VOL 16
VA a’iaVA
(:11 17aVETT.V 1N.VTI T[JTE
LouIs X.
OF TltY:l[NOL()(;
RIDENOUFI, Editor-in-Chief
I -x7
Board of Editors
LOUIS N. RIDENOUR, Editor-in-Chief
3. RADAR 13EAcor$s-Roberls
4. LORAN—%?PCe, McKenzie,
and Woodward
and Lebacqz
and Kuper
and Purcell
TECHNIQUE OF MICROWAVE [email protected]
and Montgomery
CRYSTAL Rectifiers—Towey
and Whiimer
MICROWAVE hkcms—?ozmd
ELECTRONIC 1NsT12uhfENTs~reenwood,
Holdam, and J4acRae
Starr, and Valley
and Wcdlman
VACUUhi TUBE Amplifiers—~a//ey
WAVEFORMS— Chance, Hughes, hfacNichol,
Sayre, and Williams
and Williams
and Uhlenbeck
Nichols,and Phillips
and Turner
With a chapter I)y ERIC
1948, IIY THE
1>7 THE
.-1!1rights reser(wf.
in iJ7L!)
ffitho,(l prtlll?~..ll)f[
the pubtlshers.
HE tremendous research anti development effort that went into the
development of radar and related techniques during World War 1I
resultecl not only in hundreds of rack- sets for military (and some for
possible peacetime) use but also in a great body of information and new
techniques in the electronics and high-frequency fields. Because this
basic material may be of great ~alue to science and engineering, it seemed
most important to publish it as soon as security permitted.
The Radiation Laboratory of MIT, which operated under the supervision of the National Defense Research Committee, undertook the great
The work described herein, however, is
task of preparing these volumes.
the collective result of work done at many laboratories, Army, N’avy,
university, and industrial, both in this country and in England, Canada,
and other Dominions.
The Radiation Laboratory, once its proposals were approved and
finances provided by the Office of Scientific Research and Development,
chose Louis lN. Ridenour as Editor-in-Chief to lead and direct the entire
An editorial staff was then selected of those best qualified for
this type of task. Finally the authors for the various volumes or chapters
or sections were chosen from among those experts who were intimately
familiar with the various fields, and who were able and willing to write
the summaries of them. This entire staff agreed to remain at work at
MIT for six months or more after the work of the Radiation Laboratory
was complete.
These volumes stand as a monument to this group.
These volumes serve as a memorial to the unnamed hundreds and
thousands of other scientists, engineers, and others who actually carried
on the research, development, and engineering work the results of which
are herein described.
There were so many involved in this work and they
worked so closely together even though often in widely separated laboratories that it is impossible to name or even to know those who contributed
Only certain ones who wrote reports
to a particular idea or development.
But to all those who contributed
or articles have even been mentioned.
in any way to this great cooperative development enterprise, both in this
country and in England, these volumes are dedicated.
HIS volume describes the design of the \-arious microwa~e circuits
that have been used as mixers in the microwave region at the Radiation Laboratory.
The mixers convert the microwave signal into a
signal at a lower frequency, where conventional lumped-constant circuits
and multiple-element vacuum tubes are used. For information concerning the design of a complete microwave superheterodyne receiver,
of which the mixer is a part, VO1.23 of this series is recommended.
Lowfrequency amplifiers of many types, for use following the mixer, are
described in Vol. 18. A complete treatment of clystal rectifiers, which
are the hearts of the mixers described in the present volume, is given in
Vol. 15, Duplexing circuits often required in pulse radar, and the tubes
used in them are described in Vol. 14. Low-level oscillators, which are
used as local oscillators for the mixers, are t rested in Vols. 7 and 11.
Because the frequency of the local oscillator determines the sensitive
frequency of the mixer, automatic frequency control has been considered
to be closely related to the mixer; for this reason, the chapter on this
subject by Eric Durand has been included in this volume.
I wish to take this opportunisty to thank H. F. Webster for his cooperation in the design of the mixers developed at the Radiation Laboratory
from 1943 to 1945, and Florence M. Carroll and Rosemarie Saponaro
for their very great assistance in the preparation of the manuscript.
R. V.
June, 1946
. . . . . . . . . .
. . .
. . . . . . . . . . .
. . . . . . .
. . . . . . . . . . . . . . . . . .1
11. Drfinitiono
. .
. .
Effect of Type of Signal on Receiver Design.
Qualitative Discussion of Duplcxing (~omporwnts
Figures of Merit for Rwmivcrs.
. . .
OF M1cnowAv~
. ..2
. .
The Square-1aw Detector.
The Minimum Dctcrtablc
Signal Power.
The Superhctcrodyrm
The Frequency Converter.
l.lO. The’I’riode
hlixcr . . . . . . .
. . . . .
111. TheDiodcAlixrr
. . . .
. .
1.12. Thc(’rystal
il[ixcr . . . . . . . . . . . . . . . . . .
1,13, The I.ocal Oscillator
. . .
114. TheRcfIexK
. .
. .
115. Radio-frequency
1.16. Recciversof
Other Types.
CHAP. 2.
. . .
Physical Description of Rectification.
Effects in Crystal Rectifiers.
Figure of Nfcrit of ( ‘r,vstal-video Receivers
The Crystal (’onvertm
. . . . . . .
of the (!rystal (kmverter
The Three-terminal-pair-network
The Relation
the Input Admittance
and the
Admittance . ...,.,...
. . . . . . . . . . . . .
The Dependence of Input Admittance on the I-f Load Admittance
Dependence of the I-f Admittance upon R-f Matching Conditions
Dependence of Conversion Loss on Image-frequency
ilteasurement, with an Admittance
Bridge, of the Dependence of
Conversion Loss on the Image Reflection
The Effect of Reflection of the Second Harmonic.
The Welded-contact
The Converter Noise Temperature.
Crystal Burnout . . . . . . . . .
. . .
. . .
. . .
. . . . . . .
. . . .
between TR Leakage Power and Crystal-burnout
Power . . . . . . . . . . . . . , .,
. . . . . . ...97
CHAP. 3.
on Available
The Basic Mixer Circuit.,
The Design of a Crystal Mount
Crystal Mounts for the 3-cm and the 10-cm Bands.
The Filter in the I-f Output Lead
Tunable Crystal Mounts
Scatter in a Mount of Fixed Tuning.
Coupling Mechanisms
Capacitive Local-oscillator
Coupling in Coaxial-line Mixers
A Local-oscillator
Coupling Circuit for Coaxial-line Mixers
Coupling in Waveguide Mixers.
A Directional
Coupler for Coupling the Local Oscillator to the
Mixer . . . . . . . . . . . . . . . . . . . . . . ...146
A Single Channel for Local-oscillator
An Exact Equivalent Network for the Coupling Channel.
An Iris for Local-oscillator
Signal-input Circuit.
Mounts for 1N26 Crystals and a Waveguide Mixer for the lo-cm
Band . . . . . . . . . . . . . . . , . . . . . . . ...171
of the Mixer Crystal
Harmonic Chokeb and Shutters
. . .
I-f Output Admittance.
The Completed
. . . . . . . . . . . . . . . . 185
CHAP. 4.
Conversion-loss Measurement
Burnout-test Apparatus.
The D-c Crystal Checker.
Specifications and Relevant Information
. .
The Beacon Problem . . . . . . . . . . . . . . . . . . . . 190
Single-charmel Automatic
Frequency Control
AFC . . . . . . . . . . . . . . . . . ...193
The Coupling of the Transmitter
Mixers for A1l-waveguide Systems
A Mixer Employing
Directional Couplers.
. .
The Rieke Diagram . . . .
. . . . . . . . .
Frequency Discontinuities Caused by High-Q Load Circuits.
The Design of Load Circuits Containing Transmission Cavities
4.10. Load Circuits with Reaction Cavities.
4.11. The Prevention of Frequency Discontinuities
by Padding.
for Beacon
R-f Pr&sion
for Beacon AFC.
Mixers with Multiple
CHAP. 6.
CHAP. 7.
. . . . . . . . . . . . , 223
. . .
, .
. . .
Generation and Effect of Local+mcillator
Magnitude of Locakmcillator
Noise for Typical Tubes
Effect of bcal-oscillator
Noise on Over-all Noise Figure
Reduction of Local-oscillator
Noise by the TR Cavity
of heal-oscillator
Noise by Resonant FiIters.
Reduction of Local-oscillator
Noise by the Use of a Cavity
of the Oscillator Tank Circuit.
Effect of D-c Bias on the Mixer Crystal.
Results of Experiments on the Effect of D-c Bias
. . . . .
. . . . . . . .
. 243
as Part
, 249
. . . . . 257
Simple Microwave
Balanced Mixer.
. . . .
General Properties of the Magic T. . . .
The Matching of the Magic T.
Description of the Magic T in Terms of Voltages and Currents
The Magic-T Balanced hlixer.
Additional Features of the Magic-T Balanced Mixer
Special Crystal Mounts for the Balanced Mixer
A Double BaIanced Mixer for Separate-channel
Other Special
The AFC Feedback Loop.
. .
The Transmitter
Mixers, Local Oscillators, and I-f Amplifiers.
. . . . . . . . .
. . . .
. . .
Frequency Drift
Properties of Local Oscillators for Frequency
Classification of AFC Systems.
. . . . .
Circuits for Nonhunting
. . . . . ..
7.14. Background
. .
. . . . . . . . . . . . ...314
7.12. Design Theory for Gas-discharge-tube
7.13. Diode-transitron
Control Circuits
7.10. Baeic Theory.....,..
711. Standard Gas-discharge-tube
. 235
. 237
, 223
. . 227
, . . , 231
Control Circuits.
. . . . . . . . . . . . . . . . .,331
and Basic Theory.
7.15. The Whitford AFT . . . . . . . . . . . . . . . . . . ...333
7.16. Nibbe-Durand AFC System.
. . 341
7.17. The Beacon Problem. . .
. . . . ...341
7,18. Reflector-modulationSchemesfor ReflectorAFC.
. .
7.19. Beacon AFC for ThermallyTuned Tubes.
. . . .
CHAP. 8.
. . .
ProductionTests for Lossesof SignalPower.
Over-all Noise-figureMeasurements
Radio-frequencyNoise Generators. .
Apparatusfor Measurementof the Effect of Image Reflection.
An Apparatusfor Measurementof the AdmittanceLassof a Mixer
Testiof the AFC Mixer . . . . . . . . . . . . . . . ...372
INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
iscustomarily applied toanentire device which,
when connected to a source of radio-wave energy, converts the information conveyed by the radio wave into a form in which it is directly
usable. By this understanding, a conventional radio broadcast receiver
includes everything from the antenna to the loudspeaker.
In a television
receiver, the information is presented on a cathode-ray tube; in facsimile
transmission, the receiver supplies energizing voltages to a suitable
reproducing device.
It is conventional to discuss the design of such a
receiver as a completely unified system, because similar techniques and
components are used throughout the receiver.
The problem of design of receivers for microwaves, however, falls more
naturally into two subdivisions: first, the design of components involving
microwave techniques, and, second, the design of those involving more
conventional, low-frequency techniques.
Because these two categories
of components are so widely different in nature, it has been thought
advisable to treat these two aspects of microwave receiver design in
separate volumes of this series, with the present volume restricted in
scope to those components that involve microwave techniques.
23 of this series covers the details of assembly of the microwave and lowfrequency components into a complete receiver unit for use in specific
microwave radio systems.
In addition, the details of amplifier design
are covered in Vol. 18 of this series. The scope of the present volume will
include a discussion of those components of a microwave receiver which
involve microwave energy.
If a transmission system from a receiving antenna is connected to the
input terminals of an assembly of these microwave components, energy
in a form to be treated with lower-frequency techniques is derived from
the output terminals.
There are many different ways in which such an
assembly of components can be made, the choice being dependent upon
the particular requirements that the receiver must satisfy.
Since the
experience upon which this volume is based is largely with receivers
specifically designed for radar, by the Radiation Laboratory in conjunction with outside companies, the emphasis will be rather heavily weighted
toward the design of microwave components for this service.
It is
hoped, however, that the information will be found of value to those
interested in the design of microwave receivers for other applications.
1.1. Definition of Terms.-Before
proceeding with a discussion of the
properties of microwave receivers, it wilJ be well to make specific statements as to the meaning of certain terms that will be used frequently in
the following sections.
Most of these terms are in common usage in
radio practice, but they will be defined more generally here, in some
cases, to make their application to microwave devices apparent.
other cases, a confusion exists in the meaning of terms, and their usage
in the following sections will be clarified by these definitions.
The conventional meaning of the term receiver has already been discussed and this meaning will be used throughout the present volume.
The classification may be begun by analogy to low-frequency techniques,
and by the definition of those terms which have relevance to the present
work. A conventional radio receiver usually begins with a radio-frequency amplifier.
This term, abbreviated “r-f amplifier,” will be used to
denote a device that reproduces at its output terminals a signal having
the same frequency and modulation components as those impressed
upon its input terminals, but at a higher power level. The r-f amplifier
must be operative directly for signals at the frequency of the received
wave, which means, for the present discussion, that it must be a microwave device.
It will frequently be necessary to use the concept of “bandwidth”
the following sections.
In a qualitative sense, this term will be used to
mean the extent of the range of frequencies within which the particular
device in question has a relatively uniform amplitude-response characteristic. The exact amount by which the amplitude response may vary
within thk band will be defined in a manner which depends upon the
device in question. An exact definition of” noise bandwidth” will be given
in a later section of this chapter dealing with figures of merit for receivers.
By the “tuning range” of a component will be meant the extent of the
range of frequencies to which the component can be adjusted with uniform
response. The question of tolerances arises in this connection and the
specification of tolerances will be discussed when particular devices are
If a component is tuned to a frequency within its tuning
range, the magnitude of its response and its bandwidth should be substantially independent of that tuning.
Any microwave circuit which, unless it is retuned, restricts the tuning
range of the receiver to a range less than that of most microwave circuits
will be considered as a preselecting circuit.
A tuned r-f amplifier would
thus be a preselector—a concept which is in agreement with common
usage at low frequencies.
Also under this definition would be included
any selective filter in the microwave section of the receiver which must be
tuned as a part of the tuning procedure for changing the frequency setting
of the receiver.
In conventional radio practice, the superheterodyne receiver is the
most widely used and most flexible type of receiver. A fundamental
group of components used in a receiver of this type is the group making
up the frequency converter, often called simply the “converter.”
group of circuits can be defined as one that has the property of giving,
at its output terminals, a signal containing the same phase and amplitude
relationships among its components as those found in the signal impressed
upon its input terminals, but having a center frequency differing from
that of the input signal. As usually employed in a superheterodyne
receiver, the converter changes the frequency of signals from the radio
frequency derived from the antenna into a lower, or intermedbte,
In some applications, however, it is desirable to use a converter that increases the signal frequency.
The bandwidth of a converter
specifies the range of frequencies at the input terminals which will be
converted into the same range at a different center frequency at the
output terminals.
The most common converter is one that combines a wave from a local
Because the comoscillator with the signal wave in a “mixer” circuit.
ponent derived from the mixer is usually the difference, or beat, frequency
between the signal and the local oscillator, an oscillator so used is often
called a beating oscillator.
In low-frequency practice, a tube containing
elements that, when associated with the proper circuits, can be used as a
mixer, as well as elements that can be used to form the beating oscillator,
is termed a converter tube. A tube that does not contain elements to
form a beating oscillator, but that does contain separate elements for
the injection of signal voltages and for the injection of local-oscillator
voltage, is called a mixer tube. Often, the two sets of voltages are
injected on a single element after their superposition has occurred in a
common circuit.
The tube may then be considered as a detector, and
for this reason the term “first detector” is often applied to this part of a
superheterodyne receiver.
A ‘(detector 7’ will be defined, therefore, as a device that produces in its
output circuit a voltage that has a-c components derived from amplitudemodulation components of the wave, or superposition of waves, at its
input terminals.
In addition, there is a d-c component of the voltage at
its output terminals which depends upon the averaged amplitude of the
T$7hena detector of this sort
superposed waves at the input terminals.
is used as a part of a mixer, only the a-c components in the desired
Since a detector usually consists of a
frequency range are utilized.
device in which the currents induced are not linearly related to the
exciting voltages, components of many other frequencies are also generated, but these are not utilized.
It is for this reason, however, that the
element that functions as a detector can also be used as a harmonic
generator, since both functions are the result of its nonlinearity.
detector is used directly as a receiving element in nonsuperheterodyne
receivers in which the incoming wave is converted directly from a microwave signal to a voltage containing only the modulation components.
1.2. Effect of Type of Signal on Receiver Design.-The
great majority
of receivers for microwaves in present use are designed for the reception of
signals consisting of pulses of short time duration.
In applications such
as pulse radar, the pulses are usually
not longer than a few microseconds
(10-6 second) and in some cases are
as short as one-tenth microsecond.
An understanding of the factors that
enter into the design of receivers for
short pulses may be gained from the
consideration of a single pulse of microwave energy, as shown in Fig.1.l.
If the amplitude of the pulse is
taken as unity and its time duration
as T, the pulse amplitude can be described as a time function which is
zero for \tl > 7/2 and is equal to
cos(ud + +) for Itl < 7/2, where UOis
of a
27rtimes the frequency of a continuousrectangularr-f pulse.
wave signal that has been turned on
at t = —7/2 and off at t = 7/2.
The term @ is an arbitrary phase factor
included for generality.
The Fourier transform, g(u), for such a function
is given by
The limits of integration are – 7/2 and +7/2 because the time function
is zero everywhere outside this range. The result of Deforming the
integration is
which shows that the postulated pulse or wave train contains frequency
components extending infinitely far in both directions from uiJ2ir. If
the carrier frequency, MJ27r, is large compared with l/~, the second term
in Eq. (2) is negligible, and the frequency components have amplitudes as
shown in Fig. 1.2.
The response of a receiver to a pulse of this sort obviously depends upon
A detailed discussion of this dependence
the bandwidth of the receiver
Suffice it to say that, usually, the
is outside the scope of this volume.
optimum bandwidth is approximately the width of the principal maximum of the frequency spectrum.
The best width and shape for the
bandpass characteristic of the receiver depend primarily upon the
degree of fidelity with \vhich the
pulse must pass through the receiver and the sensitivityy requireI’m, l.i!—-l.’mmr.r
of :L
ments that must be met. In any
rectangularr-f pulse,
case, most of the energy in the pulse
In order to rec~ive most of the
is contained in the principal maximum.
energy carried in pulses from 0.1 to 1.0 psec in duration, the recei~er
bandwidths reauired are 20 to 2 Jlc/see,
The effect ~f this requirement on the design of the microwa~-e comBecause the carrier frequencies
ponents must now be considered.
~oncerned are usually from 3000 Me/see upward, it is apparent that w
microwave component must have a loaded Q of 100 to 1000, for the
bandwidths stated, before it begins to affect the rereiver bandwidth.
Circuits as sharply resonant as t his are rare]y encountered. and t he ixmdwidth requirement for the microwave components is theref ore seklom
difficult to meet. On the other hand, it is relatively simple to achieve
resonant circuits that are sufficiently sharp to obtain a certnin degree
if desired. The bandwidth requirernmt affects the
of preelection,
microwave receiver because it is so small rather than bwause it is large.
For a band~vidth of 2 Me/see, the receiver must remain stalk in t’requency to 2 M c/see in at least 3000-and
perhaps as many :M 30.000-iMc/sec.
Thus a frequency stability of 1 part in 15,000 may be re(~llired.
This would correspond to maintaining an ardinary broadc:mt receiver
to within 50 cps at a receiving frequeuey of 750 kc we. which require+
some care, For this reason, automatic fre.auencv
. control 11:1sbecome a
standard part of almost all micro]vare receivers, nnd thus pro~’ision t’or
it is an important factor in the design of microwavp comporrrnts.
In receivers for radar service, the automatic frequenq- contnd is w
arranged that the recei~’er is maintainrcf at the 10CO1tmnsmitt iug frequenc.v, although thk frequency may vary. Hence, iu the t’oll(,[riug
chapters, great emphasis will be placed on the ~ar’ious met hLidsby \~hii5
automatic frequency control of this kind can be achirn-ed. Th,re will
aiso be a discussion of the various techniquw tlmt im~-e berm deYiw{l t’tw
absolute frequency control for receiver brmdu-idt hs oi thi< orxicr. .+11
exception to the polic.v of excl{ding the discussions ot’ l~>j!--frt,(lllt,r]c~-
circuits from this volume is made in the case of automatic frequency
The low-frequency circuits used as a part of the frequencycontrol schemes are discussed in Chap. 7. The reason for including
this discussion is that frequency control and stability are fundamentally
connected with microwave oscillators and for that reason may be considered a part of a microwave component.
If microwave frequencies are ever to be used for transmission and
reception of ordinary audi~frequency
signals, and, therefore, conventional audio-frequency receiver bandwidths are desired, the frequencyIt may then be
stability problem will become of prime importance.
necessary to maintain a receiver at an absolute frequency within 1 part
in 106 or more. For this service, an entirely different approach to frequency control is required, and a certain amount of work in this direction
has been done. Circuits developed for such purposes are fully discussed
in Vol. 11 of this series because their major application, so far, has been
in special laboratory equipment.
Because most of the receiver components discussed in this volume were
designed to operate in pulse radar, the effect of a “ duplexing system”
A duplexing system includes those
on their design will be prominent.
parts of a radar set which make possible the use of a common antenna for
transmission of large signals and reception of weak signals at different
times. Such a system makes use of the fact that the amounts of transmitted and received power are of very different orders of magnitude, to
facilitate the flow of transmitted power to the antenna and not into the
receiver, and the flow of received power into the receiver circuit.
these duplexing components are of very great importance in the design of
modern radar, and because an exposition of the problems and design of
the many types that have been developed is a large task in itself, only a
rudimentary discussion of their functions and general nature will be
given here. For a complete discussion of this subject the reader is
referred to Vol. 14 of this series where it is treated in detail. Because
duplexing systems have had so great an influence upon the design of the
microwave receiving components, however, it will be necessary to give a
qualitative description of some of the more important types.
1.3. Qualitative Discussion of Duplexing Components.—As stated in
the previous section, the duplexer components form a unit that makes
possible the use of a common antenna for transmission and reception.
In pulse radar this is done by making use of the fact that transmission
and reception are accomplished at different times and at different power
levels. The great majority of the receiving components to be described
have been designed to work with duplexers of this kind, but it might be
well to digress for a moment to add a few words about the more general
SEC. 13]
class of duplexers with which transmission and reception may be accomplished simultaneously.
It is not the task of the present volume to discuss the desirability of
common transmitting and receiving antennas, for this is certainly a
question that must be decided for a particular system.
At microwave
frequencies, small but highly directive scanning antennas are usually
employed and the exact alignment of two such antennas is not easy to
In addition, the usual desire is for maximum directivity
compatible with the available space, and, therefore, a single large antenna
is more desirable than two antennas of half the area each. The further
fact that this single antenna has twice the gain of the two smaller ones for
both transmitting and receiving, makes the use of a duplexer, even with
the loss of some transmitted and received power, definitely advantageous.
A box representing a generalized duplexer is shown in Fig. 1“3. The
box has three pairs of terminals.
One of these pairs is to be connected
to the antenna, one to the receiver, and one to the transmitter.
the best duplexing action the product of the available transmitted power
sent to the antenna and the available received signal power delivered to
the receiver should be as large
-. as ~ossible
and none of the transmitter power should
be coupled into the receiver.
It can be
shown that if the duplexer contains only
linear circuit elements and if the received
and transmitted frequencies are identical,
Fm. 1.3.—Genera1ized
representathe maximum value this product can have
tion of a duplexer.
is 0.25. For example, if one-half the
available transmitter power is radiated by the antenna, not more than
one-half the available received signal power can be delivered to the
This loss just compensates for the gain obtained through the
use of a single antenna instead of two, each one-half the radiating area.
Duplexers of this kind can be made up from such bridge circuits as the
“magic T” and its equivalent circuits, described in Sec. 6.2.
A duplexer for a radar system is different from this, in that simultaneous transmission and reception are not required.
In a radar system, the
transmitted power is very high, and the prime requirement of the
duplexer is that it protect the sensitive elements of the receiver from
damage by this power. Because of the extremely fragile nature of the
best receiver elements, great effort must be made to achieve adequate
An attenuation from 70 to 80 db is needed between the
transmitter and receiver when the transmitter is actuated.
This attenuation is realized through the use of a resonant chamber filled with an
appropriate gas at low pressure. The resonant chamber is so designed
that a narrow gap exists between two posts. In the gap, the electric
field is builtuptoa value
considerably greater than that in the normal
transmission line. If the field at this gapisless than sufficient to break
down the gas by ionization effects, the resonator transmits an incident
Because the
wave at its resonant frequency with little attenuation.
resonant frequency isadjustedto be that of the received signal, the cavity
acts as little more than a preelection
circuit for the receiver.
resonator is sometimes made up of a combination of several individual
resonators and corresponds to a multituned circuit passing a wide band of
T-junction Flexible
\, n
1& dtam.
1“disk flange
viewof ~ 1B27 TR switch.
received frequencies.
In this case, even its preelection action may be
At the level of the transmitted power, the field in the gap of the
resonator far exceeds that necessary to produce electrical breakdown,
and an arc is therefore maintained at the gap for the duration of the
transmission period.
The principal field in the resonator at this time is
that necessary to sustain the arc; thus, if the output coupling of the
resonator to the receiver is sufficiently small, insufficient power is coupled
into the receiver to damage it. Because the voltage required to strike
the arc is always greater than that needed to sustain it, a somewhat
higher power is transmitted for a very short time at the beginning of
each transmission period.
This power is called the “spike” power and
has been found to be the part most likely to damage the receiver.
a resonator is called a TR switch, because of its function as a self-actuating
transmit and receive switch.
The design of this switch always involves a
compromise between the leakage power that reaches the receiver during
transmission and the attenuation suffered during reception.
For a
detailed discussion of this problem and for details of the design and gas
content of the resonator, the reader is referred to Vol. 14 of this series.
Fig. 1.4 shows a cutaway perspective view of a resonator commonly used
as a TR switch.
When the arc of the TR switch is firing, a wave incident at the input
side of the TR cavity is almost completely reflected.
The cavity may
therefore be placed in a side arm, as a T-connection to the main line that
The phase of the reflection
connects the transmitter to the antenna.
coefficient is such, with an iris-coupled cavity, that it is equivalent to a
short circuit in the plane of the input iris. To obtain transmission of the
transmitter signal past the junction without reflection, the length of line
from the wall of the waveguide to the input iris is chosen to be approximately an integral number of half wavelengths.
For coverage of a wide
frequency band, the cavity is mounted with its input iris in the wall of the
main waveguide.
With a loop-coupled TR switch the phase of the
reflection coefficient is determined by experiment, and the cavity is
connected in such a way as to act as a short circuit at the end of a stub
line, an odd number of quarter wavelengths in equivalent length, on the
side of the main coaxial line.
During reception, the duplexer must also ensure that almost all of the
available received signal power is transmitted through theTR cavity into
the receiver.
The transmitter, when not oscillating, has a resonant
frequency differing from its oscillation frequency, and it therefore
reflects, almost completely, a received signal wave arriving through the
line from the antenna.
The line length between the transmitting oscillator and the side branch that contains the TR cavity and receiver can be
chosen in such a way that waves traveling along the line from the antenna
are transmitted into the TR cavity and receiver without serious reflection
or absorption due to the presence of the piece of line terminating in the
For coaxial lines, the piece of line between the T-junction
branch and the transmitter is equivalent to a short-circuited stub line,
an odd number of quarter wavelengths in length, such as is used for a
right-angle stub support.
In early radar equipment this line length was
made variable to allow proper adjustment for the particular transmitter
tube in use. Later, it was found that a fixed length gives sufficiently
good results for all transmitter tubes in a small frequency band.
ensure this, a specification test of the “cold impedance” of transmitter
tubes intended for use with systems having a fixed distance between the
TR cavity and the transmitter was set up,
An improved method for ensuring transmission of received signals to
the receiver, is one that utilizes a second gas-filled cavity resonator,
called an anti-TR or RT switch. This switch is so placed on a stub line,
or in the wall of the main line between the transmitter and the branch
leading to the TR switch that, when an arc is struck in its gap, during
transmission periods, it causes little reflection of the transmitter wave.
The cavity is tuned to resonate at the transmitter frequency and it is
tightly coupled to the input line. As a result a large standing-wave ratio
for low-level signals is produced in the main line between the branch
containing the TR switch and the branch containing the anti-TR switch.
The spacing between these two branches is chosen in such a way that
received signal power is coupled into the receiver with little reflection
m absorption due to the line terminating in the transmitter, regardless of
the cold impedance of the transmitter.
To antenna
To transmitter
vector is 1 to plane
of the page
TR tuba
To receiver
of a duplexer.
A sketch of the relevant parts of a typical duplexer is given in Fig. 15
where the dimensions shown refer to equivalent electrical lengths.
is an example of only one of many forms in which duplexers have been
made. For a thorough treatment of the subjects of TR switches, anti-TR
switches, and complete duplexers, the reader is referred to Vol. 14 of this
1.4. Figures of Merit for Receivers.—At low frequencies, the sensitivity of a receiver can be specified in various ways. Since atmospheric
md man-made static is almost always present to some degree, the useful
sensitivity is usually considerably below any limits imposed by purely
physical or thermodynamical considerations.
At microwave frequencies,
such static is almost completely absent and the minimum detectable
signal is determined almost completely by the masking effect of random
noise. Such noise is developed because electric currents are not steady,
but are made up of the flow of large numbers of electrons.
agitation of the particles in a resistor gives rise to a random noise voltage
across the terminals of the resistor. For this reason, the quantity called
the “noise figure” has become the figure of merit for microwave receivers,
and design considerations that affect the noise figure of the receiver
are of the first importance if the detection of the smallest possible signal
strength is a prime requirement.
Within any electronic circuit there exist sources of noise in the form of
small potentials developed bythermally excikd fluctuation of electronsin
the circuit elements.
This thermal-agitation noise has been studiedly
many people and is often called “Johnson noise” after J. B. Johnson,l
It has been shown that the
one of the first to study the phenomenon.
mean square of the noise voltages in the frequency range VIto VZ,developed by a circuit element because of thermal agitation, is given by
where k is Boltzmann)s constant, T is the absolute temperature of the
circuit element in degrees Kelvin, R is the resistive component of the
impedance of the circuit element, and v is the frequency of the noisevoltage component.
For an interval of frequencies so small that R may
be regarded as constant, Eq. (3) becomes
= 4kTR
Any network made up of linear passive circuit elements such as resistors, condensers, and inductances, or their microwave equivalents, maybe
considered as a noise-voltage generator with an open-circuit mean-square
noise voltage given by Eq. (4) in the narrow frequency band d., where R
is the resistive part of the impedance measured across the terminals of the
Since the power available from such a generator is
the available noise power in the frequency band dv is
dP = kTdv.
For a linear four-terminal network with a signal generator connected
to the input pair of terminals, a gain G may be defined.
The network
may be considered as a new source of the signal developed in the signal
generator, and it will deliver maximum power when the output load has an
impedance that is the complex conjugate of that measured across the outI J. B. Johnson, “Thermal Agitationof Electricityin Conductors,” Phys. Rw., S2,
97 (1928); H. Nyquist, “Thermal Agitation of Electronic Charge in Conductors,”
Phvs. Rev., S2, 110 (1928), J. B. Johnson and F. B. Llewellyn, “Limits to Amplification,” Elect. Ettgttg., N. Y., 63, 1449 (1934); F. C. Williams, “Thermal Fluctuationsin
Complex Networks,” WirelessSection, I.E.E., 13, p. 53, March 1938.
putterminals of the network.
If SOand Sarethe available powers from
thenetwork and from the signal generator, respectively, the gain of the
signal-generator-network combination is defined as
This definition says nothing about the impedance match between the
signal generator and the network; in fact, the value of G depends upon
the impedance of the signal generator as well as on the network.
It is
a maximum when the impedance of the signal generator is the complex
conjugate of the impedance measured across the input terminals of the
network, when the output terminals of the network are connected to a
load having an impedance equal to the complex conjugate of that at the
output terminals.
Associated with the output impedance of the signal generator, there
will be thermal-agitation noise, as discussed earlier in thk section, the
available noise power being given by Eq. (6). From the four-terminal
network there will also be an available noise power in the frequency
band dv. If dN is the noise power available from the signal generator,
and dNO is the noise power available from the output terminals of the
network, it is found that
F dN
where F is equal to, or often greater than unity.
The quantity F is
called the “noise figure” of the network and is a measure of the signalpower loss in the network, as well as of the detrimental effects of additional thermal-agitation noise, vacuum-tube noise, and noise from other
sources added to the signal within the network.
This quantity is thus the
figure of merit for a receiver.
For a perfect receiver, F is equal to unity,
which means that a signal arriving at the output terminals is masked by
noise no more nor less than it was as delivered from the antenna.
noise power available from the antenna of a receiver may be regarded as
being developed in the radiation resistance of the antenna.
As a consequence, its magnitude depends upon the temperature of the region of
Since receiver noise
space from which the antenna receives radiation.
figures are usually considerably greater than unity, however, the part of
the output noise power of the receiver which arises from the antenna
resistance is small for an apparent antenna temperature near room
R. H. Dickel has designed an ingenious device that
measures very precisely the apparent temperature of the resistance of a
1R. H. Dicke, “The Measurement of Thermal Radiation at Microwave Frequencies,” RL Report No. 787, Aug. 22, 1945.
receiving antenna, as a means for measuring the attenuation of microwave
The noise figures of receivers are usually
frequencies in the atmosphere.
defined for an antenna resistance assumed to be at room temperature.
A combination of Eqs. (6), (7), and (8) leads to the result
dNo = FGkTo ifV.
Both the quantities F and G depend upon the impedance of the signal
generator, but in general, the impedance that gives minimum noise
figure is different from the impedance that results in maximum gain.
Because the noise figure is the important quantity, receiver design should
always be such as to minimize it, even at the expense of gain, for the gain
can be increased easily at high level where any noise power introduced
is negligible.
In general, the noise figure is a function of frequency.
An “effective”
noise figure for the system may be defined in the following way. The
output power from the network is read on a meter. We define GOas the
product of the gaip of the network and the fraction of the available power
from the network delivered to the output meter. Power is delivered to
the output meter only when the power available from the network
exceeds thermal-agitation noise, if the network and the meter are at the
same temperature, for otherwise the transfer of energy from one body to
another at a higher temperature would be implied.
The noise power
delivered to the output meter is
No = kT,
FGo dv.
The use of the gain GO instead of G makes the integral convergent.
can be seen from Eq. (9), the product FG must be equal to or greater
than unit y at all frequencies since, from Eq. (6), dNO must be at least as
great as kTo dv.
If F were unity at all frequencies the output noise from the network
would be
N! = kTo
Go dv.
The effective noise figureF* for the network is then defined by Eq. (12),
Go dv
An effective noise bandwidth B may be defined, for the combination, as
G, dv
B= / “Gem= ,
where GO~, is the maximum value of the gain with respect to frequency.
The effective noise figure, from Eqs. (10), (12), and (13), is then
F* =
kl’oBGo -.x”
This noise figure can be measured by determining No, GO ~“, and B.
The quantity B may be considered as the bandwidth of an equivalent
circuit having a constant gain equal to Go ~~ within the band and zero
gain outside the band.
This bandwidth can be calculated for bandpass
circuits of many types if the bandwidth between the points at which
is measured and the type of circuit is known.
—- -----
meter I
I i
I_ -----
1.6.—Blockdiagramof cascadednetworks.
It is often necessary to use two or more networks with noise figures
To discover how the noise figure of the
greater than unity, in cascade.
combination depends upon the noise figures of the individual networks,
we may consider a situation such as that shown in Fig. 1“6. A signal
generator is connected to network 1, this in turn connects to network 2,
which finally connects to the output meter. Networks 1 and 2 can be
treated as a single network, (1 + 2). From Eq. (9),
di’fo(l+!) = F(l+slG(,+.z)kTo dv
where the quantities are all the same as before except that they refer to
the combined network (1 + 2). The gain of the combination G(,+ZJmust
be equal to the product of the individual gains G1 and Gz, where G~depends
upon the output impedance of network 1, in accordance with the definition of gain, Eq. (7). Therefore,
dNo{l+z) = F(,+~)G,GzkTo
The available noise power from network 1 is
dNoi = [email protected]
whereas that part of the available noise power from network 2 caused by
noise output from network 1 is just
dN&l+z) = dNo,Gz
= l’1f4G2kTo dv.
The part of the availabIe output noise power from network 2 which
arises in network 2 and in the output impedance of network 1 is
dNoz = [email protected],kTo
The part of this originating in network 2 is
dN;l+z) = dNoz – G21cT, dv,
since the contribution resulting from thermal noise available in the output
impedance of network 1 is k 7’0 dv times the gain of network 2. These
noise components are added and subtracted directly as power because
they are completely random and therefore can have no phase coherence.
The total noise output dNO[l+z) from the combination must be the sum
dNo(l+z) = dIV&1+2)+ dWl+a.
Putting Eqs. (17), (18), and (19) into Eq. (20) we have
= F,G,GzkTo
dv -t F,G,kTo
dv – G,kTo dv.
From this and Eq. (16), an expression is obtained for the over-all noise
figure in the narrow frequency range dv given by
Again, by use of the concept of the gain of network 2 associated with an
output meter GoZ,so that the integrals may exist, an expression analogous
to Eq. (14), for the effective over-all noise figure, is
= / 0
“ [G,Go,F, + Go,(F,–
G,G02 dv
/ o
If the network 1 is very wideband compared with the combination of
network 2 and the output meter, and Gl and F1 may therefore be regarded
as constants in the above integrals, then
where F; is defined by Eq. (12).
Equation (23) suggests the possibilityy
of setting up apparatus to measure the noise figure of a single network
To do this a measurement of
used as network 1 in the combination.
[SEC. 1.4
Ftl+; andof Glmustbe made forthenetwork
~questioni nt heapparatus
so that, if Fz is known by a previous measurement, F1 may be calculated.
Since F: will be a function of the output impedance of network 1, this
function and the output impedance of network 1, under the conditions of
the experiment, must be known or measured.
To facilitate the calculation of over-all noise figures and the measurement of pertinent parameters for devices that can be simulated by linear
passive networks, the concept of “noise temperature” has come into use.
The noise temperature of a device is independent of the gain of the
device, and is directly a measure of the noisiness of the network compared
with a simple resistance.
The noise temperature is defined as the ratio
of the noise power available from the network to that available from a
It was shown by Eq. (9) that the available
resistor at room temperature.
noise power in a frequency band dv is
dNo, = [email protected],lcTo dv.
The same quantity for a resistor is
dNo = kTci dv,
and the ratio dNOl/dNo
= t, becomes
t = F,GI.
By substitution
of this expression into Eq. (23),
The noise temperature of a network may be measur~d by simply comparing its noise output power with that of a resistor. The gain of the
network may then be measured at a much higher signal level, provided
the network is the same for a signal at this level as for noise, and these two
quantities together will then be the figure of merit for the device.
effective over-all noise figure for a combination may then be computed
from Eq. (26), provided the output impedance of the first network, and
F: for the second network corresponding to this impedance, are known.
An expression of the form of Eq. (23) maybe derived in an analogous
Because the noise
manner for more than two networks in cascade.
figure and gain of each network are functions of frequency (as is also the
noise temperature), an expression for the over-all noise figure of a combination can be expressed only as an integral.
In practice, however, one
of the circuits very often has a pass band much narrower than that of the
others, and an expression similar to Eqs. (23) or (26) is useful. Microwave receiving components very often have pass bands 10 per cent or
more in width, whereas the nass hand of the entire receiver is about
therefore Eqs. (23) and (26) are useful. Ifallbut
the last
of n networks in cascade have pass bands wide compared with that of the
last network, their gains and noise figures may be regarded as constants in
integrals similar to those in Eq. (22). The effective over-all noise figure
for the combination may then be written
o . . +~*+
I’p =
Because of the appearance of the gain factors in the denominators of these
successive terms, it is clear that in a receiver, the contribution to the
effective over-all noise figure from stages occurring after a reasonable
gain has been achieved is negligible.
Another way of saying this is
simply that the noise contribution of the early stages, because it is
amplified, masks any contributions to the total output noise which might
be made by later stages. It is clear, then, that the microwave components, since they must necessarily be the first in any cascade of circuits
making up a microwave receiver, play the dominating role in determining
the figure of merit for the receiver.
1.5. The Low-level Detector.—The simplest kind of receiver at any
frequency consists of a detector followed by an amplifier, as indicated in Fig. 1.7. At microwave frequencies, the detector for such a
receiver must respond directly to the microwave energy. The detector
produces, at its output terminals, voltages derived from amplitudemodulation components in the envelope of the radio-frequency waves
impressed upon its input terminals.
All of the amplification in such a
receiver occurs at the modulation frequency.
A receiver of this kind
responds to signals having carrier frequencies anywhere in the pass band
of the r-f components, including the detector.
The ability to reproduce
modulation voltages is determined primarily by the characteristics of
the detector and modulation-frequency
amplifier, since the pass band of
the other r-f components is usually wide compared with the frequency
spectrum of the received signal.
A number of devices mav be used as detectors for a receiver of this
kind. Because they must ~espond directly to the microwave signal,
however, only special kinds of vacuum tubes, in which the interelectrode
spacings are very small, are useful. Transit-time effects make ordinary
In addition,
vacuum tubes almost completely unresponsive.
vacuum tubes must be built in a form that enables them to become integral parts of thecircuits associated with them.
There exist afew tubes
that meet these requirements—the GE “lighthouse” and “oilcan” diodes
and triodes for example.
Such tubes, however, even with their small,
but not negligible, interelectrode spacings, are useful only in the lowfrequency part of the microwave region, principally above 10 cm. The
design ~f circuits for the use of these tubes is too strongly dependent on
the specific nature of the tube available to be described here. The primary problem associated with the design of detectors using these tubes is
the matching of the signal energy available from the antenna into the
r-f input circuit.
This problem can be solved by the use of standard
microwave techniques, and circuits for this purpose will be found in
literature dealing specifically with such tubes. A tube intended for use at
microwave frequencies is so designed that it may be used as an integral
FIG.1.7.—Blockdiagramof receiverwithlow-leveldetector.
part of the microwave circuit.
In the lower-frequency part of the microwave region, only diodes are used as detectors; in the higher-frequent y
part of the region (10,000 Me/see and above), no satisfactory diodes exist.
The diode is not the most satisfactory detector for most purposes, and is
widely used only in applications where its ability to withstand high-power
signals without damage is an important property.
A detector for microwave signals can be made from one of several
devices that change in electrical resistance when heated by incident microwave energy.
One such device is a Wollaston wire. An ordinary 5- or
10-ma Littelfuse contains such an element and can therefore be used as a
Another device of this sort is the thermistor, which also suffers
a change in resistance when heated by microwave energy. The thermistor has a negative temperature coefficient of resistance, whereas the fuse
wire has a positive coefficient.
Either of these devices may be arranged
in a circuit with an r-f matching transformer, in such a way as to absorb
signal energy from an antenna.
A steady current is passed through
the fuse or thermistor, and incident r-f energy causes a change in the
voltage produced across the element.
The use of a detector of this kind is restricted primarily to laboratory
Its power sensitivity and noise figure are not so good as
those of some other devices, and it cannot be used to detect modulation
frequencies above a few thousand cycles per second because the thermal
time constant limits the rate at which it can respond.
Detectors of this
kind are widely used in test equipment, however, because they are easily
procured and have some convenient properties.
Because these detectors
are capable of absolute calibration when used as bolometers in bridge
circuits, they are most frequently used in low-level power-measuring
A discussion of these applications is outside the scope of
this volume, and is to be found in Vol. 11 of this series.
A sensitive detector for microwave power is the very highly developed
microwave version of the familiar crystal detector.
Crystal detectors
were early recognized as being especially suited to microwave circuits
because of their extremely small physical size. A large amount of
research has been devoted to the development of crystal detectors in
fixed adjustment and packaged in small cartridges.
A large advance in
the understanding of the mechanism of operation of these devices and
studies of the factors making possible the manufacture of high-quality
crystals have led to mass production of cartridge units that are considerably superior to their earlier prototypes.
The principal work on these
devices has been toward the development of rectifiers for use as frequency
converters, but advances in the development of low-level detectors have
also been significant and have benefited considerably from the other
Because the development of crystal detectors and units
for mixers is a very large field in itself, it will not be possible to give it more
than a cursory treatment in the next chapter.
The reader is referred to
Vol. 15 of this series for a thorough review of the subject.
The use of
receivers of the variety under discussion here is not sufficiently widespread or complex to warrant a separate treatment in this volume.
the following section some of the considerations that affect the figure of
merit for such a receiver will be discussed.
1.6. The Square-law Detector.—Both diodes and crystals function as
detectors because of the nonlinear relationship between the current
induced in them and the magnitude of the voltage impressed.
In general,
a smaller current is induced by a voltage of one sign than by a voltage
of the other sign. If the current through a crystal is plotted as the
ordinate on a linear scale, and the impressed voltage is plotted as the
abscissa, a curve of the type shown in Fig. 1.8 is obtained.
This plot will
be seen to show considerable curvature or nonlinearity in the region of
the origin, and it is upon this curvature that the action as a low-level
detector depends.
If an alternating voltage, such as is shown on the
negative current axis, is impressed across this crystal, the current that is
passed through the unit has the form indicated in the plot on the righthand voltage axis. Because there is less current flowing during the
negative half-cycles than during the positive ones, there is a net positive
[SEC. 1.6
current having magnitude related to the magnitude of the impressed a-c
If the envelope of the a-c voltage varies with time, the net
current varies in a related fashion and so has components derived from
the amplitude modulation of the impressed voltage wave. This is a
picture often used to explain detecz
tion and can be found in any reference book.
The current in a nonlinear device
can be expressed, analytically, as a
function of the voltage, and expanded in a Taylor series. The
nonlinearity is expressed by the
terms in powers of the voltage
higher than the first. For very
small voltages, the term in the
second power of the voltage is large
compared with the higher-power
FIG. 1.S.—Graphical representation of terms. Therefore the rectified curdetection.
rent produced from a very small
signal must be proportional to the square of the impressed a-c voltage.
For this reason, low-level detectors are often referred to as “square law”
The induced current is proportional to the incident r-f power.
A diode or crystal detector is an entirely passive circuit, in that there is
no source of energy other than the input signal. The maximum possible
gain of such a detector, according to the definition of gain in the previous
section, is unity.
Because the detector is a square-law device, its gain
decreases with decreasing signal strength unless a change of the output
impedance accompanies the decrease in current flow.
The detector, as a generator of modulation-frequency
signals, may be
considered as a current generator producing a current i, in shunt with an
admittance g, as shown in Fig. 1.9. The value
of i is proportional to the input power to the
detector and the value of g is also dependent
upon the input power level. At very low
levels, the value of g is relatively independent
of the power level, and an effective measure
FICI.1.9.—Modulation-frequency equivalentof a detecof the gain of the device can be obtained.
Because of the square-law dependence of the
magnitude of the current generated, this gain is directly proportional to
the input r-f power.
It is clear that the concept of the noise figure for
such a detector is not very useful sinw the noise figure, too, depends
upon the input-signal level. A quantity ihat is a measure of the quality
of a square-law detector can be defined in terms of the magnitude of the
current produced by the generator per unit of incident power and the
magnitude of the generator conductance associated with it.
1.7. The Minimum Detectable Signal Power.—Because the conversion efficiency (gain) of a diode or crystal detector at low level is so small,
the device may be described in terms of a two-terminal-pair network in
which the transfer admittances are very small compared with the selfadmittances associated with the input and output terminal pairs. In
such a network the input admittance is almost completely independent of
the load admittance presented to the output terminals.
Maximum power
is therefore delivered through the network when the admittance of the
r-i generator connected to the input terminals is the compiex conjugate of
the self-admittance of these terminals, and the load admittance is the
complex conjugate of the self-admittance of the output terminals.
design of the microwave unit associated with the detector is largely concerned with transforming the self-admittance of the input terminals into
line admittance so that the detector may be connected to a matched
This specific subject will
antenna line with maximum power transfer.
not be discussed explicitly in this volume, but the techniques involved are
similar to those outlined in following chapters on crystal-mixer design.
One special problem connected with the experimental design comes about
because admittances must be measured with signals sufficiently small to
If the signal strength is sufficiently
approximate the low-level condition.
small, no change in the measured input admittance should result from a
Since, to satisfy this condition
further decrease in the signal strength.
for crystal detectors, the power delivered to the crystal must usually be
less than 1 gw, equipment for measurement of the input admittance by
the standing-wave-ratio method must have high sensitivity.
In the absence of currents through a crystal the noise voltage at its
output terminals is thermal-agitation noise, as discussed in See: 14 and
given by Eq. (3). To evaluate the degree of sensitivityy possible with a
receiver using a crystal detector, the detector can be considered to be
connected to a noise-free amplifier, and the amount of r-f power necessary
to produce a signal power equal to the noise power at the output terminals of the amplifier can be found.
It has been shown that the current
induced in the crystal is proportional to the r-f signal power. This statement may be expressed as
where i is the short-circuit current, P is the available r-f signal power,
and b is a proportionality constant dependent on the crystal.
Since P
is defined as the available power rather than that dissipated in the crystal,
b includes any losses caused by mismatch between the signal source and
[SEC. 1.7
the crystal,
If the output terrninalsof thecrystal areconnected to the
input terminals of the noise-free amplifier of gain G, the output signal
power from the amplifier will be
For this quantity to be equal to the output noise from the receiver it is
required that
= GkTB,
where B is the effective noise bandwidth of the amplifier, as defined in
Sec. 1.6. This equation can be solved for the required r-f power, giving
where the expression has been separated into two terms because the first
This expresrelates to the detector unit and the second to the amplifier.
sion holds only for a noise-free amplifier, which cannot be achieved in
practice; therefore an expression for a realizable situation must take the
amplifier noise into account.
The expression can be used, however, to
obtain some qualitative information about receivers with low-level
A more rigorous treatment of the subject will be found in
Vol. 15 of this series. In Chap. 2 of this volume, an extension of this
dkcussion to include the effect of amplifier noise will be given.
Equation (31) may be compared with a similar expression for an ideal
receiver—that is, one with a noise figure equal to unity.
For such a
receiver the r-f signal power required to equal noise power in the output
terminals is just
P, = kTB,.
The bandwidth B1 is the effective noise bandwidth of the over-all receiver.
For a square-law detector, B, is the effective noise bandwidth of the
This immediately
brings out one
feature of a receiver of the detector type.
Because the efficiency of the
detector is so small, the output noise is independent of the r-f bandwidth
of the receiver.
In reality, there are two different pass bands to be
considered: first, the width of the region of radio frequencies to which the
receiver is sensitive, and second, the pass band of the amplifier, which
determines the kind of modulation components to which it will respond.
For an ideal receiver, the effective noise bandwidth is equal to the square
root of the product of the bandwidth before detection and that after
detection, because it is the fluctuation in detected noise power, which can
pass through the circuits following the detector, that tends to mask a
small signal. The performance of a receiver in which a low-level detec-
tor is used approaches that of the ideal receiver more closely if the r-f
bandwidth is large compared with the amplifier pass band than if the two
‘l’his is the type of service in which
pass bands have similar widths.
receivers of this kind have been most widely employed.
For use at
beacon stations, for instance, a receiver that responded to pulses of
about 2-psec duration anywhere in a frequent y band of about 120-.Mc/sec
width, was required.
The simplicity of a receiver with a crystal detector
was considered worth the loss in ultimate sensitivity compared with
other receivers.
For very large bandwidths, greater than about 150
Me/see, only receivers with the low-level detectors have so far been used
to receive in the whole band continuously, because amplifiers have not
yet been made for bands wider than about 70 Me/see.
If intermittent
response to each frequency in the band is acceptable, a sweeping superheterodyne may be used.
If the receiver is to be responsive to a band of frequencies only sufficiently wide to carry the desired modulation components, then the bandwidth before detect ion and the over-all receiver band width are similar.
The smaller this quantity, the more closely does the receiver having a
low-level detector approach the ideal noise-free receiver.
It will be seen
that, again, wide pass bands are favored; thus, for example, the low-level
detector might be satisfactory for receivers designed to respond to
extremely short pulses. In general, however, for receiver bandwidths
of 1 or 2 M c/see (before detection) the minimum detectable signal power
is larger, by a factor of about 105, than that obtainable with receivem of
other types. Receivers of the low-level-detector type have not been used
extensively, except at beacon stations.
One way of reducing the minimum detectable signal for this type of
receiver is to precede the detector with r-f amplifiers having sufficient
gain to make noise generated ahead of the detector contribute a significant part of the total output noise from. the detector.
In this case the
over-all noise figure of the system becomes dependent on the noise figure
of the r-f amplifying system.
If the amplification is sufficiently great
to make r-f noise contribute all but a negligible part of the detector output noise, the receiver noise figure is completely determined by the noise
figure of the r-f amplifiers.
Since these amplifiers are usually made
with resonant circuits, they also act as preselectors.
The receiver is then
similar to the tuned r-f receivers commonly used at lower frequencies
before the advent of the superheterodyne.
Because the minimum signal
power detectable by a low-level detector is relatively large, a high gain
would be required of a noise-free amplifier.
In the example cited, the
gain would have to be greater than 105. A gain this large would require
several stages of amplification by tubes available even at the lowest freIn this low-frequency region, improvequencies in the microwave region.
ment can be made by use of r-f amplifiers, but the system becomes
relatively complex and a smaller minimum detectable signal can be
obtained with a superheterodyne receiver.
It would be advantageous
to use noise-free amplifiers ahead of a superheterodyne receiver.
a superheterodyne receiver having a moderate bandwidth can detect a
much smaller signal than can the low-level detector, less gain would be
required of a noise-free amplifier to make the over-all noise figure
approach unity.
A discussion of existing types of r-f amplifiers will
therefore be deferred until the superheterodyne
receiver has been
1.8. The Superheterodyne Receiver.—The superheterodyne receiver
makes use of a frequency converter, which changes the signal into one
Radiofrequency +
Frequency +
frequency +
FIG.l.10.—Blockdiagramof a superheterodyne
The signal is then amplified at this
centered at a different frequency.
Because the amplinew frequency before demodulation by a detector.
fication usually occurs at a frequency lower than the signal frequency
(that is, the converter produces a downward frequency conversion), the
amplifier is called an intermediate-frequency or i-f amplifier.
A detector
at a relatively high level is used, follo\ving the amplifier, to detect the
modulation components carried by the signal, and modulation-frequency
amplifiers are usually used to make the signal large enough to drive the
reproducing device.
A block diagram for such a superheterodyne
receiver is shown in Fig. 1“10.
At conventional frequencies. the advantages of a superheterodyne
over receivers of other types are numerous.
The fact that the i-f amPlifier is operated at a fixed frequency allows the receiver to be designed
with almost any shape of bandpass characteristic desired, with full utilization of the gain available from the tubes used, compatible with the bandpass circuits.
The r-f selectivity, except for image-frequency effects, is
completely determined by the selectivity of the i-f amplifier.
this amplifier need not be tuned, highly selective circuits can be used.
The tuning of a superheterodyne receiver is accomplished by adjustment
of the frequency converter and of anyselective circuits occurring between
the receiver and the antenna terminals.
Another property of this receiver is that the signal level at the second
detector is sufficiently high to make the noise contribution from this
part of the system completely negligible.
Under this condition, the
detector may be chosen on the basis of its fidelity in reproducing modulation, rather than on the basis of its noise figure. Relatively
amplification is needed because the output level
of the detector is high.
As a receiver for microwave signals, the superheterodyne has anothe~
prope~y, which is not so important at other frequencies.
the radio frequency and intermediate frequency are of the same order of
magnitude but this need not be so. For a microwave receiver, the frequency converter is usually made to convert the microwave signal into
one at a relatively low frequency, with the result that conventional
circuits and ordinary pentode and triode vacuum
tubes may be used in the i-f amplifier.
A receiver having a noise figure
approaching that of a low-frequency amplifier can be made, provided the
frequency conversion can be accomplished with a device having a small
noise figure. Under such a condition, an r-f amplifier would not improve
the over-all noise figure of the receiver unless it had considerable gain and
a noise figure smaller than that of the frequency-converter
and the i-f
amplifier combined.
Another property of the superheterodyne receiver, especially for
In most
microwave frequencies, is its susceptibility to frequency control.
microwave receivers, the intermediate frequency is less than 1 per cent
of the radio frequency; consequently, the effect of time and temperature
drifts in the highly selective circuits upon the receiver frequency setting
is smaller, by a factor of 100, than it would be if the selectivityy were
Furthermore, since there is little
accomplished at the radio frequency.
to be gained in making any r-f circuits as selective as the i-f ones, the
control of the receiver frequency can be accomplished by control of the
converter alone. Thus, the superheterodyne receiver is especially well
adapted to microwave frequencies and has been used almost exclusively
except in cases where the receiver bandwidth must be greater than can be
The recent advances in the developaccomplished with i-f amplifiers.
ment of i-f amplifiers (see Vol. 18 of thk series) have resulted in amplifiers
with noise figures near unity and bandwidths much greater than were
previously used. The emphasis of this volume will be on the subject
of circuits for frequency conversion and the circuits associated with the
frequency control of the frequency-conversion
The design of
miwowave low-level crystal-detector circuits will not be discussed speci-
fically, but the method of attack should be apparent from the methods
discussed in connection with frequency converters.
1.9. The Frequency Converter.-In
low-frequency superheterodyne
receivers the frequency conversion is accomplished through the combined
use of a local oscillator and a mixer. The local oscillator is simply a
continuous-wave oscillator operating at a frequency somewhat different
from that to which the receiver is to be sensitive.
In the mixer, a superposition of the local-oscillator wave and the input signal takes place. A
beat, or heterodyne, frequency equal to the difference frequency between
the two waves exists as an amplitude-modulation
component on the
superposition of waves within the mixer. The mixer produces at its
output terminals a voltage or current corresponding to thk heterodyne
Signal frequencies that differ from the local-oscillator frequency by the intermediate frequency, produce a heterodyne frequency
equal to the intermediate frequency and so are amplified by the i-f
If the signal is not a continuous wave but is a modulated
wave, it may be considered as a
of Fourier components, each of which produces its
output signal from the mixer con‘Wnheterodwefrequency’he
a component for each component in the incoming signal. The
amplitude, frequency, and phase relations between these components
are preserved as the signal passes through the mixer. The signal
entering the i-f amplifier therefore contains the same modulation as
the r-f signal, but is centered at the intermediate frequency.
those components lying within the pass band of the i-f amplifier will
continue through the receiver, and it is for this reason that the bandwidth of the receiver is just the bandwidth of the i-f amplifier, provided
no narrower circuits are used in the mixer, or ahead of it. A block diagram for a converter of this type is shown in Fig. 1.11.
If the local-oscillator frequency is fm there are two frequencies that
give rise to the intermediate frequency jp. These are f. + jd and ~. – jd,
since the difference between each of these and j“ is equal to the intermediFor this reason, the combination of a converter and an i-f
ate frequency.
amplifier is sensitive to two r-f bands, each of a width equal to the bandwidth of the i-f amplifier, and differing in center frequency by twice
the intermediate frequency.
This situation gives rise to one of the
principal imperfections encountered in the superheterodyne receiver,
the so-called image response.
At ordinary frequencies, there is usually a
tuned circuit associated with the signal input terminals of the mixer,
which is adjusted to favor one of the two signal frequencies, and which is
FIG.Ill. -Block diagramof a converter.
caused to follow the tuning of the local oscillator in such a manner as to
The frequency to which this
maintain the required frequency difference.
circuit is tuned is termed the signal frequency for the receiver. The other
frequency to which the converter unit is sensitive, and which is discriminated against by the input circuit, is called the image frequency.
is no particular convention as to which of these is the higher frequency.
Sometimes the choice is made so that the image frequency falls in a region
where there are few strong singals to be expected.
In this way, interference by signals at the image frequency is minimized.
In low-frequency
receivers, the intermediate frequency is often chosen to be quite high to
secure a large image suppression, without requiring highly selective circuits in the r-f part of the receiver. However, the condition that the
intermediate frequency be low enough to allow the use of conventional
tube$ and lumped-constant circuit elements limits the choice of intermediate frequencies for microwave receivers.
Ii should be noted that, if no difficulties with interference or confusion
of signals are encountered because of the two frequency bands of sensitivity of a converter, there is little to be gained through the use of preelection unless the noise figure of the converter is nearly unity.
If a converter
has a noise figure of unity, the entire noise power available at its output
terminals originates on the r-f side of the converter.
The ratio of a signal
to noise power at the output terminals of the converter can be doubled by
the use of a preelection circuit that eliminates the noise contributed
from the image-frequency region. If a large part of the output noise from
an imperfect converter arises within the device itself, however, preelection can have little effect on the available i-f noise power. Since this is
true of all known frequency converters for microwave signals, the effective
noise bandwidth of such a receiver is considered to be that of the i-f
amplifier, whether or not preelection
is used. In addition, a circuit
that reduces the sensitivity of the receiver to image-frequency signals
from the antenna does not necessarily suppress the i-f noise power available from the converter and may even increase it. Some of the small
variations in converter noise figure which can be produced by special
treatment of the image-frequency voltages are discussed in Chap. 2 in
connection with the linear-network representation for a converter.
Because a mixer usually contains a nonlinear circuit element for the
detection of the heterodyne frequency, there exist in its output circuit
many frequency components of second and higher orders, corresponding
to sums, diilerences, and products of all of the input frequencies and their
These components, too, can give rise to spurious responses
in the receiver, especially if very strong signals outside the receiver band
are allowed to enter the mixer. Preelection, which restricts the allowed
frequency range to one comparable with the i-f bandwidth, is very desira-
Meif such signals are anticipated, even if the fidelity and the minimum
detectable signal, in the absence of interfering signals, are unaffected.
Since most of thecircuits to bediscuswd were designed foruse in pulseradar systems, preelection
is achieved by means of the resonant TR
If the receiver is to
cavity of the duplexer that precedes the converter.
be used for some other purpose, the design should therefore include
a preselecting resonator that has characteristics similar to those of the
TR cavity but need not be capable of electrical breakdown.
Many of the
circuits demand the use of such a resonator, independently of any preelection function for the over-all receiver, to allow satisfactory operation
of the LO coupling circuit.
For this reason, the TR cavity used with each
mixer discussed will be indicated.
As mentioned in Sec. 1“1, in which the terms “mixer”
and “con~erter” were defined, some special vacuum tubes have been developed for
performing these functions at conventional frequencies.
Converter tubes
combine the function of local oscillator and mixer in one envelope.
Mixer tubes and the mixer sections of the special converter tubes accomplish the mixing in the electron stream flowing to the plate of the tube.
All of these electronic mixer tubes require that the drift time of the
electrons through their many elements be short compared with the period
of the r-f waves which they mix. Their performance consequently falls
off at even lower frequencies than does that of the simpler conventional
At moderately high frequencies, it has been found advantageous
to return to the older technique of accomplishing the superposition of
waves in circuits external to the tube and using a tube of simpler construction, such as a triode or diode acting as an amplitude-modulation detector,
At microwave frequencies there is almost
to perform the mixer function.
no other course, and even the drift time between cathode and grid in a
triode, or cathode and plate in a diode, is excessive except in some very
specially designed tubes in the lower-frequency part of the microwave
region. Since the developments to be described in this volume are
chiefly concerned with the frequencies from 3000 Me/see upward, these
tubes will receive practically no attention elsewhere in this book, but it
might be well for historical purposes and for purposes of orientation to
mention briefly some of the more successful types.
1.10. The Triode Mixer.-The
effective noise figure of two cascaded
networks, given in Eq. (26), depends inversely upon the gain of the first
network, and directly upon the noise power available from it, as measured
by t. If a triode or multielement tube is to be used as a mixer, the gain
that can be realized falls off with increasing frequency because of the time
required for the electrons to cross the gaps between the elements.
phenomenon caused by the transit time is an apparent grid-to-cathode
conductance, which increases as the frequency is increased.
This con-
ductance sets an upper limit to the grid-to-cathode voltage that can be
developed from a given signal power, with the result that the gain decreases
with increasing frequency,
In order that this effect may be minimized,
the interelectrode spacings must be made very small, and in order that
the grids may function as electronic shirlds, they must then be made of
very fine mesh. The manufacturing tolerances that must be maintained
R-f by~ss
shell to cathod
Grid structure
Low-1oss glass
Base and cathode
Fm. 1.12.—flkoss-sectional
viewof a typicallighthousetuba
and the difficulties of working with such extremely small parts have prevented the development of usable tubes of this sort for frequencies higher
than about 3000 Me/see, except on a restricted, experimental basis.
At frequencies up to 3000 or 4000 Me/see, tubes of the lighthouse
type (plane-parallel electrodes) have been used as mixers. The noise
figure of a mixer using such a tube
has never been made so small as the
noise figure for crystal mixers.
Hence, the use of lighthouse tubes
in this service has never become
widespread except in the very lowfine2
@ =
est frequency region (below 1000
R.fbypass ~ +
in thetube
The design of the circuit
Fw. l-13.—Circuit diagram of a lightfor such a device is determined
largely by the particular tube available. Usually a resonant circuit between the grid and cathode is employed
to matih the available signal power into the grid conductance of the tube.
A sketch of a typical lighthouse tube, such as the GL446, or the 2C40
tube, is shown in Fig. 1-12. The grid of this tube is a rectangular wire
mesh, mounted on the grid ring and made of wire 0.002 in. in diameter,
with the centers of the wires spaced 0.010 in. apart. The cathode-togrid spacing averages 0.005 in. and the grid-to-plate spacing is 0.010 in.
All of the elements are plane-parallel, including the cathode which is
[SEC. 1.10
indirectly heated.
A typical low-frequency circuit using a lighthouse
triode as a mixer is shown in Fig. 1.13.
The tube is biased near cutoff by the self-biasing resistor in the cathode
circuit and then driven relatively hard by the injected local-oscillator
Consequently, on the negative half-cycle very little change in
plate current occur”, whereas on the positive half-cycle considerable
plate current flows. The average pl~te current, therefore, depends
upon the magnitude of the voltage at the grid, and since this voltage is
composed of the local-oscillator voltage pl(ls a small signal voltage, the
beat or difference frequency will exist as a component of the plate current.
As long as the signal voltage is small compared l~ith the local-oscillator
voltage, as measured at the grid, the beat-frcqllency current flo]~ing in
the plate circuit must be directly proportional to” the signal amplitude.
The mixer, therefore, is a linear device, as contrasted \}-iththe square-lalv
low-level detector.
Bccausc the tlmcd circuit must be resonant for the
signal frequency, the efficiency of transfer of the local-oscillator signal to
the grid is relatively low. Considerably greater local-oscillator power
must be available than }vould be other\ \”isenecessary.
310reover, the loss
of signal power into the local-oscillator circuit must be kept small. This
particular requirement is one that has an important influence upon the
design of all mixers to be described, for it must be met if the minimum
noise figure possible with a given type of mixer element is to be achieved.
The resonant circuit in the plate lead of the mixer tube of Fig. 1.13 serves
to develop an i-f voltage from the beat-frequency component of the plate
current and so is made to resonate at the intermediate frequency.
A sketch of the basic parts of a microwave mixer circuit designed by
P. A. Cole for operation near 3300 Nc/see, which is equi~alent to the
low-frequency circuit, is shown in Fig. 1.14, The resonant grid-tocathode circuit is made up of the radial cavity, which is somewhat lessened
in radius by the lumped-capacitance
loading due to the grid-to-cathode
capacitance of the tube at its center. The signal voltage is coupled in by
means of the coaxial line, the center conductor of ~vhich crosses to the
opposite wall of the resonator.
The signal power may be matched into
the cavity by proper choice of the distance from the center of the cavity
to the point at which the coaxial line enters the cavity.
The greater this
distance, the larger the voltage stepup from the coaxial line to the grid.
The signal line also affects the resonant frequency of the cavity, and,
consequently, the cavity diameter is not independent of the position of
the input line. These two dimensions are determined experimentally.
To achieve the small coupling between the grid-to-cathode region and
the LO input line, the distance from the outside edge of the resonator to
the LO input line is made considerably shorter than the distance to the
signal line. This procedure may be considered to be analogous to the use,
in the circuit of Fig. 1“13, of a much larger stepup ratio for the localA matched termination on
oscillator circuit than for the signal circuit.
the local-oscillator line then contributes only a small admittance at the
grid of the tube.
Consequently, little signal power is lost in this con-
ductance, compared with that delivmxxl to the grid-to-cathode conductance of the tube. To ensure that the local-oscil[:ltw line is matched, a
cable with a distributed loss of several dccilmls l)ctwm’n the loral oscillator
and the mixer is used. In addition, the cal)lc smww to minimize the
effects on the local oscillator of the large rdlwtions at the mixer of local-
oscillator signals. Such reflections exist because the local-oscillator line
is not terminated in the characteristic admittance of the line. In this way
the behavior of the local oscillator is less affected by the mixer circuit than
it would be in the absence of the dissipative cable, but the available localoscillator power required is increased.
The circuit of Fig. 1~14 includes no provision for tuning the resonator
This particular
as would, in general, be required for a tunable receiver.
circuit was designed for operation with a very wide i-f amplifier to cover
the entire range from 9.0 to 9.2 cm with fixed tuning.
The Q of the resonant circuit was found to be just low enough to allow this. The resonant
wavelength was 9.1 cm with a tube of average input capacitance.
If the mixer must be tunable, provision for adjustment of the effective resonator radius can be made. This can be done by the inclusion of
screw plugs of large diameter so placed around the outside wall of the
resonator that, when they are screwed into this wall, they fill the region
bet ween the top and bottom resonator walls for a part of the circumference. The average radius is thus reduced, and hence the resonant freThe coupling ratio for the signal input
quency of the circuit is increased.
line will not remain constant, nor will the cavity losses. It is not advisable therefore to attempt to cover a very great tuning range by such a
means. Because triode mixers are not used extensively in the microwave
region, the m~ny methods by which tunable cavities and measurements
on them may be made will not be discussed here. The reader who is
interested in this subject is referred to Vol. 7, which deals with microwave vacuum tubes, and Vol. 14 on TR tubes, where these matters are
considered in detail.
The triode mixer of Fig. 1.14 was found to have a noise figure of about
100 or, as usually expressed since it is a power ratio, 20 db at the center
of the band and about 23 db at 9.0 cm and 9.2 cm. The exact value
depends, of course, on the particular tube used, but this value is not so
small as the noise figure of receivers using other types of mixers. The
noise figure of the triode mixer is high because, although it has a larger
conversion gain than some other mixers, the noise pow-er available in the
plate circuit is large. All tubes develop noise through the “ shot effect”
and because some electrons are stopped by the grid. The over-all
noise figure of a triode mixer decreases if the radio frequency is decreased,
because the grid-to-cathode conductance decreases \vith frequency as a
This allows a larger
result of the decreased transit angle of the electrons.
gain to be obtained \vith the mixer ]vith almost no change in the available
noise poww-, if the intermediate frequency is held constant.
1.11. The Diode Mixer.—Another
tube that can be used in a converter is a diode.
At low frequencies, \vhere the transit angles are negligible, both the gain and the noise of the diode mixer are smaller than those
of a triode mixer. Like the triode, the diode, to be useful at microwave
frequencies, must have a small interelectrode spacing, in order to minimize the transit time. The diode must be so constructed that the tube
The construction
can be made an integral part of the microwave circuit.
of diodes with plane-parallel elecPlate structure
trodes, such as are used in the lighthouse tubes, has proved to be one
of the most successful methods.
Figure 1.15 shows the construcR.f bypass
shell to
tion of a typical diode.
The cathcathode
ode is plane, and forms the top of a
cylinder that contains an indirect
heater element, as in the triode.
The anode is a cylindrical post,
separated by a very few roils from
the cathode, with its face parallel
to that of the cathode.
A typical
FIG. 1.15,—CrOss-sectiOnalview of a
low-frequency circuit for a mixer
typicaldiodeueedfor a diodemixer.
containing a diode is shown in
Fig. 1’16. In addition to a d-c component, the diode plate current
contains the beat-frequency
component, because the diode passes a
current only during the positive half-c ycles of the input voltage, ivhich
consists of the superposition of the small signal on a relatively large
local-oscillator voltage.
If the beat frequency is equal to the intermediate frequency, an i-f voltage is developed across the i-f resonant circuit in
the plate circuit.
As is true for the triode, the magnitude of this voltage
is proportional to the amplitude of
the signal voltage if the signal voltinput
age is very small compared with the
The circuits
l-foutput local-oscillator voltage.
used between the cathode and plate
= )
of the diode may be the same that
used between the grid and cath% bypass =
ode of the triode.
If the shell of the
FIG.1.16.—A circuit for use of a diode
tube is actually connected to the
as a mixer.
cathode, a bypass condenser must be
built into the circuit between the resonator and the shell to prevent shortcircuiting of the i-f voltage.
In some tubes, this condenser exists within
the tube itself. This allows the resonator to be connected directly to the
The same is true for the triode circuit, where bias
base part of the tube.
voltage must be developed for the cathode.
The noise figure of the diode mixer used in combination with an i-f
amplifier of noise figure Fz is given by Eq. (26), where the gain G is always
less than unity, representing actually a loss, and the noise temperature t is
greater than unity.” Since thegain isless than unity, thenoise figure of
the succeeding i-f amplifier is relatively more important than for a mixer
with a large gain. The best operating point, with respect to driving
power from the local oscillator, results if a compromise is made between
gain and noise temperature.
The gain increases with increasing driving
power, but the rate of increase becomes small for large local-oscillator
drive. Thenoise temperature alsoincreases \\-ithincreasing driving po\ver
because of the larger current flow in the plate circuit of the tube. In
addition, the output impedance varies with driving power, and there exists
a limit to the amount of driving power that can be coupled into the mixer
from a given local oscillator.
If this limit is exceeded, the signal loss into
the local-oscillator circuit becomes significant.
The optimum driving
power must consequently be chosen—usually experimentally—for
particular combination at hand. At 3000 Me/see, the minimum over-all
effective receiver noise figure that can be achieved with a diode mixer is
about 18 db. At higher frequencies, poorer noise figures are found,
because of the increased transit angles.
As a consequence of its relatively poor noise figure the diode mixer is
not widely used; therefore it will not be discussed in detail here. For
information about cavity circuits, the reader is referred to literature
dealing with tube design. Diode and triode mixers may be successfully
used in the lower-frequency regions if noise figure is not a primary consideration and if resistance against damage by excessive input power is of
great importance.
A disadvantage in addition to that of noise figure is
that these tubes must always be used in resonant circuits, in order that
the shunting effect of the grid-to-cathode or plate-to-cathode capacitance
may be eliminated.
If a wide tuning range is desired for the receiver, the
resonant circuit must be tuned at the same time as the local oscillator.
To accomplish tuning, the physical size of the resonators must be variable,
and the manufacture of the circuits and the operation of the receiver are
therefore difficult.
These difficulties can be eliminated by the use of
mixing elements of other types.
1.12. The Crystal Mixer.—The crystal rectifier has been developed
to the extent that it is the most effective mixer element for the superheterodyne receiver at microwave frequencies.
The qualitative description of the operation of a crystal as a mixer is similar to that of the diode
and, as in the case of the diode, the i-f voltage is linearly dependent upon
the signal amplitude, for signals small compared with the local-oscillator
Because the part of the crystal in which rectification takes place
is physically very small, transit-time effects are minimized and may be
neglected, for most purposes, even in the microwave region. The considerable effort that has gone into the design of crystal-rectifier elements
~ EC. 1.13]
for this purpose during the war has resulted in a very great improvement in
the various parameters that determine the usefulness of a crystal mixer.
At the beginning of the development the crystal was found to be slightly
better in over-all noise figure than any vacuum-tube mixer then available.
The subsequent improvement has been so great that the crystal now compares even more favorably with the improved vacuum tubes now available. In fact, one result of the improvement in crystal rectifiers has been
the replacement of vacuum-tube r-f amplifiers and mixers by the simpler
crystal mixers, even at frequencies as low as 700 Me/see.
The subject of
the design of the crystal unit is treated in Vol. 15 of this series. A short
discussion of the properties of these units relevant to the design of mixer
and converter circuits, as developed at the Radiation Laboratory, is to be
found in Chap. 2 of this volume.
In subsequent chapters, specific mixer
designs are discussed.
Suffice it to say, here, that rugged receivers using
crystal units as mixers can be made that have over-all noise figures as low
as a factor of 5 (7 db), at frequencies up to 25,000 Me/see.
When it is
realized that such noise figures were rarely achieved, even at frequencies
of a few megacycles per second, before the war, the significance of the
crystal as a mixer element for use at microwave frequencies and the j ustification for placing the emphasis of this volume almost completely on a
receiver of this type become apparent.
1013. The Local Oscillator.-An
important component of the superheterodyne converter, which has not yet been discussed but the existence
Here, again, is a field
of which has been assumed, is the local oscillator.
of development which is so highly specialized and so extensive that it can
not be discussed from the point of view of tube design in this volume.
The physical and electrical characteristics of the available local-oscillator
tubes, however, have a considerable influence on the design of the mixer
units that will be discussed.
It is necessary, therefore, to describe
briefly tubes of the more common types.
The usefulness of the triode and of the more complex space-charge
tubes is limited by the transit times between the various elements when
the tubes are to be used as oscillators, just as when they are used as amplifiers and converters.
If a tube of thk type is to be used as an oscillator,
it is necessary that the gain of the tube as an amplifier be greater than
The only
unity in order that positive feedback can sustain oscillations.
tubes of this type which can be used successfully as oscillators are those
that are specially designed with small interelectrode spacings and with a
shape that allows them to be made an integral part of the cavity type of
oscillator circuit.
The lighthouse tube is probably the best example of
this construction available in quantity, but the highest frequency at
which most lighthouse tubes oscillate is in the neighborhood of 3000
In order to make an oscillator for frequencies higher than this,
it isnecessary tomake use of entirely different principles.
At present the
most widely used local-oscillator tube is the klystron.
This tube utilizes
the principle of velocity modulation of an electron beam.
In addition to
its ability to oscillate at very high frequencies, the velocity-modulation
oscillator, through the introduction of the reflex principle, has become the
simplest kind to manufacture and to operate.
It also has the advantage
of being both electronically and mechanically tunable in a very simple
A klystron oscillator of the original two-cavity kind is shown
schematically in Fig. 1.17. An electron gun, similar to those used in
cathode-ray tubes, with focusing electrodes to form a small-diameter
beam directed upward through the grids of the cavities, is indicated at
the bottom of the figure. The beam isaccelerated bythe large potential,
positive with respect to the cathode, on the cavities.
The field is so
shaped, and the grids of the cavities are so constructed, that the beam
_- Output
Drift dmtance Cav(ty2
----- Buncher
FIG.1.17.—Schematicdiagramof a two-cavityklystronoscillator.
passes on through all of the grids with very small interception of electrons
by the grids. The beam is finally collected on the positive electrode at
the upper end of the tube. The cavities are made to be resonant at a
common frequency and their shape is such that, if they are excited by a
wave of the resonant frequency, a large field is developed between the
two grids of each cavity.
These grids may be considered as forming the
capacitive part of a shunt-resonant circuit.
The electric field, if it exists,
is directed parallel to the path of the electron stream, and so will alternately accelerate and decelerate the electrons passing through the grids.
In accordance with the usual procedure in describing the operation of an
oscillator, the excitation of the cavities will be assumed to exist and the
device will be examined to see if the excitation can be maintained.
Suppose that cavity (1) contains some r-f energy. This cavity will velocitymodulate the stream sinusoidally with the frequency of the resonance of
the cavity.
As the stream drifts on toward cavity (2), the density of the
electrons will no longer be uniform, since those slowed down by the field
in the grid space of cavity (1) will be overtaken by those accelerated in that
region. The spacing between the two cavities can be so chosen that there
are bunches of electrons passing through the grids of the cavity (2) with a
recurrence frequency equal to the resonant frequency of cavity (l).
first cavity is therefore called the buncher cavity.
If the second cavity
is resonant at the same frequency and if, furthermore, the phase of the
voltage in this cavity is properly adjusted, the field between its grids
opposes the transit of electrons between them at the time the bunches
arrive. In this way the electron stream is made to give up energy to
the r-f field, since very few electrons transit the grids at a time when they
would be accelerated and so take energy from the field. The second
Thus the passage of electrons
cavity is therefore called the catcher.
through cavity (2) is made to maintain the energy in this cavity in suficient strength to allow some of this energy to be coupled out to excite
cavity (1) and some to be coupled out as the useful power from the oscillator. The proper drift time between the first and second cavities is
obtained by choice of the acceleration voltage on the beam, and by the
spacing between the cavities.
It is, of course, influenced by the relative
phase of the excitation of the two cavities, which in turn depends upon
the line length of the feedback loop.
A simpler embodiment of the
: velocity-modulation
principle, for use as a low-power local oscillator is
the reflex klystron.
This tube operates in much the same fashion, but
has only one cavity, used as both buncher and catcher, and is therefore
easier to make and to operate.
The two-cavity klystron, and even threecavity klystrons, are used as power oscillators, amplifiers, and even as
The various oscillator tubes and their uses are
frequency multipliers.
dkcussed in Vol. 7 of this series.
1.14. The Reflex Klystron.-The
reflex velocity-modulation
may be described with the aid of Fig. 1.18. The beam of electrons passes
through the cavity grids and enters
the retarding field of the reflector
--which is at a negative potential
with respect to the cathode.
retarding field is sufficiently strong
not only to prevent the electrons
from arriving at the reflector but
also to return them through the
FIG. 1.18.—Functional drawing of the
grids of the cavity.
If an r-f field
between the grids of the cavity, the electrons will be velocitymodulated by this field, and thus will be caused to form bunches as
they drift toward the reflector and then back to the grids. The time
between the first and second passages of a particular group of electrons
is dependent upon the magnitude of the retarding field, and this field can
be chosen to make the arrival of bunches back into the grid region correspond to the times when the field is directed against the backward
transit of the electrons.’ The bunches, therefore, give up energy to the
[SEC. 1.15
r-f field and maintain oscillation at the cavity frequency.
The bunches
form around electrons which, while traveling toward the reflector, pass
through the cavity at a time when the r-f field is going through zero from
the accelerating to the decelerating direction.
This is because the accelerated electrons penetrate more deeply into the reflecting field and therefore take a longer time to return to the cavity than do the unaccelerated
The decelerated electrons, correspondingly, take a shorter
time to return.
For oscillations to be maintained, the total drift time
of an electron that is not acted on by the field in the first transit must be
(n + $) cycles, where n is an integer.
For a given acceleration potential,
there are several values of the reflector potential which will give rise to
oscillations, corresponding to several different values of n. These are
referred to as.reflector-voltage modes.
As the reflector voltage is increased
in the negative direction with respect to the cathode, the mode number
n decreases and, because the electrons are returned at higher backward
velocities as the reflector voltage is increased, the output power increases
There is a limiting reflector voltage,
with increasing reflector voltage.
however, for which the drift time becomes too short to give good bunching. Thus, for a particular tube and accelerat or voltage, there is a reflector-voltage mode that gives maximum output power.
It may be said
that the velocity-modulation
tube surmounts the difficulty of transittime eflects, first by causing the pertinent electrode gaps to be transited
by accelerated electrons instead of by electrons starting from rest and,
second, by making use of the drift time outside of these electrodes as
the means of producing bunching.
The reflex oscillator is simpler in operation than the two-cavity tube
because there is only one adjustment that must be made to satisfy the
condition for oscillation.
This adjustment consists of setting the reflector
Oscilvoltage to give the proper phase to the reflected electron bunches.
lation occurs not only for a discrete set of voltages corresponding to an
exact integral value for n, but also if the reflector voltage is varied
Operation under this condition
slightly either side of the exact value.
reveals one of the most useful properties of the reflex oscillator, namely,
that of electronic tuning.
The slightly incorrect reflector-voltage
setting gives rise to slightly out-of-phase currents in the cavity resonator
and these currents can be resolved into components, one in the correct
phase and one at 90° to this. The 90° component is purely reactive in
character and results in a change in the oscillator frequency in just the
same way as would a change of the capacitance between the grids. Since
the orthogonal component can either lead or lag the in-phase component, the frequency may be altered in either direction from the cavity
frequency, depending upon whether the reflector voltage is made slightly
greater or slightly less than the value making n exactiy an integer.
the reflector voltage is altered from this value, there results, in addition
to the frequency change, a decrease in the amplitude of oscillation,
because the in-phase component of the induced cavity current falls off,
and the oscillator finally falls out of oscillation.
.Most of the reflex
oscillators currently used as local oscillators in frequency converters are
so designed that aconsiderable range of frcqucney can recovered by the
electronic tuning before the output power falls to half its value at the
center of the reflector-voltage mode.
Figure 1.19 shows a typical plot of
the reflector-voltage modes of a reflex oscillator.
The abscissa is the
reflector voltage, increasing in the negative direction toward the right.
The ordinate for the solid curves is the output poww, and the ordinate for
the broken curves is the frequency relative to the resonant frequency
of the cavity.
Since the mode ofhighest output powcrdomnotgi vethe
maximum tuning range, the choice of the operating moclc is macle as a
Output power
--Reflector voltage
for a reflexklystron,
compromise between large output power and large electronic-tuning
Since the reflector does not collect electrons, it draws no current.
Consequently, the electronic tuning device can be a very-high-impedance
source of voltage.
For this reason, the provision for frequency control
of a converter can be accomplished very simply and effectively through
the control of the reflector voltage of the local oscillator.
in many
cases, of course, the frequency range of the refiector tuning is not sufficient
to cover the required tuning range of the receiver and mechanical tuning
must be incorporated as well. Mechanical tuning is accomplished by
altering the size or shape of the cavity of the oscillator.
In some cases,
the tube itself contains only the grids, and the rest of the cavity is
attached to flanges external to the glass wall of the tube.
The tuning of
such a tube is accomplished through the use of plungers or tuning screws
in this external part of the cavity.
There are usually several such screws
around the circumference of the cavity as well as an output loop and
coaxial line, or an exit iris with a waveguide, by means of which power
is extracted.
The tube now most commonly used is of metal construction and contains the entire cavity as an integral part. The tuning of
Type No.
23fW&24400 Internal
[email protected] Internal
minus to
BTL, W13
BTL, Wl?
this tube is accomplished through mechanical deformation of the cavity,
which alters the grid spacing and, therefore, the capacitance and resonant
Across-sectional viewof atypical tube of this kind is shown
in Fig. 1.20.
A recent development in reflex oscillators is the incorporation of a
means for accomplishing the mechanical deformation of an internal
cavity by an electronically controlled mechanism.
One method consists
of the inclusion of asmalltriode,
with a separate cathode, grid, and plate,
within the envelope of the oscillator tube. The plate of the triode is
made of a bimetal strip, the shape
or dimensions of which are determined by its temperature.
temperature is, in turn, controlled
by the triode grid voltage \vhich
determines the current passing into
the plate and, consequently, the
power dissipated by it. The plate
is so connected to the cavity of the
oscillator that the temperature of
the plate determines the grid spacing of the cavity and, consequently,
the frequency of the oscillator,
this way, electronic tuning over a
very wide range—10 per cent or
more—has been accomplished
through the control of the triode
grid, which draws no current.
frequency control cannot be used
FIG. 1.20.—Cross-sectional
view of the
if the response must be instantane2K25 reflex klystron.
ous, because it involves a thermal
time constant.
When the triode tuner is used in combination with reflector-voltage control in a frequency-control circuit, however, completely
automatic frequency control over a wide region can be accomplished.
Thk subject is discussed in Chap. 7.
Table 1.1 is a list of some of the tubes available at present which are
useful as local oscillators.
All but the first of these are reflex klystrons.
Information is given concerning the frequency range, beam voltage and
current, negative reflector voltage, output power, and the electronic
tuning range for a typical tube. These numbers are the average and not
the limiting values acceptable under the specifications of the tubes.
the specification limits the manufacturers’ technical sheets or the ArmyNavy specifications should be consulted.
Present manufacturers are
listed with the following abbreviations:
BTL. . . . . . . . Bell Telephone Laboratories, 463 West St., New York, N. Y.
Western Electric Co., 120 Broadway, New York, N.Y.
Sperry. . . . .Sperry Gyroscope Co., Great Neck, N.Y.
Raytheon. . . Raytheon Manufacturing Co., Waltham, Mass.
RCA. . . . Radio Corporation of America, Camden, N.J.
GE. . . . . . . General Electric Co., Schenectady, N. Y.
1.16. Radio-frequency
might be wondered whether
the superheterodyne receiver could not be improved in noise figure by the
addition of a preselecting r-f amplifier.
It was pointed out in Sec. 1.9
that the only advantage afforded by preelection alone is the suppression
of spurious frequency response, and that the noise figure is changed
very little. The preelection
can be accomplished without tubes as
amplifiers, with only small loss in noise figure, through the use of approThis feature is not of importance unless
priately selective r-f circuits.
image rejection is needed.
Tubes such as two-cavity klystrons can be used as r-f amplifiers and,
in fact, were so used in some of the very early experimental radars in the
microwave region. This was done, however, because of the lack of good
duplexing components.
The minimum detectable signal for the receiver
probably was not decreased by their use. These tubes usually have poor
noise figures and are now rarely used as r-f amplifiers except at high level
for transmitting purposes.
The only other types of amplifier available are the triode and the
more complex space-charge tubes.
At frequencies of 3000 Me/see
and below, the 2C40 tube can be used successfully as an r-f amplifier,
giving an increasing r-f gain and decreasing noise figure as the frequency
is decreased.
An effective over-all noise figure, at 700 Me/see, of 5 db
has been achieved with two such r-f amplifiers in cascade, each tuned,
In view of the fact that a receiver with about
preceding the converter.
the same effective over-all noise figure can be made with a crystal converter, however, it hardly seems worth while to add the complexity
of such amplifiers to a receiver, since all such cavity circuits are relatively
difficult to tune and power must be provided for the tubes.
It is true
that excellent image rejection can be achieved with such a receiver, and
that the receiver is considerably less susceptible to damage by excessive
input power.
If these considerations are important, the use of r-f
amplifiers may be desirable.
The simplicity of tuning and of operation of
the crystal converter, without r-f amplifiers, might be considered worth a
sacrifice of a few decibels in noise figure. In any event, it is more difficult
to maintain a Rceiver using two r-f amplifiers at its optimum performance, and it is likely that in actual use the simpler crystal converter
When the r-f amplifiers
will have abetter noise figure than the amplifiers.
were first developed they were incorporated in many existing receivers,
and improved performance resulted.
This was true, however, largely
because those receivers had very poor noise figures in comparison with
what can now be achieved with the crystal converter.
For use at frequencies of 3000 Me/see and higher there are no vacuum
tubes commercially available that can be used as r-f amplifiers to give
noise figures even comparable with those easily achieved with the crystal
A project at the Radiation Laboratory for the development
of such a tube led to the construction, by H. V. INeher, of a few experimental models of an amplifier tube for the 3000-Mc/sec region. These
are the only tubes known to the author which can be used as r-f amplifiers in receivers with noise figures comparable with those achieved with a
crystal converter.
These tubes were tetrodes, having a screen grid in
addition to the cathode, grid, and plate. The construction was a planes
parallel one similar to that of the lighthouse tubes.
The resonant cavitie.
were built into the tube envelope, which was the size of that of the 6L6
As an example of the extremely fine worlananship involved in them, the
fact may be cited that the grid structures were made with wires 0.0002
in. in diameter and spaced 0.001 in. apart.
At the time these tubes
were first available on a laboratory scale it appeared that some decrease in
over-all receiver noise figure would be possible through the use of one as
an r-f amplifier with the existing crystal-mixer superheterodyne receivers.
Before any large-scale production was accomplished, however, improvement in the crystals available in quantity production and reduced i-f
amplifier noise figures had resulted in a smaller noise figure for the simple
crystal-mixer superheterodyne receiver than could be achieved with
the amplifier tube. The intended production of this tube in factory
quantities was consequently dropped to make the production facilities
The details of the design
available for more urgently needed devices.
and results achieved with this tube are described in a Radiation Laboratory report. 1
1s16. Receivers of Other Types. —Other receivers are sometimes used
at lower frequencies.
A brief description of them is given to show why
they have not as yet been commonly used at microwave frequencies.
Some development work has been done on the design of frequency
converters of basic types other than the space-charge tube.
tubes using accelerated electron beams have largely replaced other types
as local oscillators, it might be supposed that some sort of tube using this
principle could be designed to solve the mixer problem.
Thus far no
development along these lines has given results comparable with the
crystal mixer, and little need be said about them here. As with the
1H. V. Neher,“The RadiationLaboratoryS-BandAmplifier,” RL Report No. 306,
July 10, 1943.
low-level amplifier, the major limitation of beam tubes seems to lie in
the excessive noise they introduce.
A very large conversion gain would
overcome this ditliculty, but sufficient conversion gain to achieve noise
figures comparable with those of the crystal converter has not yet been
It appears that the limiting frequency of the ac.celeratedelectron-beam tube might be met before that of the crystal mixer. The
transit angle of the electron beam must be kept small, as the frequency is
increased, either by a corresponding reduction in the grid spacings or by
an increase of the velocity of the beam through the use of higher potentials. Both of these expedients make the tube increasingly difficult to
Although the crystal probably does have an ultimate limiting
frequency where transit angles become significant, this frequency has not
yet been approached.
So far, the application of the crystal mixer has
been successfully extended to higher-frequency bands through the use of
smaller parts in the cartridge construction and a smaller contact area on
the crystal.
By this means it has been possible to extend the frequency
range of crystal mixers up to 25,000 M c/see with almost no sacrifice in
noise figure over the best value that can be achieved at the lowest microwave frequencies.
The sacrifice that is made in doing this is in the
resistance of the unit to damage from high-power signals.
A receiver that has been common in the ultra-high-frequency
is the superregenerative receiver.
As a simple receiver, using a minimum
number of tubes and having a high sensitivity, it is useful in that frequency range. Because it requires a detector that can be made to
oscillate, however, it has not been very extensively used in the microwave region. Lighthouse tubes can be made to oscillate up to 3000
Me/see and higher, but the noise figure that can be obtained as a superregenerative detector does not appraoch that of the crystal mixer.
Because the output level is high, and, therefore, little amplification is
needed, a superregenerative receiver is useful for some applications where
the noise figure and bandpass characteristics are of less importance than
compactness and small power consumption.
No attempt will be made
in this volume, however, to describe circuits of this kind, and the reader
who is interested in this subject is referred to Vol. 23 where the developments in superregenerative receivers are discussed.
The simple regenerative detector has few advantages over the superregenerative detector and is less reliable and not so simple to operate.
Consequently, circuits of this type have received no serious attention as
microwave detectors.
An interesting possibilityy in connection with regenerative and superregenerative receivers for frequencies higher than about 3000 Me/see has
very recently arisen in connection with a development in crystal rectifier
units, It has been discovered that a crystal rectifier unit, designed
byH. Q. North at General Electric Company, which uses avery small
welded contact between a germanium-crystal element and a platinumruthenium “cat whisker, ” can be made to show a negative output conductance at the intermediate frequency when placed in a very special
microwave circuit, with local-oscillator power incident upon the rectifier
unit. Thecrystal unit used inas~lpcrheterodyne
converter could therefore bemadeto
oscillate and, consequently, could beusedas aregenerative or supperregenerative frequency converter.
Attempts to achieve,
with this crystal, a better over-all receiver noise figure than can be
produced with more conventional crystal mixers have not yet been
On the other hand, it may be that the rather large power
gain that can beachirved willbe of sufficient importance in reducingthe
required amount of i-f amplification to make some application of this kind
worth while. Since this crystal unit is a relatively recent development,
it may be that further work will make possible an improved noise figure,
although the exploratory measurements showed that the noise figure
obtained in the condition of negative i-f conductance was somewhat
greater than that for the same crystal operating in the conventional
Thenoise figure wasnot, however, solarge as fora tube mixer
atthe same frequency (l0,000hfc/see).
In order to indicate the method
in which this unit can be made to act as a regenerative converter, a
discussion of frequency conversion by a local oscillator and crystal
mixer must first be given. Further reference to this subject will be
made in Chap. 2, following the linear-network representation of the
crystal mixer. It\vill beseenthat thespecial tuning conditions necessary
in the microwave circuit may render the operation of such a regenerative
converter impractical, or at least not worth the decrease obtained in the
i-f gain required.
Since the subject is in such a rudimentary state of
development, no final conclusion can be made, except to say that at the
present time there has been no indication of much to be gained witil the
present crystal units.
Early in the development of radio communication,
the crystal
rectifier was used almost universally as a detector for radio signals.
After the introduction of the three-element vacuum tube, receivers
having crystal detectors were replaced by receivers using vacuum-tube
r-f amplifiers, detectors, and audio amplifiers and, finally, by superheterodyne receivers.
The performance of receivers having vacuum
tubes throughout was very much better than that achieved with the best
This fact, together with the need for
crystal rectifiers then known.
frequent adjustment of the common galena crystal detector led to the
complete abandonment of the crystal for use in serious radio practice.
With the extension of radio techniques to higher and higher fredue to electron transit time, lead
quencies, however, complications
As a result,
inductance and distributed capacitance became apparent.
the crystal rectifier, which can be made in a very small package, has
become reinstated.
An important reason for the return of the crystal,
in addition to the great improvements in its performance which have
resulted from intensive research and development during the war, is the
fact that the crystal has been widely used as the nonlinear element of a
superheterodyne mixer. In thk application, the crystal rectifier units
now available give mixer noise figures that compare very favorably, even
at 25,000 Me/see, with those of the best vacuum-tube mixers and converters at low frequencies.
Service in mixer circuits places requirements
on the characteristics of the rectifier which differ from the requirements
The major part of recent developimposed in low-level-detector circuits.
ment has been directed toward the production of units for superheterodyne mixers; however, some units have been designed specifically for
use as low-level detectors.
Other low-level detectors have been selected
by appropriate tests from production-lots of mixer crystals.
It is not the purpose of this volume to consider, in detail, the subject
of crystal-rectifier design but, in order to clarify the later material,
the present chapter will be devoted to a brief discussion of crystalrectifier units. A rudimentary discussion of the physical mechanism
of the units, and of the linear-network treatment of frequency conversion
by the crystal mixer, will be given. This will be follo!ved by sections
giving characteristics and Army-Navy specifications of the units com47
All of these subjects are
mercially available at the time of writing.
treated in greater detail, and more rigorously, in Vol. 15 of this series.
2.1. Physical Description of Rectification.-The
electronic theory of
matter, applied to crystalline structures, shows that the electrons associated with the atoms of the material possess energies in discrete levels,
In a crystalline solid, however, the
just as they do in single atoms.
coupling among the various constituent atoms or molecules causes the
energy levels corresponding to particular quantum numbers in each atom
to be split, and a band of very closely spaced levels results. Some bands
may overlap, but there are always regions of energy which may be
occupied by electrons, and regions between these bands which are
forbidden to electrons.
In substances made up of moderately heavy
atoms, the available energy levels associated with the most tightly
bound electrons are completely filled. Above the uppermost completely
occupied band there is a band of energy levels that may be either completely empty or partially filled, depending upon the nature of the atoms
making up the crystalline solid. For a monovalent alkali metal, for
instance, all of the electron shells
except the last are completely filled
and the energy bands associated
with these inner shells are fully
occupied when the atoms are in
their lowest
The band
associated with the outermost shell,
howcxxn-, is occupied by only one
FIG. 21.-Electronic e,,ergy levels of a
electron per atom and an energy]nctal.
level diagram for such a substance
would be like that shown in Fig. 2.1. The energy difference & between
the maximum energy of an electron in the material and the energy of an
electron outside is the work function for the material, or the minimum
energy that must be imparted to an electron to cause it to escape from the
material in the absence of thermal energy.
Crystals in which the uppermost occupied bands are completely
filled at O“K and those in which thrse bfinds are only partially filled form
two fundamentally diffmmt classes of materials.
Those of the first class
are insulators and those of the srcond, as shown in the diagram, are
metals or conductors.
If the uppermost b:md is completely filled,
the electrons are not free, and elect ric con(luct,ion cannot take place.
Because of the forbidden region bctlvmm the uppermost filled band and
the next higher band, an electron, to become free, must acquire a considerable amount of energy.
In a metal, electrons are easily excited into
adjacent states within the band itself, where they act as free conduction
‘‘ Tntrinsic semiconductors, ” ~vhirh ctin be used in crystalelectrons.
~Ec. 2.1]
units, would be perfect insulators at absolute zero temperature,
since at that temperature they possess only completely filled and completely unfilled energy banda. At the temperatures at which they are
used, however,
the intrinsic semiconductors possess a few conduction
electrons in an otherwise empty band.
This situation exists because of
thermal excitation of electrons from the highest filled band to the next
higher band and, therefore, a condition for conduction of this kind is that
the forbidden region between the bands have a width not much larger
—— Ck3nators
Highest —
normally full
Fm. 2.2.—lZnergy-leveldiagraxuof two ty~es of impurity semiconductors. (a) n-type.
(h) &type.
than kT energy units, where k is Boltzmann’s constant and T is the
absolute temperature.
In order to facilitate the existence of a few conduction electrons, a
semiconductor may contain a very small percentage of an impurity.
In fact, this is very difficult to prevent.
The impurity centers give rise to
either because electrons normally associated with the
impurity atoms, in levels just below the normally vacant band, are
thermally excited into the vacant band, or because electrons in the top
levels of the highest normally full
band are thermally excited into vacant levels associated with the impurity centers.
In the latter
instance, vacancies are left in the
uppermost occupied band and these
can conduct.
both these types are called “impurity semiconductors”;
those in
~IG. 2.3.—Ener&v-levelrepresentationof
which the impurity acts as a donator,
as shown in Fi~. 2.2a, are often
called ‘<n-type, ” whereas those in which it acts as an acceptor for electrons
as shown in Fig. 2.2b are called “p-type.”
A crystal rectifier usually consists of a small contact between a metal
whkker and a semiconductor crystal.
In view of the foregoing energylevel considerations, the junction between the metal and the semiconductor may be described in terms of the energy-level diagram of Fig. 2.3.
The carriers of electric charge will flow from one material to the other
until the energy levels are so altered that equal currents cross the junction
in the two directions.
By this mechanism, a space charge is produced
in the region of the contact.
In the metal, this space charge resides in
a very thin layer (about 10–8 cm) at the boundary, but in the semiconductor the space charge is distributed through a broader region,
because the material has a much smaller number of available carriers of
current. The thickness of the space-charge layer in the semiconductor
can be calculated from a knowledge
of the dielectric constant of the
semiconductor and the density of
p~f~ Votige the carriers of current far from the
Such calculations show
the width of this region in the semiconductor to be of the order of 10–6
con- cm, or about a hundred times the
tact withappliedvoltagein high-resistance
width of that in the metal.
A curve
of the potential as a function of
distance from the boundary has a very steep barrier on the metal side of
the junction, in which narrow region the potential rises abruptly by the
amount 4. which is the difference between the work functions of the two
There is a thin layer near the surface in the semiconductor
in which a potential gradient exists because the curve of the ~otential is
less steep. - The dia~ram of Fig. 2.3
applies to contacts for which the work
function of the metal is greater than
that of the semiconductor.
The relative potentials of the levels
in the metal and in the semiconductor,
when equilibrium is established, can
be shown to be such that the top of
the filled region in the metal is at a
potential approximately half way between the donator level and the
relabottom of the vacant band in an
tion for crystalcontact.n-type semiconductor.
This is the
type of contact to which Fig. 2.3 applies.
If the equilibrium potentials are altered by the application of a
voltage between the metal and the semiconductor, the shape of the
potential barrier is altered.
When the semiconductor is made positive
with respect to the metal, the levels in the semiconductor are depressed
with respect to those in the metal, as shown in Fig. 2.4. The potential
barrier, which may be considered as a thin layer having a high resistance
because of a dearth of free electrons, is enhanced and, consequently, it has
a still higher resistance to the flow of electric current. The amount of
A limit to the rise is
resistance rises if the applied voltage is increased.
reached when electrons from the metal begin to tunnel through the
barrier in a manner analogous to that of field emmission.
A curve
showing the current passed through the contact as a function of the
applied voltage, with the semiconductor positive, is therefore, similar to
the left half of Fig. 2.5.
Application of a voltage of the other sign across the contact reduces
the insulating effect of the potential barrier by raising the potentials
in the semiconductor relative to those in the metal, as shown in Fig. 2.6.
The effective resistance of the contact decreases until the voltage is
reached for which the insulating layer no longer exists, as in Fig. 2“7.
The resistance of a contact at this voltage and higher is primarily what is
called the “spreading resist ante, ” which is determined by the area of the
In the semicontact and the bulk resistivity of the semiconductor.
contact with applied voltage in direction of
FIG. 2.7.—Energy-leveldiagram with
applied voltage correspondingto linear
part of high-currentcharacteristic.
conductor, only a small cross-sectional area near the small contact is
effective for carrying the current, but inside the semiconductor the
effective area rapidly increases with distance from the surface.
right-hand side of Fig. 2.5 shows the current as a function of an applied
voltage of this sign (semiconductor negative).
The steepest slope of the
straight part of the curve is a measure of the spreading resistance.
From this description it can be seen that a nonlinear current-voltage
relationship exists for a metal-to-semiconductor
The device
cannot be used as a rectifier unless a voltage can be applied across the
It might be argued that the second contact this requires
would exhibit characteristics that are the reverse of those of the first
contact and that the net effect would be a linear resistance.
Thk would
indeed be so if the two metals were the same, and if identical contact areas
were used. The rectifying junction results when the connection to the
back of the semiconductor is made through a very much larger area.
This back contact could indeed be nonlinear in the reverse sense to the
small contact, with respect to voltages applied to the unit, but, because
the area is large, the resistance of the barrier layer is very small, even
The d-c
compared with the spreading resistance for the small contact.
characteristics of a crystal rectifier unit, therefore, do resemble Fig. 2.5,
and the effect of the back contact can be entirely neglected.
In practice, the crystals used for microwave work are usually made of
silicon in which has been dissolved a small amount of aluminum, which
The back
acts as the acceptor impurity for a p-type semiconductor.
contact is made by soldering the piece of crystal into a cartridge unit,
as sketched in Fig. 2.8, and the small metal contact is made by light
pressure of a tungsten whisker, carefully prepared with a very small
The research and development work that has
been done toward the perfection of techniques for the
production of these units is described in Vol. 15 of this
Conseries, to which reference has already been made.
siderable work has been done toward perfecting crystals
with germanium semiconductors but these have not yet
been widely used in microwave applications.
The same
principles are involved in the construction of microwave
circuits for the use of such units and, in fact, the design
of circuits for crystal units of any type could follow the
methods to be outlined in the follo~ving chapters
FIG. 28. Typical crystal- of this book.
Specific designs may have to be altered in
details for the best utilization of crystals of other types,
but this can be done if the pertinent characteristics of the units to be
used are known.
2.2. High-frequency Effects in Crystal Rectifiers.-The
of the performance of vacuum tubes at high frequencies is a result of their
large physical size. The crystal rectifier can be made very much smaller
because of its inherent simplicity and, therefore, proper design of the
cartridge allows the effects of lead inductance and distributed capacitance
to be neglected at very much higher frequencies than for any vacuum
tubes so far constructed.
Since only the barrier region in the semiconduct or is effective in producing the nonlinear characteristic, the device
could theoretically be made microscopic in size. In practice, of course,
considerable skill is required to assemble the small parts. Also, to
achieve a whisker contact that has an appropriate area and that will
remain stable, some spring action in the whisker is required.
The quantity in the crystal-rectifier unit analogous to the interelectrode spacings of a vacuum tube is the thickness of the barrier layer.
The carriers of electric charge must be able to cross this barrier in a time
short compared with a quarter cycle of the applied r-f voltage if the
high-frequency behavior is to be simply related to the d-c characteristic
shown in Fig. 2.5. Since this barrier thickness is of the order of 10-’ cm,
it is obvious that transit-time effects may be neglected at very much
higher frequencies than would be possible in any device in which an
interelectrode gap must be obtained by mechanical means.
A simple equivalent circuit for the crystal-rectifier unit, exclusive of
the transformation effects of the cartridge, may be used for illustrative
purposes. Such a circuit, shown in Fig. 2.9, includes the nonlinear
resistance R of the barrier, a linear resistance Rb equal to the spreading
resistance, as measured by the linear part of the d-c characteristic, and a
capacitance C shunted across the nonlinear resistance.
This capacitance
arises because the barrier laver.
., althouch it
has very small conductivity, does have a
considerable dielectric constant, and it can
be shown that the effect on an” applied r-f
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voltage is similar to that of a small conFIG.2.9.—Equivalentcircuit for
denser shunted across the barrier region.
The magnitude of this capacitance is not
independent of the applied voltage because the effective thickness
of the barrier varies somewhat with the value of the applied voltage.
For most purposes, however, the capacitance may be regarded as fixed.
Because of the presence of the spreading resistance Rb, the capacitance
of the contact cannot be resonated out by an external inductance and,
consequently, this capacitance has a real effect upon the high-frequency
behavior of the crystal rectifier. The capacitance acts as a shunt that
lowers the effective impedance of the barrier at high frequencies.
its presence has the greatest effect for the highest barrier resistance, the
nonlinearity of the resistance, on which the usefulness of the crystal unit
depends, is reduced.
A voltage applied to the crystal in the direction of high resistance is
said to be applied in the backward direction, and one in the low-resistance
direction is called a forward voltage.
The ratio of the voltage to the
current for a backward voltage is called the back resistance and for a
Because of the barrier capacitance,
forward voltage the front resistance.
the ratio of the back to front resistances is not so significant, as a measure
of the quality of the crystal, as it would be if there were no capacitance
present. Since the capacitance increases with increasing contact area,
it is important that the area of the contact be kept as small as is comThis is one of the reasons for the care
patible with other requirements.
with which the whisker is prepared and brought into contact with the
The small contact area Used is produced by the flattening of the whisker which occurs if a small force is applied across the contact. Crystals designed for the highest frequencies usually have a
smaller force applied to the whisker and have, consequently, smaller
areas of contact than those designed for lower frequencies.
By this
means, it has been found possible to maintain about the same sensitivity
over the microwave range, but the higher-frequency units are, consequently, mechanically and electrically Iess rugged.
The back resistance of a microwave rectifier unit can be used as a
measure of its quality, provided that a lower limit for the value of the
back resistance of acceptable units of the same type is known.
statistical studies, it has been found that a lower limit to the back resistance of crystals of a given type, measured at a given applied voltage,
can be set. Crystals of that type which have back resistances below this
limit are probably damaged, whereas those having resistances above the
limit are almost certainly still acceptable.
The measurement of the
back resistance at the given voltage is a test by which it is possible to
eliminate practically all inferior units at the expense of losing some
acceptable ones. In view of the difficulty of measuring, directly, the
quality of a crystal, and in view oft he large numbers of crystals available,
such a loss has been considered a small price to pay for simplicity of
testing the crystals.
The back resistance of a crystal unit that is in electrical use may
become lower over a period of time. Such a change has more significance
than the absolute value of the back resistance at any one time. Any
change in the back resistance must mean a change in the contact or in the
semiconductor and should, therefore, be looked upon with suspicion.
In the past, a lack of realization of the significance of the back resistance
or of a change in it has led to the continued use of damaged crystals in
Because of the simplicity of a back-resistance test the importance of performing it at frequent intervals, if high-quality performance
I,imiting values of the
is to be maintained, cannot be overemphasized.
back resistance for crystals of various types are included in a table at the
end of this chapter.
2.3. Figure of Merit of Crystal-video Receivers.—In Sees. 1”5 to 1.7,
a discussion of the quality of a rcccivcr with a low-level detector was
For completeness, this discussion shouhl include the definition
and method of measurement of the “figure of merit, ” which is used as a
measure of the quality of crystal cietcctors availalde commercially.
order to correlate the figure of merit with the minimum signal detectable
by a receiver consisting of a Iow-level dctrctor and an amplifier, it is
necessary to have the definition include a parameter that takes into
Two crystal detectors
account the noise power arising in the amplifier.
that are identical in performance when used with a noise-free amplifier
do not necessarily make equally sensitive rccrivers when used with
practical amplifiers.
Therefore, the figure of merit of a crystal detector
is a quantity that is related to the quality of the over-all receiver, when a
typical video amplifier follows the detector.
As stated in Sec. 1.6, a crystal upon which a signal is incident may be
represented, at the output terminals, by a current generator i in shunt
with a conductance equal to that measured between these output terminals. It has been found that the noise generated in a video amplifier
can be represented as the noise of a resistance between the grid of a
perfect amplifier and the input terminal, as shown in Fig. 2.10. Over a
wide range of impedances across the input terminals, the noise power
available at the output terminals of the amplifier, in excess of that arising
from the circuit connected across the input terminals, can be considered
The entire circuit at the
as arising as Johnson noise in this series resistor.
amplifier input terminals may then be represented by Fig. 2.11, where R
is the resistance of the output terminals of the crystal detector and RA is
the equivalent noise resistance of the amplifier tube.
The relation
Fx~. 2.1l.—Modulation-frequencycircuit
of low-leveldetector.
circuitof firstamplifiertube withnoiseresistance.
between the output voltage E of the amplifier, caused by an r-f signal,
and the r-f signal power P is
where b is the proportionality constant defined in Sec. 1“7 and A is the
Since the rms output noise voltage of the
voltage gain of the amplifier.
amplifier now originates completely as Johnson noise in the two resistors
R and R*, its value is
R = A 441cTB(R
+ R.),
where B is the equivalent noise bandwidth of the receiver, as defined in
Sec. 1.4, and the remaining symbols have the same significance as previously stated. The signal-to-noise ratio at the output terminals of the
receiver is thus given by the ratio of Eq. (1) to Eq. (2),
E __
% – ~41cTB
b 4R
+ R.”
The right-hand side of Ea. (3)
., has been divided into two factors, the
second- of which includes the quantities descriptive of the detector.
This quantity,
is called the figure of merit of the video crystal and has been used to
evaluate the acceptability of production crystal units intended for use
as low-level detectors.
Before the figure of merit may be evaluated from measurements of the
and Rfor the crystal, the vdueof h?A mmt be known.
value is, of course, dependent upon the particular amplifier tube and
varies somewhat among specimens of the same type and widely among
different types.
The amplifier tube most commonly used in video
receivers that have crystal detectors is the 6AC7 tube in pentode ccmnection.
Tubes of this type have been shown by measurement to have
equivalent noise generating resistances of 1000 to 1200 ohms. The
specifications, under which the various types of video
crystals have been produced and tested, are based on calculations for
the figure of merit in which the value for It.4, in ]’;q. (3a), is taken to be
1200 ohms.
At the end of this chapter is a list of the various types of crystals for
which Army-Navy specifications existed at the time of writing.
in the list are several types of low-level detector crystals, designed for
specific frequency regions as indicated in the table.
It will be observed
that these so-called video crystals have, in addition to a specification of
figure of merit, a definite minimum or maximum value of output resistance. The resistance of the crystal determines the bandwidth of the
first circuit of the amplifier, because the capacitance of this circuit is
largely outside the control of the designer.
If the resistance becomes
too great, the pass band of the amplifier becomes too narrow; therefore,
the receiver does not respond properly to signals of the type for which it
was designed.
2.4. The Crystal Converter.-The
crystal rectifier, when used as a
frequency converter, is operated under conditions rather different from
those in the low-level-detector application.
For this reason, an entirely
different set of parameters are used for the evalutaion of the qua!ity of a
unit intended for use as a frequency converter.
This can be seen from
a simplified consideration of the mechanism of rectification based on the
d-c characteristic of Fig. 2.5. Although an analysis based upon the d-c
characteristic gives a poor picture of the microwave behavior of the
contact as a frequency converter, because of the barrier capacitance,
it does serve as a qualitative description.
In Fig. 2.12, a typical d-c characteristic is drawn.
In addition,
there is shown, as a function of time along the negative ordinate axis, a
voltage corresponding to the superposition of the local-oscillator voltage
The output terminals of a crystal mixer are
upon a small signal voltage.
so arranged that no microwave-frequency
components of the current in
the crystal appear at them.
The output terminals carry only the direct-
current and the beat-frequency components, as indicated by the curve
representing this current as a function of time plotted along the nghthand part of the horizontal axis. The magnitude of the beat-frequency
component in this current is related to the efficiency of the device as a
frequency converter.
From the diagram it is evident that the magnitude
of this beat-frequency component depends primarily upon the ratio of the
slopes of the d-c characteristic at
the negative peak and at the positive peak of the local-oscillator
It is apparent that the
curvature of the characteristic in
~ ~ Signalamplitude
the vicinity of the origin is of
little direct importance compared
with the ratio of what might be
called the differential impedances
at two p o i n ts symmetrically
FIG.2.12.—Grapbicalillustrationof frequency conversionon basis of d-o characchosen at some distance on either
I l—
side of the axis. From this con‘eri’tic ‘f crystal”
sideration, it would be expected that the crystal rectifiers that make the
best low-level detectors do not necessarily make the best units for use as
frequency converters, and vice versa.
Another significant relationship that can be qualitatively determined
from this simple analysis is the dependence of the ccmversion efficiency
on the magnitude of the local-oscillator voltage applied.
If the signal
voltage is kept small compared with that of the local oscillator but
of constant magnitude, and the amplitude of the local-oscillator voltage
is varied, the magnitude of the modulation component in the linear superposition of the two voltages remains
Because of the curvature
of the d-c characteristic, particularly
on the positive side of zero voltage, the
ratio of the differential impedances on
the two sides diminishes with decreasLocal-oscillatorpower
ing local-oscillator voltage and, as a
FIG.2,13.—Typicalcurve for conversion efficiency vs. local-oscillator result, the conversion e5ciency of the
device should be less with small localoscillator amplitudes than with large amplitudes.
The conversion efficiency, plotted as a function of the local-oscillator power, maybe expected to
behave as in Fig. 2.13, where the abscissa is the local-oscillator power and
the ordinate is the relative conversion efficiency.
There is no longer
any significant increase if the local-oscillator power is increased beyond
that which utilizes the straight portion of the d-c characteristic in the
forward direction.
At larger amplitudes, there may even be a decrease,
because the differential back resistance may decrease.
This situation has
not been indicated, however, in either Fig. 2.12 or Fig. 2.13.
The conversion efficiency is usually specified as the gain of the converter unit, considered as a network, between the signal input terminals
and the i-f output terminals.
This gain, as defined in Sec. 1.4, is the
ratio of the available i-f output power to the available signal input power,
and, for a crystal converter, it is almost certainly less than one. Consequent y, it has become customary to use the reciprocal of the gain,
called the “loss” L of the converter and to express it in decibels.
order to specify completely the quality of the converter, it is necessary to
know the value of the output noise power from the converter, considered
as a network, as discussed in Sec. 1.4. From these two quantities, the
effective over-all noise figure of a receiver in which such a converter is
used in conjunction with an i-f amplifier of known effective noise figure
may be estimated.
The noise temperature t,as defined in Sec. 14, has
been most commonly used as a measure of
the noise. In order to specify the local?!3
oscillator power for optimum effective
over-all noise figure, it is necessary to
know both the dependence of the noise
of the crystal on the local;
and the noise figure of the
i-f amplifier for a generator impedance
FIG. 2.14,—Typical curve of equal to the impedance of the output
mixernoisetemperaturevs. 10calterminals of the crystal converter.
impedance also depends somewhat on the
local-oscillator power, although it varies only slowly for local-oscillator
drive sufficient to give a conversion gain near the maximum.
The noise temperature of a crystal converter is found to be approximately linearly dependent upon the incident local-oscillator power, as
indicated in Fig. 2.14. Equation (1,26) may be used to calculate the
effective over-all noise figure if F?, the effective noise figure of the i-f
amplifier, is known for the range of output impedances possessed bjj the
crYstal converter.
Since the over-all noise figure is usually expressed in
decibels and since the loss L, also usually expressed in decibels, is used
instead of the gain, this equation may be rewritten as
F;+, a = La + 10 log,, (F: + t – 1),
where t and F; are numerical ratios, not expressed in decibels.
2.15 shows a typical curve of the effective over-all noise figure of a receiver
resulting from the combination of the three quantities in Eq. (4). It will
be observed that the noise figure decreases in about the same way as the
conversion efficiency increases, for small local-oscillator power. For
high local-oscillator power, the conversion efficiency no longer increases
so rapidly but the noise temperature
continues to increase; therefore the
over-all noise figure goes through a
minimum value and then increases
again. The noise figure does not vary
rapidly in the region of the minimum
value and, therefore, a reasonably
large deviation
in local-oscillator
power from the optimum value can be
The optimum local-oscillator power is usually about 0.5 mw
into the crystal, which results in a
continuous rectified crystal current of
about 0.5 ma. More specific informaLocal-oscillator power
tion about conversion losses and noise
FIG. 2.15.—Over-aUnoise figure vs.
temperatures, as well as about i-f impedances of typical units, will be given in later sections of this chapter.
2.5. Linear-network Representation of the Crystal Converter.-The
use of the terms loss and noise temperature, to describe the crystal
frequency converter, suggests that the device may be considered as a
network that possesses two pairs of terminals: one pair to which the signal
is applied, and one pair from which the i-f signal is obtained.
the converter depends for its action upon the nonlinear relationship
between voltage and current in the crystal unit, a linear relationship
exists between the i-f output voltage and the microwave input signal
voltage, provided the signal amplitude is vw-y small compared with that
of the local oscillator.
This is
true because the voltage-to-current
relationships of the crystal, which
are effective for the conversion from
of crys- the signal frequency to the intertal converter.
mediate frequency, are differentials
of the d-c and r-f characteristics, and these maybe regarded as constant for
very small signal amplitudes and for a given local-oscillator power.
The converter may then be regarded as a box containing a pair of signal
terminals and a pair of output terminals for the i-f voltages, as indicated
in Fig. 2.16. A considerable number of relationships that help to
clarify the complex behavior of crystal converter units can be derived
from this representation.
It might be wondered what would result if the device were worked
If an i-f voltage were impressed upon the i-f terminals,
would an r-f signal be produced at the signal terminals?
A return to a
consideration of the d-c characteristic will help to answer this question.
If, as in Fig. 2“17, the local-oscillator voltage is impressed upon the
crystal, in the absence of an r-f or an i-f signal, and a d-c bias is added in
series with the crystal, then the operating point shifts, with the result
that a different part of the characteristic determines the r-f impedance
of the crystal.
If the bias voltage is made to vary through zero sinusoidally at the i-f frequency, the effect is to modulate the r-f impedance
of the crystal at the i-f frequent y or, in other words, to amplitude-moduIt is well known that, an amplitudelate the r-f current in the crystal.
modulated r-f current or voltage may be considered as equivalent to the
unmodulated current or voltage plus two other r-f components; one
above the original frequent y and one below it. These two added
components differ in frequency from
the incident radio frequency by an
amount equal to the modulation fre1/
In the crystal converter,
where the modulating voltage is supLocal-oscillator
posed t o b e at t h e intermediate
due to
one of these new radio
bias voltage
frequencies will correspond to the
signal frequency and the other to
FIG, 2 17.—Graphical illustration of the image frequency.
When an i-f
effectof bias voltageon r-f admittance.
voltage is applied to the i-f terminals
of the converter of Fig. 2.16, voltages of equal magnitude, at the signal
and the image frequencies, appear at the r-f terminals.
This assumes,
of course, that there is contained in the box between the crystal and the
input terminals nothing that is sufficiently selective with respect to
frequency to favor one of these voltages over the other.
To return to the use of the converter in the direction for which it was
intended, the application of a signal voltage to the input terminals gives
This voltage in turn
rise to an i-f voltage at the output terminals.
produces, at the input terminals, a voltage at the signal frequency and
one at the image frequency.
The presence of the signal-frequency
voltage serves only to determine, in part, the signal-frequency impedance
of the converter, but the image-frequency
voltage has considerable
It is clear that the behavior of the converter cannot be
independent of the image-frequency impedance of the generator circuit
connected to the input terminals; a reflection of the image-frequency
wave from the generator back into the converter unit will produce a
The phase and amplitude of this
voltage at the intermediate frequency.
component, relative to the one produced directly
by the signal, is dependent on the phase and amplitude of the reflected
image-frequency wave. The signal-frequency impedance, the output
impedance and the conversion loss must all be dependent, to some
degree, upon the impedance presented by the generator circuit to the
image-frequency wave.
Because the crystal is a nonlinear clement, there must be developed,
in addition to these voltages, many other higher-order components
corresponding to harmonics and products, sums, and differences of these
A rigorous analytical treatment of the device must include
In addition to the
all of these components as well as the image voltage.
process just described, the image-frequency voltage may be developed
as the difference frequency between the second harmonics of the localoscillator frequency and the signal frequency.
The effects of the higherorder frequencies, however, are smaller than those produced by alterations
in the crystal impedance.
They are, moreover, analytically and experimentally, very much more difficult to handle.
To estimate the effects of
these voltages, it is useful to consider the image frequency alone because
it is probably of the greatest importance, and relatively simple experiments can be made to verify the analytical predictions.
The effect of
varying the impedances presented to the higher-order frequency components, such as the second harmonics, may be anticipated to be qualitatively similar, but less pronounced.
2.6. The Three-tenninal-pair-network
Representation. -Let us suppose that the only voltages of significance in the converter circuit are
those at the signal, image, and intermediate frequencies.
Although the
first two of these appear on the
input terminals of Fig. 2.16, it is
convenient to assume that there
exist separate terminals for them,
as shown in Fig. 2.18. This could
be achieved in practice
by an
appropriate splitting net work, comconverterwith separateeignal-and imageposed of frequency-selective
cuits, within the box. A three-terminal-pair
network, in which the
voltages and currents are linearly related, as they are for small voltages in
the crystal converter, may be described by a set of three transformation
equations involving a total of nine independent coefficients characteristic
of the network.
Because of the symmetry between the signal- and imagefrequency components in the converter, assuming the converter to hav~ a
low Q in terms of the frequency difference involved, the number of
independent coefficients may be reduced to five, provided the equations
take account of the phase relation between the signal- and imagefrequency components.
These equations may be written as,
where the subscripts ., ~, and ~ refer respectively to the signal, intermediate, and image frequencies, and the asterisks denote the complex
The i-f current due to the image-frequency voltage eYhas a
value that is the complex conjugate of that produced by the signal
Therefore the complex conjugate of the term yPaeTis taken,
in the second equation, to be the cent ributi on of the image-frequency
For this reason, the complex conjugate
voltage to the total i-f current.
of the image voltage is used throughout, and the third equation gives the
complex conjugate of the image-frequent y current.
If the image terminals are connected, independently of the signal
terminals, to an external admit tancc YT, the relationship between the
image-frequency current and voltage is
– YY
If this expression is substituted into Eqs. (5), and if e, and i, are eliminated between the resulting equations, the relations between the voltage
and currents at the signal and intermediate frequencies become
Equations (7) show, through their dependence upon the image
termination yy, that the behavior of the device as a converter from signal
to image frequency cannot be specified independently of the treatment of
the image-frequency component.
Specifically, the conversion loss, the
signal input admittance and the i-f output admittance can all be calculated from Eqs. (7) in terms of Y=-, Yap, Yfla, and I’pp, plus the signalgenerator admittance ya and the i-f load admittance at the output
terminals, YP.
To find the signal input admittance
Y. for an i-f load admittance
Y?, Eqs. (7) may be written as,
(Y.. – Ya)ea+Ya8ep
Ydae=+ (YP~ +y~)e~
= O,
To be consistent, the determinant of these equations must vanish, or,
The i-f output admittance Yp, by analogous steps may be shown to
depend upon the signal-generator admittance y., as
These two relations, Eqs. (14) and (15), reveal a point about the design
of crystal mixer circuits which must not be overlooked if the best possible
performance from a given tryst al unit is to be obtained.
The choice of
the r-f and i-f matching conditions cannot be considered to be independent
or to be completely a property of the crystal alone. Because of the interdependence, the design of the input circuit of the i-f amplifier should
take into account the effect on the i-f output characteristics of the signalfrequency and image-frequency admittances that are connected to the
In turn, the signal- frequency admittance
r-f terminals of the converter.
of the converter is dependent both upon the i-f load admittance presented
to the converter by the i-f amplifier and upon the admittance presented
If the image-frequency termito the converter at the image frequency.
nation is fixed, the coefficients of Eqs. (7) may be regarded as constants
descriptive of a particular converter unit. There is, therefore, a great
similarity between the converter and an ordinary piece of transmission
line, with respect to the dependence on the signal-generator and outputload admittances.
In the representation of a transmission line by equations analogous to Eqs. (7), it can be shown that the transfer admittances
That this is also true for the
analogous to Yti~and YP. must be equal.
network representing the crystal converter cannot be proved without
making some restrictive assumptions.
Dicke’ has shown that, if certain assumptions about the time dependence of the voltage across the barrier in a crystal rectifier unit are true, a
relation bet ween Y.~ and Y~mexists such that
= Il’~m].
1R. H. Dicke, “A Reciprocity Theorem and Its Application to Measurementof
Gain of MicrowaveCrystal Mixers,” ILLReport No, 300, Apr. 13, 1943.
On the basis of this relation, the conversion loss of a crystal converter can
be calculated from measured values of the signal or i-f admittances of
the converter, for each of several different admittances connected to the
other pair of terminals.
Comparisons have been made between the
values of the conversion loss found in this way and the values measured
on the same units by the standard method that involves the measurement
of the ratio of the available input power to output power.
It is found
that the reciprocity condition holds very closely for silicon crystals, but
that it does not hold for germanium crystals.
If this condition is not
obeyed, the efficiency of conversion of r-f power to i-f power is not the
same as that from i-f power to r-f power.
It has been found that units
that do not obey the reciprocity conditicn are usually more efficient as
converters from low to high frequency than in the opposite sense. The
agreement between the measured conversion loss and that calculated
from the admittance data, for silicon units, is excellent confirmation
of the usefulness of the linear-network representation of the crystal conEven for units that do not sho~v reciprocity, the same qualitative
interdependence of r-f and i-f admittances is found.
The conversion loss of the converter in terms of the parameters of
Eqs. (7) may be derived in the following way. The output power from
the converter unit is the real part of – ~iped*, whereas the power entering the unit is the real part of &.eti*; therefore the loss is
~ =
which, by Eq. (13), becomes
~ =g.e.’
Here, G. and gB are the real parts, or conductance parts, of Y= and yj,
If the second oi I;qs. (12) is solved for lem/[email protected] the
solution substituted in Eq. (17), the expression for the loss becomes
If the value of G. from Ilq. (14) is substituted in this expression, the loss
in the form
where the G’s and B’s are the real parts and imaginary parts of the Y’s
with the same subscripts.
In addition, Ga88. and Baddaare, respectively,
the real and imaginary parts of YadY~a. The gain of the network which
appears in the expression for the effective over-all noise figure of a cascade
of networks, is defined (see Sec. 1“7) as the ratio of the signal power
available from the network to that available from the signal generator
connected to the input terminals of the network.
The full po)ver available from the converter is obtained when the load admittance yd is so
chosen that the loss L is a minimum.
There are two orthogonal quantities, [email protected] bfl,in Eq. (20) which must be adjusted to make L a minimum.
The quantity bb can be given any value from plus to minus infinity.
minimum of L will occur for a minimum of
(% +
(Bdd + bp),
which is obtained when
as is evident if the derivative of Eq. (21) with respect to (Bdd + b~) is set
equal to zero. Thus Eq. (20) becomes
If the partial derivative of L with respect to g~ is taken, the value of gp
resulting in minimum loss can be found to be
where only the positive root has physical significance.
The optimum
load admittance, from the combination of Eqs. (22) and (24), is
Upon substitution of Eq.
minimum loss becomes
(24) into Eq.
(23), the expression
for the
By algebraic manipulation,
Eq. (26) can be put into the form
is given by
The second factor in Eq. (27) maybe called the impedance loss, because it
can be,evaluted from direct measurements of the impedance of one pair of
terminals of the mixer for each of two different load conditions at the
other pair, This loss and the actual minimum loss encountered in practice are the same only if the first tern, in the expression is unity.
This is
true if the mixer obeys the reciprocity condition.
If the mixer is worked backward, that is, caused to generate the signal
frequency from an applied i-f voltage, the 10SSfor this process may be
calculated in a similar manner.
The loss L’ from low- to high-frequency
power is found to be identical with Eq. (27) except that the reciprocal of
first term appears; that is,
If the ratio of Eqs. (27) and (28) is taken,
_ ly.#12
This ratio of the losses in the two directions reveals to what approximation
reciprocity holds.
Since, as mentioned earlier, the loss is usually greater
in the direction from r-f to i-f power than in the other direction, when
the reciprocity theorem is not obeyed the relation between Ymfland Y6.
can be stated to be, almost without exception,
[Ym~l> /Y&J.
2.7.The Relation between the Input Admittance and the Load Adrnittance.-The
representation of the mixer as a linear network makes it
apparent that the input admittance cannot be independent of the load
admitt ante, and, in fact, the relationship between them may be calculated with the aid of Eq. (27).
This is most easily done for cert ain simple
cases from which the general interdependence may be discovered.
example, suppose that the i-f output terminals are connected to a pure
susceptance which can be adjusted through all values between negative
and positive infinity.
Suppose, further, that the mixer includes r-f
matching devices such that, under the condition of infinite load suscept-
ante, the signal admittance is real. From Eq. (14) it is evident that this
may be written
Y,. = G= = G...
The load susceptance may then be adjusted to make the input admittance
mismatched to Y= by as large an amount as possible.
This may be
expressed, by use of Eq. (14), as
= G.. –
[email protected]=
GBR+ j(Bdp + bJ”
The mismatch between Y~ and Y.. may be expressed in terms of the
absolute value of the reflection coefficient r of Y~ relative to Y,., which is
The maximum loss due to mismatch, corresponding to the maximum
of Ir [2, can be found by setting the partial derivative of Ir 12with respect to
([email protected]+ bp) equal to zero. The result of this is
This expression is identical with Eq. (22), which gives the optimum load
susceptance from the standpoint of conversion loss. If this susceptance
value is used in Eq. (32), the result is
The r-f signal is applied to a microwave converter through a coaxial
line or a waveguide.
The position in this input line at which the
signal terminals of the equivalent network are located is, as yet, arbitrary. It is convenient to choose these terminals to be at a point
at which Y.. is real. This is not incompatible with making Y.. real,
because, for instance, the r-f matching in the mixer could be such that
G.. is the characteristic admittance of the transmission line. Then Y..
would be real at all points along the input line. Choosing the position of
the input terminals to make Y., real makes the imaginary part of the
second term of Eq. (36) equal to zero, or
~EC. 2.8
This is satisfied if
2G.a GD8= G.w.l
B.R8. = O.
The first of the conditions of Eq. (38) results incgreater than one and,
therefore, it does not have real significance.
The second of these conditions, however, resultsin
Y.. = Gm. -
From Eqs. (31) and (39),
Under these conditions, however, Eq. (28) for c may be used to show that
Therefore Eq. (27) becomes
It is now clear that the measurement of these two admittances at one
pair of terminals of the converter, under each of two conditions at the
other pair, constitutes, according to Eq. (42), a measurement of the
mimimum conversion loss of the converter, except for the reciprocity
The result of this measurement, sometimes called the impedance
loss Lz, is given by
This expression is identical with one which can be derived for the transmission loss of a piece of transmission line an integral number of half
wavelengths long. For the transmission line, G.. is the conductance of
the input terminals with the output terminals open-circuited and G,. is
the conductance with the output terminals short-circuited.
An experimental apparatus to be described in Chap. 8 has been designed and used
to measure the impedance loss of crystal mixers, by measurement of
The results, for silicon crystals, have been in good agreement with those obtained by more dh-ect methods.
2.8. The Dependence of Input Admittance on the I-f Load Admittance.
The characteristic admittance of a transmission line may be shown to be
just 4G8CG0.. That the same expression holds for the converter may be
verified by putting Eq. (24), for gd, into Eq. (14), under the condition
that the choice of the position of the input terminals is the same as
before, and therefore B.dflti is zero, as in Eq. (38).
It is now possible
to discover the range of input admittances which will be shown by the
converter for all possible values of i-f load admittance, by use of Eq.
It is a general theorem for linear networks that a circle on an
admittance diagram is transformed by the network into another circle.
It is known that, under the special conditions here assumed, two points
2.19.—Limitingr-f admittancecontoursvs. i-f load admittancefor severalvaluesof.
impedanceloss in dccibcls.
of the admittance contour at the input terminals, resulting for output
load admittances along the circle yd = jbu (a circle of infinite radius in a
cartesian plot of conductance vs. susceptance, or the outside circle on
a Smith chart), fall upon the conductance axis. It has also been shown
that G.. differs from G,. by the maximum amount for this range of load
admittances and, therefore, it follows that the conduct ante axis is a
diameter of the input-admittance circle.
If, further, the r-f tuning is so
chosen that ~G..G.. corresponds to a matched input line, the circle will
be centered, on a Smith chart, at Y,. Several such circles are shown in
Fig. 2.19, corresponding to various values of L. between O and 10 db.
Under these conditions, only points inside the circle corresponding to
the Lz of the converter in question can be produced as the input admittance to the converter by choice of the load admittance.
The center
point of the circle Y, is obtained when the load admittance has the optimum value, as given by Eq. (25).
One of the important tasks in the design of converter and mixer circuits is the adjustment of the tuning of the’input circuit in such a way that
minimum loss is obtained for the largest possible number of crystal units.
In this connection it is important to realize the significance of the definition
of the gain, and its reciprocal the loss, as it appears in the expression for
the over-all noise figure for the cascaded converter and i-f amplifier.
input circuit of the i-f amplifier does not need to provide for the converter
a load admittance such that the converter delivers maximum power. The
conversion loss of a given converter, therefore, is not necessarily minimized by a tuning that matches the signal generator to the converter,
with the converter connected to the i-f amplifier.
The i-f input circuit
is so chosen that the smallest possible noise figure compatible with the
desired bandwidth and the amplifier tubes is achieved.
As a result,
the input admittance of the mixer lies nearer to the boundary of the region
inside the appropriate circle of Fig. 219 than to the center.
Nevertheless, for minimum over-all noise figure, the mixer tuning should be
such that the characteristic admittance of the mixer is matched to the
admittance of the r-f signal generator, since this gives minimum conversion loss. Therefore, a load admittance having the value such that the
mixer delivers maximum power should be used in experiments intended
to establish optimum r-f tuning conditions for the mixer.
For converters in which IYtiB\# IYd.l, and the actual loss therefore
does not equal the impedance loss, the dependence of the input admittance
upon the load admittance is greater than would be expected if reciprocity
were assumed because of the relation of Eq. (30).
With such units it is
even more important that the input matching is achieved under the
proper load conditions than for units of equivalent actual 10SSbut foi
which reciprocity holds.
Because the values of the parametric admittances, Y.n of Eqs. (7) are
dependent, through Eqs.
(8), (9), (10), and (11), upon the imagefrequency termination VY, the characteristic signal input admittance as
well as the loss are to some extent determined by this image-frequency
In a converter unit that is, in itself, insensitive to frequency
but that is to be used with a high-Q resonator such as a TR switch, the
measurement of the characteristic input admittance should be made with
this resonator in place. The input admittance is less dependent on the
image-frequency load admittance, however, than on the i-f load admit-
tance. The mismatch encountered if the tuning is made optimum
without the resonator in place is not large because an increase in loss of
only a few tenths of a decibel would result even if the mixer were matched
to the signal generator with an incorrect admittance connected to the
i-f output terminals.
A calculation of the magnitude of the interdependence of the signal admittance and the image-frequency load admittance
requires a knowledge of the values of the parametric admittances yn~ of
Eqs. (5). Although these can be measured, this subject will not be
discussed here.
2.9. Dependence of the I-f Admittance upon R-f Matching Conditions.-In
a fashion exactly analogous to that of Sec. 2.8, the admittance
of the i-f terminals of a converter may be shown to be dependent upon the
The symmetry of I;qs. (7) suggests that an
signal-generator admittance.
expression similar to Eq. (43) could be written down immediately, where
G.. and G.. refer respectively to the conductance of suitably chosen i-f
terminals for the conditions of open-circuited signal terminals and shortcircuited signal terminals.
It is more convenient, however, to keep
the previous choice of the position of the r-f signal terminals and the
r-f matching conditions previously defined, to allow a single set of
terminals to be used for the description of the converter in either direction.
In practice, a special r-f circuit is required to allow variation of the admittance connected to the signal terminals independently of that connected
It will be assumed that this can be done, howto the image terminals.
ever, and with this assumption a useful relation can be derived.
The three conditions set up in the previous section were:
1. R-f matching such that 1’.. is real, and equal to G~a.
2. Choice of the position of the r-f signal terminals such that (Y.6Y~.)
is real, and equal to Ga~8..
3. Addition of a susceptance, bp, to the i-f terminals, which resonates
out the imaginary part of YPP. This is the condition of Eq. (35),
which was used to calculate the quantity denoted by Y...
By the use of these three conditions, the expression for the impedance
loss may be calculated for measurements of the i-f admittance for shortcil cuited and open-circuited signal terminals.
From Condition 3 and
Eq. (15) the i-f admittance for short-circuited signal terminals may be
Y ..a = Gf18= G,...
From Conditions 1 and 2, the i-f admittance
terminals may be written
for open-circuited
The ratio GM=/G,.mis therefore identical with that given by Eq, (40), and
the impedance loss can be written in I ~~ms of this ratio in the same way as
for the r-f terminals
1 – ~Go.m/G..a”
This relation reveals a point that is important in the design of converters and i-f amplifiers.
The i-f output admittance of the converter,
which plays an important role in determining the i-f amplifier noise
figure and bandwidth, can fall anywhere inside the appropriate circle on
Fig. 2.19 depending upon the admittance of the signal generator conIf a resonant circuit
nected to the input terminals of the converter.
is included in the converter or in the line between the converter and the
antenna, the i-f admittance may be expected to vary with the intermediate frequency.
If the signal generator is matched to the crystal
converter, the i-f admittance will be the characteristic admittance of the
i-f terminals, which corresponds to the center point of Fig. 2.19 for that
particular crystal, image-frequency termination, and harmonic-frequency
If the image-frequency termination is identical with that
at t-he signal frequency, the i-f admittance of most crystals now available
is between 2000 and 3000 micromhos.
This value for the i-f conductance
of the converter is valid only when the signal and image terminals are
both connected to admittances matching the input admittance of the
Since the converter is tuned for minimum conversion loss, the admittance of the signal generator is nearly matched to the characteristic
At the image
admittance of the signal terminals of the converter.
frequency, however, the signal generator admittance may have a different
value, and this, too, affects the i-f admittance of the converter.
circuits involving an r-f resonator, the image-frequency load admittance
is usually very different from that at the signal frequency.
A TR cavity
having a loaded Q of 300 at a signal frequency of 3000 Me/see almost
completely reflects the image-frequency
wave if the intermediate frequency is 30 Me/see.
Because of the symmetry, shown by Eq. (5),
between the signal and image frequencies, an expression may be written
which expresses the impedance loss of the converter in terms of the i-f
measured with the image-frequency
terminals opencircuited and short-circuited.
This expression is
The impedance loss L, is the minimum loss that could be obtained if the
roles of the signal and image terminals were interchanged.
It is, therefore, the same as the conversion loss between the signal and i-f terminals
when the image-frequency terminals are connected to an admittance
Again, Fig. 219 is
equal to the admittance of the signal generator.
The center point now corresponds to the admittance
resulting if the image terminals are connected to an admittance equal
to the optimum signal-generator admittance.
Since the termination at
the signal frequency will be near this value, a Iow-Q circuit would provide
the same admittance at both signal and image frequencies.
The i-f
admittance would then correspond to the center of the chart and would
be between 2000 and 3000 micromhos, as mentioned above.
If the termination at the signal frequency is kept constant and the
phase of a complete reflection of the image-frequency wave is varied, the
resulting i-f admittance should move along a circle, such as the appropriate one in Fig. 2-19. This could be done by varying the length of a
transmission line, matched both ways at the signal frequency, connected
between the converter and the TR cavity.
An incomplete reflection of
the image frequency would give rise to admittances on a smaller circle.
It is thus apparent that any mixer or converter circuit, or any circuit
preceding the converter, which reflects at the image frequency may be
expected to give rise to an i-f admittance that varies with the operating
For this reason it is advantageous to make the line length
between the crystal and TR cavity, or other device reflecting the image
The variations encountered in the i-f
frequency, as short as possible.
conductance are of sufficient magnitude to affect seriously the bandpass
characteristic of the input circuit, and the variations in capacitance can
have a serious detuning effect on the i-f input circuit.
In order to evaluate these variations it is convenient to put Eq. (47) into a different form.
If Eq. (47) is multiplied through by v’G,.,
the result is
and then by (=+<G~.7),
Since 4G.TG..7 = Go (the center point of Fig. 219, or that value of the
i-f admittance with an image-frequency admittance equal to that at the
signal frequency), it may be shown that, for losses greater than 5 db,
the equation
– Go., = ~
holds, within about 10 per cent. Since 5 db is about the minimum loss
found for available crystal units, the maximum variation of i-f conductance is from about one half to twice the mean value for open-circuited and short-circuited image-frequency terminations, respectively.
In a given r-f circuit, the variation with different crystal cartridges, at a
fixed frequency, is determined by the variation in GOfrom unit to unit
and by the fact that the effective phase length, and so the position of the
apparent terminals satisfying Condition 2, is not the same from cartridge
to cartridge.
A consideration of Fig. 2.19 shows that small variations
in the phase of the reflection of the image frequency give rise, primarily,
to changes in i-f susceptance, for lengths giving either minimum or
maximum conductance.
In the region between these values, small variations give rise, primarily, to changes in conductance.
The choice of the
length of line used could, in part, be determined by which of these two
kinds of variation has the less objectionable effect upon the receiver noise
figure and bandpass characteristic.
Because the complex conjugates of the image voltage and admittances
appear in Eqs. (5), it can be shown that the i-f admittance resulting
from given signal-frequency and image-frequency terminations is the
complex conjugate of that resulting if the signal-frequency and imagefrequency admittances are interchanged.
For instance, if the signal
terminals are connected to a signal generator of the admittance that
gives minimum loss, and if the image terminals are connected to a
variable length of line, short-circuited at its far end, the i-f admittance
goes around a circle such as the appropriate one of Fig. 2.19, as the line
length is varied.
If the roles of the signal and image terminals are
interchanged the same circle will result but it will be traversed in the
opposite direction as the line length is varied.
From this it can be shown that, if the signal and image terminations
are kept equal to each other but are changed together, the i-f admittance
will remain real provided Condition 3 is satisfied.
The connection
between the impedance loss and the limiting values of the i-f conductance, for complete reflection of both signal and image voltages, for all
phases, is
I – dGtin/G.u
Experiments to measure conversion loss by means of this relation
For silicon crystals, where recihave been performed by R. H. Dicke.
procity is found to hold, good agreement with the conversion losses
Instead of a complete reflection
measured by other methods was found.
of the signal- and image-frequent y waves, Dicke’s method made use of a
post protruding into the input waveguide of the mixer, giving a known
reflection coefficient less than unity, to allow transmission of the localIt is necessary in such an
oscillator wave through the same waveguide.
experiment to use such a low intermediate frequency that a reflection
some distance back from the crystal in the input waveguide gives rise to
identical load admittances at the mixer, at the signal and image fre-
If the i-f wavelength is not very much longer than the distance
in the waveguide between the crystal and the point at which the reflection occurs, the phase lengths of the waveguide at the image and signal
frequencies are different and the imaginary parts of the i-f currents
excited by the reflected signal and image waves are not exactly equal
in magnitude and opposite in phase. There will be, consequently, a
variation of the imaginary part of the i-f admittance as the line length is
In Dicke’s apparatus the i-f frequency used was 60 cps and,
therefore, this condition was well satisfied.
However, with intermediate
frequencies of 30 Me/see and line lengths of several feet, variation of the
susceptance component is observed.
In summary, it should be emphasized that the i-f admittance of a
crystal converter is not a function of the crystal unit alone but is dependent to a considerable degree upon the details of the design of the mixer
The range of admittance values that are possible is determined
by the crystal unit and by its minimum loss as a converter.
However, a
reasonably good crystal unit can be made to show conductance
as much as a factor of 8, as can be seen from Eq. (48), the factor depending
In addition, the susceptance of the i-f
on the nature of the mixer circuit.
terminals of the converter is not completely determined by the distributed and lumped capacitances and inductances of the physical
structure, since the susceptance can be affected to a considerable extent
These effects become rapidly more
by the design of the r-f circuits.
pronounced as the crystal units are improved and, therefore, increasing
care must be taken to obtain optimum performance from improved units.
The input circuit of the i-f amplifier must be designed to give satisfactory
performance with all values of the i-f output admittance of the mixer to
be expected with different crystal units in the whole band of operating
It may be found advisable to restrict some receivers to the
use of crystals having more than the minimum loss, just to gain the added
independence in the r-f and i-f circuits such crystals would give. The
effect would be similar to that of adding an attenuator to increase the
total loss by the same amount, in either the r-f or the i-f circuit.
2.10. Dependence of Conversion Loss on Image-frequency Termination.—The minimum loss for a particular image termination, as defined
by Eq. (27), depends upon the value of the image-frequency
through Eqs. (8), (9), (10), and (11).
The magnitude of the variation
in the minimum loss which can be produced by changes in the imagefrequency load admittance depends upon the values of the parameters
Y.., Y.A Y.?, Y~., and YM of Eq. (5), and cannot be simply related to the
minimum loss wit h a particular image-frequent y load admittance.
That there should bean effect of this kind, however, can qualitatively be
seen from simple arguments.
The most pronounced effect of the image-frequency admittance on the
conversion efficiency might be expected to occur with crystals with the
smallest loss. Suppose, for instance, one had a converter that had
unity loss, with a dissipative load connected to the image terminals.
device is said to have unity loss if the signal voltage develops the same
available i-f power as is available from the r-f signal generator.
existence of the i-f voltage across the i-f terminals, however, must give
rise to an image-frequency
voltage across the image terminals and,
therefore, to some dissipation of power in the image-frequency load.
The signal is thus responsible for the generation of more total power than
is available from the signal generator and this is incompatible with the
assumption that the converter can be represented by a linear passive
net work. A perfect converter, for which the passive network represent ation is valid, has a loss of 3 db if the signal-generator and image-load
admittances are equal and are matched to the characteristic input
admittance of the converter.
One half the available signal power is
transferred to the image frequency and dissipated in the image-frequency
If there is no isolation of the signal- and image-frequency waves
by means of tuned circuits, the minimum loss which a crystal converter
representable by a linear passive network can have is 3 db.
If, on the other hand, the image terminals are provided with a load
having no conductance component, there will be some value of the
susceptance of the load which will allow the converter to have no loss
It can be shown that this will occur,
between the signal and i-f terminals.
if the terminal positions are chosen in accordance with the conditions of
Sec. 29, for the image terminals either open-circuited or short-circuited.
The i-f admittance will be a pure conductance, if the signal generator is
matched to the characteristic admittance of the signal terminals and if
the conditions of Sec. 2.9 are fulfilled.
Such a perfect converter has not so far been made, but the crystals
now available for use as converters do give losses as small as 5 db. The
dependence of the loss on the image-frequency load would not be expected
to be so pronounced as in an ideal lossless converter.
A reduction of less
than 3 db in the conversion loss from the value obtained with an imagefrequency admittance equal to the signal-frequency admittance, therefore, could be obtained through the use of an image-frequency load
reflecting in the optimum phase. The magnitude of the effect depends
on other parameters of the crystal as well as on the loss measured under
the matched condition of the image, and an analysis will not be given
here. This subject is discussed in detail by H. C. Torrey in Yol. 15 of
this series. This discussion shows several possibilities for the dependence
A plot of the loss as
of the loss on the image-frequency load admittance.
a function of the image load admittance can be made in the form of a
,;urface, where the height of the surface almvc a particular point in the
complex half plane corrcspomling to positive image load conductance
gives the loss associate[l \vitll that particular VUIUC of the image termination. For some crystal units, the loss is highest for open-circuited image
terminals and falls to a minimum at large absolute values of the load
For other possible crystals, the reverse might be true,
and for still ot,hcrs a maximllm 10S+,or a highest point of the surface,
might occur for a load consisting of a pure conductance, with the minimum loss at open circuit.
The determination of the best image-frequency load admittance for a
There are
crystal of a particlllar type mllst bc done experirnrntally.
t~vo ways in ~~hich this can Ilc done. onc JVay is to measure certain
differential codficicnts drwriptivc of the crystal mixer. R. H. Ilicke and
S. Robmts~ have shoi~n that the coefficients of thclinear-network
representation of the crystal convcrtcr can bc expressed in terms of these
differentials, which in turn can bc follnd b.v meastwement of the r-f
admittance at the local-oscillator
lm-el and memurement of the d-c
Exa,mples of differentials to which the description of the
converter has been rcd~lced arc the rate of chango of direct current ~vithan
applied d-c voltage, the rate of change of the direct current with the r-f
power, the rzte of change of r-f cond~lctance with the applied d-c voltage,
It was possible
and the rate of change of r-f Conductance with r-f power.
to show that from these differentials, the coefficients of Eq. (5), descriptive of the converter in question, can be evaluated and therefore the
conversion !OSSfor any particular image-frequency load can be evaluated.
Also from these measurcrnents, the value of II-.61/l lrp~l can be found and,
therefore, the loss can be calculated for the conversion of an r-f signal
to an i-f signal, or of an i-f signal to an r-f signal. This treatment has
been extended by H. C. Torrey and is discussed in detail in Vol. 15 of
this series.
The magnitude of the variations in the minimum loss of a converter
with ordinary crystal units, resulting for different image-frequency
loads, has been found by calculation from the differential coefficients to be
about 1.5 db. The loss can usually be made either greater or less than the
value obtained with an image-frequency load equal to the signal-generator
The loss with equal signal and image loads is usually about
Thus there might be a reduction of
midway between the two limits.
about $ db in conversion loss to be gained by choice of the best phase of an
Because the noise temimage-frequency reflection in the converter.
perature of the converter may also be affected by the reflection of the
1R. H. Dicke and S. Roberts, “Theory of Radar Mixers,” FL Report No. 287,
Jdy 16, 1942.
image frequency, the effect of the image-frequency reflection on the overall noise figure is not determined by the loss alone.
Another measurement that can be made to determine the effect of the
image-frequency load on the loss is the direct measurement of the loss
for various values of the image-load admittance.
Direct measurements
of the available i-f power, for a particular value of available signal power,
are difficult to make because the i-f output admittance and the signal
admittance of the mixer depend on the image-load admittance.
each experimental value of the image admittance, the r-f matching must
be adjusted for minimum loss, since otherlvise the effect of a mismatch
may give rise to a change in the measured loss, which obscures the effect
under investigation.
If the available i-f power is found by measurement
of the power delivered to an i-f load, the admittance of the i-f load must
be such that the load absorbs all the i-f power available, or the power lost
because of mismatch must be known for each value of the admittance of
the image-frequency load.
Experiments of this sort have been carried out at the Radiation
Laboratory and elsewhere, and the results ~vere substantially in agreement with the predict ions from the measurements of the differentials.
In the experiments a variable length of line }vas used between the mixer
The TR cavity provides almost a
unit and a resonant TR switch.
complete short circuit of the input line of the mixer at the image frequency, whereas it provides a matched generator at the signal frequency,
when the signal generator is connected to the input side of the TR cavity.
The r-f tuning of the mixer was such that when the TR cavity was not
present and the image frequency was therefore not reflected to the mixer,
the mixer represented a matched load on the waveguide.
Under this
condition, the signal admittance of the mixer with the TR cavity in
place should fall on a circle of constant reflection coefficient for all lengths
of the line between the TR cavity and the mixer. Variation of the length
of this line, therefore, should not change the reflection loss on the r-f
side of the mixer. The i-f load admittance was made equal to the complex
conjugate of the i-f output admittance of the mixer when the TR cavity
was removed and the input line was thus matched at both the signal and
the image frequencies.
With the TR cavity in place, the i-f output
admittance measured relative to the i-f conductance with no TR cavity,
should then fall, for all lengths of the line between the TR cavity and the
mixer, on a circle about the center of a Smith chart.
In this manner, the
reflection loss on the i-f side is made to be independent of the r-f line
length. With these precautions the results were still not considered to be
very dependable, but no gross disagreement with the results of other
methods was found.
According to the calculations based on the differential coefficients, the
mtilmum and maximum values of the loss should occur when the susceptance has the same value as when the TR cavity is not present.
prediction was not verified, however, and therefore, measurements
were made of the i-f output admittance as a function of the line length.
Instead of a circle on a Smith chart, a curve reproduced in Fig. 2.20
was found, where the experimental points are indicated by the crosses and
the closed contour is a smooth curve drawn through them, consistent
FIG.220.- Locusof the i-f adn,ittanccof a ro,,vcrtcras the phaseof theimagereflection
k V:uied.
with the probable experirnrntal error. lt will bc ohscrved that there is a
considerable departure from a circle in the values of the susceptance for
higher than the charactc ristic conductance.
The values of
the maximum and minimum concfuctanccs, however, if put into Eq. (47),
give a loss for the mixer tvhich agrees WC1lwith a previous direct measurement of the conversion loss of the same crystal.
A circle representing the
expected locus of the i-f admittance as a function of the r-f line length is
also drawn in the figure for comparison.
In addition, the value of the
conductance was measured with the TR cavity removed, and it was
found to be exactly the geometric mean of the minimum and maximum
values, or tiG~.y/G,,v, aspredicted from thelinear-network representation.
Thus the only disagreement is in the susceptance values of the i-f admittance, andnoexplanation
forthis has been found.
Apossibility isthata
variation in a harmonic-frequency load is responsible, but, since the line
length was changed by the use of a long split waveguide of variable
width, it is improbable that the variation of the effective length of thelinc
at harmonic frequencies would bear a simple relation to that at the
fundamental frequency.
Since the figure appears to be closed, such a
relation would be necessary if a harmonic frequency were responsible
forthe distortion of the circle.
2.11. Measurement, with an Admittance Bridge, of the Dependence
of Conversion Loss on the Image Reflection.-Another
measurement of
the dependence of the conversion loss on the image-frequency
admittance was carried out for several crystal units by means of measure-
c, ==
C,= if bypass-1000u#f
C = 5-20 tipf variable condenser
FIG.2.21.—Apparutusfor measm’cment
of effectof retfectionof theimage-frequencywave
on conversion10ss.
ment of the impedance loss of a mixer ~vith several different lengths of line
between the crystal and the TR ca~-ity, The apparatus with which this
was done was an admittance bridge, }vhich will be described in Chap. 8,
The TR cavity and the variable length of line betlveen it and the crystal
were considered to be included in the circuit, represented by a linear
The resulting impedance loss therefore included the loss in the
TR cavity.
Figure 221 sholvs a block diagram of the converter and
variable i-f load circuit that lrerc~used. Since the shunt admittance of
the i-f resonant circuit appears as a part of the converter circuit and
contributes to the loss, pains ]vrrc takcm to make it sufficiently small to
contribute only a negligible amo~lnt to the loss. With the coil used, the
shunt admittance was less than t\vcnty micromhos and this is very much
smaller than the several thousand mirromhos usually encountered as the
output admittance of a crystal convcrtcr.
The procedure of the experiment \vas as follo~rs. For a particular
setting of the variable line length, the slritch ,S’was first set in position
(1), giving an i-f load admittance eqlml to the complex conjugate of the
i-f output admittance of a mixer \vitll an a~-er~Ke Crvst:ll and no TR
Then the mixer timer \vas so :Mlj(Istwl that a small signal at the
At the same time
signal frequency was not mflectcd from the ‘1’lt cavity.
the coupling and frequency of the local oscillator were set to the correct
This tuning serves to establish nearly the proper loading on the
TR cavity.
If a large standing-wave ratio existed in the line between the
mixer and the TR cavity, the part of the total conversion loss contributed
by the TR cavity would be large, and a variation in it might obscure the
effect under investigation.
Next, the switch S was put at position (2) and the tuner on the input
side of the TR cavity was adjusted to make the small signal pass into the
tuner and converter without reflection.
This made G.. equal to the charNext, the switch was put into
acteristic admittance of the waveguide.
position (3) and the variable condenser adjusted for maximum reflection
of the small signal at the input terminals of the first tuner. Under these
conditions, the ratio G..P/G..8 is equal to the voltage standing-wave ratio,
and Eq. (43) may be written as
From this expression, the impedance loss was calculated for that particular setting of the variable line
The line length was adjusted in units of about 15° of phase
and the whole procedure was re.;
: 9.0
peated for each setting.
showing the impedance loss of the
~ 8.0
converter, including the loss of the
z 7.0
TR cavity, as a function of the setting of the variable line length, for
three _representative crystals, are
‘;O 40 80 120160200 240 2S0 32o
shown in Fig. 2,22. Because the
S?ttmgof the var<ableIme length in arb)trary umts
loss measured by this apparatus,
with the TR cavity removed, agreed
fortheimpedancelossof a converterinclucfwell with the calibration of the
ing a Tfl cavity,as a functionof theI-ngth
of the line betweenthe TR cavity and the
crystals by other methods, it was
assumed that reciprocity held and
the impedance loss was the same as the loss for conversion of the signal
from radio to intermediate frequency.
It will be observed that the curves do not show a cyclic variation of
the loss as a function of line length, as would be expected.
one reason for
this might be that, for each line length, the mixer tuner was, adjusted to
establish the proper load admittance for the TR switch and this adjustment has some effect on the phase length of the line between the TR
switch and the crystal.
It is therefore possible that the actual phase
length of the line was not a simple function of the setting of the line-length
Another possibility
is that the harmonics and other
high-order waves developed by the crystal, which would be reflected to a
large extent by the TR cavity, are responsible for the irregularity.
These higher-frequency components would be affected in various ways
by the setting of the line-length adjustment.
The line length was
varied by means of a polystyrene wedge that could be slid from the side
This explanation of the irregularity
to the center of the waveguide.
would be in agreement with some measurements made at the Bell Telephone Laboratories on the effect of the image-frequency
load on the
It was
conversion loss by the direct measurement of output power.
reported that, in these experiments too, very irregular results were
obtained untif harmonic chokes were installed in the mixer unit. These
chokes prevented the transmission of the frequency componentsin the
region of the second harmonic back into the adjustable line and so to the
TR cavity, and the curves obtained for the loss as a function of line length
The peak-to-peak
with the chokes in place were simple and periodic.
variations were about the same as in the curves of Fig. 2.22, although,
since they did not apply to the same crystals, no exact comparison could
be made.
An attempt was made to discover which line length corresponded to
minimum loss. For each point of the curves of Fig. 2.22, the setting of
the i-f condenser which maximized the standing-wave ratio was observed
and from this the imaginary part of the i-f admittance could be estimated.
The maxima and minima all seemed to correspond to real i-f admittances,
in accordance with predictions from the linear-network representation,
and independent measurements of the admittances for some of these
points showed that, in most cases, the minimum loss occurred for the
point of the i-f admittance
however, was not always true; that is, with some crystals the maximum
conductance point gave minimum loss. It thus appears that considerably more data must be obtained before it will be possible to include, in
the design of converters, the image-frequency termination giving the
minimum possible conversion loss. NToneof the designs to be described
in later chapters includes this feature.
Before it could definitely be stated
that the converter should be designed for minimum loss in this way, the
effect of the image-frequency load admittance on the noise temperature of
the converter would have to be measured.
Also, the fact that a low i-f
conductance is usually associated with the best conversion efficiency
makes the ,design of input circuits having a wide pass band difficult
because the i-f capacitance of the output terminals of the mixer unit
cannot be correspondingly reduced.
If, on the other hand, there is a
further decrease in the conversion loss of available crystals, it will become
more important to include the proper image-frequency
load in the
At present, it appears that with ordinary crystals only a
fraction of a decibel is to be gained by the reflection of the image wave in
the best phase. An experiment on the effect of image reflection on both
the noise temperature and the conversion loss has been performed by
E. R. Beringer, M. C. Waltz, and C. P. Gadsden.
The apparatus used
for this experiment is described in Chap. 8. The results show that
the over-all noise figure can be definitely improved by the proper choice
of the phase of the image reflection, because the noise temperature did not
change to compensate for the decrease in conversion loss. Experiments
similar to this should be done for large numbers of crystals to determine if
a fixed image-frequency reflection could be used for all crystals and over a
broad band of frequencies.
2.12. The Effect of Reflection of the Second Harmonic.-As
already been stated, the crystal mixer contains frequency components
The treatment of
at the second harmonic and at higher frequencies.
these harmonics is likely to have some effect on the i-f admittance, the
Some manifestations of these freloss, and the signal admittance.
quencies have already been mentioned in Sec. 2.11 but a few remarks
about some experiments that dealt independently with the higherfrequency components are in order. These experiments have been
primarily concerned with the effect on the conversion loss of the load
admittance at the frequency of the second harmonic.
The first observation of an effect of waves having frequencies at the
second harmonic of the local-oscillator or signal frequency was made at
the Bell Telephone Laboratories in conjunction with experiments on a
coaxial-line mixer designed by W. M. Sharplessl for 3000 LMc/sec. one
of the design parameters was the position of an abrupt change in the
diameter of tbe center conductor of the coaxial line connecting to the
The signal generator could be matched into the mixer, for any
position of the step change in diameter, by two other adjustments.
Data were taken of the conversion loss as a function of the position of the
step, with the signal-generator admittance adjusted for minimum los~ at
each position.
When these data were plotted it was found that the
conversion loss varied cyclically, with a repetition occurring for a motion
of about 2.5 cm. Any variation caused by changes of admittances at
the fundamental frequency would have repeated at each half wavelength,
or 5 cm, of motion.
Therefore, the observed variation was attributed to
The magnitude of the variation was
between 0.5 and 0.75 db from minimum to maximum.
The final mixer
design was chosen with the step in the position of minimum loss, and this
1W. M. Sharpless,“The Influenceof Harmonicson lo-centimeter Performanceof
Silicon Crystal Converters,’”BTL Report MM-42-166-SO,July 24, 1942.
mixer has since been used as the standard test mixer for acceptance tests
of 1N21, 1N21A, and 1N21B crystals.
In the process of establishing the crystal-test specifications, measurements were made of large numbers of crystals in mixers of many different
None of the other mixers had dimensions specifically chosen for
optimum second-harmonic effect and yet no large disagreements were
observed between the average values obtained with the various types as
long as the signal-frequency matching was made to correspond to the
same tuning condition.
It might be that an effect due to the second
harmonic is very frequency-sensitive,
and also requires individual
adjustment for each crystal unit because of variations in the effective
It appears that equally good conversion
phase length of the cartridges.
losses are obtained on the average with 3000-Mc/sec
mixers that have
If it were
no provision for reflection of the harmonics in the best phase.
considered worth while to include adjustments in a mixer which would
allow the best possible performance to be obtained from each individual
crYstal, it would perhaps be reasonable to include, in addition to adjustments for the signal matching, the local-oscillator injection, and the
termination, an adjustment to give the best load
It is doubtful that
admittance at the frequency of the second harmonic.
the termination for the second harmonic could remain optimum over the
wide band of frequencies in which most mixers are now designed to be
used. A mixer that contained all these adjustments would probably be
very difficult to tune, unless each of the adjustments could be made
independently of the others.
There have also been experiments in the 3-cm region (9000 to 10,000
Me/see) for the purpose of finding the effect of second harmonics on the
conversion loss. For one of these experiments, also made at the Bell
Telephone Laboratories, a mechanism indicated in Fig. 2.23 was used.
A common crystal mount in this frequency range has a crystal mounted
The waveguide
across the waveguide, along the narrow dimension.
extends a short distance beyond the crystal and is then short-circuited by
The distance to this short circuit determines,
a plate or a sliding plunger.
Instead of an
in part, the tuning of the mixer at the signal frequency.
ordinary plunger, the mixer of this experiment had a thin plate extending
across the waveguide along the narrow dimension in the center of the
wide dimension and continuing in this position a considerable distance
back along the waveguide.
Except for a small phase shift, this plate
acts in the same way, at the fundamental frequency, as a short-circuiting
plate or plunger filling the whole cross section of the guide, since the
half-width waveguides on either side of the diaphragm are waveguides
beyond cutoff for the fundamental-frequency
At the frequency
of the second harmonic, however, these half-width guides are wide
enough to allow propagation.
Short-circuiting strips in the small guides
can be adjusted to control the admittance of the waveguide at the
harmonic frequency.
Observation of the output power from the converter, with fixed input power, revealed a cyclic variation which repeated
with the proper distance of motion of the two side strips to correspond to a
second-harmonic effect. The variation observed totaled about 0.5 db
from minimum to maximum.
When the two, side strips were replaced by
resistive cards, tapered to give small reflections, the observed output
Fundamental. frequency short circuit
FrQ. 2.23.—Back plunger, independentlyadjustahlc for fundamentaland harmonic
power was about midway between the maximum and minimum values
found for the metal strips.
A similar experiment was undertaken in which the apparatus used for
the measurement of conversion loss by the admittance method was used.
This apparatus also operated at about 3.2 cm and contained waveguide of
0.400 by 0.900 in. inside dimensions.
A short-circuiting plate was used
over the end of the waveguide behind the crystal mount.
To detect an
effect due to the harmonic admittance of this part of the mixer circuit,
this plate was replaced with one in the center of which was inserted a
waveguide of 0.170 by 0.420 in. inside dimensions, as shown in Fig. 2.24.
Because this waveguide was beyond cutoff for the fundamental frequency, the motion of ashort-circuiting
plunger in the small waveguide
would not affect the fundamental waves but would be expected to affect
the admittance to the second harmonic and higher frequencies.
the second experiment, the tuner
for the harmonic couples to a harmonic wave in the dominant mode
only, whereas the tuner in the first
experiment couples to both the
dominant and the second modes.
A change in the conversion loss
of the mixer, caused by a change in
the position of the small plunger,
FIG. 2.24.—Harmonic-frequency“ back- would produce a change in the
admittance measured with the i-f
leads either short-circuited or open-circuited,
or for both conditions.
When this experiment was tried, with several representative 1X23A and
1N23B crystals, however, it was found that the effect on the admittances
of moving the plunger was much smaller than could be measured, for both
conditions, although the apparatus
had sufficient sensitivity to detect a
change in conversion loss as small as
0.05 db. The effect of harmonic
frequencies would be expected to be
larger for crystals designed to operate at the frequency of the second
An adapter was made
to try 1N26 crystals normally used
in the 1.25-cm band and for these
tryst als also, a negative result was
In an effort to make the tuning
of the load admittance at the harmonic frequency cover a wider
range, a tuner illustrated in Fig.
admit2.25 was tried. This tuner contancetuner.
sists of two small wavcguides connetted at right angles to the full-sized wavcguiclc, about five-eighths of a
harmonic wavelength apart.
Sliding plungers in the small waveguides
affect only the admittance at the harmonic frequencies because the waveguides are too narrow to s[lpport Ivaves at the fundamental frequency.
The section of waveguide containing these side arms was placed in the line
between the signal generator and the mixer.
In this experiment no
measurable effect of the position of the plungers on the value of the
admittance of the converter at ttw signal frcqurmcy was found.
In both
these experiments, a slight changein the admittance of the mixer, which
repeated at scttinys of the plun~ers corresponding to half-wavelengths
at the second-harmonic
frequency, was detected.
The change was
not large enough, however, to allow measurement of a change in the
impedance loss.
Unfortunately, a direct measurement of output power was not tried
with these same harmonic tuning devices.
It may be suggested, hoivever,
that the reflection of the second harmonic appears in the reciprocity term
lYafll/lY~a{, in the expression for the conversion loss and thci-efore
affects the actual conversion loss hlit not the impedance loss. This
possibility may have further foundation in the fact that I)icke’s proof
of the reciprocity theorem requires certain relations to hold between the
phases of the harmonic and fundamental frequency components in order
that a time zero can be chosen shout which the potential across the
barrier may be expressed as an even function of time.
Like the image-frequency
effects, the harmonic effects cannot be
evaluated in terms of the possihlc improvements in the over-all noise
figures of receivers without parallel experiments on the effect on the
No such experiments are known to
noise temperature of the converter.
the author.
It appears, at the present time, that the image-frequency
termination has a greater influence on the over-all performance than the
The effects of the load admittance at
harmonic frequencies are small compared \rith the variations among
.Making a converter circuit that has a wide pass band and
includes optimum terminations for the image and harmonic frec[uencies
throughout this band is not a simple task. Whether a fixed setting of
these terminations would give, even at a single frequency, optimum or
nearly optimum performance with the majority of crystal units, cannot be
decided until further data have been accumulated.
These are some of the
questions that were not answered satisfactorily during the war because
they were of less importance to radar development than was the development of converters and mixers for new frequencies and types of service.
2.13. The Welded-contact
Gerrnsnium Cfystal.-A
recent development in crystal units, reported by H. Q. NTorth of the General Electric
Company, has resulted in crystal rectifier units that behave very differently from any others previously observed.
A description of their
behavior is most easily given by an account of the experiments that led
to the discovery of the unusual properties.
These crystal units were originally intended for use at 25,000 Me/see,
and were developed as a part of a program of research on germanium
Very great care was taken in the preparation of the germanium and the cat whisker and these parts were assembled into a
cartridge resembling that of the lhT26 crystal (to be described in a later
section of this chapter) to allow their use in the standard r-f circuit.
The whisker was supported on a glass bead which \vas sealed into the
outside cylinder of the cartridge, and the contact \\as made }vith very
light pressure. It has been observed ~vith other germanium units that
some improvement in the conversion characteristics could be obtained
if the crystal was subjected to a rather large direct current for a short time
before it was used. In making an experiment on this effect, Xorth
discovered that a current of several hundred milliamperes in the forward
direction could be passed through the unit \rithout apparent damage to its
The result of this large current was that
high-frequency characteristics.
the tip of the platinum-ruthenium-alloy
cat whisker became so hot that
That such a w-eld l~as
it fused and became welded to the germanium.
produced was verified by measurement of the force required to pull the
This force was found to be sufficient
whisker away from the germanium.
to break the whisker itself. The crystal units resulting from this process
seemed at first to be comparable, in their behavior at 25,000 Me/see, with
If for no other reason,
silicon units of more conventional design.
welded crystals would have been interesting because of their great
mechanical and electrical stability.
Because these units did not have the same r-f characteristics as the
1N26 units, it was thought probable that their conversion loss, as measured in the test set for the 13’26, suffered considerably from reflection of
the signal. As a consequence, they were tried at 3.2 cm. The 3.2-cm
test set was equipped with a tunable crystal holder and it was found that,
when the crystal holder was tuned for maximum delivered power, the
losses of the welded units were as small as 3 db. An additional adjustment was used in the form of a d-c bias voltage in the forward direction.
This bias voltage had a considerable effect on the minimum conversion
loss obtainable and was retained as part of the converter circuit in all the
subsequent experiments.
Since the test set has the same load admittances at the signal and image frequencies, it was thought that these
crystals were exhibiting the smallest loss compatible with the representation as a passive network.
Therefore, a few readings of a few tenths
of a decibel less than 3-db loss were considered to indicate a small error in
the absolute calibration of the test set.
To verify the result obtained with the test set, the loss of a few of the
best units was measured by the admittance-bridge method, described in
Sec. 2.11. No resonant circuit was used to separate the image termination from the signal-frequency termination, but the result of the experiment was that the reflection coefficient, for the open-circuit switch
position and optimum load susceptance, was as large as unity for some
The impedance loss was therefore unity, indicating that the
same power should be available from the i-f terminals of the converter as
For some crystals, the
was available from the r-f signal generator.
reflected wave from the crystal seemed to be a little larger in amplitude
than the incident wave, but this was thought to be an experimental error.
In order to obtain the best results it was necessary to adjust the level of
Z.26.—I-fadmittanceof a welded-contactcrystal,
the local-oscillator power and the magnitude of the forward d-c bias
voltage, and with each crystal several tests were made in search of the
optimum combination of %hese adjustments.
The experiment definitely
confirmed the result of the earlier one.
In the experiment with the test set it had been found that the conversion efficiency was better if the 400-ohm i-f load resistance normally
used was changed to 800 ohms. The test set measures the ratio of the
available r-f power to the i-f power delivered to the load, and not the true
conversion loss. Further experiments with this test set showed that
still more i-f power was delivered to even larger i-f load resistances.
loss factors became less than3 dbformany
crystals and, for some, were
even less than O db. This corresponds to an actual power gain, and it
An experiment
occurred without any isolation of the image terminals.
was done to determine the i-f output admittance of a converter using
these crystals, to discover the optimum load admittance.
Since such a
low loss must depend markedly on the r-f tuning, provision was made to
include tuning of the r-f circuit by means of a sliding-screw standing-wave
Local-oscillator power and a d-c
generator in the r-f-input waveguide.
bias voltage were provided.
With the tuning screw inserted for a large
reflection, the i-f (30 Me/see) admittance was measured for various
positions of the screw along the waveguide.
The result of this experiment
is shown in Fig. 2.26, plotted on a Smith admittance chart. The significance of the extension of the contour outside the circle representing the
ordinary complex half-plane, is that negative conductance
\vere encounThe circle of zero conductance
tered for some conditions of r-f tuning.
is the normal boundary of the Smith chart, but if negative conductance
are included these become circles of larger diameter and, like the circles of
constant positive conductance, have centers on the real axis and pass
through the infinite-admittance point.
The discovery of the negative i-f conductance of the welded-contact
germanium crystals explained the experiments in which a con~-ersion loss
of less than unity was found, as well as the fact that this ~vas obtained
.$ din-ice having a
only under critical conditions of the r-f tuning.
negative conductance can be made into an oscillator if it is loaded by a
positive conductance of absolute value smaller than that of the negative
conductance itself. The same device may be used as an amplifier ~~ith a
true power gain if it is loaded with a conductance just too large to
allow oscillation.
The crystal, when used as a converter, drlivered
an increasing amount of power to the load as the load conductance
was increased,
When a resistance of several thousand ohms Tyasused
as the i-f load, a conversion gain of more than 10 db was obtained.
The crystal ~~as therefore acting as a regenerative converter.
confirmation of the existence of the negative i-f conductance was
obtained by connecting the con~-erter to a shunt-resonant circuit, which
had a shunt conductance smaller in absolute \-alue than the measured
Oscillation at the resonant
negative conductance of the converter.
frequency of the tuned circuit was obtained for all frequencies from
5 to 45 lIc lsec, and a later experiment at the General lZlectric ~ompany
revealed oscillation near 10,000 lIc/see, when the crystal was tried in a
converter with a local oscillator at 25,OOO 31c/sec.
A negative i-f
conductance has not been produced with crystals of other types.
The d-c characteristic of the welded-contact units is also different
from that of other units. A curve resembling the d-c characteristic of a
The slope of the curve in the vicinity
typical unit is shown in Fig. 227.
of the origin corresponds to a resistance of several megohms whereas the
steepest part of the curve on the right side has a slope corresponding to
a resistance of about 3 ohms. As
mentioned previously, this part of
the curve is a measure of the spreading resistance of the crystal and,
with ordinary silicon units, it is
vabout 50 ohms.
On linear scales,
the d-c characteristic appears to
have a sharp bend in the forward
direction, but the position of this
FIG. 2.27,—D-c characteristicof weldedbend on the voltage axis depends
upon the scale of the current coordinates, A formula deduced on theoretical grounds, which expresses the
relation between current and voltage applied across the barrier of the
crystal in the forward direction is
I =
where e is the electronic charge, k is Boltzmann’s constant, and T is
the absolute temperature.
The constant A is related to the density
of current carriers in the semiconductor and the area of the contact, and
V is the voltage across the rectifier unit minus the drop in the spreading
resistance. The d-c characteristic of the welded-contact crystal has been
measured carefully and it is found to follow this formula closely over a
wide range of current.
When the logarithm of the current is plotted
against the applied voltage on a linear scale, the plot is a straight line
over six decades of current.
Similar curves for other crystal units follow
the formula over only two or three decades at most, and the slope does not
For the welded-contact crystal, H. C.
agree closely with the formula.
Torrey has shown that the d-c characteristic can be used to calculate the
value of the electronic charge. Using a more precise formula than Eq.
(50), Torrey obtained a value for e agreeing with the accepted value
within ~xperimental error. The d-c characteristic of the welded-contact
crystal thus agrees more closely with the theoretical prediction than do
the d-c characteristics of the more common types.
If the d-c characteristic of a welded-contact crystal is displayed on an
oscilloscope when the crystal is mounted in a converter with local-oscillator power incident, the presence of the negative conductance can be
For ordinary crystal units, a curve similar to that shown in
Fig. 2.28 is obtained.
The intercept with the current axis is the rectified
current caused by the incident r-f power, and the plot shows the total
current for bias voltages of both signs. The shape of the curve for z
is not very much affected
r-f tuning but, when
the welded-contact units are tried, the situation is changed.
upon the r-f tuning, a variety of curves can be produced and among them
are curves resembling those of Fig.
2.29a and b. The curve of Fig.
2.29a is not much different from
the curve for an ordinary crystal,
due10Lo but that of Fig. 2.29b clearly demonstrates the negative conductance
and the fact that it is most easily
FIG,2.2S.—D-Ccharacteristicof normal obtained with a small forward bias
cwstal wit]l loc~l-oscillatorpowerincident voltage applied to the crystal.
Other effects on the d-c characteristic could be obtained by adjusting harmonic-frequency admittances in
specially designed r-f circuits.
A theory of the source of the negative i-f conductance of these crystals
He has shown that the i-f conductance of a
has been given by Torrey.
crystal can be made negative under certain conditions of r-f tuning, if the
variation of the barrier capacitance with the voltage applied across the
The negative conductance should show up
barrier is taken into account.
only in units which have very small spreading resistances, as have th-e
welded-contact crystals, and for high-frequency local-oscillator voltages,
Normal rectified current
of weldedgermaniumcrystalfor two conditionsof r-f tuning.
where the effect of the capacitance on the rectification efficiency is considerable.
There is no possibility of producing the negative conductance
in the absence of local-oscillator voltage, because it is from this source
that the necessary energy associated with the negative conductance must
Ifj because its conversion gain can be made large, a crystal of this
type could be used to obtain a receiver having a smaller effective over-all
noise figure than is obtained with conventional crystals, it would be of
great importance as a converter for a microwave receiver.
by E. R. Beringer, M. C. Waltz, and G. P. Gadsden, with an apparatus
similar to one described in Chap. 8, showed that the noise power available
from the converter, when the convcrtcr is opcrtitc(l in the c(mdition oi
negative i-f conductance, was also lflrge. i\s a rrsl~lt, it lV:M not found
possible to obtain ~vith these crystals, in any of the many tllninx conditions tried, an effective over-al~ noise figure Snudlcr th:m C:LUbc obtained
The tuning conditions tried included the use
with conventional crystals.
of separate tuning of the signal-fmqllcncy and image-frequency circuits,
but the only advantage of the convmtcr over one ilsing a con~-cntiomd
crystal was that the greater output po\vrr aNo\ved the usc of somewhat reduced gain in the i-f ampli[icr.
l\”hcn operated in a tuning condition in which a negative i-f conductance was ubtaincd the over-all noise
figure was not very much larger than tlmt ol)tained v-ith conventional
crystals. The tuning is critical, howcverj and :L rcccivcr, the pmformance of which depends on the large conversion gain, J\-ouldbe difficult to
keep in proper adjustment.
Some attempts to make regenerative and supcrrcgencrative converters
were made but they \vere not carried very fm. The use of germanium
crystals for such converters may lmve importance in lightweight apparatus, because the i-f amplification required could be considcrnbly reduced.
The noise power available from crystzls of this type may bc rccfuced by
further research, and such a development \vould allow lower rccciver
The treatment of the image and harmonic
noise figures to be obtained.
frequencies in converters designed to operate ~1-ithgermanium crystals
would be much more important than it is with the crystals in use at
present. A more complete discussion of the welded-contact crystals, is
given in Vol. 15 of this series.
2.14. The Converter Noise Temperature.—The
noise temperature
was defined in Chap. 1 and reference to it has been made in connection
with the effect of the image load admittance on the loss and in the discussion of the welded-cent act germanium tryst ~d. The magnitude of the
effect of a given noise temperature on the over-fill noise figure of a receiver
depends on the magnitude of the noise figure of the i-f amplifier.
N-ith an
i-f amplifier having a noise figure of unity, a change in the noise temperature of the converter by a given factor produces a change in the over-all
noise figure by the same factor.
Since amplifiers with noise figures
smaller than two can now be made, it is important that the noise temperature of the converter be as small as possible.
The noise temperature of a crystal converter is never less than unity.
By definition, it would be unity if no excess noise were developed in the
crystal itself and the noise power available from the converter were only
the Johnson noise associated with the i-f output admittance.
If the
conversion loss of the unit were very small, the i-f admittance of the converter would have a temperature determined by the objects and the
When the noise
absorbing media in the field of view of the antenna.
temperature of a converter is measured, however, the antenna is replaced
by an r-f resistance at room temperature and, if no excess noise were
developed in the converter, the noise power available from the converter
would be kTB, where T is room temperature.
As a result of the research on semiconductor crystals and on techniques
of preparation and manufacture of rectifier units, the noise temperature of
units now available has become considerably smaller than that of early
units. The excess noise developed by the crystal unit is associated with
the flow of current through the borrier; this current consists of a flow of
discrete charges and, consequently, has a nonuniform character.
approximatcl y linear relationship bet wecn the noise temperature of the
converter and the crystal current, which is rou~hly proportional to
the incident local-oscillator po~ver, bears out the theory that the noise is
If there is no incident localsimilar to the shot-effect noise in a diode.
oscillator power, the crystal no longer acts as a frequency converter, and
the available noise power is just .Johnson noise.
In order to specify the quality of a crystal as a converter, it is necessary to give the conversion loss and the noise temperature corresponding
to the same amount of local-oscillator power. The magnitude of localoscillator drive should be chosen to be the magnitude for which optimum
over-all noise figure is obtained in a receiver using the crystal as a converter. The optimum local-oscillator power depends on the noise figure
The local-oscillator drive
of the i-f amplifier following the converter.
chosen for the specification of the loss and noise temperature is that which
results in the minimum over-all noise figure in a receiver using an i-f
amplifier with a noise figure typical of present production.
If a receiver
uses an i-f amplifier with a smaller noise figure, the optimum value of the
over-all noise figure is obtained with less local-oscillator drive. For
best results, the optimum local-oscillator level should be determined
Since the over-all noise figure does not vary rapidly
with local-oscillator drive in the region of the minimum, a small departure
from the optimum local-oscillator drive does not entail a large increase in
over-all noise figure.
It has been found that the noise temperature of a crystal converter,
unlike the conversion loss, is not independent of the intermediate frequency at which it is measured.
In general, it is found to be lower at
high intermediate frequencies than at low ones, although at frequencies
above a few megacycles per second the variation with frequency is not
very pronounced.
Since 30 Me/see is the most common intermediate
frequency, the noise temperature of most crystals is measured at that
frequency, although some are measured at 60 Me/see, also a common
intermediate frequency.
For some purposes it is desirable to have a receiver with an i-f amplifier at a frequency lower than this, or even to connect an audi~frequency
It is easier
amplifier to the output terminals of a frequency converter.
to make an i-f amplifier having a very narrow pass band at low frequencies
than at high frequencies, and for this reason a low intermediate frequency
might be desired. An audio-frequency amplifier might be used in an
application such as c-w radar, where the reflected wave received differs
from the transmitted frequency because of the doppler effect with a
moving target. It is important to realize that the noise temperatures
usually quoted for crystal converters apply at 30 Me/see and that the
temperature at low frequencies is considerably higher.
If a narrow pass
band is desired, it is usually better to use a double i-f system, where the
first amplifier stages operate at 30 Me/see or more, and a second frequency conversion is made to allow the use of a narrower, low-frequency
Measurements, made at the University of Pennsylvania, of the noise
temperature in the video- and audio-frequency range, show that the noise
temperature of a crystal converter increases as 1/j in this range. The
values common at a low audio frequency are very large. At 100 cps, a
noise temperature as large as 105 is common.
The noise figure of a
receiver using an audio-frequency amplifier would be correspondingly
large. The minimum signal power detectable with such a receiver would
be very much larger than that detectable with a receiver having the same
bandwidth but a high intermediate frequency.
This same limitation is
encountered when crystals are used as rectifiers for experimental purposes
and small changes in the rccti fied current are intended to show smail
changes in the incident r-f power. Because of the low-frequency noise,
there are slow changes in the rectified current with a fixed incident r-f
power, and the fractional change in incident power which can be detected
is therefore limited to a rather large value.
Usual!y, the noise temperature of a crystal converter is raised if a
backward bias voltage (one in the direction of high resistance) is applied
to the crystal.
For this reason, it is advisable to keep the resistance of
the circuit through \vhich the crystal current flows as low as possible.
For the purpose of filtering, resistors have been used in series with the
crystal-current leads but, because the flow of crystal current through such
resistors develops a backward bias voltage at the crystal unit, it is not
advisable to use such resistors unless they are small or are shunted by i-f
A total resistance of about 100 ohms can be
chokes of low d-c resistance.
tolerated in the crystal-current path without producing an appreciable
deterioration in the over-all noise figure of the receiver. Since the crystal
current is usually less than 1 ma, a backward bias voltage of less than 0.1
volt can be tolerated.
Specific values and an outline of the method of measurement of the
converter noise temperature of crystals of various available’ types are
It must be remembered, however,
given in later sections of this chapter.
that since all the standard tests are made at 30 Me/see and at higher frequencies, the test specifications cannot be used to estimate the noise
figure of receivers using intermediate frequencies much below this.
2.15. Crystal Burnout.-In
Chap. 1, the need to protect the sensitive
part of a receiver was discussed in explaining the function of the duplexer
The amount of protection
common to all single-antenna radar systems.
the duplexer must provide depends on the amount of power that cam be
dissipated in the input circuit of the receiver without damage.
Since the
best over-all noise figures are obtained with microwave receivers using
crystal converters as input circuits, the more power a crystal unit can be
made to withstand without damage, the less protection is required from
the duplexer.
A considerable part of the work on the development of
crystal rectifiers, therefore, has been directed toward increasing the
amount of electrical shock they can withstand without damage.
increases in the resistance of crystals to both mechanical and electrical
shock have been made.
In some instances, there have been simultaneous
This improvement is
reductions in the loss and noise temperature.
valuable for crystals intended for use in isolated receivers because,
although the danger of damage from a local transmitter may not exist,
accidental mechanical and electrical shocks can occur.
The crystal cartridges now available are all hermetically sealed by
filling the region above the semiconductor and around the cat whisker
with a wax having a low r-f loss factor.
In addition to making the
hermetic seal, the wax serves to support mechanically the fine wire cat
whisker, and the contact is therefore made more stable against mechaniThere is no reason to believe that
cal shock than it would be otherwise.
a crystal rectifier unit that was never subjected to electrical power greater
than a few milliwatts, and that was never subjected to severe mechanical
shock, would ever change in its characteristics.
Nevertheless, the problem of burnout of the crystal converter has been one of the greatest
sources of trouble in a radar system, and, as a consequence, a large amount
of work has been done to reduce the frequency of occurrence of burnout.
This work has been directed toward increasing the amount of protection
and the lifetime of the TR switches, and toward increasing the resist ante
of the crystal units to damage by electrical shock. Resistance to electrical shock could be increased relatively easily at a sacrifice in the noise
figure of the receiver, but this sacrifice could not be tolerated.
A crystal rectifier, to be useful at very high frequencies, must have a
very small contact area. The barrier capacitance is partially determined
by this contact area and, with a large contact area, the nonlinear resist-
When a
ante of the contact is effectively bypassed by the capacitance.
large current is passed through a crystal rectifier, heat is generated in the
very tip of the cat whisker and in the semiconductor just below it, because
these are the regions of highest electrical resistance.
The weld of the
Unf ortuspecial germanium crystals was accomplished in just this way.
nately, ordinary tungsten-whisker silicon crystal units do not react
favorably to such heating.
Instead, the contact is destroyed, or the area
of contact is made so large, by the fusion of the tip of the whisker, that
the crystal is no longer a good high-frequency rectifier. A crystal that
has deteriorated because it has been subjected to excessive electrical
power is said to be burned out. A burned-out crystal may exhibit its
deterioration as an increase in conversion 10SS,an increase in noise temperature, or both, if it is used as a frequency converter or, if it is used as a
low-level detector, as a decrease in rectification efficiency.
2.16. Correlation between TR Leakage Power and Crystal-burnout
Power.—It has already been stated in Chap. 1 that the power that leaks
through a TR switch consists of two
components called the “spike” and
the; flat.”
The spike oc~urs at the
j~–lbeginning of the radar transmitting
pulse and builds up with that pulse
to an amplitude sufficient to initiate
FIG. 2.30.—Envdope of the r-f pUISe
a ~iewe,,
TR switchM viewedwith
the arc in the TR switch. After the
~, ,-f ,.~,elOPe
arc is initiated, the amplitude of the
leakage signal falls abruptly to a smaller value, where it remains until
The envelope of the pldse transthe end of the transmitting period.
mitted through a TR switch can be observed with an r-f envelope viewer.
This instrument consists of a crystal detector and a video-frequency
amplifier, the output voltage of which is applied to the vertical-deflection
plates of a cathode-ray tube. A sweep voltage, synchronized with the
pulse rate of the radar transmitter, is applied to the horizontal-deflection
plates of the tube.
In Fig. 230 a sketch of a typical trace produced by
the leakage power from a TR cavity, as viewed with an r-f envelope
viewer, is shown.
In this sketch, and on most of the viewing systems,
the peak power of the spike appears to be about twice that of the flat.
The average leakage power can be measured with bolometers and is
usually found to correspond to an average power for the duration of the
pulse of less than 50 mw. The power level at the peak of the spike cannot
be found from the trace on the envelope viewer alone, because the bandwidth of the video amplifier is not sufficient to ensure that the r-f envelope
viewer responds rapidly enough to show the true magnitude of the spike
relative to the flat power.
Measurements of the r-f pulse power, in l-usec pulses, required to
damage crystal rectifiers have been made. This power was found to be
considerably larger than the 50mw of average power that passes through
the TR switches during the transmission period.
Yet crystal burnout
was not at all uncommon intheradar systems in which such crystals and
TRswitches wereused.
Even after crystals that could withstands everal
watts of r-f pulse power had been developed and the apparent safety factor was very large, the burnout problem persisted.
Finally, techniques
for the measurement and viewing of the spike were developed.
of these techniques consisted of a measurement of the total leakage power,
by the” bolometer method, and a measurement involving the calibration
of the r-f envelope viewer as a power meter. Comparison of the results of
these two measurements showed that the average leakage power, as
indicated by the bolometric method, was considerably greater than that
calculated from the height of the flat part of the leakage on the viewer,
the pulse length, and the recurrence rate. Therefore, the actual peak
amplitude of the spike part of the leakage is much greater than indicated
by the viewer and, consequently, the time duration of the spike must be
very short compared with the response time of the viewer.
This was
confirmed by measurement with the other method, which was accomplished with a transmission channel bypassing the TR switch and having
the right phase and amplitude characteristics to produce destructive
interference between the waves transmitted by this channel and by the
TR switch during the time of the flat-power leakage.
The subsidiary
channel was adjusted until the flat power was completely canceled, and
only the spike remained to be seen
on the envelope viewer.
The amplitude of the spike is almost entirely
unaffected by the addition of the
Fm. 231.-Leakage of a TR switch with
flat powercanceledout.
‘interfering channel because the
spike power is transmitted through
the TR switch without much attenuation, before the arc is initiated.
The attenuation of the subsidiary channel is the same as that of the TR
switch when it is firing, and the power transmitted by it is therefore small
compared with the spike power at the time of transmission of the spike.
A sketch of the trace on the r-f envelope viewer with the flat power
canceled out is shown in Fig. 2.31. When the residual average power
under these conditions was measured with a bolometer, it was found to
correspond exactly to the discrepancy between the measurements by the
first method.
Because the duration of the spike was found to be so short (less than
10-’ see), it was not yet substantiated whether such a short pulse could
damage a crystal unit by heating, since the crystal unit must have a
The time constant had in fact been
nonzero thermal time constant.
estimated to be somewhat longer than the duration of the spike and,
therefore, it was suspected that the damaging effect of the spike might be
measured bythe energy content of a single spike, independent of its peak
power. Tests of the burnout characteristics of crystal units with videofrequency pulses, shorter than 10–8 sec but of various durations, were
made and it was found that the energy was the important parameter.
The methods of measurement of the spike allowed the calculation of the
energy per spike pulse, and it was found that there was a much smaller
safety factor of protection against burnout by the spike than by the flat
leakage power.
Inaddition, themethods ofmeasurement and of viewing
of the spike energy revealed a great dependence of the spike energy on the
functioning of the keep-alive electrode of the TR tube.
in the design of the keep-alive electrode and of the circuit supplying
the voltage for it considerably reduced the frequency of burnout of crystals in radar systems.
the research on the burnout
characteristics of crystals was directed most strongly toward measurement and improvement of their resistance to burnout by very short pulses.
It was found that the burnout of crystals by the r-f spike energy correlated
reasonably well with the values obtained from experiments with videofrequency pulses.
In some frequency bands, crystals of several different types, having
different degrees of resistance to burnout, are now available
In the
3000-Mc/sec region, for instance, the 11Y21A crystals are subjected to
short pulses containing 0.3 erg of energy, ~vhereas the lh’28 crystals are
subjected to pulses containing 5 ergs, before their 10SSand noise temperature are tested.
That the increase in resistance to burnout was not
achieved at a sacrifice in noise figure is evident from the fact that the
limits on the loss and noise temperature of the 1N28 crystals are lower
The 1N21B units, however, have a
than those of the IN-21A crystals.
burnout test at lower energy than the 1N28 units, and a lower limit on
the conversion loss.
In addition to burnout of this instantaneous kind, it has been found
that a slow deterioration
with time occurs when crystals are subjected to
pulses of considerable magnitude but containing insufficient power to
cause a crystal to be burned out by a single pulse or by a small group of
pulses. For instance, a crystal that might withstand several hundred
pulses of 2 watts pulse power sometimes shows a serious deterioration
over a period of operation of many days when subjected to pulses of a few
hundred milliwatts pulse power recurring 1000 times per second.
It is
therefore advantageous to make the leakage power of the TR switch as
small as possible and to make occasional checks of the crystal unit, even
if no failure of the TR switch has occurred and no abrupt change in
At power levels of a few millireceiver sensitivity has been observed.
watts, crystals appear to last indefinite y if handled with reasonable care.
In this connection it should be pointed out that one of the most frequent causes of damage to crystal units is the discharge through the crystal of the electrostatic charge commonly accumulated on the body.
Discharging the body capacity to the apparatus before a crystal is inserted
or removed precludes the possibility of burnout by this means.
In this
way one makes certain that no discharging current will flow through the
crystal unit. It is confusing to have a crystal burned out during the
time between its testing and its insertion in the apparatus.
The energy
stored in the charge on the capacity of the body, even for electrostatic
potentials that would not normally be noticed, is sufficient to cause burnout of some units.
In addition to damage by electrical shock, the delicate contact of the
crystal rectifier unit is subject to damage by mechanical shock.
wax filling cannot prevent motion of the whisker if extreme accelerations
are encountered, and, hence, it is advisable to make checks before use on
For this purpose and for
all crystals that are accidentally dropped.
checking for damage from electrical sources, the back-resistance meter, to
which reference has already been made, is a very useful and simple test
Information on the design and use of this device is given in Sec.
In the table at the end of this chapter, a column giving limiting
values of the back current at one volt, for crystals of the various types,
is included.
In the earliest days of the development of crystal rectifiers for use as
microwave frequency converters, the only specification of the quality of
the crystal was the effective over-all receiver noise figure resulting with
its use. The noise figure was ascertained by measurement of the r-f
input signal power required to give an output signal power equal to the
output noise power.
In addition, the width and shape of the pass band
had to be measured in order to evaluate the equivalent noise bandwidth
B of the receiver. The ratio of the required input signal power to lcTB
is the effective over-all noise figure of the receiver.
This was sufficient
description of the particular receiver for which it was measured, but it did
not allow computation of the expected noise figure for the same crystal
with a different i-f amplifier.
The conversion loss and the noise temperature of a crystal used as a
frequency converter are, together, a measure of the quality of the crystal
alone. They can be used to calculate the effective over-all noise figure of
a receiver using the crystal as a converter if the effective noise figure of
the i-f amplifier, with a generator having an admittance equal to the i-f
SEC.2. 17]
admittance of the converter, is known.
The first equipment for measurement of the loss and noise temperature of a crystal closely resembled an
ordinary microwave superheterodyne receiver. The loss was measured
by calibrating the i-f amplifier as an i-f power meter and comparing the
i-f power delivered by the crystal converter with the r-f power available
from the signal generator.
The measurement of noise temperature was
made by comparison between the values of the output noise from the
receiver with the crystal in place and with the crystal replaced by an
equivalent i-f resistance.
From this comparison the noise temperature
can be calculated, provided the effective noise figure of the i-f amplifier
is known.
The amplifier noise figure was measured in a standard manner
by use of a temperature-limited noise diode.
This method of measurement of the quality of a crystal was rather
unreliable and difficult to carry out. Simpler apparatus was subsequently developed for making the measurements of loss and noise temperature.
Moreover, a burnout test was included in the specifications
and a standard apparatus for this test was developed.
The remaining
sections of this chapter are devoted to a description of the principles of
this test apparatus.
It is not intended to give sufficient detail in this
description to enable the reader to duplicate the apparatus but only to
A table of some of the
make clear the meaning of the test specifications.
specifications and related data for crystals of the types now available is
included at the end of the chapter.
2.17. Conversion-loss
measure the conversion
loss of a crystal by the direct method, an accurately known amount of r-f
signal power, 1 pw or less, must be avadable.
Simdarly, it must be possible to measure accurately a smaller i-f power. The frequencies of the r-f
signal and the local oscillator of the converter must be such that the output signal of the converter has the frequency of the i-f amplifier that is
used as a power meter. Because the conversion loss is dependent on the
load admittances at the image and harmonic frequencies, the loss measured in this way can be different for the same crystal in different mixers,
even if all the available signal po~ver is matched into the converter.
To simplify the measurement of conversion loss, the “modulation
method” was developed.
In this method, no signal generator, separate
from the local oscillator, is used and the converter output power is measThe crystal is placed in an appropriate
ured with a standard instrument.
mount, either a waveguide or a coaxial line, depending on the frequency.
This mount is adjusted, on the basis of statistical data on large numbers
of representative crystals, in such a \vay that an average crystal has the
minimum loss at this adjustment of the mount.
Provision is made in the
crystal mount to bring out the rectified crystal current and low-frequency
voltages in the same way as in a conventional mixer. The manner in
-, - “J
[S~c, 217
which this is done will be made apparent in the following chapters.
crystal mount is placed at the end of a similar waveguide or coaxial line,
from which the local-oscillator power is applied, through a matched
dissipative attenuator, at an appropriate known level. Because of the
matched attenuator the local oscillator, as a signal generator, has an
admittance equal to the characteristic admittance of the line. A small
amplitude modulation is then introduced on the local-oscillator signal
and the magnitude of the voltage thus produced at the output side of the
crystal, across a resistance equal to the optimum load resistance for an
average tryst al, is measured by means of a sensitive a-c voltmeter.
modulation frequency is low, usually 60 CPS,and an ordinary amplifying
voltmeter having a full-scale sensitivity of 0.01 volt can be used. For a
full-scale deflection of such a voltmeter, an i-f power of 0.25 PWis required
if the load resistance is 400 ohms. If the conversion loss were 6 db, the
modulation required for a full-scale deflection would be equivalent to an
available signal power of 1 pw. This is found to be a small enough signal
to allow the converter to behave linearly.
The amplitude-modulated local oscillator is equivalent to an unmodulated local oscillator and a signal at each of the sideband frequencies
corresponding to the signal and image frequencies of a converter.
If 27r times the local-oscillator
may be shown in the following way.
frequency is CO,and 21rtimes the modulation frequency is d, the instantaneous local-oscillator voltage is
E = EO(l + m [email protected]) COSat,
where m is the fractional modulation and E,) is the unmodulated
tude. A trigonometric manipulation allows this to be \vritten
E = E, COScd + E, ;
COS[(u + WI + ~,;
COS[(u – BM.
Thus, there is a signal at each sideband frequency, of amplitude 1?, ~, or a
power equal to E~Y,, ~~
The incident local-oscillator
power is
Therefore, the signal power in one sideband may be written
P, = P, :2.
In the measurement of loss, the incident local-oscillator power can be
measured directly with a thermistor, or a Wollaston wire, in a bolometer
bridge and, therefore, the equivalent signal power can bc found, provided
that the modulation pcrccnta,gc con IK measured,
In onc form of the
loss-measurement apparatus, the modulation is produced by an eccentric
rotating disk made of cm-lxm-coated Bakclitc.
The disk projects into
the waveguide that supplies the local-oscillator powm to the mixer. The
disk is so proportioned that when it rotates at a constant speed, sinusoidal
modulation of the amplitude of the local-oscillator signal at the crystal
results. By rotating the disk slo\vly the mo(lulation percentage can be
mcasurecl. The value of the loss can bc calculated from knmvledge of P.
and of the delivered output power as mcasurccl by the voltmeter.
It is more common, however, to make the absolute calibration by what
is known as the “ incremental method” for a few crystals ~rhich are then
carcfldly preserved as standards.
If thrsc crystals are inserted in an
apparatus using electronic amplitude modulation, the ]evcl of the localoscillator power can be set to give the proper rectified crystal current,
and the a-c output meter may be made to read correctly by setting
the modulation level. The incremental d-c method may be regarded as
an extrapolation of the modulation method to zero frequency,
A sensitive current meter is so connected that it measures a small fractional
change in the rectified current. This change in the rectified current is
produced by a small, known, percentage change in the r-f power.
If the
change in current and the differential admittance of the crystal to DC are
known, it is possible to calculate the output power that would reproduced
if the change in incident power were repeated sinusoidally.
With a set of
a few crystals calibrated as primary standards in this manner, any number of crystals may be calibrated with a modulation-method
for use as secondary standards at the many locations where modulationmethod apparatus is used. The use of several standards is a protection
against changes or damage in any one of them, since a change in a crystal
will immediately be discovered because of disagreement with its calibra.
tion when the instrument is adjusted to read correctly for the others,
The loss, as measured in the test, is not exactly the loss that is used for
the calculation of noise figures, except for some special cases, although
the measured loss does not differ greatly from the loss appearing in the
formula for the effective over-all noise figure of a receiver.
The i-f load
of the testing apparatus is fixed at a value equal to the i-f output admittance of an average crystal, and the power delivered to it—not the available i-f power-is
Under the conditions of measurement, the
i-f output admittance of most crystals does not differ from the load admittance by an amount causing a loss, due to mismatch, of more than a few
tenths of a decibel.
Because the tuning of the crystal holder is fixed,
crystals having signal admittances that differ from that of an average
crystal are not tuned for minimum conversion loss. Both of these
factors tend tomakethe
measured loss greater than that which couldlw
obtained from a given crystal if both the i-f load admittance ancl the r-f
tuning were adjusted to the optimum values.
In the calibration of the apparatus, each sideband signal contributes
a component to the low-frequency output \roltage. There is a phaw
relationship between the local-oscillator signal and each sideband such
that two modulation-frequency components at the output terminals of the
crystal are in phase, because they arise from amplitude modulation.
The output voltage, therefore, is twice as great as it would bc if there
were only one signal having the same amplitude as one of the sideba ml
signals. The loss, therefore, is computed assuming a signal amplitude
twice that of a single sideband component, or a signal po~~-ert!rice that
available in the two sideband signals. When the calibration is made
in this way, the loss obtained is, except for the mismatch factors,
that which would result if conversion \vere made from a single signal
frequency to the intermediate frequency and if the r-f tuning at the signal
frequency were identical with that at the image frequency.
As ~vas
shown in Sec. 2.10 the minimum loss that a converter, representable as 2
linear passive network, can possess under these conditions of tuning is 3
db. This corresponds, in the modulation-method
test, to conversion of
all the available signal power in the two sideband signak into low-frequency power. A crystal for which this is true shows a 3-db loss according to the calibration.
Thus, a crystal that shows less than 3-db of loss
in this apparatus, as do the welded-germanium units, delivers to the load
resistor more power than is available in the input signal. Such a crystal
converter cannot be represented by a passive network, although it may
still be linear, and the excess power must be derived from the localoscillator wave, the bias supply, or both.
In the specification tests of crystals there is no explicit measurement
of the r-f admittance in a particular mount nor, except for one type of
Because the loss measured is the ratio of
crystal, of the i-f admittance.
the equivalent available r-f power to the i-f power delivered to a fixed load,
and not the ratio of this r-f power to the available i-f power, a limit is
implicitly imposed on the range of admittances possible.
Crystals having
r-f or i-f admittances greatly different from the average must also posses a.
minimum conversion loss considerably below the specified limit to pass
the loss test. Such crystals are not often found because the upper limit
on the loss is not very much greater than the average loss for crystals of a
given type. The fact that some reflection loss can occur at the single
frequency of the test does not allow much margin for frequency-sensitive
behavior in a circuit that must operate in a wide band since reflection loss
increases much more rapidly with the degree of mismatch after the first
few decibels.
If all of the mismatch loss were to occur on the output side
of the test converter, the possible scatter of the i-f admittances of many
crystals, from this cause, combined with the effect of the image-frequency
termination when a high-Q TR cavity is used, could pose a considerable
problem to the designer of the i-f input circuit.
Fortunately the i-f
admittance seems to be fairly uniform from crystal to crystal under the
conditions of the test. The loss caused by r-f mismatch is usually greater
than that caused by i-f mismatch because the crystal cartridge represents
a fairly sizable circuit element compared with the r-f wavelength and therefore its r-f admittance is determined not only by the semiconductor and
contact but by all of the discont inuities and dimensions of the cartridge.
The i-f admittance is determined by these things only in so far as the r-f
tuning affects the i-f admittance, which is very little because of the buffering effect of the conversion loss.
2.18. Noise-temperature
the noise temperature is dependent upon frequency, it must be measured at the intermediate frequency to be used. For this reason the noise-temperature
test equipment resembles a complete superheterodyne receiver much more
closely than does the loss-test apparatus.
As is also true for the apparatus used to measure loss, the noise-temperature test equipment used at
present is similar in principle for all microwave frequency ranges and
differs primarily in having r-f circuits in a medium suitable to the particular frequency.
Thus the 3000-Mc/sec test sets for loss and noise-temperature measurements utilize principally small coaxial lines, and the
crystal mounts are of a coaxial-line type. The test sets for 9280 Me/see
and that for 25,000 Me/see, on the other hand, use appropriate waveguide transmission lines and crystal mounts.
A block diagram of the present form of the noise-temperature measurement apparatus is given in Fig. 2.32. The local-oscillator power enters
the mixer through a filter cavity in order to minimize any spurious noise
that might enter at either of the sensitive sideband frequencies.
Attenuators are used on both sides of this filter, to ensure that the filter does not
pull the oscillator frequency badly and to provide a matched line looking
from the mixer back toward the local oscillator.
The mixer is identical
with the one used in the corresponding loss-measurement apparatus and
the level of the incident local-oscillator power is set to be the same as
in the loss apparatus.
The input terminals of the i-f system can be
switched from the output terminals of the mixer to a fixed dummy
Between the output terminals of the
resistor for purposes of comparison.
mixer and the preamplifier is a lumped-constant circuit.
This circuit
transforms the input admittance of the i-f amplifier to a value equal to the
complex conjugate of the output admittance of the mixer with an average
In addition, the transformer has such characteristics that it is
equivalent to a transmission line having a characteristic admittance equal
to the output
of the mixer with an average crystal and having a
length equal to five-eighths of a wavelength at the intermediate frequency.
The function of this circuit is to make the output noise of the receiver
m 1=
l-f pre.
FIG.2.32.—Blockdiagramof noise-temperature
test apparatus.
independent of the i-f admittance of the converter provided that it is
It is this circuit that makes
real and has a noise temperature of unity.
the apparatus better suited to the
measurement of noise temperature
than an ordinary receiver.
The output noise of an amplifier
may be regarded as arising primarily
in the input stage of that amplifier
and ahead of it, provided the input
stage has sufficient gain to make the
contribution to the total output noise
z mmt
from other stages negligible.
In the
apparatus under discussion, this condition is fulfilled, and if the only
sources of noise are Johnson noise
and noise arising in the tube, the cir*
FIG.2.33.—Equivalentcircuitof i-f input cuit may be represented by Fig. 2.33,
to an approximation sufficient for the
present purposes.
The grid of the
tube is considered to have no admittance, and the noise generated in the
tube is considered to be caused by the Johnson noise in the resistance R-
at room temperature.
The impedance Zi.p.t, or its reciprocal the input
admittance, may be considered to be made up of the input admittance to
the tube plus all admittances associated with the circuit connected to the
In the case in question, however, the
input terminals of the amplifier.
input circuit includes the i-f admittance of the mixer, transformed by
the special circuit between the mixer and the amplifier, and a conductance
added from grid to ground.
The total effective circuit may be represented by the equivalent circuit shown in Fig. 2.34. The i-f admittance
of the mixer is made real by an added susceptance and, for a crystal
having the average i-f admittance, the transformation effect of the input
circuit is such that the admittance at the output terminals of this circuit
is equal to g,. Thus the only elements appearing in the circuit of Fig.
2.34 are the transformed i-f conductance g of the mixer with its associated
noise-current generator i, the conductance go, made up of the input
5/ewavelength line
line andinputamplifier.
FIQ.2.34.—Equivalentcircuitof mixer,five-eighth-wavelength
conductance of the tube and an added resistor with its associated noisecurrent generator L, and the equivalent noise-generating resistance for the
tube with its associated noise-voltage generator e.. Each of the noise
generators generates a noise current or voltage given by the thermalagitation equation.
The temperature of the i-f conductance of the mixer
is t times room temperature, and the temperature of the other resistors is
room temperature.
The admittance of the output terminals of the transmission-line section may be obtained from the general transmission-line equation, which
for a line having no loss is
where @ is 2m/A for a distributed-parameter line, 1 is the line length and
YI is the admittance of the pair of terminals at one end when an admittance Y, is connected to those at the other end. In the present case, the
admittance of the output terminals of the five-eighth-wavelength line is
go +
2ggo +
j(g{ –
~~ +
A new equivalent circuit may now be drawn, eliminating the transmission
linejasin Fig. 2.35. Themagnitude of thenoise current associated with
the mixer is found from the fact that the noise power available at the
output terminals of the line is the same as that from the mixer, since the
line is lossless. The mean square ~
of the noise current induced in
the input conductance go, in a narrow frequency band dv, is
= [~
+ ~]
where Iillz and Iizj2have the values shown in Fig. 2.35.
developed across the conductance go is
+ I’d’
9?I 190
The substitution, from Eq. (56), for YI and the insertion of the values of
and ~
in terms of the conductance,
reduces Eq. (58) to
The mean square of the total input noise voltage lS the sum of this voltage
and the voltage arising from the noise resistance of the tube, or
(1 ~a)’
where the ratio g/g. has been written as a. The admittance transformation of the input circuit is used to make the value of l/2g, comparable
with that of R., which, for a typical pentode 30- Mc/sec amplifier tub,
is about 2500 ohms.
Equation (60) describes the behavior of the test set. I?h-st, let us
suppose that the mixer has a noise temperature of unity, or that a resistor
at room temperature is substituted for the mixer at the input terminals of
the coupling net work. ‘l%c term that depends on the conductance at
the mixer terminals is then zero and the output noise power of the amplifier is independent of the conductance, provided that the noise examined
is only that contained in a narrow frequency band, in which the transformation effect of the input circuit maybe considered to be independent
of frequency.
In practice, a fairly narrow-band communications receiver
If the noise temperature of the mixer
is used, fo11owing a preamplifier.
is not unity, the contribution is a maxiTo Dreamriifler
mum if a is equal to unity.
The contribution falls to 80 per cent of the maximum
value, for the same value of f, if a is as
much as a factor of 2 larger or smaller
than unity.
The increase in the outpllt
noise power from the amplifier w-ith a
crystal in the mixer, OVCYthat with the
amplifier connected to the resistor, is
proportional to t – 1.
To calibrate the apparatus, the value
of R.v could be measured and an output
meter measuring noise po~ver at the output
terminals of the amplifier could be used.
Instead, the apparatus is calibrated in
such a manner that the value of R., need
not be known, and a meter having any law
of response can be used at the output
terminals of the amplifier.
For this purpose the noise diode is included in the
This diode is a specially concircuit.
FIG. 236.-Possible
circuit for
structed tube having a tungsten filament
utilization of noise diode.
C = bypass condenser (1000
and short leads. The magnitude of the
#pfd at 30 Me/see).
plate current of the diode is controlled by
RFC = i,ntcxmediate-f requency
the temperature of the filament, and a
R = filament rheostat.
plate voltage sufficient to ensure saturation current for all filament temperatures is applied.
Thus, spacecharge smoothing of the plate current is eliminated.
Under these
conditions, the mean-square fluctuation components of the plate current,
in a given frequency band, caused by the shot effect can be calculated.
Diodes that are used for the measurement of amplifier noise figures in
this way are called temperature-limited
Figure 2.,36 shows a
possible circuit for utilization of such a noise diode, where RI is the i-f
resistance of the mixer, equal to l/g, and R2 is the resistor included for
comparison purposes.
The noise diode may be considcrccl
mean-square noise current given by
as a noise generator
~,lz = 2cI d.,
with a
where 1 is the diode plate current, c is the electronic charge, and dv is the
narrow band of frequencies being examined.
If a resistor of conductance
g is put into the mixer in place of the crystal, the mean-square thermal
noise current in this resistor is
Iitilz = -4 k?’g dv.
Therefore, the total mean-square noise current in the resistor is
Iitl’ = li~l’ + ]i,l’ = 2cZ dv + 4kTg dv,
The resistor may be regarded as having a noise temperature t given by
The standard temperature for purposes of sLIch calibrations is taken as
that which makes c/kT equal to 40 per volt and corresponds to a temperature just less than 20°C. Thus Eq. (64) becomes,
The calibration of the noise-temperature measurement apparatus
can thus be made by observing the olltput meter at several values of
diode current with each of several
resistors having different conductdeflection
antes in place of crystals in the mixer.
-_----—-— .-_____t:5
--A typical calibration curve for an
-—-- ———-—-—-—--output meter giving readings pro1,5 —-–__L=3
portional to power is shown in Fig.
---__ -----—-2.37, where the ordinate is the outt=2
——-— _——______
_— --put-meter reading on a linear scale
and the abscissa is the value of a on
a logarithmic scale.
In practice, the input transformer
measurement set,
for noise-temperature
is a lumped-constant
This circuit contains several variable
condensers which must be tuned properly.
When the condensers are
correctly adjusted, the output-meter reading is independent of the con.
ductance of the resistor placed in the mixer and is the same for the switch
in the position that connects the dummy resistor to the amplifier input
SEC. 2.19]
Unfortunately, this special input circuit does not work so well for the
measurement of the noise temperature of a mixer that has a reflection
It has been shown in Sec. 2.11 that such a
of the image-frequency wave.
reflection can give rise to a susceptance component in the i-f admittance
of the mixer and such a component would upset the adjustment of the
special input circuit.
For mixers not having reflections at the image frequency, the noisetemperature measurement apparatus can be used to measure the i-f
conductance as well as the noise temperature, by use of the temperaturelimited diode.
The diode plate current required to cause a given deflection of the output meter is dependent on the magnitude of the conductance at the output terminals of the mixer. A calibration can be obtained
using resistors in the mixer. Then a measurement of the diode current
needed to produce a given deflection on the meter with a crystal in the
mixer constitutes a measurement of the i-f conductance of the mixer,
if a square-law (po\vcr) meter is used.
2.19. Burnout-test Apparatus.—To
simulate the spike energy as a
cause of tryst al burnout, the apparatus used to test tryst als for susceptibility to burnout subjects a crystal to a very short video pulse. The
specifications for most types of crystals require all units to be subjected
to a pulse of this sort before they are tested for loss and noise temperature.
Crystals intended for use as low-level detectors, on the other hand,
because they are not commonly used in systems having duplexers, are
rarely subjected to “spike” p~l.lses but are more frequently burned out
through the presence of po~verful radar transmitters in the immediate
Therefore, the p(dscs to which such a crystal might be subj ected would more likely bc ordinary radar pulses of about l-psec
Less attention is paid to the burnout characteristics of such
crystals, as a consequence.
The apparatus developed by H. C. Tomey for the burnout test of
mixer crystals consists of a short piece of coaxial line, connected at one
end through a high resistance to a source of d-c voltage which charges the
line to that d-c voltage.
The crystal to be treated ~rith a burnout
pulse is inscrtmd into a holder at the other cnd of the line but, not put
into contact with the center conductor.
A sudden contact of the center
conductor with the pin cnd of the crystal cartrdgc is made by dropping
the center conductor a short distance onto the cartridge tip. This
discharges the line in a single pulse through the crystal in a time approximately equal to 21/c where 1 is the length of the line and c is the velocity
of light. The length of the line is made such that the pulse length is
about 5 X 10–’ sec. This time is so short that the burnout of the crystal
depends upon the pulse energy and not upon the pulse power.
energy delivered to the crystal is just the energy stored in the capxitance
[SEC. 219
of the line and this is easil,y calculable from the size of the line and the
In this way a single pulse of uniform energy is delivered to each
If it has
crystal before it is tested for loss and noise temperature.
been damaged appreciably by this pulse it will not pass these later tests
and therefore no electrically fragile crystals should find their way into
The correlation between burnout by a video pulse of this kind
and burnout by an actual r-f spike pulse has been found to be good and,
therefore, this simple technique has been adopted in preference to an r-f
burnout test.
The value of the energy of the pulse used depends on the type of
crystal being tested, as will be evident from the table at the end of this
The lower-frequency
units can, in general, stand a larger
amount of energy before burnout occurs because the area of the contact
of the cat whisker and the semiconductor is larger. Also there are
available, in some frequency ranges, units that have high burnout
resistance and high loss, as well as units that have the lowest possible
loss and reduced burnout resistance.
This is not obvious from the
table, however, because some types with high loss and noise-temperature
limits but with small burnout energy, or no specification of burnout at all,
are also listed. These are obsolete or obsolescent types having characteristics inferior to the more recently designed types designated by the
same code number followed by a letter A, B, or C. The lower limits on
the loss and noise temperature as well as the higher resistance to burnout
of later types are illustrative of the progress made in the design of crystal
units through the intensive research that was carried on during the war.
For the burnout test of crystals for which the burnout specification is
given in terms of watts of pulse power in a l-psec pulse, a video pulse
is also used, but the pulse is formed by a lumped-constant pulse-forming
The pulse power
network which is discharged through the crystal unit.
delivered depends upon the admittance of the crystal unit at this level
The specificarelative to the characteristic admittance of the network.
tion is the available power, but this power is dissipated by the crystal
only if the crystal admittance matches that of the network.
network admittance is chosen to be approximately equal to the crystal
admittance at this power level and, therefore, the available power is not
greatly different from the power actually delivered.
The burnout specifications, like the other specifications, were determined on the basis of tests of representative units, rather than being
When research
arbitrarily set up as minimum acceptable requirements.
and improved manufacturing techniques indicated that it was easy to
produce large numbers of crystals passing existing specifications without
large “shrinkage,”
a new set of specifications was written for a crystal
with a different type number, usually the old number with the added
A or 1?. In this way the improvements found possible on a laboratory
The result
scale were quickly reflected in improved production types.
is that the crystals available at present represent a great advance in
both burnout and noise-figure characteristics relative to those available
only on a laboratory scale in 1942.
2.20. The D-c Crystal Checker.—The fact that there has been shown
to be a reasonably good, if not perfect, correlation between the back
resistance of crystal units of one type and their noise-figure characteristics has been mentioned earlier. The correlation is sufficiently good to
enable it to be said that a crystal of a particular type, passing more than a
given back current at a given applied voltage, has probably been burned
out. Perhaps more important is the fact that a unit passing less than
this given current has almost certainly not been damaged severely.
Without a check as simple as this, the service problem of microwave
receivers u n d e r field conditions is
rendered very difficult because there
are many possible sources of trouble
1000 ‘~- Crystal
other than the crystal.
By this test
S* -->--the condition of the crystal can be
quickly determined; if the crystal is
not at fault, another source of trouble
o-1 MA
may be investigated.
In addition, a {
simple check makes possible periodic
~lG.23S.-D-C crystal checker.
checks of operating crystals, allowing
slow deterioration which might otherwise go unobserved to be watched
and not allowed to proceed far enough for it to be detrimental to the
performance of the receiver.
The limiting back current is known, for most of the available crystal
units, for 1 volt of potential difference across the unit. A circuit
diagram of a test unit that can be used to make this check is given in
Fig. 2.38. A switch SI is used to turn the unit on and off, and a second
switch S2 enables the single meter to be used, with the switch in the upper
position, to adjust the potential across the test crystal to 1 volt.
the lower position the current through the crystal is read on the meter.
The position in the circuit of the meter and of a resistance R, equal to
the meter resistance, are interchanged by the switch Sz and, therefore,
the current through the crystal is the same for either switch position.
The value of the maximum back current at 1 volt for a relatively.
undamaged crystal, has been found to be dependent upon the crystal type
only, and not upon the manufacturer, with one exception.
For the
1N26 crystal, it was found that the limit on the current was sufficiently
different for crystals of the two manufacturers towarrant the use of a
value for each. These values as well as the single ones for the other types,
where known, are included in the table of specifications at the end of this
chapter although they are not to be considered as specifications.
It is
possible that the safe currents will change for crystals produced in the
future under the same specifications, because there is nothing included in
the specifications which relates directly to them.
If it is desired to
guard against any amount of deterioration no matter how small, it is
perhaps best to keep a record of the back current at 1 volt for each
crystal; from the time it is first used and to be suspicious of the crystal if it
shows anv tendency to pass greater current with use. If a number of
crystals show such a change upon insertion into an operating mixer it is
to be taken as evidence that the TR switch or some other part of the
circuit is allowing the crystal to be damaged by excessive electrical power.
It is worth while to repeat the caution about static charge on the body
when handling crystals, and the importance, therefore, of grounding the
body to the apparatus through a path other than the crystal while it is
Care should be taken to be sure that the
being inserted or removed.
A considerable a-c voltage with
apparatus is electrically grounded.
respect to ground may be present, especially if the apparatus contains a
filter in the a-c line. Many crystals have become damaged because of
this, and it is advisable to take appropriate precautions to eliminate such a
2.21. Specifications and Relevant Information on Available Types.—
Table 21, to which reference has been made many times throughout the
chapter, follows.
The table gives the specifications as well as other
information on the various types of crystals currently available for use as
detectors and mixers in the microwave region.
There are two general
types of cartridge, and the one applying to each crystal is indicated in
the first column of the table as A or B. These symbols refer, respective] y,
to cartridges like those shown in Figs. 239 and 240.
An outline of the
physical dimensions, with tolerances, is given for each of these cartridges.
This is an important factor in the design of mixer and detector mounts
since considerable nuisance is encountered if the mount is designed on
the basis of the dimensions of only a few units. The large ceramic unit
was originally used at 3000 Me/see in a coaxial-line mount where it is
small compared with the dimensions of a convenient Iine, or compared
with the wavelength.
Later, crystals for the 3-cm region were built in
the same cartridge.
In this region the cartridge is still not large compared with the dimensions of conventional rectangular waveguides in
which it is mounted.
For 25,000 Me/see, this unit is excessively large
compared with either the waveguide dimensions or the largest single-mode
SEC. 221]
Consequently, the coaxial type of cartcoaxial line at that frequency.
It has
ridge of Fig. 2.40 was developed by Bell Telephone Laboratories.
much smaller internal dimensions in accordance with the use at shorter
There has been some use of this same cartridge for units
recently designed for lower frequencies because of the shielding of the
sensitive contact from stray radiation and because of the smaller physical
There is, in addition, less probability of damage thr u
(. ..$
0.046’’max, rad.
O.010’’max rad.
.005’’max. rad.
.. .;
e.. :! ‘;
in this end
~ :;LJ
FIG. 2.39,—Ceramic crystal cartridge.
Note 1. Eccentricity between tip and base shall not exceed 0.0075.
Note 2. Metal parts shall be silver-plated min. 20 mg/inz or gold-plated min. 10 mg/in2.
Note 3. Usedfor types: 1N21, IN21A, 1N21B, 1N23, 1N23A, IN23B, 1N27, 1N2S,
This drawingis takenfrom BuShipsDwg. RE 38A192.
static discharge from the body, since the mount is so constructed that
contact to the outside cylinder will almost certainly occur before the
discharge can go through the crystal.
The table gives, next, the use for which the crystal is intended, either
detector or as a mixer unit. The next column is
as a low-level “video”
the frequency of the specification tests. For mixer crystals, the localoscillator power level to which the loss and noise specifications refer is
given, then the minimum rectified current, measured by a meter of 100ohms resistance, and then the maximum acceptable values of loss and
noise temperature.
For some crystals the i-f resistance under the conditions of operation in the test set is specified, and, if so, it is given in
Formost crystals thisisnot specified and, forthese, the
value of the load resistance used in the loss test is indicated by the
Note 2+0002
Alternate shape’for end
ofpin O.012’’radius @
FIG, 2.40.—Shielded coaxial crystal cartridge.
Note 1. F]nish: plate with O.00002 tin over nickcl flash or O.0001 gold orsifver.
Note’2. ODdimemion applies tolengthindicatcd.
Note 3. Axis of cer,tcr conductor not todeviatefmm axis of outer conductor referred
to its outside diameter more than 0.004.
Note 4. The polarity is such that sleeve is positive when current flows in the pass
(forw:wd) cfircction.
Note 5. Crimp pcrmi~sible but adjaceut surface shall not be bulged beyond maximum
Thisedgcto bc sharp a,itifrccfrol]lburrs.
Note7. Slidlt cl,:ir,)fer pcrillittcd.
Typctc>t followin~: 1+’,H, note. 1 and 4, 5, nnd 7.
Oesiuntest follow.i,lg:B, D,J, K,G.
P~od,&.t, test :L1lother ditne,lsio!)sa])cl,,otcs.
This dra\vi,,gistakcllfrol,~ BuShips Dwg, IU3 3SA208.
numbers accompanied by TL for “test load. ” The “video”
resistance is given in this same column for low-level detectors and the
next column gives the figure of meritf.
Following this comes a column
Type of
rype Of
... .,.
. .
1-f or
noisefig. current
j-db am- limit at 1
)lifier,db volt, ma
O.l erg
. .. .
0,11 WE
0,23 SEP
5.0 erg
0.3 erg
...... ..
.. ... . .
300 TL
400 TL
400 TL
300 TL
300 TL
300 TL
200 TL
300 TL
0.3 erg
2.0 e-g
fig. of
. . ...
.. .
... .
0.36 watt
giving the pulse energy of the burnout test, or the peak power where
For some types the number in this column is labeled
‘‘ design. ” This means that the test is made only on a few sample units
and the number then represents only the approximate power that units of
this type may be expected to withstand.
Next comes a column of over-all
noise figures for a receiver using mixer crystals that just pass both
the loss and noise-temperature tests and having an r-f amplifier with a
noise figure of 5 db. This i ~ by no means to be considered as the best
noise figure possible with that type of crystal since some units show
losses as much as 2db less than the maximum values, and noise temperatures effectively equal to unity.
Moreover, the 5-db i-f-amplifier noise
figure is by no means the lowest obtainable; values as low as 1.5 db have
been obtained with some recent circuits.
A combination of such an
amplifier with the best 1N21B crystal at 3000 Me/see would give an
over-all noise figure of about 6.5 db. At 10,000 Me/see such noise
figures are also possible with the 1N23B and at 25,000 Me/see over-all
noise figures of about 7.5 db have been observed.
Finally a column
of maximum back current at one volt, as discussed in Sec. 2,20, is given.
For the 1N26 crystal, two numbers are given, one followed by SEP
standing for Sylvania Electronic Products Company, and the other by
WE for Western Electric Company, the two manufacturers producing
these units at present.
The region of freq~~encies near the test frequency is not the only region
in which a unit may be used. In general, however, the units would be
expected to show greater conversion loss at higher frequencies, although
an increase of frequency of 10 or 20 per cent would not produce a serious
effect. The use of the units at lower frequencies will certainly not
result in a greater loss and can, in fact, result in slightly lower loss,
especially for the high-burnout units having relatively high loss at the high
frequent y. Because the units are not tested at these lower frequencies,
however, there is no implicit control over the r-f admittance characteristics. Therefore, the admittances of the various units would not necessarily be very uniform or have any relationship to that of units designed
for this frequency.
In addition to the development of microwave crystal rectifiers, there
has been considerable work done on units for special purposes at lower
As an example, there are units for use as diodes in such
applications as second detectors in superheterodyne receivers and as d-c
restorers in special circuits where their characteristics and small physical
This subject is not
size make them more desirable than ordinary diodes.
within the scope of this volume and for details of the properties of such
crystals the reader is referred to Vol. 15 of this series.
,Some of the rlrviccs
come to bc kno)vn as “mixers”
or “converters”
in the microival-c range prrforrn the flinction of converting a rcccivccl signal at a micro\rtive frequency into onc at a lo~ver
intermediate frequency, in addition t<) several other secondary functions
which arc special rml~lircrncnts of their application in micro~vave radar.
Some of these additi(mal functions trill bc drscribml in Iatcr chapters; the
purpose of the present cliaptcr is to dixmsin
some detail the consicferations involved in the dcsigu of crystal mixers that perform, in conjunction
with the local mcilltitor, the single function of frequency conversion of a
microlvavc signal.
There are many possible variations in the design of a mixer for a
particular frc(lucncy region and it \rill not he possible to Rive details of
each of the typesin current USC. ‘1’hc examples cited \rill usually be those
of designs m’(jlvcd at the Itadiation I,abmwtory and these cannot be
considered as the only possible ones. It has been the attempt, in designing these circuits, to make a single unit as a basic design for each frequency
range for }vhich a particular type of transmission medium is used in order
to avoid the much greater Iahor involved in designing a particular
unit for each piece of c(luipmcnt and to alloiv as ~videa tuning range in the
equipment as possible.
The problem of the design of crystal-mixer circuits cannot be treated
with any degree of finality because the details of the mixer best suited to a
particular task depend, to a larger degree than do other microwave
circuits, on things outside of the control of the designer.
The design
must, for instance, be influenced primarily by the physical and electrical
characteristics of the available crystal units. Since there is reason to
believe that improvements may lead to units considerably different from
those available at present, one may expect that mixer designs for such
future units will be correspondingly changed.
The frequency ranges
covered by designs for radar use are by no means the only important ones;
hence, for many purposes, the details of these designs are not of general
interest. Unlike the purely microwave circuits, the mixer cannot be
adapted from one frequency band to another by a simple scaling process
because the crystal unit, which plays such a dominating role in the
operation of the circuit, will neither have the same characteristics in
the scaled circuit nor be scalable in itself. The detailed designs that will
be given as examples, therefore, will probably be of less general interest
than would warrant the inclusion of a large number of them.
emphasis will be put on the general mrthods and ideas that have been used
in the design of the mixers, in the belief that analogous courses may be
taken for frequency bands and uses other than those encountered in the
Radiation Laboratory experience.
3.1. The Basic Mixer Circuit.—one of the simplest possible circuits
that a mixer can have is that of Fig. 3.1. In this circuit, the antenna or
signal generator is represented by the current generator delivering a
current z’. and having an internal admittance Y., and the local oscillator
by the current generator producing a current i. and having an internal
These two generators are connected in parallel through
admittance Y..
Signal generator
Local oscillator
r 1
l-f output
R-f choke
Yu /
adm)ttar, c?
l-f load
FIG. 31.-Equivalent
circuit of simple mixer.
the crystal unit to the i-f output terminals which, in use, would be
connected to the input circuit of the i-f amplifier.
In the diagram,
a load circuit presenting an i-f load admittance Y8, and a low-resistance
d-c circuit are shown.
As shown in Chap. 2, the r-f tuning of the mixer
should be set with a matched i-f 1oad ad mitt ante in place.
The functions of the various parts of the circuit are the following.
The magnitude of the local-oscillator current establishes, in conjunction
with the i-f load admittance, the input admittance of the mixer to the
small signal from the signal generator.
The r-f choke on the one side
of the crystal unit and the i-f choke on the other provide a low-resistance
path to the rectified current.
The tryst 31, therefore, does not become
appreciably biased by the rectification of the local-oscillator signal. In
order that the r-f voltages of both the signal and the local oscillator may
be impressed primarily across the crystal unit, an r-f bypass condenser is
provided across the i-f output terminals.
For maximum power delivered
to the i-f load, this capacitance must either have a negligible susceptance
at the intermediate frequency or be resonated with an opposite susceptance component in the i-f load admittance.
The basic mixer is most easily understood when the conversion loss of
the crystal is large. Under this condition the r-f and i-f aspects of the
mixer circuit may be considered separately because the effect of the load
Local oscillator
[email protected]’
R-f choke
R.f ~{pa&
R-f admittance of
i.f load circuit
FIG.3.2.—Simplified representation of r-f aspect of high-loss mixer,
admittance on one pair of terminals is negligible at the other pair. Thus,
both the signal admittance and the i-f admittance are dependent only
on the crystal unit and the amount of its local-oscillator drive.
r-f circuit and the i-f circuit may be considered separately as illustrated in
Figs. 32 and 3.3, respectively.
The i-f load circuit influences the r-f
conditions only in so far as, in combination with the r-f bypass circuit, it
develops an r-f voltage drop.
Similarly, the r-f circuit influences the i-f
admittance only in so far as, in combination
with the i-f bypass circuit, it produces an i-f
voltage drop and so detracts from the i-f voltR-f bypass
age appearing at the output terminals.
r ---- 1
The best performance of a mixer of this ~
I Crystal
kind, as a frequency converter, is obtained
\ ____~
when the signal power is caused to develop
the maximum possible voltage across the crysa
tal unit. This condition is satisfied if the
ff’lG.3.,3.—I-f circuit of highsignal-generator admittance is made equal to
the complex conjugate of the input admittance to the crystal mixer, and if no r-f signal power is dissipated
in the admittance of the local oscillator or of the i-f load. To satisfy
this last condition, the local-oscillator admittance must be zero and
the admittance of the bypass circuit must be infinite.
In practice, it
is necessary only to make the local-oscillator admittance so small, and
the admittance of the r-f bypass circuit so large, compared with the signal
admittance of the crystal, that the amount of signal power that is dissipated in them is a negligible fraction of the available signal power.
design of the r-f portion of ahigh-loss mixer, therefore, reduces to three
parts which are:
1. Design of a signal-coupling mechanism to match all available
signal power into the tryst al unit.
2. Design of a local-oscillator-coupling
mechanism that has negligible
effect on the signal admittance.
3. Design of an r-f bypass circuit for the i-f output terminals that will
not allow the r-f power to couple to the i-f 1oad circuit.
Usually, the signal generator to which the mixer should be matched is
The antenna, in turn, is so made
the antenna of the receiving system.
that its radiation admittance terminates a transmission line in its characteristic admittance.
The desirable signal-input circuit, therefore,
would be a transmission line of the same type, with the mixer so arranged
that the crystal provides a matched load to this transmission line,
In addition, there must be
whether it be a coaxial line or a waveguide.
terminals to supply local-oscillator power, across which only a negligible
part of the available signal power appears, and there must be terminals
for the i-f output voltage.
Experimentally, the admittance of a high-loss
crystal unit for the small signal in the presence of the local-oscillator
drive, is found to be approximately the same as for a signal of the same
magnitude as the local-oscillator signal in the absence of the localoscillator drive.
It is possible, therefore, to begin the task of mixer
design by designing a crystal mount that contains only the crystal unit
and the i-f output circuit without incorporating the LO coupling circuit.
The mount is so adjusted that a signal at the local-oscillator level is
matched into the crystal unit. Moderate corrections may be required,
for low-loss crystals, to obtain minimum conversion loss from the crystal
mount, when finally operated as a mixer. By such a procedure the task is
made straightforward even if there is no previous information as to the
input admittance of a particular crystal in the desired mount and frequency range.
3.2. The Design of a Crystal Mount.-The
physical form of the
mount for the crystals in ceramic cartridges is arbitrary.
The only
features that all such mounts have in common are contacting elements for
both ends of the cartridge unit. The unit can be made to be a part of a
coaxial line, or it can be mounted in a waveguide or in a resonator.
Nothing in the basic mixer circuit requires or excludes f requency selectivityy in the r-f circuit, except for the separation of i-f, d-c, and r-f voltages.
Hence, any form of the mount will operate equally well at the frequencies
for which the signal-input-line admittance matches the antenna-line
resonant mixers were at first considered
necessary, but only because admittance transformation was obtained
through their use. The more recent designs of mixers use nonresonant
coaxial-line and waveguide mounts for the crystal.
Any r-f preelection,
or separation of signal- and image-frequency terminals, has been accomplished through the use of a resonant TR cavity or of a resonator added
between the crystal mount and the input terminals.
The crystal is mounted in either waveguide or coaxial line, in such
a way that it does not represent a large mismatch as a termination of the
line when r-f power at the local-oscillator level is incident in the line.
If, with an experimental crystal mount, a large mismatch is found, a
measurement of the apparent admittance of the crystal allows a correcting
change to be made.
If the mismatch is not large, tuning elements, such
as sliding-screw tuners, stub tuners, plungers, and sliding quarter-wavelength transformers, may be added to cause the crystal to match the line.
An investigation of the admittance characteristics of a large number of
representative crystals will show whether al! ‘ mits can, by means of the
tuning elements, be made to match the line.
The tuning of most recently designed crystal mounts has been fixed.
Fixed tuning is possible because the crystal units are made to pass the
conversion-loss test in a mixer having fixed tuning.
As a consequence,
it should be expected that the crystal units should behave identically
in the receiver mixer, provided its tuning is fixed at the same point as that
of the test mixer. A crystal mount identical with the one used in the
mixer of the crystal test set would be properly tuned only for the frequency of operation of the test set and with a circuit in which the imagefrequency wave is not reflected to the mixer. If fixed tuning is desired at
a single frequency of operation different from that of the test set, it may be
achieved through fixing the tuning adjustments of the mixer on the basis
of best results with a large number of representative crystals.
On the
other hand, if the mixer is required to operate over a wide band of frequencies, the same tuning may not be adequate, and tuning elements
might be required for a mixer intended for use in a broad band if not for
use at a single frequency.
If fixed tuning over as wide a frequency range as possible is desired,
the crystal mount itself should come as close as possible to a matched
termination of the input line. Any additional transformer is then
required to give only a small transformation effect and it is, consequently,
As a general rule, the larger the
relatively insensitive to frequency.
transformation effect of a simple microwave admittance transformer,
the more sensitive to frequency it becomes.
This effect is obvious for a
transformer employing a quarter-wavelength section of transmission line.
There is, of course, in addition to the frequency-sensitive character of the
admittance-matching circuit, frequency dependence of the admittance of
the crystal unit itself, although it is difficult to separate the two effects.
It is often possible to combine a mismatched crystal and mount with a
matching circuit in such a way that the frequency sensitivity of the two
tend to compensate each other. The match can then be held over a
wider band than would be possible for a mount that was perfectly matched
at the center frequency of the band.
With a mount that is perfectly
matched at a given frequency, it is often possible to add a resonant
circuit that, at the resonant frequency, has a transformation effect of
unity, and hence no effect, but that compensates for the frequency
dependence of the crystal admittance at other frequencies.
It should be noted here that the only difference between a crystal
mount designed for a mixer and one designed for a low-level detector is
in the level of the input signal for which the admittance measurements
are made. For a low-level detector, these measurements must be made
at a signal level of 1 pw or less, and the resultant admittance of a particular mount is consequently different from that at the local-oscillator
Must be d-c return
100. or stub.
(a) Coaxial-line crystal mount for 10-cm band.
(b) Crystal mount for 3-cm band.
FIG. 3.4.—Cartridge-crystal mount.
level of signal. The design of a low-level detector, however, is completed
when a satisfactory mount has been achieved for the small signal level,
because there is no need for a local-oscillator circuit, and the efficiency is
so small that the load admittance does not affect the r-f match.
A mount
for use in a mixer must ultimately be checked as a mixer with the localoscillator injection operating and with an appropriate i-f load admittance and d-c circuit as well as any preselecting resonant circuits in place,
because all of these things have some effect on the resultant small-signal
The preliminary admittance measurements with the single
signal at local-oscillator level must be made with a low-resistance path
for the rectified crystal current, in order to avoid the generation of a
backward bias voltage across the crystal.
That the level of power
actually being dissipated in the crystal unit is about the same as the
recommended local-oscillator level can be assured by use of a milliammeter in this d-c circuit.
The incident power may be appropriately
increased if the mount has a large reflection loss.
3.3. Crystal Mounts for the 3-cm and the 10-cm Bands—Two
crystal mounts commonly used for crystals in ceramic cartridges are
illustrated in Fig. 3.4a and b. The first is a coaxial-line mount used in
the range from 4000 to 2500 Mc/scc and the second is a \vaveguide mount,
in rectangular waveguide 1 by ~ in. Olj by 50-mil wall, used in the range
from 9600 to 8500 Mc/scc.
The diagrams are only symbolic of the r-f
characteristics of the mount, for they show no provision for bringing
* 0.001
0.248 ‘
Fm. 3.5.—Coaxial-1ine crystal mount for lo-cm band.
out the low-frequency voltage or rectified current.
The mounts in
which this provision is included are shown in Figs. 3.5 and 3.6. In the
coaxial-line mount it is necessary to have a path of low d-c resistance to
and of low i-f impedance between the center and the outer conductors of
the coaxial line, to correspond to the r-f choke of Fig. 3.1. Provision
for this return path has not been shown because its nature is dependent
MI CR(l}i ’A 1’1< (’I(YLSTAI>
upon the rest of the mixer. In some mixrrs the retllrn path is provided
by a loop that excites the coaxi:d line. If there is no sllch loop, a quartcrwavelength side stub, ~vhich is :dso useful for supporting the center
conductor, can provide this d-c return. The diameter and characteristic
admittance of the coaxial line shoum in I~ig. 3.4a arc sIIch that the line
fits over the cartridge unit cwnvcnientlv , and connects l~itho~lt serious
mismatch to the st:mdartl ty[l-~-N coaxial-line fittings (Iscd for lo\v-level
cables. The crystal mlmitt:mcc rmlllting ]rith a line of this size and no
transformers is not greatly different, at 3000 Me/see, from the line
FIG.3.6.—Wa}.eguide crystal mount for 3-cm band.
If this had not been true, a line having some other characteristic admittance would have been preferable.
There are several
parameters in the mount for 9000 Me/see which can be chosen to make
the average representative crystal unit terminate the line in its characteristic admittance.
The position of the crystal unit, both reiative to the
center of the broad dimension of the waveguide, and axially along the
narrow dimension, may be adjusted to control the resultant admittance.
The distance along the waveguide from the axis of the crystal cartridge to
the short circuit at the back end of the unit is also such a parameter.
None of these parameters afford strictly independent adjustment of the
resultant admittance.
It s found, however, that if Lhe admittance
determined from the mwwurement of the standing-wave ratio in the
waveguide leading to the crystal is referred to the plane of the axis of
the crystal cartridge, the adjustment of the length of waveguide beyond
the crystal unit results essentially in variation of the susceptance com.it a length about equal to one half of
ponent of the crystal admittance.
the wavelength in the waveguide, the crystal unit is completely shortcircuited by the reflected short circuit at the end of the waveguide and
the reffec~ion coefficient of the mount is unity.
The crystal current
becomes zero for this length, since no voltage is built up across the
crystal barrier.
It is not advisable to achieve a match with the waveguide crystal
mount by using a length, betn-een the short circuit and the crystal, near
to a half wavelength, since the susceptance introduced by the back part
of the waveguide is then large. The susceptance raries very rapidly
with frequency and the crystal mount is correspondingly sensitive to
The adjustment of the length of u-aveguide beyond the
crystal is the design parameter most easily determined, because a sliding
short-circuiting plunger in the wavcguide can be used. If the suscep tance componmit of the crystal admittance can be tuned out only \vith a
length nearly equal to the length for }vhich the crystal is short-circuited,
it is preferable to change the mount in some u-ay to allofv the use of a
length more nearly cq~lal to onmplarter ~~avelength in the \raveguide.
It has been found that a change of’ the position of the crystal along the
primarily in the susceptance
line through its axis a]so CLLUSCS a chtinge
The position may be so chosen
component of the crystal admitt~ncc.
that the crystol mount has only a snmll slwceptance ll-ith a short circuit a
The effect of moving the crystal
(lllarter-\\-avelcllgtll Imyond tlm crystal.
cartridge across the ivavcguide in the plane perpendicular to the waveguide axis is primarily to ~rtiry the cumluctancc component of the
This Variation occlws Iwcause the voltage (integrated field
intensity) between the top and bottom of the ]raveguide is a sinusoidal
function of the crosslrihc pwition, ~vith ~ maximum at the center and
zeros at each side. C(lrrcslJ{)ll(lirlgly, the presence of the crystal unit
has the greatest effect OILthe c]cctric field when the crystal is at the center,
and bfis less inffucncc \vllra tllc crystal is moved totvard the side of
the waveguide.
Tllc con(l~lctancc of the crystal mount thus falls from
a maximum vduc \vith tlw crystal at the center to a minimum with the
crystal at either si(lc.
In this )vtiy it Ims linen f{nln(l p,)ssil)lr to make a crystal mount for the
9000-11 c/scc frequency region \vhich has an admittance with a crystal
representing an average \ritll respect to tllc a(lrnittance scatter of all
units, equal to the clmracteristic admittance of the tvaveguide at the
level of signal e(lual to the optimum iocal -oscillator drive. The crystal
units used in this region are the 1X23, 1N23A, and lN23B types, all of
which show approximately the same spread of admittance since they are
tested, in production, in identical mixers.
It is more difficult to make the desired adjustments of admittance in
the coaxial-line mount than in the waveguide mount.
Although the
wavelengths for which the coaxial-line mount is used are longer compared
with the dimensions of the tryst al, the crystal cannot be treated as a
lumped-circuit element because it appears as part of the center conductor
of the coaxial line. It is largely fortuitous that a coaxial line of a convenient size and characteristic admittance can be used as a crystal mount
in the 3000-M c/sec region, since the early crystal mixers used for production testing were not at all similar to the present mount.
An r-f
impedance of 40 to 50 ohms in the coaxial-line mount must be de~ived
from the effect of the barrier capacitance and from the transforming
At a frequency as low as the
effects of the various parts of the cartridge.
intermediate frequency, the crystal unit would exhibit an impedance to a
The i-f
small signal of the same order as the i-f output, impedance.
output impedance is usually several hundred ohms, and a crystal baring
an r-f impedance this high would be difficult to match to a 50-ohnl line.
At 9000 Me/see, the aspect of the crystal in the waveguide mount is
such that it can be considered approximately as a lumped admittance
connected across the waveguide.
3.4. The Filter in the I-f Output Lead .—The r-f bypass at the lowor direct-current)
frequency (i-f, video-, or audio-frequency
terminals is, in neither of the mo{mts under discussion, completely
accomplished through the Ilsc of a simple lumpmi capacitance, as would
be inferred from the basic equivalent circuit,
The function of this
circuit may be considered as twofold: (1) it provides a path of high r-f
admittance, compared with that of the crystal, with the result that the
loading of the transmission line is the same as if the crystal were shortcircuited to the line at this point; (2) itprevents leakage of any appreciable amount of r-f polver—p:imarily
power, since its
level is so much higher than that of the signal—into the input circuit of
the i-f amplifier.
The requirements set on the effectiveness of the filter
circuit by the first of these f~mctions might at first appear to be much
smaller than those of the second.
Since the r-f admittance of the input
circuit of the i.f amplifier to which the mixer is to be connected is arbitrary, the effectiveness of the filter circuit could be reduced considerably
if a resonance were to occur when the two were connected together.
to avoid such effects, a large capacitance or a more
complex filter is required.
It is felt that the circuit of the filter type
is more effective, per unit of capacitance introduced at the i-f terminals,
than the lumped capacitance, in a restricted band of radio frequencies,
Since most applications of microwave mixers have been in receivers
having wide i-f pass bands, the i-f capacitance of the mixer is important
in determining the maximum pass band of the input circuit of the amplifier. The lo~~-erthis capacitance, the wider the input circuit can be made.
The operation of the filter is similar to that of many filters used as
joints for r-f lines. In the filter used with the 3000-hIc/sec
mount, a spring-metal cent act is used to make connection to the large
end of the crystal cartridge.
The spring contact is mounted by a rivet
on the base of a cylindrical metal cup that has an open end toward the
i-f outlet.
The center conductor of the i-f line extends into this cup and
terminates at the solid end of it. The inside of the cup, which is filled
with a polystyrene dielectric , is thus a concentric line short-circuited
The open
at one end and a quarter wavelength long, in the dielectric.
A wave progressing
end, therefore, has a vanishing y small admittance.
along the coaxial line formed by the outside conductor and the outer part
of this cup induces currents in the outer wall of the cup, and, in order
for the wave to travel out the i-f line beyond the open end of the cup,
the current of the inner conductor must pass through the small admittance of the cup. Thus, unless the r-f admittance of the i-f output line
seen at the open end of the cup is also very small, the major part of the
voltage drop at this point appears across the end of the cup or choke.
The r-f current in the i-f output line is kept small, because of the small
admittance of the choke and, therefore, the r-f power getting into the
i-f circuit is kept small.
In order that the choke system be equivalent
to an r-f bypass at the base of the crystal, the length of the coaxial line
formed by the outer conductor and the outside surface of the cup or
choke is made equivalent to a quarter wavelength.
Because this line is
terminated in an admittance at least as small as the admittance of the
choke, a large r-f admittance results between the base of the crystal
and the outer conductor of the crystal mount.
In the waveguide crystal mount used at 9000 lJIc/see, the r-f filter
on the i-f output lead operates in much the same way, except that the
addition of a small lumped capacitance just beyond the quarter-wavelength choke gives further assurance that the r-f admittance of the i-f
The choke occurs, for mechanical
output line is large at this point.
reasons, in the outer conductor of the coaxial i-f output line. The point
at which the choke appears in series with the output line, however, is a
quarter wavelength along the line from the point at which the large
bypass admittance is desired, in this case between the pin end of the
The reasons
crystal cartridge and the bottom wall of the waveguide.
governing the choice of a circuit containing both a distributed-parameter
filter and a lumped capacitance are largely mechanical, since the center
conductor of the output line must be supported.
The capacitance of
the lumped condenser is not large compared with the distributed capaci-
tance of the output lead. The total i-f capacitance, consequently,
could not be reduced greatly by elimination of the condenser, and its
inclusion makes the tolerances on the dimensions of the choke filter less
rigid. The filter action is also less frequency-sensitive than it would be
without the condenser.
A choke joint or a filter of this kind is most effective over a wide
frequency range if the characteristic impedance of the coaxial line
forming the choke is as high as possible, and if that of the line forming the
quarter-wavelength transformer is as low as possible.
At the frequency
for whith the effective lengths of the choke and of the transformer are
exactly one-quarter wavelength the filter is perfect, since the impedance
The impedance bet~veen the
at the open end of the choke is infinite.
crystal and the outer conductor of tke crystal mount is therefore zero, if
dissipation in the filter itself is neglected.
At a frequency differing from
this by a small amount, however, the impedance at the open cnd of the
choke is a large reactance.
The larger this reactance is, compared ~~ith
the characteristic impedance of the transformer section and compared
with the r-f impedance of the i-f line, the smaller are the leakage of r-f
power into the i-f circuit and the impedance between the end of the
The reactance of
crystal and the outer conductor of the crystal mount.
the choke is proportional to the characteristic impedance of the line
forming the choke.
In the coaxial-line mount, therefore, the ratio of the diameters of the
outer and inner conductors of the line forming the choke is made relatively
large and the ratio of the diameters of the outer and inner conductors
of the line forming the quarter-~vavelength transformer is made small.
The maximum usable line size for the 9000-Mc/sec
crystal mount is
one in which the mean circumference of the inner and outer conductors is
nearly 3 cm, for other modes than the principal mode may be propagated
in a larger line. The characteristic impedance of the choke, therefore,
cannot be made very high and, consequently, the addition of the condenser across the i-f line helps to reduce the leakage of r-f power in a
wide band of frequencies.
The only effect of the filter on the i-f characteristics of the crystal
mount is to produce a capacitance, provided the section is short compared
with a quarter wavelength at the intermediate frequency.
Since this
is true, the i-f capacitance is just the static capacitance between the
inner and outer conductors of the output line. In the coaxial crystal
mount the capacitance is contributed primarily by the quarter-wavelength section of the cup and increases with decreasing characteristic
impedance of this transformer.
The desire for a small i-f capacitance
in the mixer sets the limit on the diameter ratio of this section of line, and
the bandwidth of the choke is therefore restricted.
Each of the crystal
mounts illustrated has an i-f capacitance of about 11 p~f. The effectiveness of the chokes in eliminating leakage power can be measured by
inserting the crystal mount, with a crystal in place, between a signal
generator at the local-oscillator level and an output indicator such as a
spectrum analyzer.
By comparison of the leakage power with the power
available directly from the signal generator, the insertion loss of the
crystal and filter is found, and if it is also known that the crystal mount
matches the signal-generator impedance, it may be
concluded that the incident power is almost completely delivered to the
crystal, if the insertion loss is large. Just how large this insertion loss
must be is difficult to determine, but with the mounts described it is
greater than 30 db in the frequency bands for which they are intended
and with a matched coaxial-line r-f load at the i-f output connectors.
Two cups differing in length but otherwise identical have been used in filters
in the coaxial-line mount.
One of
these cups has an outside length of ~
in. and gives maximum insertion loss
at a wavelength of about 10.7 cm.
The other has a length of + in. and
gives a maximum effect at about 8.8
cm. The longer cup is used between
9.5 and 12 cm and the shorter one
between 7.5 and 9.5 cm. A curve
FIG. 3,7.—R-f leakage of choke vs.
typical of the ratio of the power inciwavelength.
dent on the crystal to that leaking into
an r-f load matching the line admittance on the i-f output connector is
shown in Fig. 37.
The ordinate is the power ratio in decibels and the
abscissa is the wavelength expressed in units of the resonant wavelength
of the choke.
3.5. Tunable Crystal Mounts.-A
technique commonly used in the
9000-Mc/sec band to make the crystal mount tunable, after it has been
designed to give an approximate match, is illustrated in Fig. 3.8. The
position of the short circuit behind the tryst al is made adjustable through
the use of a plunger of the choke type and, thus, the effective susceptance
of the crystal is controlled.
Two tuning screws, one situated three
eighths of a wavelength and the other five eighths of a wavelength ahead
These screws allow adjust of the center line of the crystal are provided.
ment primarily of the conductance component of the admittance referred
The admittance of the crystal itself
to the center line of the crystal.
is, of course, not changed by the insertion of the screw but the admittance
at a point an integral number of half wavelengths toward the generator
from the center line of the crystal is changed, primarily in the conductance
component, for a small insertion.
That this is true can be seen with the
aid of an admittance diagram, with the knowledge that the effect of the
tuning screw is to add a capacitive susceptance in shunt at the center line
of the screw. Thus, if the crystal were matched to the waveguide, a
small insertion of the screw three eighths of a wavelength from the
crystal would make the crystal appear to have a conductance larger than
A small insertion of the other screw would decrease the apparent
crystal conductance.
Only one screw is used at a time, the choice of
screw depending upon whether the apparent conductance must be
increased or decreased.
The adjustments of the screw and of the plunger
FIG. 3+3.—Tunable crystal mount for the 9000-Mc /see band.
are completely independent only for very small insertions of either
screw. A large range of tuning is available from the adjustment of the
plunger and one screw. If, however, the crystal is severely mismatched
to the waveguide with no insertion of the screw and with the plunger set a
quarter wavelength from the crystal, some dissipative loss may result
in the tuning screw and in the plunger when they are used to match the
In addition, the frequency sensitivity
crystal mount to the waveguide.
of the resulting admittance is large. Both the plunger and the tuning
screws have choke systems similar to that of the i-f output lead, to
prevent leakage and to decrease contact losses. Only a small current
flows at the points where metal-to-metal contact occurs and the design
considerations of these choke systems are similar to those of the filter.
The best operation over a wide band is obtained for a high characteristic
impedance in the line forming the choke and a low characteristic impedAttempts have been
ance in the quarter-wavelength transformer section.
made to design plungers and screws that actually make contact and thus
have not the constructional complication of the chokes, but no designs
have been found which are as satisfactory under service conditions as
those using chokes. This is particularly true of the tuning screws, if
smooth continuous operation is desired. For experimental purposes, an
ordinary screw can be put into a threaded hole in the top wall of the
waveguide and locked by forcing a nut on the screw above the waveguide
against the top wall. This simple screw, however, cannot be adjusted
continuously because it depends for contact on the clamping effect of the
The only tunable crystal mounts of the coaxial-line variety that have
been built have used standard coaxial-line tuning elements.
One of these
mounts contained, in the line ahead of the crystal, a pair of polystyrene
cylinders filling the space between the inner and outer conductors of the
coaxial line. The length of each of the cylinders was one quarter of the
wavelength in the dielectric.
The cylinders could be slid together along
the line, and the spacing between them could be varied from zero to
This device constitutes what has been called a
one-half wavelength.
“double slug” tuner. Since the characteristic admittance of the section
of line in which one of these dielectric cylinders appears is v%. times the
normal line admittance, where k. is the dielectric constant of the cylinder
material, it is apparent from an admittance chart that the maximum
transformation effect occurs for a spacing between the cylinders of
one:quarter wavelength.
An admittance corresponding to a voltage
standing-wave ratio equal to k: can be made to match the line. With
the cylinders together or one-half wavelength apart, there is no transformation effect because a half-\ravclcngth section of transmission line is a
one-to-one transformer.
Thcrcforc, any transformation from unity to
The phase angle can bc controlled by the position
& can be achieved.
of the pair relative to the crystal mwmt and, in this \vay, any voltage
standing-wave ratio lCSSthan lc~can bc matched out.
Under special conditions, tuners having tuning ranges smaller than
this have been used. ‘l’his is true, for instance, for some crystal mounts
for low-level detectors, where the stimc I)asic mount was used but where
measurements of the admittuncc of the mount Jvith large numbers of
representative crystals showed that it NW possible to bring all of the
crystals sufficiently C1OSC
to L match over the required 10 pcr cent band of
frequencies with a single sliding metallic slug. Such devices can be
designed only by mcasurcmrnt of the admittances to bc matched to the
line. Thus, if the required tuning range is known, a satisfactory tuning
device can bc found.
One frequent suurcc of tmublc in crystal mounts that have had
several changes of crystals is in the contact to the pin end of the crystal
Experience has shown that contacting fingers such as those
shown in Fig. 3.5 have been the most satisfactory ones tried, especially
Similar contacting fingers
when made of tempered beryllium copper.
have consequently been used in all mounts used for crystals in ceramic
cartridges, in both the 3-cm and the lo-cm regions. Saw cuts 0.020
in. by 0.375 in. were found to give a good compromise between large
contact pressure and ability to withstand reasonable deflections without
becoming bent through distortion beyond the elastic limit. Although
the specifications of the crystal cartridge call for a rounded end on the
pin, it has been found well worth while to include an internal bevel in
the end of the contacting fingers to assist in the centering of the pin
during insertion of a crystal in the mount.
3.6. Admittance Scatter in a Mount of Fixed Tuning. -Because
of the
desire to make crystal mixers that are fixed in tuning, a large part of the
design of the crystal mount is concerned with finding the best fixed
adjustment for all crystal units that are expected to be used. This can
be done by measurement of the admittances of very large numbers of
crystal units representative of those which Ivill be used in the mount, and
by adjustment of the mount in such a way that the scatter of admittances, when plotted on a Smith admittance chart, covers an area centered
at the characteristic admittance of the input line. In order to reduce the
labor involved in making these measurements, a special procedure of
crystal selection has been used.
To ensure that the crystals to be used in the tests were representative
of those to be encountered in scrvicc, crystals were chosen at random from
stocks of the various typcs made by each of the several manufacturers.
A tota’ of one or two hunch-cd crystals was used and the r-f admittance
of each was measured in a crystal mount that was found to be reasonably
well matched for a few randomly chosen crystals.
Then these admittances were plotted as points on an admittance chart and from this the
area and, therefore, the proper tuning of the mount could be determined.
Once this had been done it NZMnot considered necessary to use the large
number of crystals in further work for this frequency band, since the
entire admittance region could bc rcprcscntcd by a few crystals having
admittances on the boundary of the region and by one or two having
admittances in the ccntcr of the region.
It was found that 10 pcr cent
changes in frequency or small changes in the mount affected the admittances of all the crystal units in about the same way. Their positions
on the margins or in the ccntcr of the admittance spread were consequently prcscrvcd, even though the whole region was transformed to
another part of the admittoncc chart. These rcprcscntative crystals were
preserved for use in tests of many kinds and such tests could then be
regarded as showing the results to bc obtained with crystals of almost any
characteristil~s to be encountered among production units. Since the
crystal units of one type number but different suffixed letters (lN21,
1N21A, 1N21B) were usually used interchangeably, the original selection
There was, usually, less difference
included samples of all such types.
found among the chfferent types than among crystals of the same types
Almost all of the design considerabut from different manufacturers.
tions of the fixed-tuned mixer are dependent UPOn this admittance
FIO.3.9.—Impedance scatter of 1N21A and 1N21B crystals in a coaxial-line mount at
8.5 cm.
spread. The borderline crystals, therefore, were used in many tests
besides the admittance measurement of the mixer.
In Fig. 3.9 a typical spread of impedances for a coaxial-line 8.5-cm
mount is shown with the borderb ~le crystals selected as representative
marked with circles. An admit iance scatter at 3.3 cm in a mount
resembling the standard one of Fig. 3.6 is shown in Fig. 3.10.
outlines of the ,pread at 3.13 cm and at 3.53 cm are also shown, with
the positions for the representati .w crystals at these wavelengths indicated by the circles on these coat ours. It will be observed that the
admittance change occurs almost entirely in the susceptance component
and is in the direction which would be found if the crystal unit were
representable as a shunt-resonant circuit connected across the waveguide
at the position of. the centerline of the crystal unit,
3.10.—Admittance scatter of 1N23, 1N23A, and 1N23B crystals at 3.13, 3.33, and
3.53 cm.
3.7. Local-oscillator Coupling Mechanisms.-As
discussed in Sec. 31,
the prime requirement of the method of coupling the local-oscillator signal
to the crystal is that it does not cause a significant loss of received signal
FIG. 3.1I.—Simplifiedequivalentcircuit
of a mixer.
cuit of Fig. 3.1 this was shown to
require that the shunt admittance of
the local-oscdlator cmcult measured
in the mixer be small compared with
and crystal
For this to be possible the power available from the local
oscillator must be much larger than that which is actually transmitted to
the crystal, because a large mismatch exists between the local oscillator
and the mixer circuit.
In Fig. 3.11, an equivalent circuit illustrating this
situation is given. The signal-generator admittance g, has been assumed
to be pure real and the crystal admittance g. has also been assumed to be
pure real. If the local-oscillator admittance were zero, maximum power
would be delivered to the crystal if g, were equal to g.. The simplest
case to analyze is the one in which these admittances are the same at the
signal and local-oscillator frequencies, and the mixer may therefore be
considered to have a low Q. It is easily shown that the fraction of the
signal-generator power that is delivered to the crystal when the localoscillator coupling is added is
7’s. = 4Q,g./[(g* + g. + 91)’ + m
where gi and bZare the real and imaginary parts of the admittance of the
local-oscillator circuit as measured at a point in the mixer line. Correspondingly, the fraction of the available local-oscillator power which is
delivered to the crystal is
7’t. = 4919./[ (9. + 9. + 91)’ + b?].
The fraction of the signal which is lost through the introduction
Iocal-oscillator circuit is
of the
which is
‘s2= (9s + 9.)2[(98 +“9.
+ 97 +
Under the condition that g, = g. this is
T81 =
49s91+ g? + M
(% + g, ‘+ 91)’ +
If the admittance of the local-oscillator circuit is smaI1 compared with g,,
the last two terms in the numerator maybe neglected and the equation
then is identical with ~q. (2). This means that, for small local-oscillator
coupling, the fraction of signal power which is lost because of the presence
of the local-oscillator circuit is approximately equal to the fraction of the
available local-oscillator power which is delivered to the crystal.
therefore, it is desired that not more than 5 per cent of the signal
power be lost because of the local-oscillator circuit, 20 times the required
local-oscillator drive for tha crystal must be available from the localoscillator circuit in the mixer. Since the local oscillator is often coupled
through a circuit that has loss, for reasons that will be discussed in a later
section, the local oscillator must be capable of delivering more power than
this, and the design of the LO coupling circuit is not so simple as it might
Even if the local oscillator can deliver 100 times as much power
as is required to drive the crystal, precautions against deterioration in
mixer noise figure caused by interaction between the signal circuit and the
local-oscillator circuit must be taken.
An additional complication t o the problem of the design of an LO coupling circuit is that the output power available from different oscillator
tubes of the same type can differ by large factors.
Usually, the tube
specifications set a lower limit to this output power but many tubes can
be found which give two or three times as much power as this minimum.
When this variation is added to the variation encountered as the tube is
tuned through a wide band and to the variation in the amount of coupling
with crystal admittance, the total variation of local-oscillator power
delivered to the crystal under all conditions of operation is more than can
be tolerated if the mixer is to operate within a few tenths of a decibel of
optimum noise figure. It has therefore been considered necessary to
have an adjustable local-oscillator coupling in order that the optimum
local-oscillator power at the mixer crystal may al)~ays be obtained.
so-called fixed-tuned mixers this adjustment is retained and is the only
adjustment required for operation ~vith any crystal of the proper type
and with any local-oscillator tube in the specified band of frequerrcics.
If the amount of local-oscillator power deli~’ered to the crystA is varied
by adjustment of the coupling circuit, the values of g, and bt in 1+s. (2)
and (5) vary.
Equation (5) applies if the tuning of the crystul mount is
For a fixed amount of
optimum in the at>sence of the 1.0 coupling circuit.
coupling, the tuning of the crystal mount could be such tliat the susceptance component of the admittance of the local oscillator ~ras canceled
by a susceptance of equal magnitude and opposite sign in the crystal
The conductance of the crystal mount could bc mwlc
equal to g, + gt to obtain maximum signal powri- in the presence of the
LO coupting circuit,
If this ww-e done the perccntagt= of the available
local-oscillator po~ver dcli~-ered to the crystal l~ould be exactly eqlud to
the percentage of available signal power lost because of the presence of the
A practical 1,0 coupling circuit must be adjustlocal-oscillator circuit.
able and the correction in the tuning of the crystal mount cannot be made.
The signal loss is therefore increased because of reflection.
The simplest LO couplillg circuits are inefficient because the added
susceptance b~ is large comparrd \vith the conductance gl. Because of
this, the signal po~~-erlost by reflection is larger at a given effective coupling than it would be if the admittance of the local oscillator \\-crekept
real at all adjustments.
Jlost of the mixer circuits that have been designed for radar ser~,ice
have been operated with a TR cavity preceding the mixer in the signal
line. The most commonly used TR cavities m-e highly resonant, and the
circuit representing the local-oscillator coupling is not the same m thiit for
the signal,
Many TR cavities have sufficiently high Q’s to be treated as
SEC. 3.7]
completely reflecting circuits at the local-oscillator frequency, when
If such a TR cavity is used the localresonant at the signal frequency.
oscillator injection can be made at a point in the mixer line, between the
TR cavity and the crystal, where the admittance of the line terminated
by the cavity is almost zero. In a waveguide, for instance, the TR cavity
appears as though it were a short circuit, at frequencies sufficiently
removed from resonance and, therefore, the admittance of the line terminated by the TR cavity is very small at a point a quarter of a waveguide wavelength toward the crystal.
If the local-oscillator signal is
injected at such a point, as a signal from a generator having a small admittance, the fraction of the available local-oscillator power delivered to the
crystal is
“c = (g. +4;$
+ b;
Therefore, the effective coupling is greater by a factor of about four
than the coupling obtained without the TR cavity for the same gl and
bl, if g, is equal tog. and if gl and bl are small compared with g.. This can
be explained in another way by supposing the local oscillator to excite a
wave that travels in both directions from the injection point in the mixer
line. Without the TR cavity the wave that travels toward the signalinput end of the mixer is lost, but with the TR cavity present, it is
reflected. The choice of the injection point at a quarter of a wavelength
from the position of the short circuit that is equivalent to the TR cavity
at the local-oscillator frequency corresponds to a position such that the
wave reflected by the TR cavity has the same phase as that traveling
toward the crystal.
Hence the total amplitude of the wave traveling
toward the crystal is twice as great as it would be without the TR cavity.
Therefore, four times as much local-oscillator power arrives at the crystal.
Besides giving greater local-oscillator coupling for a given amount of
interaction of the local-oscillator circuit and the signal circuit, the addition of the TR cavity causes another change in the operation of the mixer
For a small coupling without the TR cavity, the power delivered
to the crystal by the local-oscillator circuit is a stationary function of the
crystal admittance when the cry~tal is matched to the signal generator.
Only the ordinary reflection losses are involved when the crystal admittance is different from this value, because the reflected local-oscillator
wave is almost entirely dissipated in the signal-generator admittance.
When the TR cavity is used, however, the local-oscillator power delivered
to the crystal becomes very strongly dependent on the crystal admittance.
If g~is small compared with g., the power delivered by the local oscillator
to the crystal is proportional to 1/g..
This requires that the available
range of adjustment of the local-oscillator coupling be much greater than
without the TR cavity, to allow the optimum local-oscillator power to be
delivered to crystals of all admittances occurring in the representative
TWO crystals having conductance
differing by a factor of four
would require adjustment of the local-oscillator
coupling by almost
this factor for the same power delivered to the crystal.
It is, therefore,
even less satisfactory to use a fixed LO coupling adjustment in a mixer
having a resonant TR cavity in the signal line than in one having a comThus, although in the crystal test sets a
pletely nonselective circuit.
fixed LO coupling adjustment is used with a single oscillator tube at a
single frequency of operation, it is impractical to attempt fixed adjustment
in a mixer for use with a TR cavity.
3.8. Capacitive Local-oscillator
Coupling in Coaxial-line Mixers.—
At 10 cm, where the small coaxial-line crystal mount is used, the common
1,0 coupling circuit is a small capacitive probe, terminating a coaxial line
that is coupled to the local oscillator
To C1’@l
Input line
and projecting into the main coaxial
line of the crystal mount.
~form of such a coupling mechanism
L.,., r,..,.<
is shown in Fig. 3.12. This device
allows adjustment of the probe insertion without movement of the
To local
line, which is a conoscillator local-oscillator
venience when frequent adjustments must be made.
It is simpler
to construct a coupling probe that
is adjusted by sliding or screwing
the whole coaxial line of the localFIG. 312.-Adjustable
in a sleeve
coupler for a coaxial-line mixer.
mounted on the mixer line. An
adjustment of this type has been used in mixers such as those used
for crystal testing.
In the mixer for testing, however, the level of the
local-oscillator signal is changed only if the local oscillator is changed;
otherwise the coupling adjustment is locked.
It is important that good
electrical contact be made through the screw threads or in the sliding
section; therefore, a clamping arrangement or a lock nut is usually provided.
In a circuit like that shown in Fig. 3.12, the center conductor of
the side arm ending in the probe makes a sliding contact with the center
conductor of the LO input line, and the spring used for this contact has
been somewhat troublesome.
The spring, which has slotted ‘‘ fingers”
at each end to contact the rod sliding in it, must be carefully soldered so
that the temper is not lost. Beryllium copper is a very satisfactory
material for a spring of this sort because it can be hardened after the
soldering is done. The length of the stub line supporting the center
SEC. 343]
conductor changes with adjustment of the probe insertion, but, since
the probe represents a severe mismatch at the end of the line, the small
reflection due to this stub is not serious.
In order that the local-oscillator tube will oscillate with this probe as its
load, it is necessary to arrange that the actual load admittance presented to
the oscillator is compatible with the characteristics of the oscillator.
way in which this can be assured is to use such a length of line, between
the oscillator and the probe, that the adrn!ittance presented to the oscillator at the other end of the line lightly loads the oscillator.
If this is done
and if the system is to be continuously tunable, the line must be so short
that the phase length of the line does not change appreciably in the
required tuning range. If the equivalent electrical length of the line
does change by a quarter wavelength, the loading will be very heavy and
the oscillator may not operate satisfactorily.
Another way of avoiding
load admittances which upset the operation of the oscillator tube is to use
lossy cable to couple the oscillator to the mixer circuit, to attenuate the
wave reflected from the probe.
Thus, the range of admittances that
are presented to the tube as the
phase length of the line changes
with frequency is reduced and can
be made small enough for the tube
to operate satisfactorily.
In view
of the difficulty in getting sufficient
local-oscillator drive without suffering from signal loss, however, this
can be done only if a large excess of
I?1o. 3.13.—Loca1-oscillator coupler with
power is available from the tube.
For operation with a 2K28 tube and
with a nonresonant mixer circuit, 6 db of attenuation can be used but
there is very little extra coupling available, with the most powerful tubes,
before interaction and signal loss become serious.
A third way in which the load admittance of the local oscillator can be
maintained at a reasonable value over a wide frequency range and with a
long coupling line is illustrated in Fig. 3.13.
Here a “resistor disk”
which is a disk of Bakelite~ coated with a carbon resistance material, and
having silvered inside and outside rings for contacts, is put into the line.
The resistance between the contact rings of this disk is the characteristic
impedance of the coaxial line, 50 ohms in the local-oscillator circuit,
disk would be a reflectionless termination for the line if its r-f characteristics were such that it loaded the line with a resistance alone and if the
admittance of the remainder of the line beyond the disk were zero. In
practice there is a capacitive susceptance due to the large dielectric con-
stant of the Bakelite base of the resistor disk, as well as the conductance, in
shunt with line in the plane of the disk. The line may still be terminated
by the disk, however, if it is placed in a position where the admittance of
the line beyond it contains an inductive susceptance of the same magnitude as the capacitive susceptance of the disk. Thusj the susceptance
is resonated out and the load terminating the local-oscillator line has the
conductance of the disk plus a small conductance caused by the small
power transfer from the probe to the crystal-mixer line. The small
capacitive susceptance of the probe and of the disk makes the resonant line
length between the probe and the disk somewhat less than a half wavelength.
A resistor disk has been provided in all coaxial-line mixers of
recent design to secure a reasonable load admittance for the local oscillator. This circuit is less wasteful of local-oscillator power than that
using attenuating cable. The local-oscillator power available at the
mixer is reduced by a factor of approximately 2 (it cannot be specified
exactly because the oscillator is not a linear generator) but the line may be
made very nearly matched.
In the design of Fig. 3.13, the admittance
of the line between the probe and the disk varies as the probe is adjusted.
Consequently, the termination is also varied but the voltage standingwave ratio is less than about two for all adjustments and over a plus
or minus 10 per cent band in the region of 10 cm. Since the half-wavelength section of line beyond the disk is frequency-dependent,
bandwidth is correspondingly
The useful bandwidth is
determined by the excursion in admittance that can be tolerated by the
oscillator tube.
At 10 cm, where the capacitive susceptances of the
probe and the disk are small, the admittance of the termination is
given approximately by
Y. =YO
For small deviations from Au,the resonant wavelength, the admittance is
‘T= ‘J+4-1)1
From this the wavelengths on each side of LO for which a given reflection
coefficient would be encountered can be calculated to estimate the usable
For a voltage standing-wave ratio of 1.5, a reflection
coefficient of absolute value 0.2 is required and the wavelengths for
which this standing-wave ratio would be encountered are approximately
10 f O.12x,; hence, a bandwidth of plus or minus 12 per cent is possible
with that tolerance in the standing-wave ratio.
3.9. A Local-oscillator
Coupling Circuit for Coaxial-line Mixers.—
A very useful LO coupling circuit for coaxial-line mixers in which rigid
connections between the local oscillator and the mixer can be used is
illustrated in Fig. 3.14. This circuit has some very great advantages
over the capacitive-probe
coupling circuit, especially if the LO output
power is low. A direct connection is made lwtwccn the mixer line and a
coaxial line terminating in the pickup loop of the local oscillator.
line includes a movable section, with spring ,contacts in both the inner
and outer conductors, so that the orientation of the loop with respect
to the mixer can be adjusted and then clamped.
For decoupling of the
signal from the local oscillator, the resonant nature of the local-oscillator
cavity is utilized.
Because the local oscillator is tuned to a frequency
differing from the signal frequency by the intermediate frequency, the
local-oscillator cavity is not resonant
To crystal
input line
at the signal frequency,
A signal
down the local-oscillator line is therefore almost completely reflected at the loop.
So far
as the signal frequency is concerned,
the local-oscillator line is just a stub,
and if it is made the right length it
has practically
no effect on the
The line is
signal-frequency wave.
a’p p r o x i m a t e 1y of nonreflecting
length if the distance from the inside
wall of the outer conductor of the
mixer line to the end of the loop,
F]{:. 314.-Ad justable local-oscillator
including the perimeter of the loop,
coupling circuit in which the resonance of
the LO cavity is utilized for decoupling
is an odd number of free-space quarthe LO circuitfrom the signal.
ter wavelengths.
A single quarter
wavelength would allow a reflection in the mixer line producing a
voltage standing-wave ratio of less than 1.2 over a band of plus or minus
10 per cent.
The load presented to the local-oscillator line is nearly matched in this
If power enters the mixer through a resonant cavity or a TR
cavity, the reflection of power at the local-oscillator frequency by this
cavity must reinforce the local-oscillator
wave traveling toward the
In other
crystal, just as it does in the capacitive-probe coupling circuit.
words, the section of line from the junction to the cavity must behave as a
The local-oscillator
line is terminated by
the crystal and is usually not seriously mismatched.
If no resonant cavity is used, the mixer line is matched in both
directions—at one end by the crystal and at the other by the antenna.
The local oscillator line might be made to have a characteristic admittance twice that of the mixer line and the standing-wave ratio in it might
therefore be nearly unity.
With a line only one-quarter wavelength long,
however, this would not be necessary, since the load presented to the
oscillator would change very slowly with frequency, although the voltage
standing-wave ratio would be about two.
The coupling of the local oscillator is adjusted by rotating the loop
A range in coupling from zero to full
in the local-oscillator cavity.
coupling is achieved for a rotation of 90° from a position with the loop in
the plane of the magnetic field to a position perpendicular to the magnetic
field in the local-oscillator cavity.
The great advantage of this circuit
is that full coupling between the local oscillator and crystal can be
obtained without danger of interaction with the signal circuit of the
mixer, provided the intermediate frequency is high compared with
VO/Q~,where Q~ is the loaded Q of the oscillator cavity and vo is the radio
Thus the local-oscillator power required is reduced from 25
or more milliwatts to about one milliwatt.
For mixers that have no
resonant cavity in the input circuit, this coupling circuit is especially
useful, since the capacitive-probe type does require large oscillator power
in that case. It is also simpler than the probe coupling circuit when
it is necessary to include a resistor disk for maintaining a matched
local-oscillator line.
3.10. Local-oscillator
Coupling in Waveguide Mixers.-In
waveguide mixers for the wavelength region for which the previously discussed
waveguide crystal mount is used, the LO coupling problem is similar
to the coaxial-line problem, but is complicated by the fact that the local
oscillators commonly used (723A/B, 2K25, and 2K45) have coaxial-line
output leads of a very special type. These output lines end in a small
dielectric-encased antenna which is supposed to couple as a probe to the
In many early mixers that were built and put into service,
this antenna was used to couple local-oscillator power directly to the
mixer by allowing the antenna to project by an adjustable amount into
the mixer waveguide at an appropriate place. The adjustment of the
probe insertion was made by using a tube mount, on the broad side of
the rectangular waveguide of the crystal mount and mixer, which could
be adjusted in spacing from the waveguide.
In this way the antenna
at the end of the coaxial line projecting from the base of the tube was
made to extend into the waveguide by a variable amount.
Localoscillator coupling of this kind has recently been completely abandoned
because it does not afford a controllable load admittance at the oscillator
Only enough coupling is needed to ensure that a few per cent of the
available local-oscillator power is coupled into the waveguide of the
mixer, in accordance with the preceding discussion.
Decoupling of
the signal from the local-oscillator circuit is thus assured but, because
only a small percentage of the available local-oscillator power is coupled
out of the LO output line into the waveguide, a large standing-wave ratio
can exist in the output line. Since the line has a physical length of about
3 in., it is electrically about 2.5 wavelengths long and the electrical length
is strongly dependent on the oscillator wavelength.
Thus, the load
admittance prese~ted by this output line to the oscillator cavity varies
rapidly with wavelength.
Wavelengths are found, consequently,
which the oscillator operates very erratically or not at all. If the same
Insulating material
FIG. 3.15.—Test mount for a 2K25,
tube is used in a circuit in which the tube is operated into a reasonable
load admittance, it can be tuned smoothly through these same wavelength
regions. The fault, therefore, can definitely be attributed to the load
With a given tube, a coupling circuit of this type operates satisfactorily at some wavelengths, and its simplicity would recommend it for a
simple mixer even if the tuning range were restricted.
It is found, however, that the wavelengths of satisfactory operation are not the same for
various tubes of the same type, because the electrical length of the
output coupling line is not controlled.
Thus, many other]vise satisfactory tubes must be discarded in favor of others which have output
lines of different electrical lengths, when the tube is coupled to the mixer
in this way.
As a result of the difficulties of this kind which have been encountered,
a definite circuit for coupling these oscillators to a wa~-eguidc has been
l~ith this circuit, almost the
made a part of the oscillator specifications.
full power available from the oscillator is coupled to a matched load
Continuous tuning of the oscillator over its
terminating the waveguide.
specified tuning range results if the waveguide has a nonreflecting
To be certain that this is true, the specifications require
that each tube be tested or this property in the specified mount, and
the tube must pass a test for minimum output po~t-erin the same mount.
A mixer that is to use one of these tubes as a local oscillator must
present to the tube the same admittance as is presented to it in this test
mount if cent inuous tuning and reasonable output power are to be assured.
Thus, the tube must be mounted ~rith the same probe position, as regards
insertion and position laterally and longitudinally on the waveguicfe, and
the waveguide must be approximately matched at its load end. Figure
3.15 sholvs the important features of the test mount or the 2K25 tubc.
In some mixers to be described in later sections, the tube mount is not
identical with this in all details because it could not easily be made so.
In these mixers, extensive tests 11-ithlarge numbers of tubes were made
to ensure that the mixers would operate satisfactorily over the required
tuning range ~;-ith the great majority of tubes.
3.11. A Directional Coupler for Coupling the Local Oscillator to the
Mixer.—.k simple mixer for the 3-cm region can be coupled to the local
oscillator in a variety of ways.
In ~-iew of the requirement that the local
oscillator operate into a special circuit it seems advisable that two
separate waveguides be used, one for the mixer proper, and one for the
local oscillator and load circuit, with a coupling circuit between these
waveguides ~vhich transmits the required amount of local-oscillator power
from the local-oscillator
waveguide into the mixer waveguide.
suggests that a “ directional coupler” would be the ideal circuit to use.
A directional coupler is a special network having four pairs of terminals
and having the property that power sent into one pair of terminals is
almost completely transmitted to a matched load on the opposite pair.
A small fraction of the power is coupled into a third pair of terminals
and none to the fourth,
The symmetry is such that if the direction of
oower flow is re~.ersed the small amount of power is available from the
fourth pair of terminals and none from the third. At microwave frequencies, the directional coupler can be realized by a structure such as
that shown in Fig. 3.16. The details of the design of circuits of this
kind will be found in Vol. 11, Chap. 14, but a qualitative description
of the operation of the directional coupler is given here to facilitate the
discussion of its use as an LO coupling circuit.
Two waveguides running parallel to one another are coupled together
by two channels of the same width as the waveguides but of smaller
narrow dirnensio nandone-quarte rwavelengthlong.
These channels are
spaced one-quarter wavelength apart, asindicated in Fig. 3.16. Both of
these dimensions are only equivalent electrical dimensions because
corrections must be made to compensate for end effects. The operation
as a directional coupler depends on the fact that each channel excites
a wave in one waveguide when a wave is sent through the other. The
excited wave propagates only in the same direction as the exciting wave
because destructive interference takes place between the two components
As a wave that is sent into the structure
traveling in the other direction.
FIG.3.16.—Waveguide directional couplel-.
at A passes the channels, a small percentage of the energy is sent down
each channel.
If the coupling is small, the amplitudes of the waves in the
two channels are almost the same. Each of these waves excites waves
propagating in both directions in the lower waveguide but the component traveling toward C arriving at 3 by way of the path through
2 and 4 is opposite in phase to that excited by way of the path through
1 and 3 because it has traveled one-half wavelength farther.
Hence, the
two waves traveling toward C interfere destructively.
The two waves
traveling toward D are in phase with each other and, consequently, a
wave of twice the amplitude, or four times the power, of that which would
result with a single channel is propagated toward D. Because of the
symmetry of the device it can be seen that a wave sent into B propagates
primarily to A with a small part sent to C and none to D, and similarly
for the other branches.
The amount of power that is coupled from the one waveguide to the
other is dependent on the width of the channels.
The characteristic
impedance for rectangular waveguides of the same broad dimension is
proportional to the narrow dimension b. The junction formed between a
channel and the main waveguide may be considered as equivalent to a
[SEC. 3.11
series connection and, therefore, the impedance loading one of the channel
waveguides is twice the characteristic impedance of the main waveguides
In units of the
if both ends of the loading waveguide are matched.
characteristic impedance of the channel waveguide the load impedance is
2b/b’, where b is the narro~v dimension of the main waveguide and b’ is
that of the channel.
At the other end of this channel, because the channel
is one-quarter wavelength long, the impedance is the reciprocal, or
Returning to units of the characteristic impedance of the main
waveguide, the impedance at the input end of the channel is (b’) z/2(b)’.
This impedance may be considered as appearing in ser”es with the load
impedance in the waveguide on the side of the channel opposite to the
If all four waveguides are matched,
side connected to a signal generator.
a fraction, approximately equal to (b’)z/2(b)2, of the power available from
a signal generator on one waveguide would be coupled by a single channel
into the other waveguide.
With two channels, a fraction of the power
approximately equal to (b’) 2/ (b) 2 is coupled into a matched load at one
end of the other waveguide.
To be used as an LO coupling circuit, the directional coupler of Fig.
3.16 would be excited by the local oscillator at A and by the received
it would be terminated
by a matched dummy load at B
and by a crystal mount at D, and a complete mixer results. The fraction
of the received signal power which is lost by transmission to the dummy
load at B is the same as the fraction of the total local-oscillator output
power which is transmitted to the mixer crystal.
One disadvantage of
the directional coupler in this application is that it is very difficult to
provide an adjustable coupling for it. Thus the only way of achieving an
adjustable local-oscillator drive is to use a dissipative attenuator between
the local oscillator and the coupling channels.
If this is done, the
coupling must be designed to give the required local-oscillator drive under
the most adverse conditions of oscillator output power and crystal admittance. The signal power lost into the local-oscillator circuit is independent of the attenuator adjustment and, therefore, is always that associated
with the amount of coupling and is not reduced when a high-power
oscillator and a good crystal are used. This is not a serious disadvantage
Many other forms of directional
but its existence should be realized.
couplers can be made and it v-ould not be 1~-orth while to go into the
details of all of these here. Any directional coupler, however, with an
appropriate coupling factor would be satisfactory.
Il”ith a 2K25 tube,
the minimum output po~~-eris specified as 15 mw and the local-oscillator
drive desired for crystals of the 11’23 type is about 1 mw. .4 directional
coupler for this combination should couple, from the local oscillator to
the crystal, T%of the available power. Such a coupler is sometimes called
an 11.8-db coupler.
It should be pointed out that there is a smaller loss of signal caused
by the local-oscillator circuit with a directional coupler than there is with
a coupler of thesimpler nondirectiorml type ciiscussed in connection with
Eqs, (2)and(5)
forthemixer circuit without a resonator.
between Eqs. (2) and (5) was stated to show that the fraction of signal
power lost could not be made smaller than the fraction of available localoscillator power delivered to the crystal, which is the same condition that
exists for the direct ional-coupler circuit.
There is’ a clifference, however,
in that, in the former example, the available power was that in the mixer,
and if a matched load such as a resistor disk is provided, only about half
the power actually availuble from the oscillator is available in the mixer.
With a directional coupler it is the total power available from the oscillator which enters into the reciprocity relation.
directional coupler results in only half as large a signal loss as the simpler
if the full coupling is being used. The fact that the signal 10SS
does not decrease with more favorable conditions, however, means that
this advantage is lost when attenuation must be used between the
oscillator tube and the directional coupler.
With the mixer preceded by a resonant circuit such as a TR cavity,
there is no such advantage from the use of a directional coupler over the
nondirectional circuits.
It was shown that the fractional loss of signal
power with a simple coupling circuit can be as small as one quarter of
the fraction of the local-oscillator power available in the mixer delivered
to the crystal.
With a matched load, such as the resistor-disk circuit
discussed in Sec. 38, provided for the local oscillator, the local-oscillator
power available in the mixer is one-half that available from the tube
alone. The fractional loss in signal power, therefore, can be as small
as one-half the fraction of the local-oscillator power available from the
tube delivered to the crystal.
Thus the signal loss with a directional
coupler is twice the minimum loss possible with the simple circuit if a
resonant signal circuit is used ahead of the mixer. Because the coupling
with the directional coupler is independent of the admittance at the
signal-input terminals of the mixer, the position of the coupler in the line
between the resonant circuit and the crystal is not important.
If the
resonator were separated from the mixer by such a long length of line that
the admittance looking toward the resonitor at the injection point of
the local-oscillator power varied rapidly with the frequency, a directional
coupler would be superior to the simple coupling circuit.
Another point
of great importance when no resonant circuit is used between the antenna
and the mixer is that the only source of signal radiated from the mixer
would be reflection, of local-oscillator
power, by the crystal, if the
directional coupler is used. With the simple circuit, the amount of
local-oscillator power radiated under these conditions would be the same
as the amount deikered to the crystal.
Directional couplers have not
been used extensively in microwave mixer circuits, chiefly because it is
diffi~il~. to make them adjustable and because they have not been
mechanically convenient for most applications.
It will be shown later
that in circuits operating with a resonant TRca~ity,
itis desirable that
the length of line between the TR cavity and the crystal be kept short.
iMost directional couplers transmit the coupled ~vave in the same direction
as the original wave, as does the one of Fig. 3.16, and this requires that
the local-oscillator tube be located at some distance from the crystal.
This requirement has not been compatible with the desire for-short
line length between the TR cavity and the crystal with the duplexer
circuits used and, consequently, other circuits have been found more
adaptable to the service. The design of amixer, whether a coaxial-line
or waveguide type, using a directional coupler for the local-oscillator
injection is straightfor~rard and any of the directional-couplers that are of
convenient shape andhave the required amount of coupling may beusecl.
3.12. A Single Channel for Local-oscillator
nondirectional circuit for coupling the local oscillator to a waveguide
mlxcr, which is similar to the directional coupler of Fig. 3.16 in principle
but contains only one coupling
is illustrated
tive argument given for the, chan‘27<0;:v::he:it:
nel width of the directional coupler,
~lG. 317 ‘–”hi C iVeCtiOnal
Coud W! circuit.
the power coupled from one ~ravegulu< ‘>5the otl ~r, with alI four pairs of terminals matched is approxi mate~y (L’) 2/2(b)’,
If this circuit is used as the LO coupling circuit
i“07 a mixer, the oscillator output .po~ver can be sent into A or B and
a matched dummy load placed on the other end of this waveguide.
The signal would be incident at C and the crystal mount would be at D.
Since the coupled power is the total po~ver taken out of the local-oscillator
waveguidej with a termination in the mixer waveguide at each end \vhich
is matched at the local-oscillator frequency, the po\\-ertransmitted to
the crystal is just half the power coupled from one guide to the (other, or
If the mixer has a resonant filter such as a TR cavity
in the signal line, the coupling depends upon the admittance presented by
this circuit, at the local-oscillator frequency, at the coupling channelBecause the junction is a series connection, the largest coupling occurs
when this admittance is very large and the coupling is then approximately (b’)’/(b)’.
All of the po!rer taken out of the local-oscillator
waveguide is transmitted to the crystal and this po~ver is twice the amount
without the resonator since the impedance terminating the cross-coupling
channel is 1 instead of 2 in units d the cha”act.eristic Impedance of the
main waveguide.
The amount of the coupling for tk single ChMME! can be made
variable by the addition of an adjustable susceptamce element in the
In Fig. 3.18 the effect of adding a capacitive ausceptance in the
coupling channel at a point midway between the two waveguides is
illustrated on an admittance chart. The load admittance in units of the
characteristic admittance
of the channel was taken as 0.25 at point (1).
FIG.3.18.—Admittance diagram illustrating effect of adjustable susceptance for coupling.
Without the susceptance, the admittance at the input end of the channel
corresponds to the point (2a) or a conductance of 4 in units of the charSince this conductance is added
acteristic admittance of the channel.
in a series circuit in the local-oscillator waveguide, the impedance is more
significant, and this is 0.25 in units of the characteristic impedance of the
Hence, the
channel or 0.125 in units of the main-waveguide impedance.
power coupled from the local-oscillator waveguide to the other would be
about 12.5 per cent of the power delivered by the local oscillator to the
dummy load. Only one half of this power goes into the crystal.
With a
capacitive susceptance of 0.5, in units of the admittance of the channel,
[SEC. 312
added at the midpoint of the channel, the admittance at the input end of
the channel is that of the point (2b). The corresponding impedance is
that of the coordinates at (2c) or 0.16 + jO.22 in units of the characteristic impedance of the channel.
In units of the characteristic impedance
of the main waveguide this is 0.08 + jO. 11. Therefore, 8 per cent of the
power delivered by the local oscillator to the load is transmitted into the
mixer waveguide and the delivered power is slightly changed because of
the appearance of the reactive term.
It might be thought that to avoid the reactive term the susceptance
should be added at a point such as (3), where the circles of constant
conductance are approximately orthogonal to the circles of constant
standing-wave ratio. Since it is just as important, however, to avoid
large reflections in the local-oscillator waveguide as in the mixer waveguide, this is not so. Although the resultant variation of the series
impedance presented to the local-oscillator waveguide would be resistive,
that presented to the mixer waveguide would be reactive and severe
reflections would result. It is sometimes more convenient to use a
channel three quarters of a wavelength long for such a coupling circuit.
Then, an inductive susceptance at the midpoint, or a capacitive suscept-.
ante at a position a quarter wavelength either side of the midpoint
would produce a coupling that deZ. creased with increasing susceptante. An inductive
used at the midpoint of the quarLocal oscillator
kgfS Line
ter-wavelength channel would give
Zl = ZOtJlb
increased coupling with increasing
The mismatch
hg/S Line
would be introduced by such a
Zl =ZOtilb
coupling device would increase with
increasing coupling and could become serious unless a limit on the
range of adjustment were provided.
It is difficult to set a limit on the
FIG. 3.19.—Equivalcnt ci, cuit of channel
adjustment since the susceptance
local-oscillator coupler.
of a structure introdticsd into the
waveguide varies rapidly with frequency when the susceptance is large.
Under most circumstances the amount of mismatch that can be tolerated
is larger for conditions requiring small local-oscillator coupling because
the crystals that have small conversion loss usually require small localoscillator drive to achieve optimum over-all noise figure.
Expressions giving the amount of coupling between the local oscillator
and the crystal, and the reflection coefficient caused by the coupling
channel, as a function of the added capacitive susceptance can be derived
from a consideration of the equivalent circuit of Fig. 3.19. All impedances and admittances are expressed in units of the characteristic impedance or admittance of the main waveguides and it is assumed that the
local oscillator, dummy load, signal generator (receiver antenna), and
crystal are all matched to the waveguides at the local-oscillator freThe series impedance introduced in the local-oscillator circuit
by the coupling channel and mixer can be calculated by transforming the
load admittance of the channel, b’/2b, through the eighth-wavelength line
by the transmission-line formula for a lossless line,
~ = ~0 Y, + jYO tan (H)
Y, + jY, tan (kl)
where YOis the characteristic admittance of the line, Y~is the terminating
admittance, k is the v-ave number equal to 27r/k,, and 1 is the length of
the line. For the eighth-wavelength
lines ld is 7r/4 and the transmissionline formula is
y = y. ;t + ~yo.
of local-oscilNext, the variable susceptance B is FIG. 320.-Equivalent
lator circuit.
added and the resultant admittance,
again transformed by this formula, gives the admittance Y. at the input
end of the channel.
The impedance Z. is the reciprocal of Y. and the
entire circuit becomes equivalent to that of Fig. 3.XJ. The fraction of
the available local-oscillator power coupled into the crystal is
and the absolute magnitude of the reflection coefficient is
[rl =
1 +(1+2,)
By algebraic manipulation,
(2 + l?.)’ +
these relations become
4A’[A’B2 + (2 + B)’]
T = [A2B2 + (2 + B)z + 4A2]’ + Azi?z [(2 + B) – AZ (2 – B)]z
Irl = ~[A’B’
16A’ + A2B’ [(2 + B) – A’ (2 – B)]’
+ (2 + l?)’ + 4A2]2 + A2B2 [(2 + B) – AZ (2 – B)]’ )
where the quantity A is the admittance terminating the channel in
The value of A z
units of the characteristic admittance of the channel.
which gives the required maximum coupling To may be found by setting
B equal to zero in Eq. (11) and solving for A‘.
If this is done,
A’ = +.
[(l –
2TO)– (1– 4To)q.
For T, small compared with ~, thk expression may be simplified by the
expansion of the second term in series and the neglecting of terms higher
than the third.
The result is
A’ = T,.
This is identical with the result obtained for the fraction of the total
power delivered to the crystal, if the series impedance of the channel
0.05 [
‘:~, ik
F[G. 3.21.—Fraction of LO power coupled vs.
FIG. 3 22. —Standlmg-wat-c
vs. sus-
ceptan<, c.
in the local-oscillator
waveguide is small compared with the characterlocal-oscillator
A typical example of a 3-cm mixer would employ a 2K25 oscillator
tube and a 1NT23crystal,
The oscillator tube maybe expected to give at
least 15 mw of power and the local-oscillator drive required for the crystal
is less than 1 mw. Hence, TO couId be 0.05,
If this value is used in
Eqs. (11) and (12), the coupling and reflection coefficient as functions
of the adjustable susceptance can be found.
In Fig. 321 the fraction
of the power available from the oscillator coupled into a matched crystal
is plotted as a function of the susceptance.
In Fig. 3.22 the standingwave ratio is plotted as a function of susceptance, found from Eq, (12)
by the relation
of the
I –
ratio hasa maximum of 1.55 atinfinite susceptance,
This amount of mismatch relative to
corresponding to zero coupling.
the optimum load admittance for the tube has been found not to cause
trouble with the great majority of tubes.
3.13. An Exact Equivalent Network for the Coupling Channel.-The
analysis of the circuit on the basis of a simple series connection to represent the junctions is not sufficiently accurate to allow exact specification
of the length and width for a particular coupling factor.
As in almost
all microwave circuits, there are end effects, associated with the excitation
of higher modes in the waveguide, or coaxial line, which cause some
departure from the results expected on the basis of the simple circuit.
However, by means of some exact equivalent circuits for a junction of
this type, developed by J. Schwinger, it is possible to calculate the length
and width for minimum mismatch (equivalent to a pure series resistance)
for a given coupling factor.
derives an equivalent network for the
junction where the terminals of the network are considered to lie in planes, in the
respective waveguides, adj scent to the
Because many modes exist in
the immediate vicinity of the junction,
the admittances in these planes cannot
be specified, but the equivalent circuit
predicts the admittances which would be
measured at planes an integral number
of half wavelengths back from the j unction in the respective waveguides.
agreement of these equivalent circuits
with experiment is very good.
By making use of them, the conventional technique of cut and try can be eliminated.
FIG. 323,-Equivalent
circuit for an
E-plane T-j unction.
For waveguide and coaxial-line structures of many other types, Schwinger’s technique has been used and the
results are being compiled in Voh 10 of this series.
In Fig. 3.23a is shown a cross-sectional view of the T-junction where
b and b’ are the inside dimensions of the waveguides.
In the same
figure the equivalent network is shown where the terminal pairs are in the
planes corresponding to the dashed lines of the structure.
The components of the network are represented as capacitances or inductances
depending upon whether the sign of the susceptances is positive or negative. They do not necessarily show the corresponding
This is evident from the relation below giving the values
of these susceptances in terms of b, b’, and k the
to %/A,.
number, equal
.[ ()1
‘1 ‘H’
All the susceptances except B, have the direction of change with frequency normally associated with a low-frequency susceptance of the
same sign but the dependence is inversely or directly with the waveguide
wavelength and not the free space wavelength.
A technique that can be used for the calculation of the length and
width of a channel for a particular coupling is to estimate the width
on the basis of the simple series-junction formula, 2’0 = (b’) ‘/4(b) 2.
Next, the admittance at terminal pair (3) with pairs (1) and (2) connected
to matched loads, or unit admittances, can be calculated.
From this
admittance the standing-wave ratio and phase in the coupling channel
can be found and from this a plane in the junction at which the load
The difference in position between
admittance would be real is found.
this plane and the plane containing the terminals of the equivalent
circuit is the end effect. The length of the channel is made to be
physically the one-quarter or three-quarters of a waveguide wavelength
If this length is used for the narrow
between these corrected planes.
waveguide, the admittance presented to the terminal pair (3) of the
second network can be calculated and hence the amount of power coupled
across found, as well as the standing-wave ratio and phase in the input
In examples the standing-wave ratio is found to correspond to that which would be found for a simple seti,es circuit coupling
out the same fraction of power, and the choice of the length on the basis
of the end-effect planes is considered to be valid.
From the phase of
the standing wave, the position of end-effect planes for the terminal pairs
(1) and (2) can be found and, thus, the circuit can be considered as
equivalent to the simple series circuit connected between these planes.
All three of the planes are found to fall inside the junction from the
planes defining the position of the terminals of the equivalent network.
The algebra of this calculation is perfectly straightforward but quite
There is no point in giving an example here, although some
results to show the magnitude of the divergence from the simple idea of
For a mixer for 1.25 cm, using
series connection may be of interest.
SEC. 313]
main waveguides 0.170 by 0.420 in. ID, the coupling and end corrections
have been calculated for several channel widths.
It was found that
the end corrections amounted to about 0.025 in. at each end of the
channel, thus shortening the length of the channel by about 0.050 in.
from a quarter-wavelength
in the waveguide for channel widths from
0.060 in. to 0.100 in. In this range of widths, the power coupled into
the mixer differed by less than 15 per cent from the value calculated
from the simple series circuit with the formula (b’) 2/4 (b) 2. A calculation
for 3.2 cm, using a main waveguide having inside dimensions of 0.400
by 0.900 in. and a channel width of 0.180 in. gave an end correction of
0.060 in. The fraction of the local-oscillator
power delivered to a
matched crystal was found to be 0.042 compared with a value of 0.051
Because the disagreement of the
calculated for the simple series circuit.
coupling factor calculated from the simple circuit with that calculated
from the exact equivalent circuit is not large, for present purposes the
choice of the width of the channel on the basis of the simple series
junction is probably sufficiently precise.
The main value of the network
representation is the end-effect correction in the length of the coupling
This is simple to calculate compared with the calculation of
the exact coupling factor.
All of the foregoing discussion applies to a mixer that has no high-Q
resonant circuit between the crystal and antenna, and the antenna,
therefore, appears as a matched load to the local-oscillator wave,
If a
TR cavity is used between the mixer and antenna, as shown previously
the coupling between the local oscillator and the crystal can be increased
by a factor of 4 by proper choice of the position of the TR cavity relative
to the coupling channel.
The TR cavity should be so positioned that a
short circuit appears in approximately the plane of the appropriate
terminal pair in the equivalent network.
The coupling can be made
very small by placing the TR cavity in a position a quarter wavelength
different from this, resulting in an open circuit at this plane, since the
circuit of the junction does correspond approximate y to the series.
Since such a position must be avoided, a mixer intended to be
operated in a wide frequency band should be designed with a line length
between the TR. cavity and the coupling circuit so short that the admittance presented at this plane by the TR cavity dots not deviate appreciably from a short-circuit admittance within the band.
The exact position of the TR cavity relative to the junction can be
calculated with the aid of the equivalent network.
The admittance at
the terminals of the network, with the complete circuit assembled maybe
The l’R cavity should then be so positioned that the susceptance of the waveguide terminated by the I’ll cavity is the negative of the
susceptance component of the calculated admit tante
The result of such
a calculation shows that the TR cavity should be positioned somewhat
closer to the junction than an integral number of half wavelengths and
an equivalent plane for the simple series circuit representation can be
For the example of the 1.25-cm waveguide cited previously, the
correction is such that the position of a short circuit due to reflection
from the TRcavity
appears almost at the center plane of the junction.
For this purpose; then, it appears that the series circuit is adequate and
that the tedious calculation required to apply the exact equivalent circuit
Fro. 324.-Curves
of constant LO power to crystal, vs. Z,, the impedance of TR cavity
plus part of network.
gives a result too little different to bc worth while, except for the calculation of the length of the channel.
When a TR cavity is used, the coupling factor is strongly dependent
upon the crystal admittance since a wave reflected by the crystal is
returned to it by the TR, cavity in a phase dependent on the reflection
coefficient of the crystal.
As an illustration of this point, two plots are
given in Figs. 3.24 and 3.25. Fig. 3.24 shows contours of constant power
delivered to a matched crystal as a function of the impedance across the
terminals of the network representing the junction in the mixer waveguide
on the other side of the junction from the crystal.
This impedance
includes the susceptance of the capacitance jll, associated with the
[email protected]
terminals and is for the 1.25-cm waveguide
0.420 in. by 0.170 in. ID
with a coupling channel 0.100 in. by 0.420 in. and 0.401 in. long.
plotted on this diagram is a contour of the terminal impedance for a
TR cavity, spaced such that the short circuit, when the TR cavity is
detuned, appears 0.261 in. from the plane of the terminals of the equivalent network.
The contour is valid for a typical 11326 TR tube having
about 1.6 db loss and equal coupling irises. The contour does not
FIG. 3.25.—Contours of constant power delivered to crystal vs. crystal admittance,
for TR admittances equal to (1.4 + j2.4) Y, at LO frequency. The TR switch is the
1B26; the intermediate frequency is 60 Me/see.
represent the TR-cavity
and signal-generator admittance alone, but
includes the capacitance associated with the terminals of the junction.
This plot is significant since the Q of the 1B26 tube, the standard TR
cavity for this wavelength, is not high enough to allow the TR cavity
to be considered as completely reflecting at the local-oscillator frequency
when the tube is resonant at the signal frequency with ordinary intermediate frequencies of 30 or 60 Me/see.
Figure 3.25 shows, for this same coupling circuit, contours of constant
power delivered to the crystal as a function of the crystal admittance as
measured at the crystol terminals of the network.
Here, the intermediate frequency lMS been ass~lmcd to be such that the TR cavity is
detuned from local-oscillator frcqllcncy to an extent sufficient to transmit
half the maximum power. A 60-Xlc/scf: intermediate frequency would
about correspond to this situation ~vith a 1B26 tube, since the loaded Q
of these TR tubes is about 200.
3-14. An Iris for Local-oscillator
operation ~vith a
resonant TR cavity, because of the more cfflcient coupling resulting, a
simpler type of circuit has been use(l
cxtcnsivcly in the 3.2-cm band and
Wide side
This coupling dcload
of waveguide adjacent regions.
vicc consists of a simple inductive
~;inclow between two adjacent paralInput line
lc1 ~\-aveguides ~~ith a common wall
Irlti. 3.26.— H-I)lane window for 10calon their narrow sides. A circuit of
oscillator coupling.
is illustrated
in Fig. 3.26.
The aperture in the vdl may bc either circular or rectangular, although
rectangular apertures running the full height of’ the common ~rall have
usually been med.
These apertures arr made less than a half wavelength in width, and, to a fair approximation, the circuit may bc considered as a lumped indnctilre susccptancc in the plane of the Irindow.
Circuits coupled to the narrow ~vall of a waveguide can bc shown to
behare approximately as shunt-conncctecl circuits ~vhcrc the admittance
at the ~vall is transformed by a quarter v-ayclcngth of \Va~-cguideinto the
center of the wavcguide.
This transformed admittance adds in shunt to
the admittances of the loads at the cncfs of the waveguicle.
The simple aperture coupling is lCSSefficient than the channel coupling
just discussed in the sense that the reflection due to the aperture is larger
than that due to the channel for a given coupling factor.
That this is so
can bc shown from the simple equivalent shunt circuit in the following
way. Suppose that all four waveguidcs in Fig. 3.26 arc connected to
matched loads representing the local
~ = 2+j4b
oscillator and a dummy load in the
upper waveguide and the crystal
FI~, 327,-Equivalent
shunt circuit for
aperture-coupling circuit.
and signal generator in the lower,
The admittance in the lower waveguide at the center is 2 in units of the
characteristic admittance of the waveguidc.
Transformed through the
quarter wavelength of waveguide to the aperture, the admittance is
~ in the same units, To this is added the inducti~e susceptance of the
aperture, –jb, and then this is transformed through another quarter
wavelength of waveguide to the center of the upper waveguide.
the admittance of the mixer waveguidej appearing in shunt in the upper
waveguide, is
_ 0.5+jb
Y. =
0.5 – jb – 0.25 + h’ – 1 + 4P’
The equivalent shunt circuit is illustrated in Fig. 3.27 and from this the
fraction of the available local-oscillator power delivered to the crystal
can be shown to be
4(1 + b’)”
A plot of this function is given in Fig. 3.28a,
on the other hand, is given by the formula
The standing-wave
1 \
FIG. 3.28 0, b,—The effect of susceptance of coupling iris. (a) Coupling factor vs. susceptance; (b) voltage standing-wave ratio vs. susceptance,
where 11’=1is the reflection coefficient for the load ( l’~ + 1) or
This is to be compared with the reflection coefficient
circuit for which the reflection coefficient is just
for the channel
Ircl = T,
LTsing the above
for a coupling factor T small compared with 0.25.
expression for Ir.1 in the equation for the standing-wave ratio, a curve can
be plotted with the result shown in Fig. 3.28b for the voltage standingwave ratio as a function of the aperture susceptance.
The symmetry of the circuit, neglecting the frequency dependence
of the local-oscillator admittance, makes it apparent that the same
standing-wave ratio would be produced in the mixer. From this it is
evident that the simple aperture coupling circuit has considerabley greater
interaction between the signal and local-oscillator circuits than is necessary. For this reason it has been found to operate satisfactorily only
under the condition that a resonant TR cavity is used, so positioned that
the admittance of the TR cavity at the local-oscillator frequency seen
in the mixer waveguide in the plane containing the center of the coupling
aperture is very small. Because the TR cavity reflects the wave incident
upon it in such a phase as to reinforce the wa~e traveling toward the
crystal, as in the other examples, the power delivered to the crystal is
increased almost fourfold, for an aperture of large susceptance.
analysis on the basis of the simple shunt circuit is similar to the previous
one except that the admittance of the mixer at the aperture is unity
s 1.75
1,30 k
FIG. 329.-The
effect of susceptance of LO coupling iris when a resonant TR cavity
is used. (a) Coupling factor vs. wmceptanoe; (b) standing-wave ratio in LO waveguide
vs. coupling susceptance.
instead of two.
case is
The coupling factor as a function of susceptance for this
* =
4(1 + b’)
9 + 5b’ + 4b’
The stianding-wave ratio vs.
and this function is plotted in Fig. 3.29a.
susceptance plot of Fig. 3.28b applies here for the signal standing-wave
ratio in the mixer, with the crystal matched to the signal, but the standing-wave ratio in the local-oscillator waveguide is changed by the presence
of the resonant TR cavity.
The reflection coefficient in the localoscillator waveguide is
m =
and for large susceptance the standing-wave ratio differs little from that
in the previous example.
Figure 3.29b gives a plot of the standing-wave
ratio due to this reflection coefficient as a function of the susceptance.
Because the space available for a radar mixer is usually limited, the
applications of this LO coupling circuit have mostly been a variation of
this scheme.
Figure 3.30 shows, in a perspective view, a mixer using such
a coupling circuit, with the positions of the coupling probe of the 2K25
local oscillator, the crystal, and the 1B24 TR cavity indicated.
oscillator tube is mounted with a tube socket above the waveguide at the
right with its antenna inserted the specified distance at an off-center
position as recommended in the test specifications.
The waveguide is
terminated with a matched load at the near end. The waveguide is shortcircuited at the other end and the iris that couples the local-oscillator
power to the mixer is located in the side wall with its center about a
quarter wavelength closer to the antenna of the tube than the short
The antenna of the tube is located at a distance from the far end
such that, at 3.33 cm, the admittance of the waveguide in this
direction is the same as that of the
equwalentto a
shott clrcuded
waveguide 1 cm
I ,, —
long, as specified in the mount for
DIUS1 cm m
the tube.
This length was chosen
by experiment and is electrically
to a short-circuited
line just less than [email protected]/4 in length,
although its physical length differs
from this considerably.
In this
way the local-oscillator
tube is
,utmt LRewstance
operated into a load circuit differStrip
ing at the midband frequency from
Fm. 3.30.—Mixer circuit with iris-coupled
the recommended one, for a small
local oscillator.
coupling to the mixer, by a small
conductance component in the admittance.
The admittance loading the
oscillator varies more rapidly ~~ith frequency than it does in the test
mount because the short-circuited waveguide is effectively a half wavelength longer than that recommended.
Experience has shown that
oscillators that operate satisfactorily in the test mount very rarely give
trouble in this circuit.
So far in this discussion the effect of the LO coupling circuit on the
admittance presented to the signal has been calculated assuming that
the local oscillator presents a matched admittance to the waveguide at the
signal frequency.
This is not true because the oscillator contains a
resonant circuit tuned to the local-oscillator frequency.
The reflection
coefficient of the local oscillator is very likely almost unity at the signal
There is a danger that this reflection may give rise to an
admittance at the coupling window which can cause serious reflection
of the signal. In the circuit of Fig. 3.30, this effect is less serious than in
the circuit in which the local oscillator and dummy load are on opposite
ends of the waveguide, since only at frequencies at which the output
coaxial line of the oscillator tube resonates by itself does the presence of
the oscillator antenna in the waveguide have a large effect. At other
frequencies the local-oscillator waveguide is loaded with an open-circuit
admittance from the side of the coupling iris away from the LO tube and
an admittance approxi.matcly matched to the waveguide characteristic
admittance on the other side of the iris.
As shown previously it is necessary to adjust the coupling of the local
oscillator if optimum results are to be achieved with production crystals
and oscillators,
With thk circuit the adjustment must be made by
FIG. 331.-Adjubtable
rectangular coupling iris.
variation of the iris susceptance.
With a rectangular iris this can be done
by making the whole side wall slidable, with spring contact between it and
the top and bottom ~valls of the waveguide.
Figure 3.31 shows such a
slidable wall made from two curved strips of phosphor bronze about
0.005 in. thick and spot-welded down the center line with their convex
surfaces together,
This spring slides in a channel between the top walls
and the bottom walls of the two adj scent waveguides and cent act is
A strip
maintained by the wiping action on the sides of these channels.
is soldered over the outside of the channels to keep the strip properly
With an adjustment of this kind, the effective position of the
iris is altered as the width is changed, but for a small adjustment the
change in position is not serious.
A more commonly used adjustment that avoids the variation of
position and the troubles usually encountered with sliding contacts is a
combination of a circular or rectangular inductive iris w-ith a capacitivescrew post.
This is shown in Fig. 3.30 mounted above the center of
the coupling ins.
The screw structure is shown in more detail in Fig.
The capacitive screw is the same type that is used in matching
transformers or in the channel coupling armngcmcnt for coupling adjustment.
It uses the {~{larter-}~’aIrclcl~gth-ch(]ke principle to minimize
In the
erratic behavior due to poor contact in the screw threads.
33-cm mixers a 6-32 screw is a
convenient size. An iris & in. in
width has been found sufficiently
narrow to allow the coupling to bc
made small enough for any combination of a 723<1/11 or 21<25 tuhc
and a 1N23 crystal with the screw
In the diacompletely retracted.
gram, a post projecting into the iris
from below is dotted in and ordinarily thk is absent from the structure. It is sometimes desirable,
however, to ha~e an adjustment in
whkh the coupling decreases with
increasing insertion of the screw,
and then the post is added.
post is sufficiently long to give a
FIG. 3~3?.-.i,ij~lst:1l]le coupling iris using
capacitive susceptance more than
enough to produce shunt resonance
with the inductive susceptance of the iris. The entire structure, therefore, appears as a capacitive susceptance that incremcs ~vith increasing
screw insertion.
For mixers that must be foolproof in operation it is important to
provide an upper limit on the coupling that can bc ac.hleved with the
This can be done with the iris and screw structure by
correct choice of the length of the screw. In applications where a wide
band of frequencies must be covered, the frequency-sensitive
of the capacitive susceptance of the screw does not allow the limit to be
chosen precisely.
A screw length that, at short wavelengths, gives the
whole structure the desired minimum inductive susceptance gives, at
longer wavelengths, a minimum inductive susceptance somewhat larger.
In such a case the device cannot be made entirely foolproof.
the structure including a fixed post the limiting coupling is, of course,
determined by the length of the post and the same arguments about the
frequency selectivity apply except that the largest coupling occurs at
the longest wavelengths.
For smoothness in the adjustment and also to protect against changes
caused by vibration, many locking schemes have been tried. The best
from the viewpoint of simplicity and permanence was a triangular spring
made from spring wire fitting into a slot in the screw mount and riding in
a thread of the screw. This is il]ustratcd in Fig. 3.32, with a top view of
the screw mount and spring JISO shoJru. The diameter of the spring
wire is about the same as the distance bct]vccn consecutive screw threads.
It is important to nmkc the slot in the screw mount at le~st as wide as two
screw thrcads in or[lcr that the spring may ride frccly in a thread, independently of the location of the threads with respect to the slot.
Many vfiriotions of thcw schemes of local-oscillator
coupling are
possible and some of thrrn ~~ill become apparent in mixers shown for
illustration m Iatcr c}mptjcrs. The general nature is the same, howe~~er,
and it would not be ~!’orth \vhllc to attempt to describe all of these
The type th:~t is best fitted to a given mixer is determined
by the shape which the mixer moy take and by some of the supplementary
functions which it is smnctimrs called ~lpou to perform.
These supplementary functions arc the sul}jmt of Chap. 4.
3.15. Signal-input
Circuit.—-Thc only remaining problem in the
design of a complete mixer is that of transferring the incoming signal
power from the circuit conncctcd to the antenna into the crystal mount.
If the line to the antenna is similar to the line in ~vhich the mixer is built,
the mixer may simply be conncctcd to the antenna line. The mixer
tuning should be such that,, l~ith the local oscillator operating at the
proper Ievcl and frequency and with a matched i-f load in place, the
admittance of the mixer for small signals with all crystals is as near
the characteristic admittance of the line to the antcuna as possible.
Measurement may show a small correction from the tuning arrived at
with signals at the local-oscillator level to bc dcsir:d)le.
For most mixers
it has been found that the small-signal admittances did not differ sufficiently from those measured at local-oscillator level to ]varrant changing
the mount.
When the mixer signal comes from a TR cavity, the mixer circuit must
be made to load the TR cavity properly.
With TR tubes having integral
cavities designed to operate between matched waveguides, the design
procedure is not greatly influenced by the cavity, but vith loop-coupled
cavities or those designed to operate between coaxial lines, a coupling
circuit must be a part of the mixer. With these cavities, the major part
of the adjustment of the tuning of the mixer for the best scatter of admittances with all crystals and over the frequency band required can not
be done independently of the design of this coupling circuit.
For this
reason the coaxial-line mixers have been designed for operation with
definite TR cavities, and the measurement of the matching conditions
has been carried out almost exclusively on the input side of the TR cavity.
If the effects, on the conversion loss and i-f admittance of the crystal,
of the line length between the crystal and the TR cavity are neglected,
the matching conditions can be completely determined by measurements
Such measurements show
of the input admittance to the TR cavity.
whether the TR cavity is properly loaded by the crystal circuit and from
these measurements the total transmission and reflection loss of the
circuit can be inferred.
A schematic view of a TR cavity and an equivalent lumped-constant
circuit are shown in Fig. 333.
The equivalent circuit applies only with a
special choice of the position of terminals on the input and output lines.
To find the position of these terminals in the input and output lines a
signal may be sent into one of these lines at a frequency far from the
resonant frequency of the shunt resonant circuit.
In the equivalent
circuit, a short circuit would appear at both the input and the output
pairs of terminals and, hence, the position at which a short circuit is found
in the coaxial lines, with the cavity detuned, is the position of the terminals.
If the cavity is then tuned to resonance, causing it to add zero
susceptance to the circuit, the admittance that is measured at this point
FIG. 3.33.—Loop-rouP]mi TR cavity and equivalent circuit.
in the output line is proportional to the sum of the admittance presented
by the load at the corresponding point in the output line and a conductance that is a measure of the dissipative loss of the cavity.
The output
admittance is transformed by the two ideal transformers by a numerical
factor and the conductance measuring the loss of the cavity is transformed
by a numerical factor by the ideal transformer representing the input
It is difficult to sho-.r that this circuit should apply exactly, but
its use is justified by very extensive experience in which perfect agreement
has been found between calculations from it of the transmission loss and
frequency dependence and measurements on actual circuits.
transformation ratio of the ideal transformers is dctrrmined primarily by
the fraction of the magnetic flux in the cavity which is linked by the loops,
and the admittance stcpup of the input-circuit loop can therefore be
increased by the use of a smaller loop or by setting it at an angle in such a
way that its plane is not perpendicular to the magnetic field of the cavity.
Iris-( mapled cavities can bc described in exactly the same way,
althoug’ the analogy betwem the iris and an ideal transformer is less
obvious than for the loops.
The position of the short circuit with the
cavity detuncd depends upon the length and diameter of the loop,
[SEC. 315
whereas with reasonably small irises it falls almost exactly in the plane
of the iris. For loops of the sort used with the fi-in. coaxial-line mixers,
the position of the short circuit is a point approximately a half wavelength
back along the line from the terminus of the loop, including the perimeter
of the loop as a part of the line.
The equivalent circuit of the TR cavity and mixer can be further
At the terminals chosen in the manner explained, the
equivalent circuit of Fig. 3.34 applies, where g. is the antenna conductance (equal to the characteristic admittance of the line), g, and jb. are
the conductance
and susceptance
parts of the cavity admittance
transformed to the terminals in the input line, and g- and jb~ are
those of the load admittance transformed to the input terminals of the
TR-cavity circuit.
From this circuit, it is apparent that, if the TR cavity
were tuned for maximum power delivered to the crystal, the resultant
susceptance of the circuit would
be zero. For such tuning b= is,
therefore, just the negative of b~.
This means that if the mixer had
been made tunable, and g% and
F]~. 3.34.—Transformed
equivalentckcuit b~ could be completely adjusted
of TR cavity and mixer.
in the mixer, there would be an
infinite number of equivalent tuning positions for the combination,
corresponding to different values of b~. It is thus apparent that
for complete tunability of a mixer-plus-TR-cavity
combination it is
only necessary to adjust g- in the mixer. Since the transformation
ratio of the output loop is influenced by its position in the TR cavity, a
completely tunable mixer can be made by using a loop of adjustable flux
linkage in combination with the tuning of the TR cavity.
To set
up a mixer and TR-cavity combination fixed in tuning, except for the
TR-cavity tuning itself, it is only necessary to choose the size of the
output loop of the TR cavity on the basis of admittance scatter diagrams.
The largest bandwidth and smallest dissipation of signal power in the
lines of the mixer are obtained when the crystals present a matched load to
the mixer line, since then the admittance presented to the output terminals of the TR cavity is no more dependent on frequency than the
admittance at the crystal.
It is on this basis that the standard 10-cm
It was made to operate with four
loop-coupled mixer &
different TR cavities covering the band from 8 to 12 cm simply by
choosing the ffange on which it was mounted on each of the cavities for
the best scatter of input admittances to the TR cavity with representative crystals.
The size of the input loop of the TR cavity is chosen on the
basis of the function of the TR cavity of protection at high level, and it is
this coupling that determines the values of g,,
The range of input admittances which can be tolerated with this
Assuming the TR cavity to be tuned
circuit can be found as follows.
such that the susceptances cancel out, the fraction of the available
signal power delivered to the crystal can easily be shown to be
(9. +9-
+ 98)’”
A measure of the input standing-wave ratio is (g~ + g,)/gg and if T
in decibels of loss is plotted against this quantity, the curve given in
Fig. 3.35 results. A typical value for g. of 0.245, resulting in a l-db total
loss with a matched output load, has been assumed.
Most TR cavities
now in use show a loss under this condition between 1.0 and 1,5 db.
+10 +12 +14 +16
SWR in db
FXG.3.35.—Transmission plus reflection loss for a TR cavity mixer, in dembels, vs. input
standing-wave ratio, in decibels.
The standing-wave ratio has been plotted in decibels, twenty times the
common logarithm of the voltage standing-wave ratio, and the positive
values correspond to a conductance at the input terminals greater than
~ the characteristic admittance of the line, and the negative values to a
conductance smaller than the characteristic admittance.
From the
plot it is evident that it is not sufficient to measure only the standingwave ratio since the curve is very unsymmetrical.
From the point of
view of the loss of signal power, a very much larger standing-wave ratio
can be tolerated with a phase corresponding to the positive side of the
plot than with a negative phase. The positive phase corresponds to a
standing-wave pattern with a minimum at the input terminals and such a
minimum has the same position when the TR cavity is tuned for greatest
transmission of signal as when the TR cavity is detuned.
For negative
values, the tuned condition shows a minimum position which is shifted by
[f3EC. 3,15
a quarter wavelength from the detuned position and the minimum
shifts rapidly with tuning.
In most 3-cm applications, the loss arising
from mismatch at the crystal has been kept below 1 db. In Fig. 3.35,
which applies to the 3<m 1B24 TR cavity, the standing-wave-ratio
limits that correspond to such a loss are – 3 db and +11 db. In a
narrow frequency band the spread need not be this great, but for the
wideband mixers covering a band 12 per cent wide, these limits were just
met using the crystals representative of the borderlines of the admittance
The ability of the tuning of the TR cavity to compensate for the
susceptance part of the load admittance has been used to reduce the
spread in transmission loss with various crystals over the required
In the course of measurement of admittance scatter of
frequency band.
large numbers of crystals in the 3-cm band, it was observed that the
scatter was not purely random about a center point but that it covered
an area longer in the susceptance direction than in the conductance
It is also found that the major direction of change of admittance with frequency is in the susceptance direction.
Because the mixers
were intended to be used with a tunable TR cavity and because the
standard tune-up procedure would be to tune for maximum received
signal, it was thought possible to use the TR cavity in combination
with the mixer to obtain a reduced resultant scatter for the combination.
Such a utilization of the TR cavity as partial tuning for the mixer has
been called” TR-aided tuning” and has been used in man y fixed-tuned 3-cm
mixers. To be most effective in reducing the admittance scatter at a fixed
wavelength, the effective electrical position of the TR cavity should be an
integral number of half wavelengths from the crystal.
This causes the
large susceptance scatter at the center line of the crystal mount to appear
as a susceptance scatter in the load admittance presented to the TR cavity.
That this should hold over the widest possible band requires the minimum
number of half wavelengths.
Consequently, most wideband mixers have
been made only one-half wavelength long from the position of the short
circuit with a detuned TR cavity to the center line of the crystal mount.
In this way it has been found possible to keep the loss caused by crystal
mismatch less than 1 db over the i 6 per cent band from 8500 Me/see to
9600 Me/see.
Iris-coupled coaxial-line mixers have been used in the 10-cm band in
conjunction with a TR cavity, and some advantages can be had through
the use of the TR-aided tuning principle.
The shape of the admittance
scatter found for 10-cm crystals does not show a decided elongation in one
direction, although there is a common direction of change of admittance
with frequency.
The actual direction of the change depends upon the
nature of the crystal mount as well as on the position in the mount at
It can be specified only for the unit
which the admittance is measured.
as a whole, and the best length of line between the coupling iris and the
crystal does not necessarily bear any integral relationship to a half wavelength.
The coupling iris loads the TR cavity with an admittance that
increases with increased height (along the lines of electric field in the cavity)
and with increased projection of the coaxial line into the cavity.
3.16. Mounts for 1N26 Crystals and a Waveguide Mixer for the
10-cm Band.-At
the end of this chapter is given a group of drawings of
several representative simple mixers. The coaxial-line mixers are all
designed for use with lN21A, IN21B, and 1N21C crystals, and the mixers
having a 1 by ~-in. waveguide for 1N23, 1N23A, and lhT23B crystals.
* a002
FIG.3.36.—1N26 crystal mounts.
(a) Turntable mounts; (b) crossbar mount.
Also included are a 1.25-cm mixer designed for operation with 1N26
coaxial-line crystals and a mixer having a similar structure designed for
lN21B crystals in the 10-cm band.
The design of the 1N26 crystal
mount for 1.25-cm operation is based on different principles from that
The 1N26 crystal was
of the two types described in p“revious sections.
designed to match a mount having particular properties at thk wavelength.
The crystal mount was, therefore, particularly easy to design.
The 1N26 is tested in a mount in which it terminates a coaxial line having
an inner conductor with a diameter of & in. and an outer conductor
with a diameter of ~ in. ID.
The mount is adjusted so that a matched
load on this coaxial line absorbs all the available power of the signal
It is, thus, necessary only to make a matched transformer to
transform from a waveguide 0.170 by 0.420 in. ID to a coaxial line of this
[SEC. 3.17
size with suitable provisions to bring out the i-f voltage and rectified
current. An average crystal unit will then terminate the waveguide in a
matched load.
Mounts of two different types or, more exactly, waveguide-to-coaxial
line transitions have been used for this purpose.
These are shown in
cross-section in Fig. 3.36 a and b. The type fabricated in ordinary
waveguide, with an adjustable plunger and screw, was adopted as standard
for testing purposes, with each unit pretuned.
The tuning adjustments
were fixed by wax, such that there was no reflection in the waveguide
The other
section, with a dummy matched load in the crystal socket.
unit, shown in Fig. 3.36b, is made from a solid block using a crossbarIn this way the
supported probe waveguide-to-coaxial-line
crossbar, with a choke a quarter wavelength from the side wall, is used to
bring out the low-frequency components.
The crossbar unit has been
used most extensively in system mixers because it fits conveniently into
complex mixers and because it is less frequency-sensitive than the other
A critical dimension on these lhT26 crystal mounts is the length of the
slotted center conductor from the shoulder in the outside conductor to
the end of the fingers. If it is too long it may strike a shoulder on the
center conductor of the crystal unit before the outer conductor of the
If it is too short, a considerable
crystal meets the shoulder in the mount.
length of the small-diameter center conductor of the crystal unit is left
exposed and this has a transforming effect on the crystal admittance.
The 10-cm mixer designed by the same principle as this crossbar
mount does not have the simplicity of being just a matched waveguideIt was developed to fill the need for a
to-coaxial-line transformer.
waveguide crystal mixer to be used with the wide bandpass fixed-tuned
TR cavity which has an output iris designed to couple to a matched
As in the 1.25-cm crossbar mount, the conduct3- by Ii-in. waveguide.
ance part of the admittance at the plane of the crossbar is controlled
primarily by the distance from the top of the waveguide to the crossbar.
The susceptance part is determined primarily by the distance from the
crossbar to the short circuit in the waveguide beyond the crossbar,
although the crystal itself projects into the waveguide.
A complete
mixer is made from this mount by the provision of the LO coupling
circuit on the opposite end of the crossbar from the end from which
the i-f signal is derived.
Several of these units having different crossbar
positions but basically the same circuit, have been designed to cover the
region from 8 to 11 cm, each covering a band about ~ 4 per cent in width.
3.17. Self-protection
of the Mixer Crystal.-Crystals
operated as
mixers in radar systems have been plagued with burnout caused by
insufficient protection from high-power signals by the TR switch.
this reason several special features have been adopted in an effort to
reduce the frequency of burnout in operating and nonoperating systems.
At the time when the flat power, lasting for the duration of the
transmitter pulse, was thought to be responsible for burnout, considerable
effort was made to include in the mixer design a feature called “selfprotection. ” This feature was based on two special properties of the
TR cavity and crystal mixer.
First, the TR tube, while firing, maintains
an essentially constant voltage across the arc, independent of the input
and output couplings.
The arc can therefore be considered as a constantvoltage generator having no internal impedance and the power delivered
by it to a load circuit is directly proportional to the load conductance.
The second property of the combination is that the crystal, since it is
a nonlinear device, shows a different admittance at high level than at low.
Because the TR leakage power is at a considerably, higher level than the
local-oscillator power in the mixer, the crystal maybe expected to show an
admittance considerably different from match and, therefore, the flat
leakage power of the TR cavity into the crystal may be considerably
different from that delivered to a matched load.
It could be either
greater or smaller depending upon the direction of change of the admittance as seen by the TR cavity.
In order to ensure that the leakage was
reduced by this admittance change, the admittance as a function of
power level was measured for many crystals.
The line length was then
chosen so that the conductance seen by the TR cavity decreased with
increasing power and a mixer designed in this way was said to have
During the early stages of the design of 3-cm mixers it was apparent
that there was something to be gained in low-level operation through the
use of TR-aided tuning described in Sec. 3.15.
This required a halfwavelength spacing between the TR cavity and the crystal.
Measurements of the change of admittance with power level showed that the
conductance at the center line of the crystal increased with increased
The two criteria for choice of the line length from the TR cavity
to the cryst,al were thus incompatible, since the half-wavelength spacing
resulted in the inverse to self-protection, because more power would be
delivered to the crystal than to a matched load. An investigation of the
magnitude of the effect, was therefore undertaken and it was found that
the crystal conductance for most units increased by about 30 per cent,
when the incident power k VC[was increased from 1 mw to 50 mw or more.
Beyond this level there ww i-cry little change.
With this amount of
change and if at least 50 mw oi leakage power is assumed, the power
delivered to the crystal woldd be about 80 per cent greater for the halfwavelength spacing than for a spacing equal to an odd number of quarter
At about this time it was learned that the spike energy was most
frequently responsible for burnout, and it was therefore apparent that the
dependence of the spike energy on the load admittance is more important.
A reliable determination of this dependence or of the effective admittance
It is
of the crystal as a function of spike energy has not been made.
felt, however, that the spike energy absorbed by the crystal is less
dependent on the admittance than is the flat power.
A serious burnout
problem has not been encountered in practice with the improved crystals
now available so long as the TR tube is in good condition and the keepalive electrode is functioning properly.
The low-level operation and
matching of the crystals have been used in almost all mixers to determine
the line length between the TR cavity and the crystal, at the sacrifice of
3.18. Harmonic Chokes and Shutters.—Another
source of crystal
burnout, especially in very-high-power radar systems (500 kw and up) is
leakage of harmonic frequencies and spurious intermittent Klgh-frequency
Since the cavities are usually heavily
radiation through the TR cavity.
capacitively loaded at the breakdown region, the lowest mode giving
unattenuated transmission with the arc firing is at a frequency two or
three times the fundamental frequency.
Frequencies this high and
higher are, however, generated in fairly large quantities, at least sufficient
to cause crystal burnout by high-powered transmitters.
For this reason,
some of the 10-cm coaxial-line mixers designed for operation with highpower systems include a filter circuit that strongly reflects the third
This filter consists of a pair of concentric-line cups on or in
the center conductor.
The cups are a quarter wavelength long at the
third harmonic (3 cm) and so spaced that the reflections at the fundaThese cups can be seen in
mental frequency cancel one another.
the iris-coupled coaxial-line mixer included in the group of drawings at
the end of this chapter.
The operation of the filter can be easily worked
out with the aid of an impedance chart. Because the reflections of the
two chokes cancel at the fundamental frequency, the effect they have on
the mixer is to produce a phase shift making the electrical length of the
line different from the physical length.
There is also some frequency
sensitivity of admittance added because their reflections cancel exactly
only at the frequency for which the electrical length of the line between
them is exactly right.
It has never been established conclusively that the incorporation of
these chokes ;reproves the protection of the crystals.
The frequent y
range in which they are highly effective in attenuating unwanted power
from the transmitter is very restricted.
In the course of design of a
particular high-powered 10-cm radar set, it was established that crystals
were being burned out by spurious high-frequency signals notwithstand-
SEC.3.18] “
Considerable effort wm expended
ing the reflection of the chokes.
in an attempt to eliminate these signals by alteration of the modulatorpulse shape, but the difficulty was not solved until a new type of gasdischarge cavity was added to the conventional TR switch.
additional cavity, known as a pre-TR switch, is simply a section of
waveguide with low-Q input and exit irises with glass windows.
cavity is filled with gas at a low pressure. When a transmitted signal
enters this cavity, the electrical breakdown that takes place is extensive
in volume and covers a large part of the input iris. ~Jndcr this condition,
it is effectively cut off for all frequencies in addition to the fundamental
frequency, although the funclamental-frequency leakage is still sufficient
to operate the conventional TR switch following it. A circuit of this
type is considerably more effective than harmonic chokes in bringing
about complete crystal protection and it is certainly the task of the
TR-cavity system and not the mixer to provide such protection from
high-level signals. The more rcccnt TR cavities having wide bandpass
characteristics, using several resonant irises as well as resonant input
and output windows, include protection of this kind. Harmonic chokes
are therefore superfluous for operation with such TR switches.
details of these two TR-switch systems and their functions will be found
discussed in vol. 14 of this series.
Another device often adclccl to the mixer in radar systems is a switch
for protection against signals coming into the antenna during inoperative
The TR cavity, when properly operating, protects the mixer
crystal from burnout not only by the signal of the local transmitter, but
also by any other signal coming iilto the antenna.
Any signal sufficiently strong to damage the crystal will cause the arc in the TR tube
to fire and, therefore, the signal power is limited to a safe level in the
mixer. Satisfactory operation of the TR switch, however, depends on
the universally used keep-alive electrode, which maintains a small steady
discharge in the gas volume of the tube, maintaining a small supply of
ions to initiate an arc when a large voltage is built up across the gap of
the cavity.
If this keep-alive arc is not operating, as it is not when the
supply voltage is shut off, the breakdown of the TR tube at high level
requires considerably greater voltage and time to occur, and the result
is that very large leakage energy is allowed.
Thus signals may be
transmitted through a TR cavity, in which the keep-alive electrode is
not activated, in sufficient strength to damage the mixer crystal.
is also possible that the first few pulses of the local transmitter, which
may occur before the keep-alive is fully operative, may damage the
For protection against these two sources of power, a mechanical
switch has sometimes been included in the mixer. The switch decouples
the mixer crystal from the TR cavity when the system is turned off,
and through the action of a magnetic solenoid or a motor the switch is
opened with a small time lag after the system is turnecl on.
Devices that are useful as switches for this purpose arc few. Many
structures can be coupled to a coaxial-line mixer or to a waveguide mixer
to reduce the signal arriving at the mixer crystal by 30 or 40 db.
Usually, however, it is found that the principal effect is one of detuning
and that the attenuation of signal po}ver at some adjacent frequency is not
many decibels greater than at the original frequency ~vith the structure
This is true, for instance, of a simple short-circuiting rod
between the inner and outer conductors of a coaxial-line mixer. Such
a rod has a large self-inductance and it acts like an inductive susceptance
across the line. Its effect can be resonated out by a susceptancc at the
TR cavity to a degree depending upon the electrical line length between
the short-circuiting rod and the TR cavity.
The most foolproof method of obtaining the required protection
during shutdown periods is to disconnect the crystal completely from
the circuit.
This has actually been done in some 10-cm coaxial-line
mixers by use of a structure like that shown in Fig, 337.
The smalldiameter rod is pulled back by a spring when the po~ver is turned off and
advanced into the fingers at the upper end by a solenoid when the power
is on. The gap between the fingers and the
end of the small rod is a waveguide beyond
o crystal
for the signal frequencies and, theremount
fore, a large attenuation is introduced if the
rod is retracted from the fingers by an
of the order of the diameter of the
coaxial line. The particular mixer in which
this mechanism was used possesses a rather
large standing-wave ratio, partly because of
the presence of lengths of line of differing
characteristic admittances.
As a c o ns e U+ ,Pulled clown to
disconnect crystal
quence, the admittance at the iris is freFIG. 3.37.—Crystaldiscon- quency-sensitive
and the mixer must be
nect mechanismin 10-cm irisretuned
is changed by 1 per
cent or more.
The tuning is provided
by making the coaxial line variable in length by a telescoping joint.
disconnect mechanism of this kind has not been applied to the wideband
mixer where the coaxial line must be of uniform impedance to avoid
large standing-wave ratios.
Figure 3.38 shows another mechanism that has been applied to
10-cm coaxial-line mixers.
A resonant stub a half wavelength long is
used to produce a short circuit across the mixer line. A short circuit
on the stub, actuated by a solenoid, makes it effectively a quarter-wave-
length stub when the system is operating.
It thus has little effect on
the circuit during operation, but during shutdown periods it is effective
in decoupling the crystal in a narrow frequency region for which the stub
produces a very large shunt admittance across the line. The systems in
which this device was used all operated inside a f 1 per cent band, and
the main protection they needed was from radiation in the same band.
The narrow band of large decoupling was therefore considered sufficient.
It does not give protection against power at other frequencies or against
damage by the local transmitter which sometimes occurs during the
first few transmitter pulses.
The most effective devices not involving an actual disconnection from
the crystal are sliding metallic shutters.
In 10-cm systems using TR
switches having external cavities, a metallic shutter macle from curved
thin phosphor bronze with two pieces spot-welded with their convex
surfaces together can be used. The shutter enters the cavity through
a slot in the side wall and slides in grooves in the top and bottom walls,
completely covering the output loop or iris. A drawing of this device
is shown in Fig. 3.39. A shutter of this kind gives very good protection
against radiation at all frequencies and has as its major disadvantage
the requirement of an operating device capable of moving it through a
large distance.
A shutter of the same kind is the most effective one for use in waveguide mixers and TR switches having integral cavities.
The shutter
enters a slot in the side wall (narrow dimension) of the waveguide between
the crystal and the TR cavity and slides in channels in the top and bottom
walls. It again requires a large motion since it must be all the way across
the waveguide when closed and completely removed when open. A
ratchet-relay motor has been used to operate such a shutter, although
it should also be possible to use a rotary motor with proper springs and
limit switches.
A simple post has been used as a shutter with fair success in the 3-cm
The post, sliding in a choke mount such as used for tuning screws,
enters the center of the wide side of the waveguide and crosses to the
bottom wall. At a given frequency, the post can be made to attenuate
most effectively when it projects just less than the full width, for it is
then resonant and completely short-circuits the waveguide.
For com-
better to make the post c’ontact
the bottom wall of the waveguide;
thereby it presents a large inductive susceptance across the wave-
increases with the post diameter,
and to minimize the danger of
resonance with the TR cavity a
spacing of one-quarter wavelength between the post and the effective
With a waveguide 1 by ~ in. OD in
position of the TR cavity is best.
the 3.13- to 3.53-cm band, a ~-in. -diameter post gives attenuation greater
than 30 db at all frequencies in the band.
3.19. I-f Output Admittance.-It
is not within the scope of this volume
to give a discussion of the circuit coupling the mixer crystal to the i-f
Such coupling circuits, however, must be designed with
knowledge of the admittance associated with the output terminals of
the mixer. The most widely used circuits are wideband doubled-tuned
admittance transformers, or their equivalent, designed to give the
best possible noise figure compatible with the bandwidth requirements.
The susceptance part of the mixer is a part of the first tuned circuit where
it is resonated in shunt.
Obviously, the circuit will be incorrectly tuned
if the susceutance
of the mixer is not the expected value and the noise
figure and bandpass characteristic suffer. The conductance part of the
mixer admittance determines the degree of coupling in the double-tuned
circuit and values smaller than the design value result in the doublepeaked frequency response characteristic of double-tuned circuits with
more than critical coupling.
It has been customary in the design of i-f amplifier input circuits to
mixer, that is, a mixer with a resistor replacing the
use a “dummy”
crystal and having the i-f resistance of an average crystal in the same
mixer under operating conditions, in place of an actual operative mixer.
Such a procedure is not strictly correct since the susceptance component
FrG.3-39.—Protectingshutterin a 10-cmTR
of the mixer is not that of the linear parts of the circuit if a resonant
As shown in
circuit is used ahead of the crystal in the r-f system.
Chap. 2, the reflection of the image frequency can change not only the
conductance part of the i-f admittance from the value obtained if the
image wave is not reflected, but also the susceptance part. This effect
with good crystals and with a 30-Mc/sec intermediate frequency can be
equivalent to adding or subtracting 3 or 4 ppf of capacitance at the output
terminals of the mixer.
Coupled with the fact that the conductance of
the crystal in the mixer may be from one-half to twice the value for the
same crystal in a nonresonant circuit, it is obvious that the i-f input
circuit must be designed on the basis of measurements on the particular
mixer to be used, with representative crystals and under operating
conditions at the frequency to be used.
FIG.3.40.—I-f admittance vs. LO frequency with the TR tuning fixed.
The situation is further complicated by the fact that the “phase
length” between the TR cavity and the crystal seems to vary from crystal
to crystal, especially for crystals made by dMerent manufacturers.
This means that, even at a fixed frequency, the i-f admittance may
vary more from crystal to crystal in a resonant mixer circuit than in the
nonresonant test mixers. For this reason, it becomes necessary to design
the input circuit in such a way that changes in conductance by a factor
of about 2, and in susceptance of about 2 ppf or more at 30 Me/see can be
When the mixer is to be used over a wide band, changes as
large as these are certain to occur, even with a single crystal, because of
the change in effective line length between the TR cavity and the crystal
and the consequent change in phase of the image-frequency reflection,
even though this effect is minimized by the choice of a line length as short
as possible.
Measurement of the i-f admittance of the mixer should
therefore be done at several frequencies scattered through the operating
band before the final form of the i-f input circuit is decided.
It was shown in the previous chapter that, if the signal-frequency
admittance connected to the input terminals of the mixer is kept matched
to the crystal and the image-frequency admittance is varied through the
full range of pure susceptance, the i-f admittance should traverse a circle
FIG.3.41.—Coaxial-line mixer with looP coupling to be used with TR cavity and IN’21A
or 1N21Bcrystalsin 10-cmband.
on an admittance chart, with a diameter related to the crystal loss.
Obviously, the effects described above are most serious with the best
It has been possible to make a receiver with optimum values, of
noise figure and bandpass characteristics by completely ignoring these
effects, with crystals having conversion losses of 10 db or more. As the
crystals improve it may become more important to design the mixer
on the basis of the i-f output characteristics than on the r-f matching
characteristics if, indeed, it is not so already with crystals having conversion losses of 5 db and less.
In order to minimize the effects of the variation of i-f admittance from
crystal to crystal and with frequency, it may be found that the line length
from the crystal to the TR cavity which gives an i-f admittance falling on
a particular part of the admittance circle may be preferred.
For instance,
the line length might be chosen in such a way that an average crystal at
FIQ.342. -Cross-sedional
view of loop-coupledmixer,
midband frequency gives an i-f admittance with the maximum conductance. Variation of frequency or of line length with different crystals,
would then result in a small variation in conductance, since the conductHowever, the largest
ance is stationary with respect to line length.
possible variation in susceptance results. The same would be true for a
line length giving minimum conductance, as a consideration of the circle
on an admittance diagram will show.
On the other hand, if a variation
in conductance is more tolerable than a variation in susceptance, the
line length can be chosen between these two values, where the susceptance
is stationary with small variation in line length, but has a value differing
There is also the desire for minifrom zero by the maximum amount.
mum possible crystal conversion loss to be considered, which may set a
different requirement on the phase of the image-frequency reflection.
In one instance in the author’s experience the variation in i-f output
admittance of a mixer with change of crystals and with frequency was
considered so serious that a makeshift remedy had to be applied to the
mixer to change its effective line length.
This mixer was a 10-cm iris-
FIG.3.43.—Mixer for lo-cm band for use with a IN21A or 1N21B crystal without a
TR cavity. The parts and dimensions are similar to those in Fig. 342. The signal
input line is supportedby a stub whichis behindthe LO couplingin the figure. The
distance from the center line of the center conductor connecting to the crystal to the short
circuit at the end of the stub is 1.000 in.
It was
coupled coaxial-line mixer used with selected low-loss crystals.
found that the line length was such that the maximum possible variation
m conductance occurred in the 8 per cent frequency band for which it was
The makeshift remedy was the insertion of a polystyrene
sleeve into the coaxial line of the mixer, in order to change the effective
length to one giving maximum conductance at midband frequency with
an average crystal.
With the iris-coupled mixer, the image is reflected
not by the TR cavity but by the short circuit in the coaxial line on the
other side of the iris from the crystal, which, in this instance, added an
extra half wavelength to the image-frequency
line. Since the crystal
was about one wavelength from the TR cavity, the total image-frequency
line length was large and the variation of admittance with frequency was
sufficient to make the susceptance change from minimum to maximum
in the 8 per cent band, after the sleeve was added.
This was less
serious than the previous large variation in conductance.
The proper
inssrtion of the coupling iris into the TR cavity had to be redetermined
50-ohm disk
F[~. 3.44.—Iris-coupIcd IN,XCU
for IN21B crystals in 8.O-to-8.8-cm band with TR cavity
sbowu in ltig. 3.45 (24–179).
after the addition of the SICCVCbecause of the effect of the sleeve on the
admittance presented by the crystal at the iris.
Figure 3.40 shotvs a qualitative picture of the result of an experiment
that was done in connection with the measurement of the variation of
i-f admittance with frequency.
IIcre many effects are obvious at one
time. The ‘H? cavity, determining the most sensitive signal frequency,
was fixed at a frequency at about the middle of the chart.
The i-f
admittance was then measured as the local-oscillator frequency was
The main effect observed is a variation of conductance in an
approximately sinusoidal fashion, except in the region of the two fre-
quencies that cliffer from the resonant frequent y of the TR cavity by j ust
the intermediate frequency.
In the example shown, these frequencies
occur near minimum conductance, and the conductance rises about half
way to the mean value at each of these frequencies.
Associated with
Ftc. 3.45.—Cavit y for 1B27 TR tube for S.6-to-S.S-cm hand and iris-coupled mixer. The
cavity is 1.400 in. ID and the mixer center line is 0.783 in. from the cavity center.
Detail of coupling.
adjustment screw
FIG.3.46.—A cross-sectional view of the u,ixer, SIWWNin Fig. 3.30 (24–126), for the
12 per cent band centered at 3.33 cm, for use with 1N23A or 1N23B crystal, 1B24 TR
tube, and 2K25 or 723 A/B local oscillator.
each is an excursion of the susceptance and its value passes through zero
in the opposite sense at each of the two frequencies.
These two frequencies are, of course, the two frequencies at which the local oscillator
could be set to obtain a receiver tuned to the frequency of the TR cavity,
and the line length and frequency of the TR cavity correspond to mini-
mum conductance variation and maximum susceptance variation with
Outside these two regions the susceptance is approximately
zero because of the compensating effect of the reflection by the TR cavity
The susceptance component appears when one of
of both sidebands.
the two sidebands is not completely reflected to the crystal by the TR
The excursion of the conductance is about twice what it would
FIG. 3.47.—Cross.section.al view of mixer for 3.2 cm, with channel for LO coupling.
This mixer is used with 1N23A and 1N23B crystals, no TR cavity, and 2K25 LO tube in
the 70-volt mode.
be if the TR cavity were kept at a frequency differing from that of the
local oscillator by the intermediate frequency and the two were tuned
This figure is given only as a sample of the possible variation
of the i-f admittance.
The effects for various line lengths can be estimated with the aid of the linear network representation of the mixer
and an admittance chart,
3.20. The Completed Mixer.-There
follows a set of drav’ings,
Figs. 3.41 to 3.52 inclusive, giving important dimensions of each of
several mixers representing applications of the foregoing circuits.
each drawing is indicated the type of crystals and the wavelength band
for which it is intended.
Those units intended for use in conjunction
with a TR cavity and those which operate directly from a wideband
antenna are identified.
For the ins-coupled 8..$cm mixer, the position
FIG. 3.4S.—Mixer for use in the 1.23-to-1,27-cm band. This mixer is used with the
1B26 TR tube, IN26 crystals, and 2K33 or 2K50 LO tube.
of the iris in the TR cavity is an important detail, since it determines
the tuning condition.
A separate drawing of the part of the TR cavity
for a 1B27 tube in which the mixer is to be mounted is included among
the drawings.
A drawing has also been included of a tunable resonant mixer known
as a “ pot” mixer. This is the only available example of a resonant
400 @q
De[all of coupling adjustment screw
FIG.3.49.—Cross-sectional view of the mixer of Fig. 3.48 (24-181).
mixer. It was used in ve-y early radar systems but was soon discarded
in favor of the simpler fixed-tuned mixers. The resonant feature is
Fm. 3.50.—Tunzble resonant mixer for 10-cm band,
unnecessary in a radar system since it already includes a cavity filter in
the fo~m of the TR, cavity.
The tuning procedure with a tunable TR
cavity and a tunsble mixer is very complicated, because these two
3?$s,&51.-Waveguide mixer for f 4 per cent b%micenteredat 10.7 cm; for use with
lNzIB crystals,2X28 LO tube. A resonrmtTF+tube is not mqired.
devices cannot be tuned independently.
A tunable resonant mixer may
be useful in other applications, however, and for this reason the drawing
has been included.
It is often desirable to have, in a radar system, a mixer that serves
several purposes in addition to the principal one of converting the
received reflected signal of the transmitter into the intermediate fre
Some of these functions are peculiar to radar systems and their
operational applications and are of little interest to the designer of mixers
for other purposes.
Since, however, a very large part of the task of
mixer design has been concerned with the problems associated with
these multiple-function mixers, anc[ since it is probable that similar needs
will exist inmany future mixers, a description of these problems and their
As is true for the simple mixer,
solutions will be given in this chapter.
there is no unique solution to a given design problem.
The material
given can only serve to show what has been done and to point out some
of the relative merits of various solutions.
4-1. The Beacon Problem.—An
example of the kind of device
described by the term “multiple function mixer, ” is the mixer with the
beacon feature for airborne radar systems.
In conjunction with the use
of radar as a navigational aid, a system of coded-pulse beacons has been
set up. A switch in the airborne radar changes the system from a radar
system to a system which sends out pulses of the proper characteristics to
trigger a response from a beacon transmitter.
The beacon response
comes back to the airborne radar after a time determined, in the same
way as for a radar echo, by the distance to the beacon, and at an azimuth
that shows the direction of the beacon with respect to the heading of the
The beacon feature requires of the receiver the same general
things as does the radar system, except that the beacon frequency is
For instance,
usually different from that of the radar transmitter.
most airborne radars for the 3-cm band operate anywhere in a frequency
band from 9320 to 9430 Me/see, the precise frequency depending upon
the particular transmitter tube used. The beacon receiver responds to
this whole band of frequencies but its transmitter replies at 9310 Mc/sec—
outside the band—to reduce confusion between echoes and beacon signals.
Thus it is required that the switch that turns on the beacon feature
change the tuning of the receiver from the local transmitter frequency to
9310 Me/see.
A similar arrangement is usedin airborne radar for the
9-cm band.
To accomplish the change in rccciver frequency, it is necessary to
In the 9-cm systems that have
alter the local-oscillator frequency.
2K28 local-oscillator tubes with external cavities this is accomplished
through the use of a switch-actuatccf solenoid that changes the position of
When the system is
a tuning plug in the cavity by the correct amount.
correctly tuned, the limiting positions of this plug are so adjusted that
the local oscillator is at the right frcqucnc y to receive the radar signal
at one limit and the beacon signal at the other. To minimize the amount
of tuning required of the plug, the local oscillator can be operated on the
low-frequency side of the transmitter frequency and on the high-frequency side of the beacon frequency, if the beacon is just outside the band
on the low-frequency side. With this choice of sidebands, however, there is
danger of interference between the beacon and the radars at the lowfrequency end of the band because, if the local oscillator is tuned for
beacon reception, the image frequent y of the receiver is in the radar band.
Because of the danger of such confusion it was at first considered necessary to tune the local oscillator to the low-frequency side of the beacon.
The difficulty of making a tuning plug that would give such a large range
was, however, very great.
With tubes of the 723A/B, 2K25, and 726 types, in which the cavity
is an integral part of the tube, a tuning plug cannot be used. In radar
sets in which these tubes are used—not abl y the 3.2-cm airbornes ystems—
two separate local-oscillator tubes and coupling circuits are therefore
provided for each mixer. The tubes are tuned, respectively, to the
proper frequencies to receive echoes or beacon signals, and the radarto-beacon switch turns one off and the other on. One of these oscillators is called the radar LO and the other the beacon LO. When the
723A tube was coupled to the mixer by the insertion of its antenna an
adjustable amount into the mixer waveguide, an odd number of quarter
wavelengths away from the effective position of the TR cavity, the
provision for the beacon feature could be made easily. All that was
necessary was to drill another hole in the same side of the waveguide or
in the opposite side and use a second adjustable tube mount.
the oscillators did not operate well in this kind of coupling circuit, and
because provision for radar and beacon automatic frequency control
(AFC) demanded more complex arrangements, such mixers are completely obsolete.
Instead, the coupling circuits described in Chap. 3
have become more extensively applied.
4.2. Single-channel
source of loss of performance of a radar system is the mistuning of the
receiver resulting in a less-than-maximum
sensitivity to echo signals.
As shown in Chap. 1, the requirement of frequency stability of the local
It has
oscillator in the supe rheterod yne receiver is very stringent.
consequently been found almost impossible to obtain as good results from
a radar system in which the local oscillator is tuned manually as from
As a consequence, all recent
one in which it is tuned automatically.
radar systems include automatic frequency control of the local oscillator.
This not only removes the frequency-stability
requirement from the
local oscillator but ensures that the oscillator wilf maintain the i-f difference from the transmitter frequency, even if the transmitter drifts. A
detailed discussion of the various electronic control circuits is given in
Chap. 7, and it is the task of the present section to present the details of
the special microwave components that are used in conjunction with
these circuits.
The simplest AFC circuit is one which branches from the i-f amplifier
after two or three stages of amplification, where such a branch has a
negligible effect on the receiver noise figure. Since the TR cavity does
not give complete elimination of the transmitted signal, an i-f beat is
produced between the local oscillator and the leakage signal from the
TR cavity.
This beat-frequency can be used to actuate the frequencycontrol circuits.
A circuit of this type was used in some of the first radar
sets having AFC but it has never been found satisfactory for fieldoperated sets. There are several possible reasons for this, no one of
which has been isolated as the prime source of trouble and eliminated.
They all stem from the facts that it is impossible to control the power
level of the leakage signal from the TR cavity, and that this leakage
signal does not necessarily have the same frequency spectmm as the
main transmitter signal. The leakage signal has a power level, at the
mixer crystal, at least 10 and sometimes 100 times the power level of
the local oscillator.
As a result, the mixer is operated at a level far
There is also the spike energy, of
above that for which it was designed.
very large amplitude but short duration, which definitely gives the TR
leakage signal a frequency spectrum different from that of the true
transmitter pulse.
In addition, spurious transmitter frequencies, which
may include a very small fraction of the energy in the main pulse, may
be transmitted through the fired TR switch to the mixer with the same
amplitude as the main pulse and the AFC circuit may lock to such a signal
instead of to the correct one.
Another argument against this simple khd of AFC is its susceptibility to interference signals. A signal, from an external source, just
large enough to overload the mixer crystal would produce an i-f signal
of about the same amplitude as produced by the transmitter.
It is
therefore conceivable that such a signal could compete for control of the
local oscillator.
Schemes involving the use of time-selective gates,
synchronized with the transmitter pulse, have been suggested to eliminate
this difficulty by making the frequency-control
circuit sensitive only
Because of other difficulties involved
during the period of transmission.
in their use, however, gated systems have not been widely employed.
The net conclusion drawn from experience with the simple AFC scheme
is that a particular radar system with a given set of components-transmitter tube, local-oscillator tube, TR tube and crystal-can
be adjusted
so that it will operate satisfactorily, but that the adjustment is not
permanent and the system requires frequent readjustment to remain
A change of any one of the components involved may
require readjustments of the circuit to eliminate spurious output voltages
from the control circuit.
The device, therefore, does not stand up well
under field conditions.
4.3. Separate-mixer AFC.—AS an alternative to the use of the AFC
system just described a completely separate mixer may be provided for
the AFC circuit.
The input signal is derived from the main transmitter
signal by way of a path having high attenuation but containing no
The input signal obtained in this way has amplitude
nonlinear elements.
and frequency characteristics that are identical with those of the transmitted pulse. The local oscillator must be the same one that is used
for the radar mixer, since it is the frequency of this oscillator that must be
The AFC circuit following the mixer is thus completely
separate from the receiver circuit and can therefore have different
All the objections to the singlebandpass characteristics if necessary.
channel system are eliminated by this scheme, provided that signals
from the TR switch in the radar mixer do not leak by way of the localoscillator path, into the AFC mixer. L’nder this condition, the amplitude
of the transmitter signal in the mixer can be set at the most desirable
level by choice of the attenuation used. The danger of losing control
to a jamming signal is eliminated because any signal in the main line of
the system suffers the same attenuation as does the transmitter signal.
A jamming signal, to cause any trouble, would have to be of about the
same strength as that of the local-transmitter signal, which is obviously
The major problem of the separate-channel-AFC
system is to operate
two similar mixers from a single local oscillator, with as large an-attenuation as possible between the signal circuits of the two mixers by way of
the local oscillator.
In addition, the signal-coupling circuit for the AFC
mixer must be designed to give the required signal level over whatever
frequency band is to be used. l~lth regard to the problem of kwaloscillator coupling, it is immediately apparent that the branching to the
two circuits must occur on the local-oscillator side of the mixer-to-LO coupling circuits, since then a signal leaking from one mixer to the other must
The percentage of leakage signal
suffer the coupling attenuation twice.
~eaching the local-oscillator circuit is the same as the percentage of
the available LO power coupled to the crystal.
From the local-oscillator
circuit to the second mixer, the leakage signal suffers the same attenuation as does the LO power.
Thus it is advantageous to have a local
oscillator with a large available power, coupled to the crystal through
a large amount of attenuation.
In the 10-em region where coaxial-line mixers are usecj, coupled to the
local oscillator by means of cables, the double-mixer scheme is provided
through the use of two simple mixers connected by separate cables to
separate pickup loops in the local-oscillator cavity.
Each of the loops is
tightly coupled to the cavity so that sufficient power is incident in the
tine of
Lme ~ In
AFC m!xer
FIG.4. I.—Block diagram of r-f circuit for separate-channel radar and AFC coaxial line
(a) Double-loop LO coupling; (b) single-loop LO coupling.
LO injection circuit of each mixer to allow reasonably weak coupling.
The attenuation between the two signal circuits, known as the “ cross”
attenuation, is increased because the signal must travel between the
Since the cavity is resonant at the localloops in the oscillator cavity.
oscillator frequency, which differs from the signal frequency by the
intermediate frequency, there is some reflection of the signal and a
If oscillator tubes having
consequent increase in cross attenuation.
only a single output line (such as tubes of the 726 type), are used, the
two mixers must be connected by a branched line or T-junction.
effect of the detuned local oscillator can be obtained through the choice
of the line length between the local oscillator and the T-junction.
this length is so chosen that the line into the local oscillator acts as a
stub when the local oscillator is detuned, the maximum
attenuation is obtained.
With tubes such as those of the 726 type,
the proper length of this line varies greatly with frequency because of the
relatively long line included in the tube.
Consequently, the amount of
attenuation gained over a frequency band of several per cent is small and
perhaps not worth the effort of determining the best line length.
Singleloop T-jmnctions have been used with cavity oscillators such as the 2K28.
For these oscillators the effective stub-line length can be made only
one-half wavelength and the attenuation gained is therefore large. A
block diagram illllstrating these two connections is given in Fig. 4. la and
b. Figure 4.2 shows the added cross attenuation due to reflection at the
T-junction as a function of frequency.
It has been assumed here that
the admittance of the stub line
ending in the loop has the frequency
30 dependence of a half-wavelength
short-circuited line, and that the
“: 20
local-oscillator cavity is completely
nonresonant at the signal frequency.
The reflection coefficient for a wave
# 10
traveling toward the cavity in this
line is therefore unity.
The line is
made to be resonant at the midband
wavelength, and the curve shows
FIC. 4. 2.—Added cross-attenuation due
the reflection loss as a function of
to reflection at T-junction vs. relative frethe ratio of the actual signal frequency, with half-wavelength line between
the T-junction and the local-oscillator
quency to this midband frequency.
In practice, somewhat less attenucavitY”
For a longer
ation than this ~~illbe achieved, especially near resonance.
line, such as would result ~~ith a tube of the 726 type, the frequency
scale may be changed by the appropriate factor.
It is important, when trying to supply two mixers with local-oscillator
power from a single oscillator, that the standing-wave ratio in the localoscillator cables be small. This can be accomplished through the use of
attenuating cables or by means of the resistor-disk terminations in the
local-oscillator circuits of the mixers, as described in Chap. 3. The
splitting of the power between the two circuits at the T-junction is
determined by the admittances which appear in parallel.
If a large
standing-wave ratio existed in the lines between the mixers and junction,
a large conductance could result for one line and a small one for the other,
with the result that one mixer would receive almost all of the available
local-oscillator power, and the other almost none. With a situation
giving equal splitting of the power, about 20 mw of power may be sent
to each mixer. Since each crystal requires about 0.5 mw of localoscillator drive, the attenuation between the mixer circuit and the localoscillator circuit is about 16 db. Thus the cross attenuation, neglecting
[SEC. 44
the contribution of the power-splitting circuit, is about 32 db.
If the
amount of TR leakage power is 50 mw, the signal that it produces in
the AFC mixer is, therefore, reduced to about 0.03 mw. Since the AF~
signal is set at about 2 mw, it exceeds the spurious signal from the TR
switch by at least 18 db. A larger safety factor than this is to be desired,
and the additional attenuation by the LO cavity or by the T-junction
is helpful.
4.4. The Coupling of the Transmitter Sample .—The sample of transmitted power that constitutes the signal in the AFC mixer is usually
coupled through a “ cutoff” attenuator to the mixer.
This consists of a
circular pipe of too small a diameter to allow unattenuated propagation
of the wave in question.
The coupling of this attenuator to the main
transmitter waveguide or coaxial line is accomplished by means of a hole
in the wall of that line; the coupling to the mixer is done by the conventional loop or iris. The action of the cutoff attenuator may be analyzed
in the following way.
The wave traveling along any waveguide is
described by the relation
E = Eoe–~(”t–k’),
where u is 27rtimes the frequency, ~ is the amplitude at the point x and
The quantity k is the
at the time t and EO is the maximum amplitude.
wave number and is equal to 27r/A0, where Ar is the wavelength in the
This is
~ =22
A. r
h. ‘_l
where 1, is the cutoff wavelength of the waveguide and XOis the free-space
Thus, the wave is described by
wavelength of the wave in question.
times the term in the time.
For wavelengths longer than the cutoff
wavelength, the quantity in the radical is negative and the ~vave does not
propagate in the ordinary sense. Equation (1) can then be written in
the form
E = EOe
showing that an exponential decrease in amplitude occurs for a wavelength longer than the cutoff value.
The ratio E~/E2 is the power
attenuation between points that are z centimeters apart in the waveguide,
if k. is expressed in centimeters.
Written in decibels, this attenuation is
For a guide of circular cross section, the cutoff wavelength of the lowest
mode is 1.71 times the diameter.
A .yJ,
If the diameter is small compared with the wavelength, the attenuation
This is a desirable property for an
is independent of the wavelength.
AFC mixer that is to be used over a wide band.
For diameters this small,
the attenuation is just 31.9 db per diameter.
The amount of attenuation needed is the ratio of the transmitted
power to the signal level desired in the mixer. For a 500-kw system and
2 mw in the mixer this is 2.5 X 106, or 84 db. It is not possible to use an
attenuator pipe giving 84 db in its length, however, because the coupling
factors between the main waveguide and the attenuator and between the
attenuator and the loop of the mixer must be taken into account.
this reason the attenuator should be designed for an attenuation about
30 db less than the total, to allow a large decoupling factor, so that the
reflection of the main signal in the transmitter line of the system will be
small. It is difficult to calculate the end effects and the final design of
the attenuator is best found experimentally.
One tentative unit can
be built and tested and then corrected, by means of Eq. (2), to give the
right power level at the mixer crystal.
A serious shortcoming of the cutoff attenuator in this application is
that it has no attenuation at wavelengths shorter than its cutoff wavelength.
In a particular example a cutoff attenuator was used that did
not transmit frequencies as high as the sixth harmonic but transmitted
the seventh and higher. It was found that trouble with the AFC circuit
was attributable to the presence of signals in this high-frequency range
in the mixer. The system operated at 10 cm but a large signal could be
detected in a crystal mounted in a 1.25-cm waveguide (O.170 by 0.420 in.
ID) of sufficient length to attenuate the 10-cm signal to a negligible level
when that waveguide was held in the position of the AFC mixer at the
It might be argued that an attenuoutput iris of the cutoff attenuator.
ator of smaller diameter would be the solution, but just how much smaller
It was thought better
it would have to be would be a difficult question.
to add to the cutoff attenuator a device that would have increasing attenuA satisfactory device of this kind was
ation with increasing frequency.
found in the form of a sheet of carbon-coated Bakelite resistance card of
500 ohms per square.
The card was cut into a rectangle of a width equal
to the diameter of the attenuator and a length about a quarter-inch less
than the distance from the waveguide end of the attenuator to the loop
of the mixer. When this sheet was inserted into the attenuator so that
its plane was in the plane of the electric field vector in the attenuator,
the high-frequency transmission was reduced well below the point of
being troublesome.
The attenuation of the power at the fundamental
frequency was affected very little and the specific resistance of the strip
was found to be of little importance to its efficiency in attenuating the
All attenuators subsequently
contained dissipative attenuators as a precaution against trouble with
high frequencies,
For the 3-cm band a short cylinder of polyiron,
inserted into the attenuator, is found to be more effective than the
resistive sheet. At 1.25 cm, a matched polyiron attenuator in the mixer
This polyiron
waveguide is used in addition to the cutoff attenuator.
attenuator is designed to give an attenuation of 20 db at the fundamental
It is used also to reduce the leakage of transmitter signal into
the AFC mixer at the joint between the cutoff attenuator and the mixer
Side wall of
FIQ. 43.—C0upliag
attenuator for AFC, used ju 10-cm, 500- to 1000-kw wavegujde
Because the polyiron pad is matched into the waveguide
from both directions, it also provides a matched generator for the AFC
signal at the mixer crystal.
The direct use of the cutoff attenuator, on
the other hand, provides essentially a constant-voltage
generator, with
the result that the power level at the mixer crystal is strongly dependent
on the crystal admittance.
The matched resistive attenuator, however,
cannot be used with a mixer having an LO coupling circuit that requires
reflect ion of the local-oscillator wave that travels toward the signal line.
Mixers intended for use with a narrow-band TR switch, therefore, cannot
be used with such an attenuator.
Figure 4.3 shows an attenuator used to derive the AFC signal in a
lo-cm, 500-kw waveguide system.
The attenuator can be coupled on
either the wide or the narrow side of the waveguide, but on the wide
side it must be in the center.
A loop-coupled mixer (see Fig. 3.40) is
mounted on the other end of the attenuator and the plane of the loop is
the same as the plane of the resistance strip and the electric field vector
in the attenuator.
445. Two-channel
for All-waveguide
1.25-cm and the 3.13- to 3.53-cm bands, where the local oscillator must be
coupled to the mixer through waveguide, the two-channel mixer is made in
a single unit. By means of the coupling circuit of the channel or iris type
described in Sec. 3.5, one mixer is coupled on each side of the localoscillator waveguide.
Figures 4.4 and 4.5 show the most commonly
used mixers employing these principles in the two bands mentioned.
All indicated dimensions are equivalent electrical lengths and must be
corrected for end effects, as discussed in the preceding chapter.
entire 1.25-cm mixer, including the coupling chokes, is machined from a
solid brass block.
Figure 4.5 shows the 20-db polyiron attenuator just
TR cavi
FIG. 44.- –Two-channel
matched load
mixer for use iu the 3.3.cm wavelength band,
described, in place in the AFC mixer. The coupling to the main waveguide is through a small hole in the wall at the end of the waveguide
running from the main guide to the mixer, and the size of the hole is
chosen to give the required total attenuation between the transmitter
and the AFC mixer crystal.
Because it would be very difficult to make the duplexer and .mixer to
such close tolerances that both the radar mixer and the AFC mixer could
be rigidly connectcc! to the duplcxcr, these t~vo pieces have been so
designed that one limit of the tolerances brings both channels into contact
with their corresponding members on the duplexer and the other limit
leaves a gap on the AF~ side. The only danger this entails is that of
leakage of signal into the AFC mixer from the outside.
As has been
mentioned, the dissipative attenuator in the 1.25-cm mixer reduces that
In the 3.3-cm mixer, this difficulty is eliminated by the inclusion
of the cutoff attenuator as a part of the mixer rather than as a part of the
In both these mixers a resistance strip is used as a matched load in
This strip has an effect analogous to
the local-oscillator waveguide.
that of the resistor disk used in the coaxial-line mixers. It has a conductance equal to the characteristic admittance of the waveguide plus a
capacitive susceptance due to the dielectric constant of the Bakelite
base. This susceptance is resonated out by short-circuiting the waveguide less than a quarter wavelength behind the strip. The specific
FIG. 45,-Persl,ective
view of 1.25-cm two.clLannel ~,,ixer,opcr,ed to show inside.
resistance used at 3,3 cm is 500 ohms prr square and the distance from the
back of the strip to the end wall is 0.265 in, In the 1,25-cm lvaveguide a
400-ohm-pcr-square material and a distance of 0.048 in. gives the best
These terminations arc very compact and simple to construct,
and give a degree of match and a handJ~idth adequate for the purposes
used here. The voltage standing-~vave ratio obtained in this way is less
than 1.10 at midband and remains under 1.4 over a band of plus or minus
5 per cent.
The reflection produced in the local-oscillator ]!-aveguide by the two
coupling devices is more serious than that produced by one. In the
3.3-cm example the coupling iris on one side has been operated with a
fixed post so that it is beyond resonance with the adjustment screw
removed, ashasbeen discussed in Sec. 3.5. With the other ins operated
as an inductive susceptance, the reflections from the two irises tend to
compensate each other. In the 1.25-cm example noserious trouble was
caused by the reflections by the coupling channels, but the reflection
could be reduced, if necessary, by placing the two channels a quarter
wavelength apart on the local-oscillator waveguide.
This would require,
however, that the mixer be asymmetrical.
The coupling channels used
at 1.25 cm are different from those discussed in Sec. 3“5 in that they are
An equivalent
connected to the mixer waveguide behind the crystals.
network for this junction has been worked out by Schwinger’s method
and may be found in J“ol. 10 of this series. Coupling of this type gives
less freedom than the symmetrical couplers between the crystal and the
TR cavity because the spacing between the crystal and the TR cavity
must be so chosen that the reflection of the local-oscillator ~J-aveby the
TR cavity does not produce a voltage node at the position of the crossbar
transition to the crystal.
All the other details of the mixers, such as the crystal mounts, the
methods of bringing out the beat frequency, and the method of adjusting
the local-oscillator coupling have been discussed in chap. 3. More
detailed dimensional drawings of these mixers will be found in the group
The cross attenuation
of drawings at the end of the present chapter.
achieved with these mixers is determined, as in the 10-cm example, by the
available local-oscillator power and, in decibels, is about twice the attenuation between the local oscillator and a single crystal.
Measurement on
the 3.3-cm mixer with a 2K25 local-oscillator tube shows that a cross
attenuation of at least 30 db can be obtained at all wavelengths in the
3.13- to 3.53-cm band.
4.6. A Mixer Employing Directional Couplers.—A mixer with greater
cross attenuation, if needed, could be made using the directional-coupler
A sketch of a mixer of this kind is shown in Fig. 46.
The TR
leakage power that reaches the local-oscillator waveguide travels toward
the dummy load, and only that which is reflected by the load passes
the directional coupler that leads to the AFC mixer. The TR leakage
power that is coupled into the AFC mixer, therefore, travels toward the
AFC attenuator and, since a matched dissipative attenuator is used,
none of this power arrives at the AFC crystal.
There is a reflection of
TR leakage power by the radar mixer crystal and some of this is coupled
into the AFC mixer waveguide, but this also travels toward the attenuator and not toward the crystal.
The only coupling between the TR
leakage signal and the AFC mixer crystal is by reflection of the wave
reflected by the radar crystal from the local-oscillator
Since the local-oscillator attenuator must have a small attenuation (only
sufficient to give the required adjustment range) the reflection may be
large. Thus, the cross attenuation is the attenuation of the two directional couplers plus an amount dependent on the reflection coefficient of
the mixer crystal at the level of the TR leakage power and on the reflection coefficient of the local oscillator and attenuator.
No mixers of this
type have been used because the simpler ones seem to have sufficient
cross attenuation with most oscillator tubes.
This mixer would be difficult to fit into the space available in the usual duplexing system.
part of AFC
TR switch
FIQ. 4.6.—Two-channe1 mixer with directional coupler, for Iarge cross attenuation.
much better two-channel mixer, which can be used with a local oscillator
of limited output power, will be described in Chap. 6.
In all of the mixer designs so far presented, provision has been made
for a very definite kind of load admittance at the local-oscillator tube.
Before proceeding with the discussion of multiple-function
mixers, the
behavior of local oscillators, as a function of the load admittance presented to them, will be qualitatively described.
From this discussion it
should become evident that the provision of a definite load admittance
for the local oscillator is a very important part of the design of a microwave
mixer. Previous to the general recognition of this fact, many
mixers were designed without such provisions (the coupling obtained
by varying the antenna insertion of the 723A/13 tube is an example),
and their operation in field radar systems was anything but trouble-free.
For the separate beacon local oscillator in one mixer, for example, a
special selection of oscillator tubes was required, since only a small
percentage of otherwise perfect tubes would operate properly in the circuit. The property of the tube which governed its proper operation
in the circuit was not included in the tube specifications.
It was there-
fore possible to design a circuit in which all tubes of a given type would
operate at the time of the circuit design, but in which later samples of the
same type of tube might be unsatisfactory.
4.7. The Rieke Diagram.-In
order to decide upon an output load
for any kind of self-excited oscillator, it is helpful to plot a “ Rieke
diagram” of the tube. This is done by measuring the oscillator power
and frequency as a function of the load admittance presented at some
point in the output circuit of the oscillator.
A plot of these data, in the
form of contours of constant power and contours of constant frequency,
on a Smith admittance diagram is called the Rieke diagram for the tube.
Suppose that the oscillator may be represented as the shunt-tuned
tank circuit of Fig. 47.
For a simple reflex klystron, this tank circuit is
The voltage built up across the
the cavity resonator of the oscillator.
From this repreresonator is not independent of the load admittance.
sentation, however, it is obvious
Oscillator tank circuit
that the power delivered to the
load must depend upon the conI
ductance of the load and must go
to zero if that conductance goes to Oscillator !
9~ ~
voltage I
zero, because of the presence of
the shunt conductance g. resultI
ing from resistive losses of the
L ----J
----If the load conductance
FIG.4. 7.—Circuit representing oscillator tank
increases unduly, the oscillator
circuit and load admittance.
may become overloaded to such an
extent that the power circulating in the tank circuit is insufficient to
maintain the oscillation through the feedback circuit and the oscillations
cease. Thus, there must be a load conductance that gives a maximum
of power delivered.
The susceptance component of the load admittance, on the other
hand, adds to the susceptance of the tank circuit.
If the susceptance
of the load varies slowly with frequency, a change in its value causes the
oscillator frequency to change until the tank circuit contributes a susThis is because the feedback
ceptance that cancels the load susceptance.
efficiency is greatest at the frequency of zero total susceptance, and the
voltage built up across the tank circuit is therefore largest at this freIt is now apparent that plots of contours of constant delivered
power and contours of constant frequency against the load admittance,
as measured in the tank circuit, would resemble Fig. 4.8. The contours
of constant power are circles of constant conductance and the contours of
The amount
constant frequency are the circles of constant susceptance.
of frequency change per unit susceptance depends upon the Q of the
The “ pulling figure” for the tube—
resonant cavity of the oscillator.
that is, the maximum frequency change when a load admittance causing
a voltage standing-wave ratio of 1.5 is varied through all phases—is
These relationships are not the
closely related to the Q of the resonator.
subjects of the present discussion; for a detailed discussion of the Rieke
diagram, the reader is referred to vol. 7 of this series. The important
region for the present purposes is the circular region of the diagram,
called the “ sink, ” in which the oscillator does not operate at all. Load
admittances that fall in this region must be avoided if the oscillator is to
be expected to operate.
4.8.—Riekc diagram for ideal oscillator. Curves of constant power are labeled rn
percentages of maximum power available.
The discussion so far has been concerned with the load admittance as
measured at the tube itself.
In practice there is some kind of output
coupling circuit and, therefore, the admittances that can actually be
measured are those at some point “in the output line. Since the electrical
distance between this point and a reference point within the tube varies
with frequency, the actual Rieke diagram is a distorted version of that
shown in Fig. 4.8. The fact that the coupling circuit cannot be completely nondissipative limits the range of admittances presehted to the
tube when the whole complex plane is covered at the point of measurement. As a result, the contours of constant power do not follow the
circles and do not close in the regions of large
Moreover, the region of the sink does not remain circular.
The contours of constant frequency are no longer the circles of constant
susceptance, but qualitatively they retain the property of being orthogonal to the contours of constant power. An actual Rleke diagram for
The admittance plotted is that
a 2K25 oscillator is shown in Fig. 49.
measured in the waveguide of a standard test mount, at the plane of
the antenna of the. 2K25.
The Rieke diagram for the 2K25 oscillator changes rapidly with the
“matched load” frequent y of the tube.
This change can be accounted
for by the relatively long length of the output coupling line between the
tube cavity and the point in the waveguide at which the admittances are
FIG. 4.9.—ltickc diagram for a 2K25 oscillator.
The electrical length of this line varies with wavelength
and, as a result, the Itickc diagram rotates cm the admittance chart as the
wavelength is altered.
If a matchwl load on the waveguicle does not
result in unity standing-wave ratio in the coaxial output line there is
also a radial shift of the diagram with wavelength.
Two things become
apparent from this consideration.
First, a given load admittance must
not be crossed by the sink for any wavelength in the band to be used.
Second, if the rotation cncountcrcd over the band bccomcs as much as
one-half wavelength, the only safe region for the load admittance is
very near the center of the diagram, provided there is not cxccssivc
translation of the diagram with wavelength.
The specification test of
the 2K25 ensures that the sink does not overlap the portion of the diagram which represents the matched-load condition of the mount when the
tube is operated in a mount identical with the test mount, because the
tube must operate continuously in this mount from one end of its tuning
range to the other. Thus, it is evident that the only load admittance
that is safe to use in mixer design is that presented by the test mount.
When the output coupiing circuit is not a part of the oscillator tube,
For a given
as is true for the lo-cm 2K28, the situation is different.
frequency the output coupling loop can be adjusted to give the required
output power, up to the maximum power obtainable from the tube.
If the loading is increased beyond the value for maximum power, the
conductance may be in the region of the sink. If, however, the output
line is several wavelengths long and there is a large standing-wave
ratio in the line, the load admittance presented by a given output-loop
adjustment changes rapidly with wavelength and a good acljust ment at
one wavelength may easily result in overload at an adjacent wavelength,
This is a good argument for the resistor-disk matched load provided in
the LO coupling circuit of the 10-cm coaxial-line mixers.
A more careful consideration of the Rieke diagram of the transmitting
oscillator is necessary, since the pulling figure is of considerable significance.
The output circuit is designed on the basis of a compromise
between pulling figure and delivered power; hcncc, some~rhat less than the
For local-oscillator applications
maximum available power is obtained.
the pulling figure is not of the same importance, although it must be
considered under some conditions.
It should be pointed out that the Rieke diagram of a reflex-klystron
oscillator is not independent of the reflector mode in ~rhich the tube is
Usually the sink covers a larger region on the diagram as the
reflector voltage is incrcasccl from one mode to the next. It is not
sufficient, therefore, to provide a load circuit identical with the test
mount unless the tube is to be opcratcxf in the same mode as that specified
in the tests. Although it may often seem that somewhat greater output
power is available in a mode of }Lighcr reflector voltage than in the one
used in the tests, designing on this basis is not safe. At some frequencies
the sink may enclose the mutchul-load point of the diagram for a highervoltage mode and there will bc no output powwr at these frequencies.
The presence of the overload condition at some frequency cannot
always be discovered by rncrcly tuning the tube through the frequency
range and observing that power is obtainccf at all positions of the tuning
The tube may jump sucldcnly over the frequencies at }vhich
it cannot oscilkitc, if the frequency sensitivity of the load admittance is
high. The tube may bc more thoroughly tested for operation in a
mixer by superimposing on the steady rcficctor voltiagc a sawtooth sweep
voltage of sufficient amplitude to sweep the tube through the desired
mode of oscillation.
If the same voltage is applied to the horizontal
deflection plates of a cathode-ray oscilloscope and if the vertical deflection
is made to show the rectified voltage of the mixer crystal, a plot of the
oscillator output power vs. frequency results. A plot of such a presentation is shown as the solid curve in Fig. 4.10. As the tube is tuned, this
mode pattern moves slowly along the voltage axis because the reflector
voltage required to maintain oscillation changes, but it maintains
substantially the same shape.
It may, of course, grow larger or smaller,
in the vertical direction, as the coupling factor for the LO coupling
circuit changes with frequency.
If, however, the overload condition
occurs at some frequency, the curve becomes suddenly smaller as this
frequency is approached and usually shows sharp drops at the sides, as
shown by the dashed lines of Fig. 4.10. The evidence of oscillation may
disappear altogether over a short range of the tuning mechanism and
reappear as the tuning is continued, but with the pattern centered at a
different voltage.
Finally, the pattern will regain its original shape as
FIG. 4.10.—Output
vs. LO
reflector voltage for normaland for over-
load conditions.
FIG. 4.11.—Overload condition, allowing oscillation at frequencies on both
sides ot a discontinuity, in a single mode
the frequency becomes sufficiently removed from the critical frequency on
the other side. In some cases the overload at a particular frequency
appears over so narrow a frequency range as to allow oscillation on both
sides of this range in a single reflector-voltage mode.
Then the amplitude falls abruptly to zero over a small range of reflector voltage, as
shown in Fig. 4.11. As the tube is tuned away from this region, the
half of the mode that corresponds to frequencies on this side of the overloaded frequencies swells and finally becomes the full mode of the normally loaded oscillator.
The other half disappears completely for a
small tuning away from the symmetrical case. The beginning of this
effect is indicated by the dashed curve of Fig. 4-11.
That the situation of a broken curve such as shown in Fig. 4.11 does
correspond to a frequency jump can be confirmed through the use of a
reaction wayemeter, coupled to the mixer in such a way that a dip in the
crystal current occurs at resonance for the wavemeter.
Since each
point of the curves of rectified crystal voltage vs. reflector voltage
corresponds to a different frequency, in accordance with the electronic
tuning principle, a dip in the curve, which moves along as the wavemeter
is tuned, results.
In a situation such as that illustrated in Fig. 4.11, the
wavemeter dip moves smoothly through one-half of the curve and then
[SEC. 4.7
disappears for a considerable range of frequency as the wavemeter is
Finally, it reappears at the insi(lc edge of the second part of the
mode and movrs smoothly on to the cud of the mode.
The region of
frequency skipped is usually much greater than that covcrecf by the
ordinary electronic tuning for a change of rcficctor vol’mgc equal to
that of the blank region. This is underst,andablc bccausc the t,fvo sides
of the sink of the R~eke diagram represent extreme values of frequency
pulling in opposite directions.
A less noticeable but very serious kind of frequcm-y discontinuity
sometimes occurs if the load on the oscillator is highly frequency-sensitive.
Such a load results with a 2K25 if the tube is tightly coupled to a ~~aveguide in which a very !argc standing-v-a~’e ratio exists. In a situation
of this kind, the test described in the pmccding paragraph may sho~v a
normal oscillator mode at all tuning conditions, except for a small cusp
which moves through the mode as the tube is tuned.
This is sho~rn in
Fig, 4.12. The cusp is often so small that it can go unnotice(l unlc,s the
observer is looking specifically for it. The rusp Tvou]d almost certairl13be regarded as of little consequence since it appears to be no more serioli>
than a small drop in available
power, similar to that produced by
the reaction wavemeter.
If, ho~vever, the wavemeter test is made,
a continuous variation of frequency
is found up to the cusp, and at this
point the wavemeter indication disReflector voltage
Before the wavemcter
FIG.4.12.—Oscillator-mode pattern, show.
indication reappears on the other
ing discontinuity.
side of the dip, the wavemeter may
have to be t~ned through 1 or 2-per cent, showing that there is a 1 or
2 per cent gap in the spectrum of available frequencies from the tube
operating into this load.
If the tube is mechanically tuned, the discontinuity moves in the mode, but the wavemeter test shows that substantially the same frequency band is always skipped with a particular tube.
This effect can also be explained as a result of the sink of the Rieke
diagram, the difference being that the load circuit is sufficiently ikequencysensitive to allow the tube to find a frequency at which it can oscillate at
any tuning condition.
As the frequency of the tube approaches the
frequency at which the load is in the overload region it simply jumps
across to a frequency on the other side of the sink. This change in
frequency alters both the position of the sink on the Rieke diagram and
the admittance presented by the load.
Attempts were made to use the 723A/B tube in a double-mixer
circuit in which the oscillator was coupled directly into a resonant
The load presented to the antenna of the tube by the resonant
cavity was very frequency-sensitive and was far from the center of the
Rieke diagram of the tube.
For any tube a frequency discontinuity of
this type could be found but the frequency region skipped varied considerably from tube to tube, corresponding to a variation, among tubes,
of the electrical length of the coaxial output line. Thus, a measurement
of the Rieke diagram of these tubes would show a considerable variation
in the position of the sink. To make a mixer that would operate with
any tube, in even a narrow band of frequencies, it was found necessary to
make the discontinuity caused by the resonator circuit fall at a frequency
several per cent outside the band, for an average tube.
As a result the
load condition on the average tube was such that only a small amount of
The coupling required between
energy was stored in the resonator.
the resonator and the mixer to give sufficient power at the crystal resulted
in a large reaction of the local-oscillator circuit on the signal circuit in
the mixer. The aim of achieving increased cross attenuation between
the AFC and radar mixers was not realized, and in fact, the mixers
designed on this principle were quite unsatisfactory.
All subsequent
designs were based on the provision of matched-load conditions for the
local oscillator, in the fashion already described.
4.8. Frequency Discontinuities Caused by High-Q Load Circuits.—
A discontinuity of another type in the operation of an oscillator results
In many cases it is
if the load circuit is highly frequency-sensitive.
desirable to couple a resonant cavity to the local oscillator of a mixer
for frequency reference.
If this is attempted it is usually found to be
very difficult to make the coupling in such a way that the oscillator may
be tuned smoothly through the cavity resonance.
For almost any
reasonable coupling a discontinuity results, if not for all tubes at least
for some samples.
At first thought it might be supposed that it would be necessary only
to restrict the admittance contour of the load circuit to a region of the
Rieke diagram not including the sink. If this is done, frequency discontinuities can still be found if the rate of transit of the load contour
with respect to frequency is sufficiently rapid.
To understand how this
comes about, let us consider an idealized example.
Associated with the
tank circuit of the oscillator there is a susceptance which changes at a
certain rate with frequency in the vicinity of resonance and which is
Tuning the tube either electronically
zero at the frequency of oscillation.
or by alteration of the cavity resonator (the microwave tank circuit)
may be considered as adding a positive or negative susceptance to the
circuit so that the zero occurs at a different frequency.
To a very good
approximation, the susceptance of the tank circuit increases linearly with
To tune the oscillator from the frefrequency as shown in Fig. 4.13.
quency corresponding to A to that corresponding to B, the addition
This statement is
of a susceptance varying from —S to +.S is required.
valid, however, only if the load offers no susceptance in addition to that
of the tank circuit.
If theload docsadd asusceptance that varies only
slowly with frequency, the effect is similar to that of the hypothetical
tuning susceptance, and the oscillator frequency is said to be pulled
by the load.
Suppose the load includes a resonant cavity, in addition to a matched
load at frequencies at which the cavity is nonresonant.
In Fig. 4.14 such
a load circuit, conforming to the load specifications for the 2K25, is
The cavity appears as a short circuit at frequencies removed
from the resonant frequency and the circuit is identical with the test
output hne
FIG.4.13.—Susceptance of oscillator tank
circuit vs. frequency.
I?lci, 4.14.—Res0nant load circuit
2K25 oscillator.
mount is those regions. In the vicinity of resonance, the cavity admittance traverses a circle on a Smith chart in accordance }vith the formula
– v,)
where 60 is the reciprocal of QO,the unloaded Q of the cavity, 61 is the
reciprocal Q of the input circuit, & is the reciprocal Q of the output
circuit, v is the oscillator frequency and VOis the resonant frequency of the
This formula can be derived from the equivalent shunt-circuit
resonator at low frequency where the admittance is given by
where u is 27rv, go is the shunt conductance of the tuned circuit, and
gz is the conductance of the output circuit.
Using the Iumped-constan&
circuit formula for Q,
and the resonance condition,
tance is
a; = l/LC,
the equivalent
circuit admit-
or, to a very good approximation,
for I(V — vO)/POl<<
The admittance terminating the input line is this quantity transformed by
an amount dependent on the input coupling, which is measured by
where ISlis the reciprocal Q of the input circuit with the input line matched
Dividing by g, thus gives the admittance in units of the characteristic admittance of the input line, as in Eq. (3).
The load presented to the antenna of the tube in the circuit of Fig.
414 consists of the sum of the matched-load admittance Y, and that of
the cavity, transformed to its reciprocal by the quarter-wavelength line.
Thus the total load admittance is
(J, + 6$+
j2Av ‘
where AJJis substituted for (v — YO)/VO,or
on an admittance chart this result can be obtained by the steps illustrated in Fig. 4.15.
In Fig. 4. 15a is shown the admittance of the cavity
alone, traversed in the direction of the arrow with increasing frequency
and with resonance corresponding to the intersection with the conductance axis. In Fig. 415b is shown the circle representing the admittance
of the cavity at the end of a quarter wavelength of line, and in Fig. 4. 15c
is shown the locus of this admittance combined with the matched-load
The point to be
admittance terminating the line in the other direction.
made now is that the contour of load admittance may lie entirely within
the acceptable region of the Rieke diagram for the oscillator, but may
give rise to frequency disc ontinuities in the operation of the tube by
virtue of an excessive rate of change of susceptance with frequency.
The tendency for this to occur is greatest, for the circuit under discussion,
if the effective length of the line between the oscillator tube and its
antenna in the waveguide is an integral number of half wavelengths.
The added susceptance of the load circuit has a negative rate of change
with respect to frequency in the vicinity of resonance for the load cavity.
Thus, it tends to counteract the positive rate of change of susceptance of
the oscillator cavity.
Since the frequency stability of the oscillator is
derived from the positive rate of change of sus;eptance of its tank circuit,
the addition of this load circuit reduces the stability by an amount
0([email protected]+i3)@’)
2 .,
,, b= -Y.
FIG. 4.15 a, b, C.—LOCUS
of load admittance vs. frequency, for cavity in place of the short
circuit in the standard tube mount.
depending on the ratio of the negative rate of change of susceptance of the
load circuit to the positive rate of change of susceptance of the tank
The situation may be illustrated graphically as in Fig. 4.16.
The susceptance of the tank circuit is the straight line, as in Fig. 4.13;
that of the load circuit is the curve passing from positive values at
frequencies less than the resonant frequency of the cavity to negative
load c“rcuit
tank circuit
- —
// — ——AV
Total – –
FIG. 4.16.—Diagram of susceptance vs. frequency, illustrating the origin of frequency discontinuities caused by a high-Q load circuit.
a frequenry
discontinuitycausedby the cavity.
values at higher frequencies; the total susceptance is the sum. In this
example the rate of change of total susceptance is negative in the vicinity
of the extermal cavity resonance; hence the oscillator must be unstable
at that frequency.
Its actual operation, using the concept of the tuning
mechanism discussed in connection with Fig. 4.13, is the following.
the tube is tuned from low frequency through resonance of the external
cavity, its frequency of oscillation must jump discontinuously from the
frequency at A to that at B.
Returning, the frequencies between C
and D are skipped.
If the tube is swept in frequency by a sine-wave
voltage applied to the reflector, and the cavity transmission is recorded on
an oscillograph as a function of this voltage, a pattern like that of Fig.
4,17 is found.
To avoid the discontinuity, the absolute value of the rate of change of
susceptance of the load circuit must be kept less, at all frequencies, than
that of the oscillator circuit itself.
It is necessary to have a measure of
the rate of change of susceptance of the oscillator circuit at a point in the
line where the maximum rate of change of the susceptance due to the load
circuit is known.
It is possible to obtain this quantity from a measurement of the pulling figure of the oscillator, since a susceptance added
to the load admittance of the oscillator must produce a frequency change
sufficient to make an exactly counterbalancing change of suweptance
in the oscillator circuit.
Thus, the quantity desired is j ust the reciprocal
of the measurable frequency pulling per unit susceptance change in
If C is defined as the frequency
the load admittance in the waveguide.
change in cycles per second per unit change in load susceptance, the
condition for continuity of oscillation is
From Eq. (4), this becomes
~ ~,
– C
or, since the left-hand side is a maximum when Av is equal to zero,
(60 + a,)’ = c“
The evaluation of this formula for some typical conditions will serve
to point out its implications.
First, it is necessary to have a typical
value of C/ UO. This quantity has been ascertained for some 2K25 tubes
by finding the values of 6,, 60, and & that give continuous operation, and
applying Eq. (5). It has been found that the value is not constant for
different parts of the same mode of the oscillator but is higher off center on
one side (low-frequency side) than at the center (maximum power) or on
the other side. In order to obtain continuous operation to the halfpower point on the low-frequency side of the reflector-voltage mode,
the left-hand side of Eq. (5) must be made less than about 103 for most
tubes, so C/v~ may be taken as 10–8. Thus C represents a frequency
change of about 11 Me/see per unit susceptance at a frequency of 9000
Suppose that it is desired to find the input coupling that can
be used with a cavity having an unloadccl Q of 20,000
and a Q of 10,000
when the mvit.v is loaded Iyy the output circuit alcmc. .lpplication of
Eq. (5), with (& + 6,) cql]al to 10-’, gives 61 less than 5 X 10-’, or the
Q of the inpllt circllit must be greatrr than 2 X 10’. Since the conductance at resonance, as seen at the antmna of the oscillator tube, is
60 -t 6,
the admittance
contour drsrribcd by the load circuit as a function of
YO far from
frwl~lency, corresp{mding to Fig. 4. 15c, mllst go thro{@
resonance and through a point somc\vhrrc bctwrcn Y~ and 1.o5 YO at
This is certainly a very snmll cxcnlrsion znd would, fit first
thought, have been regarded as an ezsily tolerable lord line for the tllbc.
Thus it is evident that this source of frequency discontinuitcs in the
operation of the oscillator must be taken into account when m resonant
cavity is to be included as a part of the load circuit of the oscillator.
A possible way in which the tendency of the ca~ity to produce frequency discontinuities can be reduced is to use a ditfercnt effective line
length between the cavity and the oscillator.
In this way the part of
the load line which is traversed most rapidly is made to correspond, at the
oscillator, primarily to a changing conductance, or, for a line differing in
length by a quarter wavelength from that in the example above, a positive
rate of change of suscept ante.
In the latter case the load circuit tends
to stabilize the oscillator frequency through increasing the total rate of
change of susceptance.
Then a much larger coupling between the
oscillator and the cavity can be used. Although discontinuities may still
be produced when large coupling is used, they will be of a different kind.
The tube may oscillate, at the resonant frequency of the cavity, with
greater frequency stability than with a nonresonant load, but two
discont.irruities, one on each side of resonance, occur for high Q’s and tight
This effect is shown on the susceptance-vs. -frequency plot
of Fig. 4.18, where discontinuities occur between .1 and B, C and D and,
The frequency
tuning from right to left, between E and F and G and H.
stabilizat ion obtained when the oscillator is operating in the region
betIveen the t~ro discontinuities is such that tuning that would ordinarily
cause a frequency change from 11 to D causes only the change from G to C.
Circuits of this type have been used for frequency-stabilization
but the dependence on’ the line length betm-een cavity and oscillator
makes them difficult to put into proper adjustment.
When using tubes
such as the 21{25, in which the coupling line is a part of the tube and
varies in effective electrical length both with frequency and from tube to
tube, it is safest to design a cavity load circuit that is satisfactory even
~vhen the line length is such that the greatest tendency for causing
discontinuities occurs, if these discontinuities are to be avoided at all
Thus Eq. (5) must be satisfied.
frequencies and lrith all tubes.
4-9. The Design of Load Circuits Containing Transmission Cavities.—
A transmission cavity nmy bc used as a part of the load circuit of the
local oscillator of a mixer to sen-c as a frequency reference, either for
If the
freqllenry mcasnrcment or for alltomatic frequency control.
presence oi the cavity did not af”fcvt the operation of the oscillator no
matter ho~r high its Q, it lwoldd be dcsirc(l to (design the circuit to load
the cavity in s~l(,h I lray as to give the maximum rate of change of
vcdtagc lvith respcrt to frct~lwncy at the output terminals of the detector
follo]ving the cavity,
This means that, lvith a cavity of given unloaded
should Im
Q, (Qo = 1/60), find ~~ith a wu:~re-l:ilv detector, the lwhg
such that ( TQ,,) is a rnaxinulm, l! Ilcrc 71 is tllc fraction of the available
input power to the cavity transmitte(l to its load and Q,, is the loa(led Q.
‘i’he qllantity T can, by arg{lmeuts similar to thusc used for l’;q. (3 15),
be s}mwn to be
~ = _____4&&
(6, + & +
so that
If the partial derivatives of TQ,,, first ]rith respect to 3, aml then !rith
respect to &, arc taken, Jnd ew:h set e(lual to z(,ro, the values of’ 6, and ~z
giving maximum T[J{. are found to be
61 = 262 – &
& = 261 – 80 I
[SEC. 4.9
61 =
Thus equal loading by the input and the output circuits is desired, and
the loaded Q is one third of the unloaded Q of the cavity.
The fraction
of available power transmitted to the load is 0.44; that is, the cavity
has an insertion loss of 3.5 db at resonance.
The situation is different in practice, however, since, in addition,
the inequality of Eq. (5) must be satisfied.
The limiting case occurs
when Eq. (5) becomes an equality, or when
& – b(c$, + 6,)2 = o,
whe rc
If the condition
of Eq. (10) is applied to Eq. (7), there results
= [b(a, + a“) + I]’(a, + 60)”
The maximum value of Z’Q~, can be found by differentiation,
val[[es of 6, and & at this maximum are
and the
Ii b is taken as the true value of the oscillator, the limiting values of
81 and ~~ we given by ll~s. (12).
M’ith these values the oscillator is
just on the ~erge of a discontinuous operation at the cavity resonanw
for the most restricti~e cavity-to-oscillator
line length.
In practice
a certain safety factor is desirable and this can best be achieved through
the use of a value for b smaller than the true value by a reasonable
Equation (12) should bc used only when b& is less than 0.25,
Application of Eqs. (12), when b& is greater than 0.25, is not desirable,
because then the inequality of l’;q. (5) holds for the optimum value of
TQL for the cavity alone.
Use of Eq. (12) would result in loading that
gives the maximum T(JZ, compatible with krcping the oscillator on the
verge of discontinuous operation.
In Fig. 419 are plotted the values of
6,/6, and &/AO vs. b& for values of MOlCSSthan 0.25 as given by Eqs. (12).
From these curves it is evident that an inrrc~sc in the output loading of
the cavity is much mow effective in reducing the pulling of the local
oscillator than is decwlpling thrwlgh a decrease in the input loading.
SEC. 49]
By the use of the condition expressed in Eq. (5), the amount of coupling which just allows continuous operation with equal input and output
irises can be calculated,
This condition maintains the maximum loaded
Q for a given transmission loss, The result is
These values also are plotted in Fig. 419.
To compare the usefulness
of the cavity loaded in these t~~o ways, the expressions for !Z’Q~may be
12 ~
61 0,6
0.002 0.0040,006 0.01
0.040 .060.080.1
0.4 0,60,81.:
4.19—Values of b,/c$oand bz/c$ogiving maximum (TQL), subject to the conditiun
required to avoid frequency discontinuities, that —
< b. The dotted curve gives
(60 + 6,)2
8,/& and &/&, as a function of b6~, for equal input and output windows.
used. When the effect on the oscillator may be neglected, Eqs. (7) and
(9) give
In Fig. 4.20 curves are plotted showing the ratio of the product TQL
obtainable through the use of Eqs. (12) and for the condition of equal
input and output loads to the maximum for the cavit y, given by Eq. (14).
The calculation for the equal-loading case is simplified for small ~,b,
since Eq. (13) can be reduced to
[SEC. 410
by expansion of the radical by the binomial theorem, neglecting terms
in 60b to powers higher than the second.
The product TQL for small
bob is reduced to
by this means.
From these curves the advantage of using larger output loading and
smaller input loading than those that give minimum transmission loss for
a given loaded Q is quite evident.
In practice, a further considera0.9
enters: that of the detuning
of the reference cavity by the in~ 0.6
put and output circuits by variaEg
tions in the admittance of the
circuit or the detector
formulas and curves
show that, if the rate of change of
FIG. 420.-Ratio
of the product TQ~,
susceptance must be lower than
obtainable without LO-frequency disconthat obtained by loading for maxitinuities, to the maximum values of TQL
obtainable from the cawty as a function of
mum TQL, the product TQL for
a given cavity suffers least if the
reduction is made by increasing the output coupling and decreasing the
input coupling in accordance with Eqs. (12). Therefore, variations in
the oscillator admittance pull the cavity frequency less than for maximum
TQ. and variations in the output admittance pull it more. In practice a
crystal is used as the detector.
To reduce the pulling of the cavity by
the change
in admittance with
changes of the crystal, a dissipative
buffering attenuator is used between the cavity and the crystal.
4.10. Load Circuits with Reaction Cavities.-One
more example
of the application of Eq. (5) may
be of interest.
It is sometimes
FIG.421.-Ciur[lit for ruu~liuga reactic]ll
desired to couple a reaction wavecavityto thelocal oscillator.
meter cavity to the oscillator.
possible circuit would be that of Fig. 4“21, which is identical with Fig.
4.14 except that the load circuit and output hole of the cavity are not
present. The condition for continuous operation with this circuit becomes
6, < b~:.
The marginal condition is given by
which a few representative numbers will show to be a very restrictive
For the example cited where b, for the 2K25, was taken as
500, a cavity with an unloaded Q of 5000 can have a value of 6,/60 at most
equal to 0.1. Thus the voltage standing-wave ratio at resonance cannot
be less than 10, with the minimum in the plane of the input iris, corresponding to the “ undercoupled” condition.
An absorption of only about
10 per cent of the available oscillator power gives the circuit, as a reaction
wavemeter, only about a 10 per cent dip at resonance in the power
delivered to the main load on the oscillator.
With a high-Q cavity,
such as the Z’EOl-mode wavemeter commonly used in the 3-cm band,
b60 would be about 0.02 so that
61/& could not exceed 0.02 and only
a 2 per cent dip could be obtained.
4.11. The Prevention of Frequency Discontiunities by Padding.
A common method of preventing
TOmatched load
discontinuities in frequency caused
FIG,4.22,—Circuitfor couplingcavity
by having a cavity as a part of the
to oscillator with clissipativeattenuator
load circuit is to provide matched
for decoupling to prevent frequency
dissipative attenuation between the
cavity and the oscillator, as illustrated in Fig. 4.22. The amount of
attenuation required may be calculated as follows. The reflection coefficient from the cavity is given, without attenuation, by
Yo– Yc
Yo + Y,
where Yc is the cavity admittance from Eq. (3). If an attenuator
inserted between the oscillator antenna and the cavity reduces the power
by a factor r, the reflection coefficient measured at the oscillator antenna
is also reduced by the factor r, since the wave must transit the attenuator
twice. Thus the admittance at the oscillator antenna is
for a total path length of an integral number of half wavelengths between
the cavity and the antenna.
The reciprocal of this admittance is the quantity desired, since it is
when the cavity and the oscillator are placed an odd number of quarter
wavelengths apart that the rate of change of susceptance with frequency
is negative and so produces frequency discontinuities.
[SEC. 411
For continuous operation of the oscillator, the condition that must be
met is that the derivative of the imaginary part of Y~ with respect to
frequency at the resonance frequency of the cavity ., is less in magnitude
than the reciprocal of the rate of change of frequency with respect to
sllsceptance, defined previously as C, for the oscillator, or
where Au, vO,and c are all as defined in the previous analysis and BL is
the imaginary part of Y..
The result is
– ?-)a
+ (1+ r)]’
< c’
where 6T is b“ + 62 and a i~ 61‘6T.
This may be written
For the marginal condition, that is, with the oscillator just on the verge
of skipping frequencies, the left-hand side may be taken as equal to zero,
and thus a minimum value of r compatible with continuous operation is
This value, designated as r-l, is
If the last term in the bracket is small compared with unity, the radical
may be expmded by the binomial theorem and an approximation may be
obtained by neglecting terms in the expansion of order higher than the
first. Thus the attenuation factor for this condition may be written
(a + 1)’
Application of these formulas to two special cases are of particular
First, for the use of a transmission cavity loaded for maximum
l“.?. in accordance \vith Eq. (9), & is 26, and a is ~. Thus Eq. (18)
‘l=(H{l-[’ )1)
( E,
and Eq. (19) becomes
A curve of these functions is plotted in Fig. 423.
This curve becomes a
straight line for small values of b60. Thus,. in this region, the real limit
on the product TTQL is imposed
by the limit in the rate of change
.s 4
of susceptance that the oscillator
can stand.
With a given value 5
of b for the tube, little is gained zz 12
by the use of a cavity of higher : 16
u n 10 a d e d Q, since additional
attenuation is required which al- g 24
0.2 0,1
most exactly compensates the in.b60
This is also true
crease in TQ~.
l~lo. 4.23,—Attcnuat,icm, in decibels,
when no attenuation is used and
required bctwccn the ravity and the oscdlator
disco ntinuities
are avoided
to avoid diwor,tirluitiw, T)lottedas a function
through the use of Ills.
(12).. , of !)!s”.
although the limit is approached less rapidly as QO is increased,
In the
limit, Eq. (21) becomesrl = ~ b&
and the product rlTQL becomes, from Eq. (14),
Without the attenuator, and with loading according
product TQ~ becomes, in the limit,
= 4b.
to Eqs. (12), the
Thus, the rate of change of output power from the cavity achieved,
in this way is 12 times as great as that which can be obtained using the
In practice the difference is not this great. For bob = 1()-:;,
the smallest value usually cncountcred, the rate of change of output
power is greater by a factor of 10 \vhcn no attenuator is used. For a
more usual value of ~ob, in the region of 0.02, the ad~~antage is only a
factor of 7. Against this advmtwge, ho~vcver, must be weighed the
greater tendency of the cavity to be pulled by the input- and output-load
susceptances when no attenuator is ~Mcd. ‘l%cre is no decoupling from
the oscillator admittance except that afforde(l by the reduced input
iris, and the coupling to the 10M1:ulmitt:mm increases as the square root
of ( 1/b60), as bbo is decrease(l.
Thus the plllling of the cavity by the load
susceptance would be about 18 times as great, for b& equal to 10–3, as it
would be if an attenuator were used.
Equations (18) and (19) may be applied also to the reaction cavity,
that is, the cavity with no output loading.
For this case, ~= = & and
a = 8,/6,.
With a coupling coefficient a of unity, which is optimum
for many applications of a reaction cavity, Eq. (19) is exact and reduces to
r] = b&.
If a is not unity, but is small compared
required is given approximately by
with l/b60, the attenuation
As in the previous examples the limit on the rate of chinge with frequency
of the reflected power from the cavity is imposed by the pulling figure of
the oscillator tube. Although an increase in the unloaded Q or a change
in the coupling factor increases the possible percentage rate of change of
the reflected power with frequency, the required increase in attenuation
just compensates for this; consequently the absolute rate of change is
As with transmission cavities, the higher-Q cavities have
the advantage of being less susceptible to pulling by the external circuits.
The presence of the large attenuation makes it possible to control the
external admittance more carefully than if the oscillator were coupled
directly to the cavity.
The maximum rate of chan,gc of reflected power, for the two methods
The reflection coefficient r for the
of decoupling, may be compared.
cavity is
Y, + Y.
The rate of change of reflected polrm- with frequency is proportional to
the attenuation factor r, and to the dcriv:ltivc of the square of the
absolute magnitude of II with rwpcrt to Au,
326, &,AII
dAv = [(6, + 6(,)’ +mvq~”
The maximum of this cxprcssitm Irith rrspcct to frequency
occurs for
Av = @8,
+ &)/[i, M is foun(l I)y setting the second derivative of
Irl 2 equal to zero. ‘1’111]st}w maximum rate of change of reflected power
with frequency iti proportional to
When an attenuator
is used for decoupling,
and 8, = Jo, this becomes
With no attenuator and with 6, = &(~,b), l+;q, (2u) becomes
‘“ = (a”b +
= 3v’’3fl.
Thus the reaction cavity, like the transmiwion cavity, has a greater
effectivrmcss (this time ~Iy [Lfw+tor uf 8 in the limit) for the circuit in
which the dccuupling is achic~rwl tl]rongh the choice of the cmvity lotiding,
In all cases the rate of changr of
without the addition of attenuation.
power with respect to frc(lucncy is also proportional to the outpllt
power of the oscillator.
The aholutc rate of change of power can therefore be increased by increasing the output pow-er of a given oscillam~ if
this can be clone \vithout clccreasing b.
All these calculations are directed toward obtaining the maximum
It is sometimes desirable to obtain
absolute rate of change of power.
the maximum percentage rate of change and the conditions are then
Calculations can easily be carried out for these or other
requirements by the use of the general condition that the rate of change
of susceptance of the load circuit must not excccd the reciprocal of the
rate of change of frequency with load susceptance for the tube.
4.12. Provision for Beacon Local Oscillator.—In the introduction of
this chapter the problem of provision for beacon reception was mentioned
and its solution for 10-cm oscillators and mixers was indicated.
only other frequency band in which a radar beacon has been used is the
As mentioned previously, the early
band from 9320 to 9430 hfc/sec.
solution to the problem of beacon provision was to add a second local
oscillator, tuned to produce the intermediate frequency when beating
with the beacon signal, and coupled to the mixer by means of the insertion
This kind of coupling
of its output antenna into the mixer waveguide.
was, for reasons already mentioned, replaced by one of the coupling
mechanisms described in Chap. 3, which provides a matched load for the
The design included the addition of a second local-oscillator waveguide and coupling iris, with an adjustment screw, on the side of the radar
mixer opposite the radar local oscillator.
Such a mixer is shown in
Tbc sepamtr .1]~’(; mixer is included in this sketch.
Fig. 4.24,
mi~:cr consists of four parallel wavcguidw \rith coupling irises between
To minimize the interaction of the two coupling-window
a{lj(lstments on the radar mixer, it
is helpful to have the screw in one
window always inserted beyond
the window resonance and the
screw in the other window inserted
lCSSthan the amount giving resonance. The two irises tend to compensate each other in their effects
the received signal. Thus a
fixed post long enough to put the
iris just beyond resonance may be
inserted into the plane of the coupling iris between the beacon local
oscillator and the radar mixer.
A mixer with an extra local oscillator can be made using any of the
coupling schemes or combinations discussed in Chap. 3. The recent
introduction of the 2K45 tube, a thermally tuned triode, has made
possible a return to the use of a single local oscillator which may be
changed from radar rcccption to beacon reception by means of a switch.
Remote control over the oscillator frequency, ~vith tunability over a
wide band, is possible with a tube
of this type.
It has so far been assumed that
~ ~~
the only change necessary to con~
; 12
vert the radar receiver to a beacon
receiver is a change in the local~ s
Most radar ~ ~
oscillator frequency.
systems, however, have some r-f
preelection in the form of the TR
9340 9370 9400 9430 9470
cavity tuned to the radar frequency.
frequency In Mc/5ec
There is some loss at the beacon
FIG. 4.25.—Beacon-signal loss due to
mistunedTR cavity vs. radar transmitter
frequency, the magnitude of which
depends upon the difference be‘req”ency”
tween the beacon frequency and the radar transmitter frequency.
loss is large for a transmitter located at the end of the scatter band
farthest from the beacon frequency.
In Fig. 4“25 is plotted a curve
of the additional loss at the beacon frequency resulting from the
fact that the TR cavity is tuned to the transmitter frequency.
value taken for the loaded Q of the TR cavity was 35&approximately
SEC. 4.12]
that of the 1B24. The abscissa of the curve is the transmitter frequency.
This signal loss is sometimes not a serious impairment to the beacon
feature of the radar set because the radar signal fails to trigger the
beacon at a shorter range than that at which the beacon signal would be
lost in the radar-receiver noise. The beacon receiver. because of its wide
pass band (the whole 110-iMc/sec scatter band), has a minimum detectIn addition,
able signal greater than that of the receiver in the airplane.
the beacon receiver has much lower antenna gain, since it must receive
Thus, if the beacon signal is received
from and radiate to all directions.
at all, it may be a signal very many times greater than noise.
In some systems there is, however, a large loss on receiving beacon
signals because the antenna spends such a small fraction of the time
pointing in the direction of the beacon.
It has, thcmfore, become
common to add to the 3-cm airborne-radar mixers a special device to
reduce the loss in the TR cavity at the beacon frequency Trhen the set is
switched to receive beacon signals. Because the beacon frequency is
outside the radar transmitter band, on the low-frequency side, the TR
cavity must be tuned in the same direction for all transmitter frequencies.
Since the beacon frequency is lower than the radar frecluency, the input
susceptance of the TR cavity is inductive at the beacon frequency and
has a magnitude proportional to the difference in frequency betfveen
the radar and the beacon.
To tune the cavity to the beacon frequency a
capacitive susceptance must be added.
To accomplish the retuning of the TR cavity to the beacon frequency,
the inverse of “ TR-aided tuning “ is used. That is, the capacitive susceptance is not added in the TR cavity, but in the mixer \vaveguide, at a
distance behind the TR tube effectively equal to one-half ~vavelength.
Thus the waveguide between the TR cavity and the tuning susceptance
contains a very large standing wave. The distance betlreen the TR
cavity and the crystal must be increased from the conventional half
wavelength to one wavelength in order to accommodate
the tuning
For a mixer to be used only in the frequency band for airborne
radar (9320 to 9430 Me/see), this is not of much consequence, since its
only effect is to narrow the frequency band over which TR-aided tuning
is effective.
Figure 4.26 shows a vertical-plane cross section of the
radar-mixer part of the converter, including the beacon tuner. The
tuner is identical in principle with a tuning screw of the choke type and
has a rod ~3 in. in diameter.
The rod is pulled out from the ~vaveguide
by a coil spring in a mechanism above the choke when the radar-beacon
When the switch is thrown to
switch is in the radar recei~’ing position.
the beacon position, an armature in a magnetic solenoid causes the rod
to be pushed into the waveguide by an amount determined by an adjustable stop. The adjustable stop becomes the tuning control of the TR
cavity for beacon reception.
It is adjusted for maximum received signal
at the beacou. frequency when, with the rod pulled out, the TR tube
is tuned for maximum signal strength at the radar frequency.
In this
way the tuner is adjusted to give the correct amount of pulling for the
particular radar transmitting frequency being used. Since the armature
of the solenoid must move the rod through about ~ in., it is found that a
starting current well in excess of the required holding current is needed.
To prevent the solenoid from overheating while holding the tuner in,
! ,,’8$
I.f output
FIc. 4.26.—Cross-sectional view of airborne-radar mixer showing beacon-TR tuner.
it has been found convenient
to cause the rod to throw a switch as it
stop. This switch causes sufficient resistance to be
placed in series with the solenoid to lower the current to a value such that
the tuner is held in place but the solenoid is not overheated.
In this
way the electromechanical part of the tuner can be made very compact.
There is a limit to the amount of pulling of the TR-cavity frequency
that can be obtained by a tuner of this kind. As the standing-wave
ratio in the section of waveguide between the TR cavity and the tuner is
increased, the circulatingg currents in the waveguide walls and in the tuner
increase. The ohmic losses due to these large currents eventually limit
the susceptance that can be added to the TR cavity as well as introduce
In Fig. 4.27 is shown a comparison
a signal loss at the beacon frequency.
of the beacon-frequency losses with and without the tuner. The plot of
loss without tuner vs. radar freG 20 quency is taken from Pig. 4.25. It
will be seen from this plot that the ~~ 16
loss for any transmitting fre$ 12
quency within the airborne band
can be held to less than 3 db by
the use of the tuner. The loss
S4 %
becomes rapidly greater than this
for a pulling somewhat larger than
that required to cover this band.
Radar frequency in Me/see
As might be expected, the action
FIG. 4.27.—Beacon-frequency signal loss
of the tuner is very sensitive to the
vs. radar frequency, with and without the
spacing between the TR cavity and
the tuner, as well as to the depth of insertion of the rod. A tolerance of
less than + O.OO5in. on the total effective distance from TR cavity to
tuner may add 1 db to the 3-db loss remaining for the largest pulling
To make possible the setting of the limit
required for the airborne band.
stop so that the tuner gives less
than 1 db additional loss to the
-TR ~uner
2 l~hok~joint
3-db minimum the adjustment
must be capable of
setting the insertion to within
‘wpling iris
and screw
0.001 in. It is thus seen that very
high precision is required in the
positioning of the tuner on the
waveguide, in the bearing surfaces,
and in the limit-stop mechanism.
In Fig. 4.28 is shown a drawing of
a complete two-channel converter
er including beacon local oscillator
and tuner for the beacon TR
Both mixers are increased
FI~.4.2S,—Functionaldrawing of mixer with cavity.
in length by the half wavelength
required for the addition of the TR-tube tuner so that the AFC attenuator
used in the con~erter shown in Fig. 4.4 may be used.
4.13. R-f Provision for Beacon AFC.-.\utomatic
frequency control
is even more necessary in beacon reception than in radar reception to
When a radar set is used to recei~e
assure satisfactory performance.
beacon signals it is because the operator does not know his location with
respect to the beacon.
Thus, the receiver must search in range and
[SEC. 413
for the beacon signal. If, at the same time, it is necessary
to search in frequency, the chance of the frequency and direction of the
receiver being right simultaneously is very small. As a result the operator
would be very lucky to find the beacon at all.
Since the system is already searching in the spatial sense, it cannot
be depended upon to search in frequency for the beacon signal, find it,
and lock onto it, in frequency, in a reasonable time. The beacon program
has therefore been based on standard beacon-transmitter
maintained wit h precision, so that the receiver may be tuned to an
absolute frequency and receive a
beacon signal if one is available.
For this purpose, a reference cavity
is used in the airborne-radar receiver to indicate when the beacon
local oscillator is tuned to the correct frequency to receive the standm-d beacon frequency.
The cavity
is pretuned to resonate at a frequmcy differing from the beacon
frequency by the intermediate frequency.
For the 9310-Mc/sec beacon, cavities re son ant at 9280
Me/see have been commerically
produced, for 30-31 c/sec intermediate-frequency receivers, and cavities resonant at 9250 hIc/sec for
receivers. These cavities, called
the 1Q23 and 1Q22 respectively, are
FIG. 4.29.—Cutaway view of the 1Q23
similar in mode to the TR cavity
but have only one post and, consequently, smaller capacitive loading.
They are evacuated and sealed, with glass input and output irises, and
include a copper and invar temperature-compensating
strut to ensure
In Fig. 4.29 a cutaway
a low temperature coefficient of frequency.
view of one of these cavities is shown. The cavity is mounted in an
aluminum block containing input and output waveguides and is put into a
circuit by connecting waveguides with standard choke joints to this block.
The specifications of this cavity are such that, when the cavity is mounted
between a matched generator and detector, the peak in its transmission
curve occurs at a frequency within about * 1 Me/see of the desired
absolute frequency (9280 or 9250) at any temperature or pressure
The cavity has an unloaded
encountered in airborne-system operation.
Q of about 5000 and the loaded Q, when matched loads are connected
to the input and output waveguides, is about 2500.
4 13]
A cavity of this sort can be used either as an indicator to aid manual
tuning of the beacon J,O or as a source of error sigmd for an AFC circuit.
For either use the r-f circuit requirements are the same if the cavity is
operated as a trtinsmission cavity.
It is also possible to block the exit
waveguide and use t]~c cavity as a rc:wtion device, although this possibility will not be discussed here. The pitfalls are, of course, similar to
those for the transmission wavcrnctcr find are c}liefly concerned with the
application of the results of Sees, 4.8 to 4.11.
Figure 430 shows an extension of the converter shown in Fig. 4.28
to include the reference covity and an output crystal detector in the
cavity, 1 Q 23
6 db attenuator r
2K25 ‘Utpu t
4,30.—Functional drawing of complete mixer witl~ be~col~ LO, beacon-TR tuner,
and refere!we cavity for beiwon A1?C.
beacon-LO circuit.
The cavity is connected as a stub line on the side
of the beacon-LO waveguide ~vith the center line of the stub ~vaveguide
one-quarter waveguide wavelength back from the short-circuited end of
the LO waveguide.
Since the cavity is completely reflecting at frequencies well removed from its resonant frequency, the length of the line
from the cavity to the wall of the LO waveguide is made one-half waveguide wavelength.
The admittance presented at the LO antenna is thus
approximately the same as in the circuit without the cavity, except for
frequency sensitivity.
Since the beacon local oscillator need function
only in the region of the beacon frequency and since this frequency
differs by only about 1 per cent from the oscillator specification-test
frequency, the added frequency sensitivity is not serious.
[SEC. 413
It is found that, with a matched load cm the beacon cavity, many
local-oscillator tubes have frequency discontinuities in the region of the
cavity resonance.
This has been interpreted as indicating that the
Experiments have shown that, if
condition of Eq. (5) is not satisfied.
dkcontinuities are to be avoided, the left-hand side of Eq. (5) must be
less than 10’. Since the cavity design was fixed, it was not possible to
adjust the coupling irises and apply Eqs. (12); instead, continuous
operation was obtained through increasing the output loading &, by
The crystal detector was mounted
means of a mismatched load circuit.
in the crystal mount of a standard mixer and was buffered with a 6-db
dissipative attenuator to reduce both pulling in frequency and variations
The input
in & due to changes in admittance from crystal to crystal.
admittance of this attenuator was very close to YO for any crystal;
the input voltage standkg-wave ratio was less than 1.25. An inductive
iris was introduced, by inserting a vane from one side of the waveguide,
a sufficient amount to produce a voltage standing-wave ratio of 4 on the
input side of the iris. The dktance from the iris to the output window
of the cavity was then chosen so that the apparent load on the cavity was
4% instead of Yo. The proper distance was found by measurement, at
frequencies on either side of resonance, of the position of the apparent
short circuit when a wave was sent toward the output iris of the cavity.
A voltage minimum in the standing-wave pattern produced by the
Thus &, the inverse
inductive iris was made to fall at this position.
With this load circuit, all oscillator
output Q, was increased fourfold.
tubes that were tried oscillated continuously when tuned through the
resonance frequency of the cavity provided that this frequency fell above
the one-quarter-power points in the reflector-tuning mode.
For thk cavity and coupling circuit, the left-hand side of Eq, (5)
can be calculated.
Since the unloaded Q is known to be 5000 and since
the Q loaded by matched waveguides is 2500,
& = 2 x 10-4
6, = !32= 10-4
for a matched-waveguide
resulted in
output load.
The output load used, however,
& = 4 x 10-4,
and the total 6 was 7 X 10-4, or the loaded Q was reduced to 1420.
Using these values in Eq. (5), it can be inferred that vO/C should be taken
to be about 5.5 X 102 to achteve continuous operation.
The quantity
b60, the abscissa of Fig. 4,19, is thus 0.055.
Figure 4.19 shows that the
input and output loadings, for maximum TQ~ should be 0.58 & and
REI’I<I!,SI<N TA TI }’1;
SEC. 4.14]
111I X E1{,S
23 L
Thus, fortuitously, the load ronditi(ms achieved arc
optimum for this consideration, since 61 was 0.5080
and & was 2.0130.
In Fig. 431 a second circuit using the Imacon rcfmwncc cavity is
This is a convcrtcr for a beacon mccivcr, and the cavity is
The cavity is so positioned that,
used only as an aid to manual tuning.
at, frequencies removccl from the resonance frequency, it presents a short
circuit at such a distance behind the resistor strip that the resistor strip
The admittance as
a~pears as a matched load for the waveguidc.
measured in the plane of the resistor strip is thus YO plus the reciprocal
FIG. 4.3 1.—Single mixer with reference wavemeter for local oscillator.
of the cavity admittance, just as is the admittance at the antenna of
the oscillator tube in the circuit of Fig. 4.14. The conditions for continuous operation of the oscillator tube are identical with those in the
previous discussion, and thus the same cavity load circuit is used.
4.14. Representative Mixers with Multiple Functions.-Included
the end of this chapter is a group of drawings showing, in somewhat more
detail than in the sketches of the text, some mixers representative of the
methods described in the text.
Fkst in the group, Fig. 4.32, is a broadband two-channel mixer for
use with a broadband duplexer using the 1B24 TR tube.
This mixer
uses 1N23A or 1N23B crystals and has a loss due to crystal mismatch
of less than 1.5 db for any crystal of this type when operated in the band
from 9600-Mc/sec to 8500-Mc/sec.
Many variations of this basic mixer
have been designed for use in particuar radar systems.
The differences
are in mechanical devices; for example, a plate may be attached to the
mixer so that the crystals and the local oscillator can be included in
the shield box with the i-f amplifier while the TR tube and AFC attenutor are outside the box. The plate thus becomes a part of one wall of
FIO. 4.32.—Double mixer for use with IB24 TR tube, 2K25 Iocal oscillator, and 1N23A
or 1N23B crystals, in the frequency band from S500 to 9600 Me/see., at a transmittm
power level of 50 kw. (For perspective view see Fig. 4.4.)
the shield box and the duplexer waveguide runs parallel to this wall,
outside the box.
Figure 4.33 is a drawing of the two-channel mixer for the 1.25-cm
This mixer uses 1N26 crystals, a 2K33 or 2K50 local-oscillator
tube and a 1B26 TR tube.
This mixer is representative of an LO coupling
circuit of the channel type applied to the double mixer and operates at
24,000 Me/see in a band ~ 2 per cent in width.
Fm. 4.33.—Cross-aect,ionalview of double mixer for use with 1B26 TR cavity, 2K33 local oscillator, and 1N26 crystal, in the 1.25 & 1 per cent
wavelength band.
[SEC. 414
The last of the drawings, Fig. 434, shows the beacon provision for
the band from 9320 to 9430 Me/see.
The beacon-tuner and beacon-LO
FIG. 4.34.—Double mixer for 9375 Me/see with beacon-TR tuner, beacon AFC, for
use with 1N23, 1N23A, or 1N23B crystals, 1B24 TR cavity, and 2K25 LO tubes. (For
perspective view, see Fig. 4.30).
circuits, with the reference cavity for beacon AFC, are included.
In this
mixer also, 1N23A and 1N-23B crystals, 2K25 local oscillators, and a
IB24 TR cavity are used.
In Sees. 14 and 2“3, the effective over-all noise figure of a superheterodyne microwave receiver was shown to depend on three quantities;
the conversion loss and noise temperature of the crystal mixer and the
effective over-all noise figure of the i-f amplifier.
At frequencies below
3000 Me/see, independent measurements of these three quantities give
results which, when applied in Eq. (1.26), are in good agreement with
the results of direct measurements of the effective over-all noise figure of
complete receivers.
At higher frequencies, however, especially when low
intermediate frequencies are used, the results of over-all measurements
are larger than those predicted by the independent measurements of
loss, noise, and i-f noise figure.
In the apparatus described in Sec. 2“13, for measuring noise temperature, a resonant cavity is included between the r-f oscillator and the mixer
The purpose of this cavity, which is tuned to transmit the oscilcircuit.
lator signal, is to remove spurious frequencies from the oscillator signal.
If such spurious signals were to arrive at the mixer with the local-oscillator
signal, they would be converted by the mixer to a frequency equal to the
difference between the frequency of the local-oscillator signal and that
of the spurious signals. Thus, any such signals lying above or below
the local-oscillator frequency by an amount equal to the intermediate
frequency of the test apparatus would be converted to the intermediate
frequency and, therefore, would increase the apparent noise temperature
of the crystal.
It is found experimentally that the result of the noisetemperature measurement, in the bands above 3000 Me/see, is always
significantly smaller when a filter cavity is used. The conclusion is, therefore, that some spurious signals in the two bands to which the receiver is
sensitive do accompany the local-oscillator signal. This must be true of
the system receiver also; in the absence of a filter cavity in the localoscillator circuit, a noise figure must result that is larger than the minimum possible for the given crystal and i-f amp] ifier combination.
6-1. Generation and Effect of Local-oscillator Noise.—The spurious
signals accompanying
the local-oscillator
signal are termed “localoscillator noise. ” The electron beam passing through the oscillator
cavity contains noise-current components at all frequencies, because it is
made up of discrete electronic charges. If a klystron oscillator tube is
operated at a reflector voltage that does not cause it to oscillate, a noise
spectrum can be detected in its output circuit.
The noise voltage in the
output circuit is largest at the resonant frequency of the oscillator
cavity, because the coupling to the electron beam is most efficient at this
A curve of the noise voltage in the output circuit as a
function of frequency closely resembles a resonance curve for the oscillator cavity.
Reflex-klystron oscillator tubes, operated in this way,
have been used as noise generators for use in the measurement of over-all
noise figures of microwave receivers.
It is reasonable to expect that when the tube is oscillating the noise
voltages in the output circuit developed from spurious frequencies will
be the same at frequencies on either side of the oscillation frequency.
In addition, low-frequency
in the electron beam
may, through amplitude and frequency modulation of the oscillator
Image frequency
Signal frequency
signal, produce noise sidebands 1ying
at frequencies above and below that
of the oscillator signal. These side! 1
[ !
bands too, will be coupled to the
U, t Frequency
output circuit with decreasing efficiP. - V,.f V. + U,.f
ency at frequencies removed inI“lG. ~.1.—Local-oscillator
creasingly far from the resonant
of frequency.
frequency of the oscillator cavity.
Thus, the oscillator may be expected to have a noise spectrum in its output circuit similar to that shown in Fig. 5“1.
Whether or not the local-oscillator noise causes deterioration in the
receiver noise figure depends upon the noise power in the local-oscillator
For a
spectrum at the signal and image frequencies of the receiver.
receiver and, for example, a 30-Mc/sec
frequency, the loaded Q of the oscillator cavity is usually sufficiently
high to reduce the signal- and image-frequency noise components from
the local oscillator to a negligible level. For a given intermediate frequency, as the receiver frequency is increased the filtering by the localTo maintain the same filtering
oscillator cavity becomes less effective.
effect with a constant oscillator-cavity Q, it is necessary to increase the
intermediate frequency proportionately
to the increase in the localoscillator frequency.
In practice, oscillator tubes at high frequencies
have cavities of lower loaded Q, because the skin depth decreases with
increasing frequency and because the volum~t~surface
ratio of the
cavity decreases. Thus, local-oscillator noise would be expected to
become increasingly apparent as the signal frequency is increased, even
if the ratio between the local-oscillator and intermediate frequencies
were held constant,
f UrK-
The presence of a significant amount of local-oscillator noise may be a
factor determining the choice of the intmmccliatc frequency.
for receivers at 9000 Me/see and above, the selection of an intermediate
frequency has involved a choice bctwccn the rcduccd local-oscillator noise
at high intermediate frcqucncics, on the onc hand, and the lower amplifier
noise at low intermediate frcqucncics on the other hand. Although the
intermediate frequent y most w idcl y used at the Radiation Laboratory
was 30 Me/see, an intcrrnc(liatc frequency of 60 Me/see was used in
manv. 3-cm and most 1.25-em rcccivers, in order to obtain a somewhat
improved over-all noise figure in the prcscncc of local-oscillator noise.
The relative merits of sm’cral possible intermediate frequencies for a
particular receiver must bc clccidcd from a knowledge of the magnitude
of the noise contribution from the local oscillator at these frequencies,
and from the i-f-amplifier noise figure that can be achieved at each
intermediate frequency.
5.2. Magnitide
of Local-oscillator
Noise for Typical Tubes.—To
facilitate the choice of intermediate frequencies and of other operating
parameters in converters, a program of measurement of local-oscillator
noise was undertaken by Kuper and Waltz. 1 Measurements were made
in the 3.2-cm band on 723A/B tubes, and in the 1.25-cm band on 2K33
tubes and on a few samples of other types. The quantity that was
measured was the apparent noise temperature of a crystal driven,
through an adjustable dissipative attenuator, from the local-oscillator
tube &der measurcrnent.
Measurements were made at intermediate
frequencies of 30, 60, and 90 Me/see, at several points in the electronic
tuning range of the tube. For each point in the electronic tuning range,
the coupling between the crystal and the oscillator ~vas set so that 0.5
The 3.2-cm crystal had a
ma of rectified crystal current ~vas produced.
conversion loss of 7 db and a noise temperature, in the absence of oscillator noise, of 1.2, and so was typical of the crystals used in a 3.2-cm
receiver. For the 1.25-cm measurements the crystal, a type 1N26,
had a conversion loss of 8.5 db and an intrinsic noise temperature of 2.
The results for a typical 723A/B oscillator are given in Table 5“1. The
data given in the table represent the increase in apparent noise temperature of the crystal over ~ts value in the absence of incident r-f noise
power (I .2). Values are given for the different reflector-voltage modes,
for each of the three conditions of electronic tuning at each value of
intermediate frequency.
The column labeled ‘‘ Center” corresponds to
the reflector voltage giving fnaximum power for each mode and the
columns labeled, “Half-power “-” High” and “LOW “-denote
rewectively the values at reflector voltages giving half maximum output power
1J. B. H. Kuper and M. C. Waltz, “ Measurementson Noise from Reflex Oscillators,” RL Report No. 872, Dec. 21, 1945.
[SEC. 52
on the high- and low-frequency sides of the center frequency.
maintain the 0.5-ma crystal current, it lvas, of course, mxxssary to
decrease thctittenuaticm between the oscillator and the crystal at these
half-power points.
intermwli:ltc frcq(lcncy.
Reflecreflector tuning
intcrmctli:ltr frcqllency,
rc[icctor tuning
i]itcrmwiiatc frequency,
reflector tuning
Center —––
Center ——
The over-all noise figure of a rccciver, using this typica1723.i/Bonds
crystal with a conversion loss of 7 db in a nonresonant mixer circuit is
found from the expression
F* = L(F:
+ /: – 1)
where t: is the crystal noise temperature {. plus the appropriate value
from Table 5“1. These values apply exactly only if the conversion loss
is 7 db, but are approximate y correct for any c ryst:d operated at O.5-ma
crystal current. This is because the rectified current is roughly proportional to the reciprocal of the conversion 10SS. A crystal having a smaller
loss would convert the incident noise power to the intermediate frequency
more effectively, but the reduction in incident power, in both the localoscillator signal and the noise sidebands, involved in reducing the
rectified current to 0.5 ma would approximately compensate for this
In systems use, the LO power level is
improved conversion efficiency.
set to give about 0.5 ma of crystal current. The values of Table 5.1,
therefore, are significant for most crystals used in systems.
Table 52 shows similar data from the experiments at 1.25 cm.
These data were taken with a 2K33 tube, operated in the 200-volt
reflector-voltage mode, and again the crystal current was held at 0.5 ma.
The data are similar to those for the 723A/B tube, in that more noise
is found when the tube is tuned electronically to the half power point
in the high-frequency direction than when it is tuned in the low-frequency
It has also been found from these experiments that the noise
intermediate frequency,
reflector tuning
intermediate frequency,
reflector tuning
intermediate frequency,
reflector tuning
spectrum is not as simple as that shown in Fig. 5.1. By means of a
cavity resonator coupled to the waveguide between the attenuator and the
crystal, it was possible to reflect the noise components in one sideband
without affecting the transmission of the local-oscillator signal or of
the other sideband.
In this way the noise in the two sidebands could be
compared by reflecting first one and then the other. It was found that
the noise power was not the same in the two sidebands and that the
relative magnitudes of the two noise powers depended upon the operating
point in the reflector tuning range. The details of this effect and the
theoretical explanation will be founcl in Yol. 7 of this series.
5.3. Effect of Local-oscillator Noise on Over-all Noise Figure.-The
amount of deterioration in over-all noise figure that results from the
existence of local-oscillator noise depends upon the other quantities that
appear m Eq. (1). TO sho~v its approximate value, however, a fe~v
It is convenient to express the noise figure
examples will be considered.
in decibels, because the relative merit of t}vo receivers is determined by
the ratio of two noise figures. Thus, in decibels,
F* = L + 10 10g,, (F: + t: – 1).
At 3.2 cm a good crystal might have a conversion 10SSof 6 db and a noise
At 30 hfc/scc it is possible to obtain
temperature very close to unity.
an i-f noise figure of abmlt 2 db, or as a numerical factor, 1.6. With such
a combination, Eq. (2) gives 8 db for the ovmwll noise figure in the
absence of local-oscillator noise. The ratio, expressed as a difference in
decibels, of the noise figure that includes loc:d-oscillator noise to the
noise figure in the absence of SUCIL
noise is
= 10 log,,,
1+ ~
Ifi.f + /.7
where t’ is the quantity tabulated in Tobles 51 and 5.2. The quantity
F~ expresses the deterioration in over-all noise figllre duc to the presence
of local-oscillator noise. Thr intcrmting r:mgc of i-f amplifier noise
figures is from 2 db to 5 db, or from a factor of 1.6 to a factor of 3. In Fig.
5.2, the quantity l’~ in decibels is plotted as a function of t’ (Ft + L – 1)
for a range from O to 10. Table 53 gives values, in decibels, of the
increase in over-all noise figure due to the presence of the amounts of
local-oscillator noise taken from Tables 5“1 and 5“2. The values given
for 3.2 cm correspond to the 170-volt mode of the typical 723A/B tube.
These are given for four assumed
values of (F2 + t. — 1) and for inter8
mediate frequencies of 30, 60, and 90
.S 6
The value of 1.6 for this
kz 4
expression could correspond to an i-f
noise figure of 1.6 (2 db), and a crysk’
tal noise temperature of unity.
higher values allow for larger crystal
noise temperatures, higher i-f noise
FIG.5.2.—Deteri0r3ti0n of effective
figures, or both.
Thus, the value 3
over-all noise figure ~.s.
t’, (F*ir +tc - 1).
could result from an i-f noise figure of
2 (3db), andacrystal noise temperatureof2.
Similar numbers arealso
given for the 1,25-cm receiver using the typical 2K33 tube used for the
data of Table 5.2.
90 Me/see
T+f, -1
‘cntc, r{IIigh
3.2 cm
723A/B in
1.25 cm
2K33 in
5.9 11.8
5.2 11.1
4,1 9.5
3.3 8.3
1.!3 ‘4.5
1,6 39
1.1 3.0
0.8 2.4
‘enter High Low-
From this table it is evident that the effect of local-oscilla,tor noise on
the effective over-all noise figure of a receiver is large, even at 3.2 cm
and with a (iO-Mc/scc intermediate frequency.
The difference between
the numbers in the columns for OOhlc/sec andthose inthecolurnnsfor
30 Me/see, in the same crosswise rowj mprescnt the decrease in noise
SEC. 5.4]
figure that could be achieved through the use of the higher intermediate
frequency, if the same i-f amplifier noise figure were obtained at these two
In practice the i-f amplifier noise figure achieved at 60
Me/see is larger than that at 30 Me/see; consequently the full advantage
For 3.2-cm receivers the
indicated by the table cannot be realized.
relative advantages of 30-M c/see and 60-Mc/sec i-f amplifiers have been
the subject of considerable controversy, and little thought has been
given to the use of frequencies higher than 60 Me/see for the purpose of
reducing the effect of local-oscillator noise. In the 1.25-cm band, it
has usually been considered advantageous to use an intermediate frequency of at least 60 Me/see and the trend was toward even higher
Another solution to the LO-noise problem, to be discussed
in chap. 6, allowed the use of 30 Me/see as an intermediate frequency,
however, even for receivers at 1.25 cm. Intermediate frequencies higher
than 60 Me/see were therefore not used extensively.
In practice, when the local oscillator is tuned off center in the electronic tuning range, the local-oscillator noise is not so large as is indicated
in the tables, because the local-oscillator coupling is left fixed at the
value giving about 0.5 ma at the center of the tuning range. The coupling at the half-power points in the electronic tuning range is thus only
one-half as great as that to which the data apply, and the crystal current
is only about 0.25 ma. Accompanying this reduction in local-oscillator
power is a small increase in conversion loss but this is less than 0.5 db in
most cases. Because the smaller coupling reduces the incident noise
power correspondingly, the increase in noise temperature of the crystal,
caused by incident local-oscillator noise at the half-power points, is only
half that given in Tables 51 and 5.2. For most conditions this gives
almost the same effect at the low-frequency half-power point as at the
center of the tuning range. The increase in over-all noise figure at the
center frequent y, therefore, holds approximately over the low-frequency
part of the electronic tuning range. In the high-frequency portion of the
electronic tuning range there is an increase in local-oscillator noise, but
its effect is somewhat less than that indicated h Table 5.3. Thus the
value at the center of the electronic tuning range is the most significant.
In order to minimize the deterioration due to local-oscillator noise it is
helpful to operate the tube principally in the low-frequency half of the
reflector mode.
5.4. Reduction of Local-oscillator
Noise by the TR Cavity.-The
measured values of local-oscillator noise and its effect on the over-all
noise figure of the receiver apply to a converter circuit only when there
are no resonant parts in the LO coupling circuit.
For most converters
used in radar, therefore, this condition does not hold, because the resonant TR cavity influences the coupling between the local oscillator and
the crystal.
For circuits in which iris coupling is used, it is required that
the local-oscillator wave reflected by the TR cavity reinforce the wave
traveling directly from the iris to the crystal.
The coupling of power
from the local oscillator to the crystal is therefore almost four times as
great as it would be if the resonant TR cavity were not present.
coupling of local-oscillator noise at the image frequency is also increased
by this factor, because of reflection by the TR cavity.
At the signal
frequency, however, the TR cavity is resonant and its reflection coefficient is small. Local-oscillator noise in the signal sideband does not
become reinforced by reflection from the TR cavity; thus only onequarter asmuch powerat thesignal frequency is coupled from the local
oscillator to the crystal.
noise powers inthe signal-and
image-frequency sidebands were equal, the ratio of total noise power to
LO signai power coupled to the crystal would be only five-eighths as large
Allowing for some reflection of signalas in a nonresonant mixer circuit.
frequency noise by the TR cavity, a value for the increase in crystal
noise temperature 0.7 times the values given in Tables 51 and 5.2 may
be used to estimate the effect on over-all noise figure in a converter
circuit of this kind. Similar results are obtained for the other coupling
schemes that depend upon reflection of the local-oscillator wave by the
TR cavity.
Coupling of local-oscillator power to the crystal through a
directional coupler, however, does not result in this reduction in localoscillator noise.
In Table 54 are given values of the increase in over-all noise figure,
similar to those of Table 5.3but computed on the assumption of a reducFOR
30 Me/see
60 Me/see
;enter Higl Low ~enter High Low
High Low
—— —— —
3.2 cm
1.25 cm
2K33 in
tion to 0.7 of the measured values, for the radar converter with a resonant TR cavity.
The noise power at the half-power points has been
reduced by an additional factor of two from the measured values of
Tables 5.1 and 5.2, on the assumption that the coupling from the local
oscillator to the crystal is set for 0.5 ma of crystal current at the center of
the electronic tuning range and held fixed when the electronic tuning is
For the 3.2-cm tube, the advantage of an intermediate frequency of
60 ~Mc/sec over one of 30 Me/see is small and can be easily lost because of
increased i-f amplifier noise figure. At 1.25 cm an advantage of more
than 1 db is obtained, and this is more than would be lost because of
increased i-f amplifier noise figure. Even with the filtering effect of the
TR cavity, however, the presence of the local-oscillator noise adds to the
over-all receiver noise figure 2 to 3 db in the 3-cm band, and 4 to 5 db in
the 1.25-cm band, with good i-f amplifiers and quiet crystals.
It is
therefore well worth the effort to try to find some method of further
reducing the effect of local-oscillator noise on the over-all noise figure.
5.5. Reduction of Local-oscillator Noise by Resonant Filters.-The
most direct method of removing the effect of local-oscillator noise would
be to use a filter cavity in the local-oscillator circuit, similar to that used
in the apparatus for measuring the noise temperature of crystals.
difficult problems are met if this is done. First, the tuning of the
receiver becomes much more complicated because the filter cavity and
the local oscillator must be kept together, as the receiver is tuned by
If an AFC circuit is to be
alteration of the local-oscillator frequency.
used it must include provision to track the cavity and the local oscillator
The second problem involves the LO coupling circuit.
As shown in Sec. 48, a cavity can be coupled to a local oscillator without
producing frequency discontinuities, only if stringent conditions on the
coupling are met. Either a large dissipative attenuation must be used
between the oscillator and the cavity or the input coupling hole must be
small. Both of these methods of avoiding frequency discontinuities
result in considerable reduction in the output power of the cavity com pared with that available from the oscillator.
The prevention of interaction between the signal circuit and the local-oscillator circuit is a
major problem in mixer design because the available local-oscillator
power is limited.
An additional reduction of available power has
It is obvious
serious consequences on the design of the coupling circuit.
that the filter cavity cannot simply be placed between the local oscillator
and any of the coupling circuits described in Chap. 3.
The tracking between the local-oscillator frequency and the cavity
resonant frequency could be accomplished by use of an AFC circuit
causing the local oscillator to be controlled at the cavity frequency,
similar to the beacon AFC circuits described n Chap. 7. With a thermally tuned oscillator such as the 2K45 or 2K50, this AFC circuit could
cause the oscillator to track the cavity frequency over a wide band.
A low-frequency
component on the mixer-crystal current could be
used to supply the error signal in the same way as in the beacon-cavity
AFC schemes.
The primary frequency control of the local oscillator
WOU’d then be the cavity-tuning
cent rol. With electromechanical
devices, this control could be made to maintain the correct receiver
frequency through a separate AFC channel operating from the i-f circuits.
For a receiver designed to operate at a fixed absolute frequency, as is
desired for beacon reception, the filter cavity would also be the frequency
standard and no further automatic frequent y control would be needed.
In Chap. 4 it was shown that the maximum value of the product of the
loaded Q and the transmission efficiency compatible with the condition
ensuring continuous operation of the oscillator, for a cavity with a given
unloaded Q and for a given pulling figure for the oscillator, is obtained
by the method of decoupling by adjustment of the cavity-load conditions,
In the present case it is desired to
without dissipative attenuation.
obtain a loaded Q sufficient to reduce to a negligible level the noise
power in the sidebands.
The goal would be to make possible the use of a
intermediate frequency without a substantial contribution
to the over-all noise figure from the local-oscillator noise. At 32 cm,
a 10-db increase in the ratio of available local-oscillator power to available
noise power in the sidebands would reduce the effect of the local-oscillator
A selectivity great
noise to less than 1 db under most circumstances.
enough to give a 10-db increase in the ratio is obtained at 9000 Me/see
with a cavity having a loaded Q of 450 or more. To be able to deliver
1 mw of local-oscillator power to the mixer, from a tube having an
available power of 15 mw, the fractional transmission must be at least
If the cavity is operated with equal input and output loading
and is decoupled from the oscillator by a dissipative attenuator, the
maximum output power from the cavity, compatible with the condition
for continuous oscillation is
TIT =.
() FO–3
from Eqs. (46) and (421).
For a 2K25 or 723A/B oscillator, the value
of b may be taken as 2.75 X 102, corresponding to the measurements
quoted in Sec. 4.14. The maximum unloaded Q that can be used under
these conditions is about 4800. The loaded Q resulting would be about
1600; thus the noise power in the 30-&f c/sec sidebands would be reduced
by 21 db. This is sufficient attenuation of the noise sidebands but
provides only sufficient local-oscillator
power to drive the crystal.
Fortunately, the resonant nature of the cavity can be used to provide
the decoupling of the signal circuit from the local-oscillator circuit.
circuit for a two-channel mixer such as that shown in Fig. 5.3 might be
used. The attenuator should have a minimum attenuation of about
9 db, and it therefore provides a load of small reflection coefficient for
the oscillator.
Since the cavity is nonresonant at the signal frequency,
the reflection of signal-frequency waves by the interaction of the cavity
in the mixer is small and the cross attenuation from the radar mixer to
the AFC mixer is large. For a larger safety factor in the available localoscillator power in the radar mixer, a cavity of lower unloaded Q could be
used and it would then be safe to use a smaller decoupling attenuation in
Since less dissipative attenuation is needed
the local-oscillator circuit.
if the output loading of the cavity is increased and the input-circuit
loading is decreased, somewhat
larger a v a i 1a b 1e local-oscillator
power could be obtained if the
cavity were coupled in this way.
An increase in the output loading
and a decrease in the input loading, in the manner indicated by
Eq. (4.12) would reduce the required am au n t of dissipative
attenuation sufficiently to more
than compensate for the decreased
efficiency of the
cavity circuit.
This, however,
~t~. 5.3.—fl~ul1lc n)ixcr with cavity filter
could be done only at some sacrifor LO noise.
fice in loaded Q, and thus in suppression of the local-oscillator noise. A combination of a higher unloaded
Q and unequal- input and output loading would give the desired result
without a decrease in noise suppression.
5.6. Reduction of Local-oscillator Noise by the Use of a Cavity as
Part of the Oscillator Tank Circuit.—Anothcr method by which a cavit y
could be used to dccrcusc the power in the noise sidebands of the localoscillator signal is to usc the cavity M a part of the tank circuit of
It wtis shown in Sm. 411 that a cavity load circuit on
the oscillator.
an oscillator can give frequency stobilizotion of the oscillator, if the line
length between the cavity and the grids of the oscillator resonator is
For very close
effectively an integral number of half }Vavclcngths.
coupling bctwccn the oscillator and the cavity, the timing of the oscillator
is discontinuous in fmqucncy but oscillfiti(m at the resonant frequency of
the extcrrud ctivity is stalllc. ‘1’his condition Lmounts to a substitution
[SEC. 56
of the external cavity for the tank circuit of the oscillator and a consequent oscillator-resonator
Q determined primarily by the external
Tuning of the oscillator can be accomplished directly by tuning
the external cavity.
Since the best control of the oscillator frequency
by the external cavity results if the external cavity has the highest
possible unloaded Q, the filtering of local-oscillator noise sidebands is
This method is rather difficult to apply because the locking of the
oscillator frequency to that of the cavity is critically dependent on the
length of the line between the cavity and the oscillator.
Because this
line has some dissipative loss, there is a limit to the magnitude of susceptance that can be developed by the external cavity at the grids of the
oscillator resonator.
This maximum susceptance sets a limit on the
frequency range over which the oscillator can be pvlled by the external
cavity without retuning of the oscillator resonator.
If the oscillator
resonator is retuned, there is a limit on the range of frequency for which
a fixed length of line between the oscillator and the external cavity will
give the desired frequency control by the external cavity.
This limit is
determined by the rate of change of the effective electrical line length
wit h frequency, and must thus depend upon the number of half wavelengths of line used. For the largest tuning range, the smallest possible
number of half wavelengths of line must be used, and reflections increasing
the dissipative loss or the. frequency-sensitivity
of the line must be
With 2K25 oscillator tubes, which have a coaxial output line
several half wavelengths long, a fixed length of line between the oscillator
and the external cavity can be used for only a small frequency range—
perhaps 2 per cent, The oscillator can be tuned, by means of the
external cavity alone, through a range of atmut 1 per cent if the
cavity has an unloaded Q of 25,000.
Because of the variation, among tubes, in the clmtrical length of the
output line, a given external circuit, containing a fixed line length between
the tube antenna and the cavity, dots not give frcx[ucncy control by the
external cavity over the same range for all tubes. This variation.
causes one of the principal difficulties in setting up the circuit, since
it necessitates a variable antenna.-to-cavity Iinc length. For each tube
this line must be adjusted to allow control hy the external cavity over the
desired range. Another difficulty cncountcrcd in setting up a circuit of
this kind lies in the fact that, although the oscillator, when it has been
locl:ed to the cavity, can bc tuned over a considcmblc range by tuning
of the external cavity L1OUC,tllc r:mge of oscillatw timing for which
locking can bc producc{l is very sm:dl. A monitoring cirulit is required
to make sure that locking h:LH (Jccurrc{l,
Oscillutor~ lockwl to cavities in tltis \v:LyIHLVC
Iwcn IIscd in the I()-cm
band for the stabilization of frequency.
With a 2K28 tube, a single
half-wavelength line between the oscillator cavity and the external cavity
can be used. The operation is considerably more satisfactory than that,
obtained at 3.2 cm with 2K25 tubes, because of this short line length.
This method is not useful in decreasing the over-all noise figure of a
10-cm receiver because, with a 30-M c/sec intermediate frequency, localoscillator noise contributes a negligible amount to the over-all noise
figure. When used with a very high-Q cavity, such as a resonant echo
box, however, it isuseful asa frequency-stabilization
In the 1.25-cm band, only enough experimentation has been done with
this kind of circuit to show that locking can be obtained and that frequency control by the external cavity can give tuning over 100 or 200
With the 2K33 tube, with its special double-resonator circuit,
Line length adjusted to suit
particular tube and frequency
; ~g
FIG. 5.4.—Circuit for tlm usc of a 2K25 oscillator locked to an external cavity for LO noise
difficulties are again encountered because the same external line length
does not gi~’e contud over the szmc frequency range for various tubes.
For the purposes of LO-noise suppression and of frequency stabilization,
this circuit offers much in the way of simplicity.
It may in the future
be developed to the point of being pr:wticablc from an operational vicJvpoint, especially if the high-Q cavity and coupling circuit are included as
parts of the tube. So fur, hoJvcvcr, it }ms not been developed to the
point of being usable in a rcccivcr intended for field usc in the wavelength
regions below 10 cm. A tube incorpor~t,ing o high-Q resonator in this
way 10SCSthe very useful property of electronic timing, through the
effect, md the t~ming mechanism must produce
a dimensional change in the l~igh-Q cavity.
In Figs. 54 and 5.5 arc shoivn ti~o possil)lc 3.2-cm mixer circuits
incorporating this type of circllit for the sl~pprcssion of local-oscillator
The circuit of Fig. 5.4 provides
noise and for frequency st:d)ilization.
for the extraction of local-oscillator po~vcr for the mixer through a
variable coupling iris in what \rould normally be a short-circuiting end
This iris must be
wall of the waveguide behind the oscillator antenna.
about one-quarter wavelength behind the antenna, to allow the antennato-waveguide coupling to operate efficiently.
A large standing-wave
ratio may exist in the line between the cavity and the oscillator, however,
especially under the condition that the external cavity causes a considerAt a given iris setting,
able pulling of the normal oscillator frequency.
the efficiency of the coupling of local-oscillator signal into the mixer is
greatest when a voltage loop of the standing-wave pattern occurs at the
antenna, and would be zero if a voltage node were to occur there. The
amount ‘of power coupled into the mixer for a given iris setting would
therefore vary considerably, depending upon the amount of pulling
by the external c~vity and upon the cavity-to-antenna
line length
FIG. .5.5.-Cavity
~~ wall for LO coupling adjustment
used as frcqum,cy control m,d soul cc of lo<,al-os.il]ator power cd the
mixer, for the Purpose of LO-l,oiw suppression.
If a voltage node occurs near the antenna, the iris must be adjusted for
large coupling between the local-oscillator circuit and the signal circuit,
with consequent reflection of rcccivcd signal po}vcr. Xo provision is
included to show when the circuit is adjusted in such a.way th~t the local
Such a provision could be made by
oscillator is locked to the cavity.
coupling a separate detector crystal to the cavity as indicated by the
broken lines in Fig. 5.4. Transmission through the cavity to this
crystal would indicate oscillation at the resonant frequency of the cavity.
In the circuit of Fig. 5.5 the cavity itself is used as the source of
local-oscillator signal for the mixer, Since the cavity must be tightly
coupled to the oscillator, a large amount of energy is stored in the cavity
and the coupling to the mixer may bc small. To accomplish adjustment
of the coupling to the mixer crystal a variable exit iris must be used an the
cavity and for this a sliding spring-metal wall between the waveguiclc
and the cavity can be used. Transmission of po]ver through the cavity
to the mixer crystal, with consequent production of rectified current by
the mixer crystal, serves to indicate that the oscillator is locked in
frequency to the cavity.
The adjustment procedure, however, is complicated by the fact that no indication of oscillation is provided when the
oscillator is not locked to the cavity.
Neither of these circuits has been developed to the point of being
practical for use in receivers. They have been included here only to
show some of the difficulties that are encountered with this kind of noisesuppression circuit and the direction in which one might proceed.
an oscillator containing a built-in high-Q cavity were available, the
mixer problem would be simpler. A separate output line from the
resonator of the oscillator would provide the useful power and this line
would be coupled into a mixer circuit in any of the conventional ways.
The frequency-stabilized
10-cm oscillators earlier referred to were used
in this way; one output loop was used to couple the oscillator tightly
to the high-Q cavity and a second to derive the useful power.
For the
present, however, the use of these circuits for LO-noise suppression
has been abandoned in favor of the more foolproof “ balanced” mixer
described in Chap. &
5.7. Effect of D-c Bias on the Mixer Crystal.-A
slight improvement
in over-all receiver noise figure can be obtained through the use of a
small bias voltage across the mixer crystal, if local-oscillator noise is
present. The effect of the bias voltage is to make the conversion IOSS
at a reduced local-oscillator level almost as small as that at the normal
level. Since thenoise sidebands areproportionately reduced, an imProvement in over-all noise figure results. Several additional advantages can
be gained through the use of such a bias voltage.
Accompanying the
reduced LO power requirement is a reduction in the reaction of the
local-oscillator circuit on the signal circuit of the mixer. The over-all
noise figure becomes less dependent upon the amount of incident localoscillator power at the crystal, because the conversion loss does not
increase so rapidly as the local-oscillator drive is decreased.
the i-f conductance of the crystal is less dependent on the amount of
local-oscillator drive.
Figure 5.6 is a graphical illustration of how the conversion loss would
be affected by a positive bias, if the d-c characteristic determined the
behavior of a crystal used in a microwave mixer. For the conditions
illustrated in Fig. 5.6a, the local-oscillator drive has been taken as
less than enough to drive the crystal to the part of the forward characteristic having the greatest slope. The addition of a positive bias
(Fig. 5.6b) increases the i-f current because the positive peaks of the
envelope drive the crystal to a region in which the characteristic has a
greater slope than before, whereas there is little change in the slope of the
There is an optimum
characteristic in the negative part of the envelope.
level since a further increase in bias
voltage would cause the negative part of the envelope to contribute an
i-f current of increasing magnitude with increasing bias voltage.
this current increases more rapidly than that duetothe
positive part of
the envelope, the total i-f current begins to drop, because the current
contributed by the negative part of the envelope has the opposite phase
to that from the positive part. The smallest conversion loss for a
particular local-oscillator amplitude usually results from the use of a
bias voltage less than the amplitude
of the local-oscillator signal.
One method of demonstrating
l-f comDOnent
the effect of a bias voltage is to
in rechfied current
measure the effective over-all noise
figure of a representative receiver
wit h various values of local-osci] later coupling and of d-c bias. Such
Envelope of signal
and local
a measurement is made by finding
oscillator waves
the available c-w input signal power
required to give an output signal
power equal to the output noise
power, when the signal frequency is
at the point of maximum sensitivity
l-t component
The effective
in the pass band.
in rectified current
over-all noisei figure is the ratio of
this signal power to kTB, where B
is the effective noise bandwidth of
the i-f amplifier. For relative noise-
figure measurements, provided B is
not changed by the parameters
FIG. 5.6.—Graphical illustration of
varied between measurements, it
decrease in conversion loss with positive
is not necessary to know B or
bias, for small local-oscillator level. The
barrier capacitance is neglected.
the absolute power level. Thus,
to demonstrate the effect of bias
voltage on the crystal it is not necessary to have an absolute calibration
of the available signal-generator power. A block diagram of a circuit
for measuring the over-all noise figure is shown in Fig. 57.
The attenuator associated with the signal generator is made to match the transmission line. A TR cavity tuned to the signal-generator frequency is
used, and a mixer with iris-coupled local oscillator.
A part of the input
circuit of the i-f amplifier is shown to illustrate the method of applying
a bias voltage through the crystal-current
metering circuit.
circuit shown is only symbolic, in the sense that a practical circuit
includes, instead of the simple condenser filter on the crystal-current lead,
a low-pass refilter of two or three sections, made up of r-f chokes and
The bias voltage is supplied from a battery and voltagedivider circuit. The best values of the battery voltage and of the resistance of the potentiometer circuit, for experimental purposes, should be
such that the series resistance introduced into the crystal-current circuit,
for a bias voltage of one volt, is small compared with the resistance of
the crystal.
For a resistance of 50 ohms per volt, the negative bias,
at 1 ma of rectified current, produced by the flow of the rectified crystal
current through the potentiometer
would be equal to 0.05 volts, a
negligible quantity compared with the forward bias applied by the
ParI of i-f input circuit and
rectified current filter
FIQ. 5,7.—Circuit for measuring the effect of c1ystal bias on over-all noise figure.
battery circuit.
The output power meter may be a thermocouple or
a square-law crystal detector with a milliammeter.
6.8. Results of Experiments on the Effect of D-c Bias.—The results
of some experiments of the kind just described are plotted in Fig. 5“8.
These data were taken on a 1N23 crystal having a measured conversion
loss of 7.9 db and a noise temperature of 1.9. The noise figure of the
i-f amplifier was about 5 db for crystals having average i-f admittance.
In this figure a curve of relative over-all noise figure as a function of
crystal current due to the local oscillator alone (with the bias voltage set
at zero) is given. The minimum of this curve is taken as the zero point,
and an increase in noise figure from this corresponds to an ordinate
below this point, a convention used since minimum noise figure is desired.
There is a set of curves each having its right-hand terminus lying on the
curve for no bias. Each of these curves gives the relative over-all noise
figure for constant total crystal current equal to that corresponding to
the abscissa of the right-hand terminus point and made up of rectified
current and current due to the bias voltage in varying proportions.
abscissa gives, for these curves, the crystal current due to the oscillator
alone. As the curve is traversed toward the left, the bias voltage is
increased, to keep the total current constant.
The curves
show that for any total current there is very little deterioration, and for
most currents some improvement, if that current is produced by smaller
local-oscillator drive and some bias, than if it is all produced by the local
The improvement possible varies considerably from crystal
/ f
—.. .
—. -
DC to rr ake 0.3
DC to make 0,4
DC to rra ke 0,5
D.c to make 0.6
DC to make 0.7
Rectified current in ma from LO alone
1 )
FIG. 5.8.—Eff ect, on over-all receiver noise figure, of a nositive bias on the crvstal.
The data are for a 1N23 crystal with 7.9-db con~ersion Ioss“and a noise temperat~re of
to crystal and data on about 10 crystals showed that as much as 0.5 db
improvement may be gained or as little as 0.1 db. The best noise figure
was obtained in most cases with an amount of local-oscillator drive equal
to that which gave minimum noise figure without bias, and with enough
bias added to increase the crystal current by a factor between 1.5 and 2.
Almost as good results are found with bias at about half the normal localoscillator drive.
The conclusions that can be drawn from these experiments are
restricted because there are many parameters that change with local.
oscillator drive which were not measured.
For instance, the r-f admittance of the crystal to the signal is affected by a change in either the bias
voltage or the local-oscillator drive, and this could contribute to the
variation in the over-all noise figure. To eliminate this the mixer
should have been tunable and adjusted for minimum noise figure for
each point.
Another source of error lies in the use of a fixed coupling
Since the i-f admittance of
circuit from the crystal to the i-f amplifier.
the crystal depends upon the local-oscillator drive and the bias voltage,
the effective noise figure of the i-f amplifier varies from point to point.
Thus the only thing that thk experiment does show is that for this
combination of crystal, mixer and i-f amplifier, some improvement in the
over-all noise figure can be obtained through the use of forward bias
on the crystal.
Of greater significance may be the fact that the range
over which the local-oscillator drive can vary without a large increase
in effective over-all noise figure is increased by the use of the optimum
FIG. 5.9.—Circuit for adding bias voltage to mixer crystal.
bias for each
with the addition
of the local-oscillator
its minimum
of an appropriate
a fixed
in the
a much
bias voltage
has sometimes
The noise
figure can be
of local-oscillator
to the microwave
Such a bias circuit is shown in Fig. 5.9. The bias voltage
applied in the absence of rectified crystal current is 0.175 volts, due
to the l-ma current through the voltage divider.
With increasing
local-oscillator drive, the bias voltage decreases because the rectified
current flows in the opposite direction through the 175-ohm resistor and
thus decreases the voltage drop across it. At 1 ma of rectified current
the bias voltage is zero. Thus the bias voltage is significant primarily
for small local-oscillator drive, where it has the most beneficial effect.
To evaluate completely the usefulness of the bias voltage, measurements should be made separately of the loss, noise temperature, and i-f
admittance of the crystal.
The data just quoted, showing a slight
improvement in over-all noise figure from an added bias when the localoscillator drive is optimum, could be explained by a decrease in the
conversion loss from the addition of the bias voltage.
The same decrease
in conversion 10SSctiuld bc achicvcd with greater local-oscillator drive but
the increase
of converted
noise apparently
results in a
of increased
range of
lies in the possibility
of obtaining
a large electron&
AFC purposes.
The addition of
bias voltage by the circuit of Fig. 5.9 allows the tuning to be carried to a
lower-power point. in the reflector mode than without the bias. Some
experiments were made to measure the over-all noise figure over the
650 - 16 -
14 -+
550 -
12 n
g 50!3 .’;10 *
.---qz 450 -$ 8 -
Conversion loss without bias
loss wth
400 -
R,., with bias
t with bias
twithout bias
250 1
0 25
High-frequency side
Per cent power
Low-frequency side
UIG. 510.-–f3ffcct
of I)ias rircuit of l’ig. 59 m] tljc ronvcrsion 10+, noise temperature.
i-f rcsist:m cc, unri ovck:~l] tvcvivcc rt<>isc
fi~,,,c ,,%t),. 1<)(:1
} <,wkll:,tc,lL&ekxtloni(’a])~r tuned
through a I’cflcl’t(, r I,)<, (IC. ‘~l)c vryst:d is :1 I N2!{; \, tl)c I.(J tulx. :i 72:}.4 /1), tl~c illtcrmcdiate
frcqucnr.y 30 Mr/sm,, wld tlio cffcctivc i-f Jtoiw figure 4 dt,.
IJias voltage is supplied from
the circuit of Fig. 5.9.
range of electronic tuning, with and IVitholit l~ius. The bias circuit was
that of Fig. 5.9 and indcprmdcnt mcasurcxncrrts of 10SS,noise temperature,
and i-f resistance of the cr.ystid wore made. The apparatus ~vas similar
to the noise-temperature test set in thtit it included the on~eighth-wavelength-line m:~tchin~ transformer bctlvccn the crystal tind the i-f amplifier.
This mrtdc the mcosllrcmcnt of the cryst:d m,isc tempcratllrc independent
of the i-f rcsistan rc t)f the cryst:d.
,i noise ~lio{ln was ~lsrtlto calibrate the
apparatus find to nlc;ml rc tlic i-f resistj! mm. \t’itll the nt)isc diode, the
diode current required to produce a given deflection on the output meter
was measured with each of several resistances substituted for the crystal.
When the crystal was in place and operating with the same amplifier
gain, the diode current required to give noise sufficient to produce this
same deflection was thus a measure of the i-f resistance of the crystal.
The conversion loss was measured by use of a calibrated low-level signal
The i-f output po\ver from the crystal was found by use of
the noise power from the noise diode as a standard of reference, since
the i-f resistance of the crystal was known.
The i-f amplifier and output
meter could thus be regarded as a calibrated low-level i-f power meter.
The results of this experiment are shown in curves of Fig. 510.
At the center of the electronic tuning range, the crystal used showed no
improvement in over-all noise figure due to the bias when the rectified
current was 0.5 ma. The over-all noise figure plotted is calculated from
the loss and noise temperature assuming an effective i-f amplifier noise
figure of 4 db. At the quarter-power points in the electronic-tuning
range, however, some improvement is found.
A crystal current of
0.125 ma would result there without bias. With the tube tul,,:l to
the quarter-power point on the high-frequency side of the center of the
electronic-tuning range, the noise figure is improved by 1.2 db by the
addition of the bias and is almost the same as at the center of the mode.
This is almost completely accounted for by the decrease in conversion
loss due to the bias, since the local-oscillator noise is almost constant in
the high-frequency part of the electronic-tuning range. On the lowfrequency side the improvement in noise figure is not so great, however,
because, although the conversion loss is decreased by the same amount by
the addition of the bias voltage, the local-oscillator noise is so large that
its effect increases significantly with the decreased conversion loss. The
bias current must also contribute to the noise temperature somewhat
but this is apparently small compared with the converted local-oscillator
noise. Since the crystal used for this experiment had a noise-temperature
of only 1.3, for about 1 ma of reetified current, small effect due to the
bias current would be expected.
The most marked effect of the bias voltage in Fig. 5“10 is the change
in i-f resistance.
Whereas without bias the resistance rose from about
400 ohms to over 650 ohms when the local-oscillator drive was decreased
by a factor of 4, with bias the i-f resistance was between 340 and 370
ohms for the whole range of local-oscillator drive. If the i-f amplifier
to be used in a receiver were sensitive to the i-f resistance of the crystal,
with respect either to noise figure or to bandpass characteristics, a
bias-voltage circuit would be of considerable value.
Provided the imagefrequency wave is not reflected to the crystal, however, the bias voltage
makes little difference in the percentage spread of crystal resistances
encountered for various crystals at a fixed local-oscillator level.
However, if the image-frequency wave is reflected to the crystal, by a TR
cavity for instance, the situation is much more complicated because the
i-f impedance varies in both resistive and reactive parts, from crystal to
crystal, as discussed in Chap. 2. A bias voltage would probably change
the relative spread of impedances very little.
Both of the experiments just described were made at 3.2 cm with a
At 1.25 cmwhere the local-oscillator
30-Mc/sec intermediate frequency.
noise is somewhat greater, a larger improvement might be gained through
the use of positive bias.
>To very reliable data have been taken to find
out how much the improvement might be, largely because the balanced
mixer was introduced as a good solution to the problem of local-oscillator
noise. Since the balanced mixer ha~. several other advantages besides
that of the suppression of local-oscillato’rnoise,
it is often tworth using,
A discussion
even if other methods of noise suppression are sufficient.
of the balanced mixer is to be found in Chap. 6.
In a receiver using bias voltage on the crystal, it is desirable to provide
the usual meter for the rectified crystal current to facilitate adjustment of
the local-oscillator coupling.
The bias voltage alone produces a rather
small crystal current but when a small amount of local-oscillator power is
added, the crystal current increases by a considerably larger amount
than it would without the bias voltage.
For the purpose of setting the
LO power level, it has been considered advantageous to use a meter jack
or switch which short-circuits the bias voltage when the meter is put into
the circuit, so that the crystal-current reading is approximately proportional to the local-oscillator power incident on the crystal.
The jack
also allows one side of the meter to be grounded, which simplifies the
The complexity of design and of operation of mixer circuitsin which
filter cavities are used for the suppression of local-oscillator noise has led
to considerable interest in the development of a microwave balanced
mixer. A balanced mixer utilizes two separate mixer units driven in
shunt by the local-oscillator signal and in push-pull by the received
signal, orvice versa. This results inabalanced
push-pull output signal
at the intermediate frequency, and the i-f amplifier input circuit is
designed to give response only to such a balanced signal. Any i-f output
signals derived from noise accompanying the local-oscillator power appear
in the same phase at the output terminals of each mixer unit and are
therefore discriminated against by the input circuits of the push-pull i-f
The suppression of local-oscillator noise is thus obtained
The operational comwithout resort to frequency-selective
plexity of the balanced mixer is no greater, and is in many respects less,
than that of a simple mixer. The many additional properties of the
microwave balanced mixer in its final form make it often advantageous
even when the suppression of local-oscillator noise is not required.
6.1. Simple Microwave Balanced Mixer.-Figure
6.1 is a schematic
drawing of a microwave balanced mixer.
If it is assumed that the
crystals may be treated as resistors across the microwave line and that
the local-oscillator power can be introduced into the microwave line by a
simple, very loosely coupled probe, it is seen that this circuit behaves as a
balanced mixer. The TR cavity is assumed to present, in the plane of its
exit iris, a short circuit to power at the local-oscillator frequency.
crystal is therefore coupled to the local oscillator in the same way, and
since the probe excites waves traveling in both directions and having
the same phase at planes equidistant from the probe, the local-oscillator
signals at the two crystals are in phase. The received signal, on the other
hand, having passed through the TR cavity, arrives at the two crystals in
opposite phase since the crystals are spaced a half wavelength apart. A
consideration of the simple addition of a small signal wave and a large
local-oscillator wave will show that the amplitude-modulation component
at the beat frequency, in the envelope of the sum of these two waves,
reverses in phase if the relative phases between the local-oscillator wave
and the signal wave are reversed. Thus the i-f voltages at the output
terminals of the two crystals are opposite in phase. By means of the
[SEC. 61
transformer, the push-pull i-f signal is changed into a signal that can be
used to excite a conventional unbalanced line or an i-f amplifier,
The local-oscillator noise arrives at the two crystals through the same
circuit as does the local-oscillator signal. The relative phases between
the noise components and the local-oscillator wave are the same at the
two crystals, and therefore the noise converted to the intermediate
frequency has the same phase at the output terminals of the two crystals.
The balanced transformer does not produce an output voltage from
equal voltages in the same phase in the two legs of its input circuit, and
thus the converted noise is not
coupled into the i-f amplifier.
over-all noise figure is determined by
the conversion loss of the balanced
mixer, its noise temperature and
the noise figure of the i-f amplifier,
without a contribution from localIf the two crystals
oscillator noise.
loss in a
A I.f &
simple mixer circuit, the conversion
loss in the balanced mixer is the same
FIG. 61.-Slmple
balanced mixer with
as that of a single crystal.
push-pull i-f transformer to unbalanced
half the r-f signal power is applied
The availabie i-f
to each cryst~l.
output power from each crystal is therefore only half what it would be for
an unbalanced mixer, but since the two powers are added, the over-all
The noise temperature
conversion loss is that of a single crystal.
associated with the output admittance of the push-pull transformer is
just that of a single crystal, provided the two crystals have identical
noise temperatures.
The advantage gained by this balanced mixer,
therefore, is the suppression of local-oscillator noise, and nothing is lost.
The degree to which local-oscillator noise is suppressed depends upon
how closely identical are the converted i-f noise components at the output
This is determined partially by the degree
terminals of the two crystals.
to which the two crystals have identical conversion losses. Since the
available output power from the i-f transformer is proportional to the
square of the difference between the voltages produced by the two
crYstals, a small difference ‘in conversion 10SSdoes not destroy the Suppression of local-oscillator noise. If the two crystals have conversion
losses L, and L, respectively, the available i-f signal power is proportional
to (W
+ v’~)
2whereas the available converted LO noise power is pro-
The factor by which the local-oscillator
portional to (W’I – @72)2.
noise is suppressed, relative to the signal, is
+ w2)2/(fil
– Wz)’.
SEC. 6.2]
If L1 = 2L.2, corresponding to a 3-db cliffercnce, the local-oscillator noise
is suppressed by a factor of 34, or by 15.3 db. This factor is sufficient
to reduce the effect of the unbalanced noise on the over-all noise figure to a
negligible amount under most conditions; therefore an unbalance in
conversion loss as great as 3 db could be tolerated, if this were the only
source of unbalance in the circuit.
A much more serious source of unbalance in this mixer circuit arises
from the possible inequality of the r-f admittances of the crystals.
power delivered to the crystals, both by the signal generator and by the
local oscillator, is divided between the crystals in a ratio dependent upon
their r-f admittances.
To the signal, the two crystals appear in parallel
so that the ratio of the signal powers delivered to them is just the ratio of
their r-f conductance, the crystal having the larger conductance receiving
the larger power.
To the local oscillator, the crystals appear at the ends
of quarter-wavelength lines and these lines are connected in parallel at
the plane of the local-oscillator probe.
If the r-f admittances of the
crystals were pure conductance,
the ratio of local-oscillator
delivered to the two crystals would be the inverse of the ratio of their
that is, the crystal having the smaller conductance would
receive the larger local-oscillator power. Since the r-f admittances of
representative crystals of a given type vary considerably, it is not unlikely
that randomly chosen crystals might differ in conductance by a factor
as large as 4. For example, a pair of crystals having admittances of
2% and YO/2, respectively, would differ by this factor, and since each
would suffer a reflection loss of only about 0.5 db in the conversion-loss
test, they would not necessarily be eliminated by the specifications.
This source of unbalance can be equivalent to 6 db or more of unbalance
in output power. When this unbalance is added to the possible unbalance
in conversion loss, it is seen that the suppression of local-oscillator noise
might not be sufficient unless crystals were selected in balanced pairs.
Such a selection would best be made on the basis of measurements of
r-f admittance, since the admittance is seen to be the more serious
source of unbalance.
A mixer that requires selection of crystals is
certainly to be avoided if possible.
For the purpose of providing a
balanced mixer that is less sensitive to inequalities of the r-f admittances
of the crystals, the “magic T” was developed.
To facilitate the discussion of balanced mixers based on this circuit, a short discussion of
the principles of the magic T and some of its equivalent circuits must be
6.2. General Properties of the Magic T.—One variety of magic T in
rectangular waveguide is a circuit consisting of a waveguide with two
other waveguides connected perpendicularly to it, one in the broad wall
and the other in the narrow wall, at a common junction plane. Each
of the joining waveguides makes, with the original waveguide, an ordinary
[SEC. 6.2
The structure formed by the branch in the broad side of the
main waveguide and the main waveguide is called an E-plane T-junction,
The arm in the
and behaves essentially as a series-connected circuit.
narrow plane constitutes, with the
main waveguide, an H-plane Tjunction and can be described in
terms of a parallel circuit.
both these side arms are present,
and have a common junction
plane, as in the magic T, the arms
on the narrow side and on the
broad side of the main waveguide
are often referred to as ~heH-plane
and the E-plane arms, respectively.
The complete structure
has some very special properties,
however, because of its symmetry,
H.plane arm
no simple series- or parallelFIG. 6.2.—Perspective view of magic T.
connected equivalent circuit can
be used to describe it. In Fig. 6.2 a perspective view of the structure of
a magic T is shown,
To understand the special properties of the magic T it is necessary
to realize the difference between the coupling of the H-plane T-junction
In Fig. 6.3a and b are shown,
and that of the E-plane T-junction.
respectively, the field configurations in the region of the junction for each
FIG. 63.-Representation
of these
of coupling in simple T-junctions; (a) H-plane T-junction; (b)
E-plane T-junction.
by a wave
into the side
to represent the wavefront
as it progresses down the side arm and through the junction.
circles with crosses represent the E-vector pointing into the paper.
It is seen that the waves traveling outward from the junction have the
same phase at planes equidistant from the center of the junction, or
from the plane of symmetry,
In Fig, 63b, which represents the E-plane
T-junction, the electric field vector is in the plane of the paper and is
arm of each.
are drawn,
in Fig.
represented by lines ]vith arrows indicating the direction.
The electric
field fringes at the junction and cxcitcs the horizontal arms with waves
having opposite phases at planes equidistant from the plane of symmetry.
Thus the waves in the horizontal arms ~f the 11-plane T-junction may be
said to possess completely even symmetry about the junction and those
in the E-plane T-junction to possess completely odd symmetry about the
Another wmy of illustrating the action of the H-plane T-junction is to draw the magnetic field vector, which fringes at the junction.
The magnetic field lMS opposite directions at symmetrically disposed
planes in the horizontal arms, but, since the waves are traveling in
opposite directions, the associated electric fields must point in the same
direction, as sholvn, at thmc tivo planes. In both of these T-structures,
with each of the horizontal arms infinite in length, there would be a
wave reflected upivard in the side arm due to the discontinuity of the
The same kind of coupling exists between the side arms and the
collinear arms of the four-arrncd structure of Fig. 6.2. Because of the
opposite kinds of symmetry associated with the side arms it is evident
that a wave traveling into the E-plane arm excites only a wave of odd
symmetry in the junction and cannot therefore excite the H-plane arm.
The result is that only waves Imving opposite phases at planes equidistant from the plane of symmetry fire excited in the collinear arms,
and a reflected wave is excited in the E-plane arm. Similarly, a wave
sent into the H-plane arm excites, in the collinear arms, only waves
having like phases at planes equidistant from the plane of symmetry
and excites a reflected wave in the IZ-plane arm. There results, therefore,
a device that transmits power to two lines from each of two independent
input lines but shows no direct coupling between these input lines.
In order that the magic T may be most useful, the input arms should
have no reflections when nonreflecting terminations are placed on
the collinear arms. Some kind of reflecting irises in the E-plane and the
H-plane arms can be provided to produce reflections that cancel the
These arms of the T-junction will then
reflections from the junction.
be reflectionless when the collinear arms are terminated with reflectionless
Provided the matching structures do not upset the symmetry
of the junction, the lack of direct coupling between the E-plane and the
H-plane arms is preserved.
Under the condition that such matching devices are used, the Tstructure takes on other special properties.
Suppose that waves of
equal amplitudes are sent simultaneously into the E-plane and the
H-plane arms. Because of the odd and even symmetry, respectively,
of the waves excited in the collinear arms, the relative phases between
the two input waves can be so adjusted that the secondary waves excited
[SEC. 63
in one of the collinear arms cancel. Then the secondary waves in the
other collinear arm are in phase and therefore add in amplitude.
the total power contained in the waves sent into the E-plane and the
H-plane arms is contained in the wave traveling outward in one of the
collinear arms. A reversal in the direction of propagation of these
waves then shows that a wave sent into one of the collinear arms excites
waves of equal amplitudes in the E-plane and the H-plane arms, and
does not suffer reflection at the junction, nor does it couple to the opposite
collinear arm. The same is true for a wave sent into the other collinear
arm. If planes arc chosen in the E-plane and H-plane arms in such a
way that the waves traveling outward in these arms, excited by a wave
sent into one of the collinear arms, have like phases, the waves due to
power entering the other collinear arm have opposite phases. Thus,
with the matching devices in the E-pkme and the II-plane arms, the
structure has the property that power sent into any arm transmits only to
the adjacent arms, and does so without reflection.
Furthermore, the
waves cxcitcd in these adjacent arms have the opposite kind of phase
symmetry if the input wave is sent into the arm opposite to the original
one. It is to this structure, including the matching irises, that the term
magic T is applied.
6.3. The Matching of the Magic T.—Any of the conventional kinds of
matching structures may be used in the magic T at a single frequency.
It has been found, however, that with inductive irises the frequency
band over which the match is good is not large. This is especially true
of the Ii-plane arm, where the voltage standing-wave ratio to be matched
out by the iris is larger than in the E-plane arm. At 3.33 cm in waveguide having outside dimensions of 1 in. by ~ in., the voltage standingwave ratio that must be matched out is about 3.6 in the H-plane arm
and 2.2 in the E-plane arm. In the 1.25-cm band with ~-in. by +in.
waveguide, it is about 7.5 in the H-plane arm and 2.8 in the E-plane arm.
With an inductive iris placed as close as possible to the junction in the
proper position to match the H-plane arm at a given frequency, the
voltage standing-wave ratio rises to about 2 with a change of frequency
of less than 1 per cent.
A structure giving a less frequency-sensitive matching effect for the
H-plane branch has been found.
In the & by ~-in. waveguide used at
1.25 cm an iris in the plane of symmetry extending outward from the
wall opposite the H-plane arm and upward into the E-plane arm has been
used. Thk and an asymmetrical inductive iris for matching the E-plane
arm are shown in Fig. 6.4. The voltage standing-wave ratio, with
nonreflecting loads on the collinear arms, is less than 1.10 over a plus or
minus 1 per cent band, in the H-plane branch.
In the E-plane branch
the voltage standing-wave ratio is less than 1.10 at the center of the band
SEC. 6.3]
and rises to about 1.30 at the edges of the plus and minus 1 per cent
For the 3.33-cm band, a post was found to give a better match, over
a wide band, than an iris of this kind, although a similar iris in the plane
FIG. 6.4.—Positicms of irises for matching
a magic T in ~-in. by ~ -in. waveguide. The
iris thickness is 0.020 in.
FIG. 6.5.—Positions of post and iris for
matching a magic T in }-in. by ~-in. wave- ().
guide. The iris thickness is +Z in., tbe(
diameter of the post is ~ in., and the lengthl
is 0.650 in.
of symmetry could be designed to give a perfect match at a single fre- ~ ~
This post, again with the single asymmetrical inductive irk
for matching the E-plane branch, is shown in Fig. &5. The vo~a~ v ~
standing-wave ratio observed in the 12 per cent band from 3.13 to s8.58
cm, for a magic T like that of Fig.
6.5, is shown in Fig. 6.6. It is
~ ,;
evident there that the match obarm ,, \
tained in the H-plane arm is al- ~ 1,3
most independent of frequency.
.. . .
Unfortunately no simple structure
‘ *“2
1.1 H.~ly::[m
_ J.- -—----z-.--: >] .“ :’4
was found that gave a wideband
match for the E-plane branch.
The voltage standing-wave ratio
Wavelength in cm
measured in the collinear arm is
~T~. &6,--Voltage standing-wave ratio
vs. wavelength, for magic T matched as
also shown.
The amount of this
shown in Fig. 6.5.
standing-wave ratio depends on
the other two but cannot
of the reflection
be derived
from them
of the
of the complete
of the magic
T, the symbols
in Fig. 6.7a and b are used in illustrating its applications.
The arms are
numbered in a definite relationship to the physical structure, because
for many applications it is necessary to know the phase relationships
between the waves in two opposing arms and not in the other two.
such cases, the collinear arms are favored over the other two since the
phase relationships between waves in them are completely defined by
the symmetry of the structure.
The lack of direct coupling between the
H-plane and the E-plane arms (henceforth arms (3) and (4), respectively)
is independent of frequency, but for arms (1) and (2) it is independent of
frequency only to the extent that the matching of arms (3) and (~) is
Measurements could be made to determine
independent of frequency.
the location of planes in arms (3) and (4) for which phase relationships
similar to those holding for arms (1) and (2) could be specified, but the
positions of these planes may vary with frequency and are dependent
upon the particular matching structures used.
One pair of planes in arms (3) and (4), which are useful for purposes of
calculation, may be defined in the following way. Suppose arms (1) and
FIc. 6.7.—Symbols used to represent tbe magic ,T.
(2) are both short-circuited in planes equidistant from the plane of
If a wave is sent into either arm (3) or arm (4), the waves
excited in arms (1) and (2) are reflected toward the junction from the
short-circuiting planes with the same kind of symmetry as they had in
A wave is therefore excited only in
traveling outward from the junction.
the input arm and the standing-wave ratio in the input arm is infinite.
For this pair of planes in arms (1) and (2) a pair of planes, in arms
(3) and (4), at which voltage maxima (zero admittance) occur may be
It now follows that, if arms (3) and (4) are short-circuited in
these planes, an admittance of zero will be seen in the planes which were
short-circuited in the previous experiment, looking into arms (1) and (2).
An equivalent four-terminal-pair network describing the action of the
magic T in terms of voltages and currents, can now be defined, where
the terminal pairs are understood to be located in these four planes.
6.4. Description of the Magic Tin Terms of Voltages and Currents.—
The relationships between the voltages and currents in the terminal
SEC. 6.4]
pairs of any linear, passive four-terminal-pair network. can be shown to be
given by the four simultaneous linear equations
iI =
yllel +
y12e2 +
y13e3 +
iz= ylzel + y22e2+ y23e3+
i3 =
y13el +
y73e2 +
y33e3 +
i4 =
y14e1 +
y24e2 +
y34e3 +
where the coefficients yn~ are constants depending on the properties of
the particular network.
For this particular circuit, the definition of the
position of the planes of the terminal pairs and the fact that there is no
direct coupling between opposite arms gives
Y1l =
Y22 =
y33 =
y44 =
ylz =
y34 =
Thus Eqs. (1) reduce to
y13e3 +
i2 = y23e3+ y24e4
i3 =
y13el +
i4 = y14e1+ y24e2I
It can further be shown that the coefficients ym~,for a network containing
no elements capable of dissipating power, are pure imaginary.
matched loads are connected to arms (1) and (2) and a current is induced
in arm (3), the symmetry condition for the H-plane branch and the
conservation of power allow the relation
to be written, where Yo is the characteristic admittance of the waveguide.
The sign is determined by the choice of the plane of the terminals
in arm (3), there being a plane, given by the definition above, every
half wavelength from the first plane. Since the sign is reversed for
consecutive planes, the definition of the terminal plane may be further
restricted to correspond to the positive sign, and thus
y,[email protected]
Similarly, a current induced
(1) and (2) gives
in arm (4) with matched
loads on arms
[SEC. 64
Again, choosing the position of the terminal plane in arm (4) that corresponds tothe positive sign, there results
y24 =
The set of transformation
_j ~
equations describing the magic T thus becomes
relations of Eq. (3) may beused, for example, to
find the power delivered from a generator of known characteristic admittance on one arm to a load of known admittance on a second arm, if the
If a generator
admittances on the other two arms are also known.
having an available power P, and an internal admittance Ys is connected
to the terminal plane representing arm (3), the power delivered to a
load of admittance Y, at the terminal plane representing arm (4) is
found to be
P, = 49394
(Y, – Y*)
(1 + Y, Y,) (1 + Y, Y,) + (1 + Y, Y,) (1 +
Y, Y,)
2 Po,
where g~ and g, are the conductance parts of Yt and Yi, respectively,
YI and YI are the load admittances connected to the terminal planes
representing arms (1) and (2), respectively, and all admittances are
expressed in units of Yo. This equation shows that the power transmitted
to arm (4) is zero if YI and Y, are equal. The magic T is therefore often
regarded as a bridge.
A similar relation showing the power delivered to
the load on arm (1) is
(1 +
(1 +
Y, Y,)
Y, Y,) +
(1 +
2 P,.
(1 +
From these expressions a similar equation for a load on any arm and a
generator on any other arm may be written down simply by proper
permutation of the subscripts.
When the load and the generator are on
SEC. 6.4]
opposite arms the equation to be used is Eq. (4); when they are on
adjacent arms, Eq. (5) is used.
There are many possible microwave circuits similar in behavior to
the magic T just described.
The conventional low-frequency “ hybrid
coil” circuit, used in wire telephony to isolate signals traveling in different
directions on the same wires, behaves as a magic T if it is arranged to
have the same characteristic admittance at all four terminal pairs. A
microwave circuit that is coming into wide use as an equivalent to the
magic T is shown in Fig. 6.8. This device may be made of waveguides,
coaxial lines, or even open-wire transmission lines. The side arms may be
connected either in series or in shunt at positions a quarter wavelength
apart along the periphery of the circular Ii-wavelength line. For the
network to be matched, the circular line should have a line admittance
FIG. 6.S.—The ring circuit.
@ times that of the branch lines, neglecting the effects of higher modes,
If the side arms are
if the side arms are connected in series, as shown.
connected to the ring in parallel, the ring should have a characteristic
admittance @/2
times that of the side arms. In Fig. 6.9, a coaxial-line
circuit of this type designed for 10 cm is shown. Since this device is
used with small cable fittings and flexible cables it is difficult to make
as precise measurements upon it as those on the waveguide magic T.
The measurements that have been made show that the output power
from one of the arms adj scent to the input arm is at least 20 db greater
than the power from the opposite arm, for wavelengths between 8 and 11
cm. Since this small amount of coupling maybe attributed to reflections
in the cable connectors on the arms adj scent to the input arm, no attempts
have been made to improve the balance.
The standing-wave ratio in
the input line is as small as would be expected with these connectors in the
circuit; thus the higher-mode effects at the junctions are apparently
[SEC. 6.4
Another possible circuit that behaves as amagic T is shown in Fig.
This circuit issimilar inprinciple tothewaveguide
version of the
magic T, in that it consists of series and shunt connections, at a common
600 ‘---l
FIG. 6.9,—Magic T equivale,]t for 10-cm band.
Characteristic admittance = Y. _
Characteristic-. ~
admttance = Y.
= Y.
admittance =2 Y.
FIG. 6.1O.—A magic T in coaxial line.
point, to a single line, the two ends of which form the other two pairs of
This circuit has been considered for use in the longerwavelength part of the microwave region, where the physical size of
waveguides might be prohibitive, for applications in which a ring circuit
Like the waveguide magic T, this
does not give sufficient bandwidth.
circuit depends on the matching devices in the series and shunt-connected
arms to obtain zero coupling between the other two arms. Like the
magic T it derives the zero coupling between the series and shunt arms
from its symmetry, and therefore this property is insensitive to frequency.
For any of the applications of the magic T, any of the equivalent
forms just described can equally well be” used. In the following discussions of balanced mixers the waveguide magic T will be used for all
I lf~u
,- .
FIG. 6.1 1.—An equivalent to the magic-T circuit, madeof coaxialline and waveguide in
illustrative purposes because it has been used extensively in this application. The mixers can be constructed from waveguide or coaxial-line
ring equivalents or from any of the other possible equivalent circuits
if space or wavelength requirements make such forms preferable.
One of
the first balanced mixers to be designed using a magic-T circuit was
made of a combination of coaxial lines and waveguide in the form shown
in Fig. 6.11.
6.6. The Magic-T Balanced Mixer.-In
order to construct a balanced
mixer from a magic T, two opposite arms are terminated by crystals
in standard waveguide mounts.
The signal enters one of the remaining
arms and the local oscillator power enters the other. Although it is not
necessary to use this arrangement, the crystals are usually mounted on
arms (1) and (2), in the terminology shown in Fig. 6.7. Thus the
resulting balanced mixer appears, for the 3.3-cm band, as shown in Fig.
[SEC. 6.5
- rol.e..of yfie [email protected]_aqd. bcai:o~tiu~to?-~nlyt. ?rrn! can_b~
interchanged, for in either case the relative phases between the incident
si~l ‘w–a-~eand the incident local-oscillator wave are opposite at the
two crystals.
Since there is no direct coupling between the signal-input
circuit and the LO-input circuit, no reactive decoupling in the localoscillator circuit is required.
Only enough local-oscillator power to drive
the two crystals is needed.
If more local-oscillator power is available,
a matched dissipative attenuator can be used in the local-oscillator arm.
The load admittance presented to the local-oscillator tube is thus well
controlled, because the crystals themselves provide the local oscillator
The fact
with a load that is approximately matched to the waveguide.
that the balanced mixer can be operated with a local oscillator having
such a small output power, without the danger of loss of signal through
To local
FIQ. 6.12.—Magic-T balanced mixer for 3.3-cm band.
interactio~ of the signal and local-oscillator circuits is one of the many
advantages of the magic-T balanced mixer.
The suppression of local-oscillator noise by the magic-T balanced
mixer is not affected in the same }vay by the crystal admittance as it is in
the simple balanced mixer earlier describwl.
If one of the crystals
reflects either the signal wave or the local-oscillator wave, the reflected
power is sent only out the signal arm and the local-oscillator arm, because
the opposite arms of the magic T do not couple directly.
If there is no
reflection of waves traveling outward in these arms, there is no way in
which the signal power or the local-oscillator power delivered to the
second crystal can be influenced by the mismatch of the first. If there is
sufficient available local-oscillator power to allow some matched dissipative attenuation between the magic T and the local oscillator, the
nonreflecting condition for the local-oscillator arm is approximated.
If there is a bandpass TR cavity, or no resonant circuit at all, in the signal
arm, a wave traveling outward in that arm is radiated by the antenna
without reflection.
If a resonant TR cavity must be used, that part of
SEC. 6.5]
the iocal-oscillator wave which, having been reflected by the crystal,
travels out the signal arm, is reflected by the TR cavity and interferes
with the direct local-oscillator wave coupled to the two crystals.
result is that the division of local-oscillator
power between the two
crystals becomes similar to the division in the simpler shunt mixer.
The power reflected from one crystal is reduced to onehalf of its value
by two transits through the magic T before it arrives at the other crystal.
However, as application of Eq. (5) will show, the form of the dependence
of the delivered local-oscillator
power on the admittances of the crystals
is the same in the magic-T circuit if the signal arm is open-circuited as
in the balanced mixer with shunted crystals.
A two-to-one ratio of conductance
causes a two-to-one split of power.
The remaining power,
originally delivered to the mixer, is reflected into the local-oscillator
This unbalance in local-oscillator power delivered to the
two crystals does not seriously affect the suppresii m of local-oscillator
noise because the crystal conversion loss is not strongly dependent on
the amount of local-oscillator
drive, provided that the amount is
sufficient to produce a few tenths of a milliampere of rectified crysd
The splitting of the signal power between the two crystals is not
influenced great{y by the presence of a TR cavity because a reflected
wave, at the signal frequency, coming from the mixer would not be
strongly reflected by the TR cavity, which is tuned to pass this frequency.
Thus the magic-T balanced mixer does not require nearly so great a
similarity between the two crystals used as does the simple balanced
mixer. If both the signal line and the local-oscillator line are nonreflecting to waves traveling outward from the mixer, tkonly
effect of
reflection by the crystals is an increase in their conversion loss by the
same amount as would be found if they were operated individually from
matched generators.
With the same tuning of the crystal mounts as in
the conversion-loss test set, and at the same frequency, the total conversion loss for each crystal in the balanced mixer, including r-f reflection
loss, would be the same as would be measured for that crystal in the test
set. Under these conditions it is unlikely that more than 3 db of unbalance in conversion loss would be found, if the crystals had a small specification value of maximum conversion loss and normal i-f admittances.
It is desirable to employ an i-f coupling circuit, such as that shown in
Fig. 613, the performance of which is not affected by a lack of balance
in the i-f admittances of the two crystals.
The transformer shown in
the figure resonates with the mixer and tube capacitances and has
the bandwidth and the impedance stepup from the crystals to the
grid required to achieve a good noise figure. To reduce capacitive
coupling between the coils, adjacent ends are made to operate at ground
[SEC. 65
and to achieve this the secondary is made of two sections
wound in opposite directions.
Ordinarily the inner ends of the two
primary coils would be grounded through the current-filter capacitances,
but in this circuit the impedances
Z are connected between the i-f
ground andthe coils. The bypass
condenser between the inner ends
of the two coils ensures that they
are at the same potential.
between the common ends of the
primary coils and ground there
appears an impedance equal to
The impedance Z is chosen
in such a way that 2/2 is the
FIG. 6.13,—Special i-f input circuit for
complex conjugate of the impedbalanced mixer. C =i-f bypass, RFC = i-f
ance that would be measured bechoke, Z = see text, MA = crystal-current
tween the junction of the two
primary coils and ground if each crystal had the i-~ output impedance of
an average crystal.
The addition of this impedance to the push-pull input circuit makes
the behavior of this circuit similar to that of a magic T. If a voltage
were impressed from grid to ground on the secondary of the transformer,
equal voltages in opposite phases would be produced across crystals
having equal impedances.
h’o voltage would result across the impedances Z. A voltage across the dummy-load impedance 2/2, on the other
hand, would produce equal voltages in like phases across crystals having
equal impedances, with no voltage produced at the grid. Thus the
terminals of the dummy-load impedance 2/2 correspond to the terminals
of arm (3) of a magic T, and the grid-to-ground terminals correspond to
those of arm (4). The choice of a dummy-load impedance in the manner
described corresponds to the use of a matching structure and a matched
load in arm (3) of a magic T. If the grid admittance of the tube were
the complex conjugate of the admittance of the secondary terminals of
the transformer, the equivalence to a magic T would be complete.
best i-f amplifier noise figure, however, some mismatch exists at these
The advantage of a circuit that is like a magic T is that a
voltage impressed across one crystal does not develop a voltage across
the other, as seen from the argument that was used to show the absence
of direct coupling between the collinear arms of the magic T. Thus
the coupling of a signal from one crystal to the amplifier tube would
be independent of the i-f impedance of the other crystal. Since the grid
is not matched to the transformer, however, the independence is not
complete so far as signal transmission is concerned.
Suppose that two crystals do not have the same i-f impedances,
but that they do develop identical output voltages when loaded with an
impedance that matches the i-f output impedance of an average crystal.
If these crystals were used in a balanced mixer connected to the present
input circuit, the suppression of local-oscillator noise would be perfect
because the equal voltages excited by the crystals would develop a
voltage only in the dummy load 2/2, corresponding to arm (3) of the
magic T. Because of the choice of this impedance, each crystal is loaded
with an impedance that matches the i-f output impedance of an average
crystal and, therefore, the equality of the developed i-f voltages is
Because the test apparatus used to measure the conversion
loss of crystals actually measures the voltage developed across a load
impedance of this kind, crystals having identical conversion loss in the
crystal test set should give perfect suppression of local-oscillator noise.
With the magic-T-equivalent
input circuit and the magic-T mixer circuit
this suppression is assured, independently of the actual i-f impedance
Because of the magic T, an inequality
and r-f impedance of the crystals.
in r-f impedance contributes little to the unbalance of the mixer and
similarly, because of the i-f input circuit, which is equivalent to a magic T,
an inequality in i-f output impedance causes little loss in noise suppression.
If these two circuits are used, there is some significance to a calculation
of the noise suppression realized for a given inequality in crystal conversion loss, as measured by a test set. The amount of LO-noise suppression
may be defined as the ratio of the effective conversion loss for the signal
to that for the local-oscillator noise, the conversion losses being measured
from the corresponding r-f input terminals to the i-f-amplifier grid.
If L, and L2 are, respectively, the conversion losses of the two crystals as
measured in a standard test set, the square of the i-f signal voltage at the
i-f amplifier, per unit r-f signal power available at the mixer, is proportional to (<~
+ W,) 2. The square of the i-f noise voltage developed
at the i-f amplifier input terminals, per unit of LO noise power available
in the mixer, is proportional, with the same proportionality constant,
The suppression of local-oscillator noise is
to (@l
– VG)2.
In Fig. 6.14 a curve of AS’,in decibels, as a function of the difference, in
decibels, in the conversion losses of the two crystals is shown.
Since more
than 15 db of noise suppression is obtained if the difference between the
losses of the two crystals is less than 3 db, it is reasonable to assume that
no selection of crystals would be required under ordinary circumstances.
[SEC. 65
A magic-T balanced mixer for 1.25 cm, with an i-f amplifier equipped
with an input circuit such as that of Fig. 6.13, was tested in the following
way. A group of 30 randomly selected 1N26 crystals were measured
for r-f impedance, conversion loss, and noise temperature.
The r-f
impedances scattered in a random fashion, within the impedance circle
corresponding to a voltage standing-wave ratio of 3. The conversion
losses ranged from 6 to 8.5 db and the noise temperature from 1 to 2.
21 .
17 ~
\ ,
13 k
\ ,
Total unbalance in conversion loss in db
FIG. 6.14.—Local-oscillator-noise suppression as a function of unbalance in conversion loss.
Pairs of crystals having almost identical r-f impedances and losses were
used and the effective over-all noise figure of the mixer and i-f amplifier
was measured.
With pairs of crystals matched in this way, the result
corresponded, within the probable error of measurement, to the calculated
value, if local-oscillator noise was neglected and if the effective crystal
noise temperature was assumed to be equal to the arithmetic mean of the
values for the two crystals.
Other pairs were formed, representing the
diametrical extremes in r-f impedance and the smallest and largest
conversion loss. For these pairs the measured effective over-all noise
figure agreed closely with the calculated value assuming a conversion
loss midway, in decibels, between the two and, again, the arithmetic
mean of the noise temperatures.
Thus the measurements showed that
the suppression of local-oscillator noise was sufficient to reduce to a
negligible amount the contribution, from that source, to the over-all
noise figure.
An independent measurement, for the various crystal pairs, of the
actual LO-noise suppression was made in the following way. A test
signal was added to the local-oscillator signal, and the output voltage
from the receiver was measured.
The result of this measurement was
compared with the output voltage from the receiver when the same test
signal was sent into the signal arm of the magic T of the mixer. The
noise suppression was found to vary from about 13 db to over 30 db
depending on the pair of crystals used. The results correlated reasonably
well with what would be expected on the basis of the data on the individual crystals.
There is, however, an additional factor depending on
how well the input transformer is balanced; consequently, the crystal
pair appearing to be the most nearly balanced with respect to conversion
loss did not give the greatest noise suppression.
6.6 Additional Features of the Magic-T
Balanced Mixer.-The
magic-T balanced mixer has been found to furnish a very satisfactory
solution to the problem of local-oscillator noise. It has, moreover,
certain features that make it useful even in the absence of such noise.
One of these features is the small LO power requirement, which makes
possible the use of a well-matched attenuating pad between the local
oscillator and the mixer, as already discussed.
This attenuation becomes
very important in the 3- and l-cm bands if a mixer must be operated
without the assistance of a resonant TR cavity.
The power available
from most small local-oscillator tubes is insufficient in these bands to
allow the reactive coupling circuits to be used without involving a
significant interaction of the local-oscillator circuit on the signal circuit,
with an accompanying deterioration in noise figure. With the introduction of the wide-band fixed-tuned TR switch in the 3.3-cm band, the
balanced mixer became the only available mixer satisfactory from this
Because the effect of local-oscillator noise on the over-all
receiver noise figure is increased if no resonant filter is used in the signal
line of a simple mixer, the balanced mixer has an additional advantage.
Another feature of the magic-T balanced mixer is that radiation of the
local-oscillator wave by the antenna of the receiver is reduced.
is because the only power coupled into the antenna circuit from the
local-oscillator circuit is a part of the power reflected by the crystals.
an ordinary single-crystal mixer, with nondirectional local-oscillator
[SEC. 6.6
coupling, as much local-oscillator power is sent to the antenna as to the
mixer crystal unless there is a resonant filter in the signal line. With
the balanced mixer, a resonant filter still attenuates the local-oscillator
power that is coupled into the s“gnal arm of the magic T. If the radiation
of local-oscillator power must be minimized for any reason, the use of a
balanced mixer, with one of the crystal mounts made tunable, would be
worth while. Since the scatter of crystal impedances is so large, it
could hardly be expected that the local-oscillator power sent to the
antenna, in the absence of a resonant filter, would always be more than
10 db below the input level to the mixer, unless the crystal impedances
were equalized by tuning.
If one crystal were matched to the waveguide,
for instance, and the other had a voltage standing-wave ratio of 2, the
power sent to the antenna would be& of that sent into the mixer by the
local oscillator.
If each of the crystals had a voltage standing-wave
ratio of 2, but with reflection coefficients having opposite phases, ~ of the
power sent into the mixer by the local oscillator would be radiated by
the antenna.
With a tuning adjustment on one crystal such that the
reflection coefficients could be equalized, the radiation by the antenna
could be kept at least 40 db below the input level of the mixer, at the
frequency for which the tuning was made.
The balanced mixer discriminates against i-f signals arising from
beats between two frequencies present in the signal channel, for the
This discrimination
same reasons that it suppresses local-oscillator noise.
is of value because it reduces the susceptibility of the receiver to interference from signals that are not at the signal- or image-frequency
Interference can be produced, in a
sidebands of the local oscillator.
receiver having an ordinary mixer and no resonant preselecting filters,
by beats between any two signals that differ in frequency by the intermediate frequency and that can propagate down the transmission line of
the receiver. The discrimination against interference of this kind is
about the same as the discrimination against local-oscillator noise and
may, unless selected crystals are used, be as small as 13 db. If such
discrimination is deemed important in view of the application of the
receiver, provision may be made to achieve an exact balance in the mixer
circuit by addition of a small adjustable r-f attenuator, for example,
The crystal having the smaller
between one crystal and the junction.
conversion loss should be used on the side that has the attenuator, and the
adjustment would have to be made on an actual set of interfering signals.
Whether the balance would be sufficiently good over the whole band in
which interfering signals can occur, however, is questionable.
If a resonant TR cavity is used in the signal line of a balanced magic-T
mixer, the i-f admittance of the crystals is influenced, as in the single
It is
mixer, by reflection of the image frequency by the TR cavity.
difficult to make the line length between the cavity and the crystals so
short that the phases of the reflected image-frequency waves arriving
at the mixer crystals
do not change very much over a wide frequency
A considerable variation
in i-f admittance
and some variation
a wide
does not seriously
the pass band
of the input
a single-frequency
and the crystal
the length
the best noise figure.
is equivalent
to a magic
the balance
of line between
and the local-oscillator
T, the line lengths
of the magic
A change
to the crystals
in the
the same
Phase angle.
TR cavity
1 %
a very
are delayed
mixer so arranged that the
both the local-oscillator
wave and the signal wave
noise figure.
be made
line length,
of i-f
but it d~s
from the
a wavelength
in the phase of the i-f voltage
by the crystal,
Qf the mixer
ever, this has not been considered worth while
and instead, consideration has been given to a
special change in the balanced mixer to allow
the effect of the image-frequency wave to be
eliminated at all frequencies.
Since the phase relation between the signal
the T-junction
to give
For most purposes,
be expected.
and the i-f-amplifier
as with
can be chosen
transmitted into the localoscillator attenuator.
It is therefore
possible to make the distance from the junction of the magic T to one
crystal a quarter of an r-f wavelength different from the distance from
the junction to the other crystal, as shown in Fig. 6.15. The result of
adding a quarter wavelength to one side of the magic T is that, if imagefrequency waves of equal amplitude are developed by the crystals,
their phase reIation, as they converge on the junction, is such that they
are transmitted entirely into the local-oscillator arm of the magic T. The
way in which this comes about is illustrated graphically in Fig. 6.16.
The vectors of Fig. 6“16a represent the waves that are excited in the
crystal arms of the magic T by the local osdlator and the signal generator. The phase of the local oscillator is taken as a standard of reference
and the vector representing it therefore remains fixed. The relative
phases between the signal wave and the local-oscillator wave, in each
arm, are determined by the angle between the local-oscillator vector and
the small vector representing the signal. Since the frequency of the
[SEC. 6.6
signal differs from that of the local oscillator by an amount equal to the
intermediate frequency, the small vectors rotate at the intermediate
frequency, in the direction indicated by the curved arrows. Because
the local oscillator is connected to arm (3) of the magic T, the vectors
representing the local-oscillator phases at points equidistant from the
junction in the two crystal arms point
f- Sig.
in the same direction.
The vectors
representing the signal are oppositely
directed, since the signal enters the
mixer from arm (4).
At the two crystals, the relative
phases are changed because one line
is longer, by a quarter wavelength,
If the vector reprethan the other.
senting the phase of the local-oscilP
lator wave at crystal (2) is directed
at crystal (1) is directed
toiv:wd the left because it is retarded
by Qoo. A like change in the relative
phases between the two signal vectors
occurs, and the situation is therefore
like that represented in Fig. 6. 16b. In
thk diagram the phases of the two
image-frequency waves generated by
FIG. 6.16.—Graphicwl illustration of
the action of the crystals are indicated
relative phases of w:~ve~ at the LO
by the dashed-line vectors.
signal, and image frequencies, when the
crystal arms differ in length by one
the image frequency diflers from the
quarter wavelength. (a) Vectors showlocal-oscillator frequency by the same
ing the relative phases of the incident
amount as does the signal frequency
signal and local-oscillator waves in
arms (1) and (2) at planes equidistant
but in the opposite sense, these vecfrom the junction.
(b) Vectors representing the relative phases between
tors rotate at the intermediate fresignal, local-oscillator, and image waves
quency in the direction opposite to
at the two crystals.
(c) Vectors showing relative phases of the two imagethat of the rotation of the signal vecfrequency waves as they converge on
tors. The relative phase between the
the junction of the magic T from tbe
image and signal waves is not uniquetwo
ly determined at the planes of the crystals, since the effective iine
lengths within the crystals may not be negligible.
However, the relative phases between the two image vectors must be as shown, if the
crystals are identical, because the phase of each is determined by the relative phases of the signal and local-oscillator voltages.
A reversal of the
p’base of the signal wave relative to that of the local-oscillator wave
must reverse the phase of the image. The relative phases have been
drawn on the basis of two assumptions.
It is assumed first that the
SEC. 6.7]
image-frequency wave is produced entirely by modulation from the i-f
voltage, and second, that the signal voltage arising from the i-f voltage is
such that the admittance of the crystal to the signal wave is reduced
by the presence of the i-f voltage.
The image-frequency waves travel from the crystals back toward the
junction of the magic T. Because the line on the left side is a quarter
wavelength longer than that on the right, the relative phases of the two
image-frequency waves are changed by a 90° retardation of the vector
representing the image wave on the left. These waves therefore have like phases, as shown in Fig. 6. 16c, as they converge on the junction, and if
they have the same amplitudes, all of the image-frequency power is
transmitted into the local-oscillator
arm of the mixer. A matched
attenuator pad in this arm allows the image-frequency power to be
absorbed wit bout reflection, and both crystals behave as they would in a
mixer without a resonant signal circuit. The i-f admittance and the
conversion loss of each crystal are not strongly dependent on the operating frequency.
A large percentage change in frequency can be made
before the difference in length of the two crystal arms becomes so diilerent
from a quarter of a wavelength that most of the image-frequency power
is not sent into the local-oscillator arm.
It is not known how well this treatment of the image-frequency wave
can be achieved in practice.
Its success depends on the equality of the
amplitudes of the two image-frequency waves generated, and on the
validity of the assumption that the effective line lengths contained within
the crystals are identical.
Since the production of the image-frequency
wave by the crystal is a second-order effect, a greater inequality would
be expected in the production of image power by various crystals than in
their conversion efficiency.
It is also possible that the effective line
length contained within the crystals, especially at 1 cm, would vary too
much, from one crystal to another, to allow the assumption about the
relative phases of the two image-frequency waves to hold. Again, it
would be possible to add a tuning adjustment, in the form of a line of
variable length on one side of the magic T, so that the correct relative
phases of the image frequencies could be obtained.
of the output admittance of the i-f coupling circuit as a function of the
line length between the TR cavity and the magic T shows how well. the
image-frequency wave is being disposed of. If all the image-frequency
power is being transmitted to the local-oscillator attenuator, the i-f
admittance should be independent of the distance between the cavity
and the magic T, unless harmonic frequencies have an effect.
6.7. Special Crystal Mounts for the Balanced Mixer.-For
receivers, the push-pull transformer of Fig. 6.13 is not suitable.
example, because mutual inductance is used and because it is not easy to
BEC. 6.7
obtain large coupling coefficients in transformers for high frequencies,
some difficulty is encountered in making such a circuit with a very wide
pass band.
It would be much simpler if the two i-f voltages could
be made to have like phases so that the output voltages of the two
crystals could be added in parallel.
If the pin end of one crystal and the base end of the other are grounded,
the crystals can be made to produce i-f voltages in like phases from the
input signal and voltages in opposite phases from local-oscillator noise.
For the ceramic cartridge crystals used in the 3-cm band, an inverted
crystal mount has been designed which aliows the i-f voltage to be
the pin end connected
taken from the large end of the cartridge,
This mount is similar to the 10-cm coaxialdirectly to the waveguide.
line mount, in that it has a polystyrene-supported
choke on the large end
of the crystal.
To obtain flexible fingers for making contact with the
pin end of the crystal, a half-wavelength
coaxial line is used. The
position of the crystal in the waveguide, and its r-f admittance, are
identical with those in the ordinary 3.3-cm crystal mount.
The disadvantage of using crystal mounts of opposite polarities in a
balanced mixer is that an i-f input circuit equivalent to a magic T is
difficult to achieve.
Direct connection of the output terminals of the two
crystals in parallel does not secure the independence of noise suppression
from the i-f admittance that is achieved with the push-pull circuit.
It is
possible to devise a shunt circuit that contains a dummy load for the
unbalance signal but such a circuit has not been tried. With a nonresonant signal circuit connected to the mixer, however, there is not a
great variation in i-f admittance from crystal to crystal, and the unbalof the i-f admittances
may not be serious.
ance ca{lsed by inequality
It is impossible
over a wide band
tmd the TR
to actiIeve
of the
of frequencies
is too
because the distance between
Because of this fact, and
is peculiarly
in systems
the crystals
because the
cavity between the antenna and the
mixer, a crystal mount that has an r-f admittance characteristic less
frequency-sensitive than that used in the simple mixers is desirable.
For the band from 3.13 to 3.53 cm, an improved crystal mount has
been designed.
It was first attempted to increase the bandwidth of the
simple crystal mount by adding a resonant iris across the waveguide, a
quarter wavelength ahead of the crystaI.
Since the susceptance of a
crystal in the simple mount increases with frequency, whereas the conductance remains approximately constant, the crystal in its mount is
approximately equivalent to a shunt-tuned resonant circuit, as discussed
in Chap, 3. If a resonant shunt-tuned iris is placed a quarter wavelength
from the center line of the crystal, to~vard the generator, the combination
or preselecting
SEC. 6.7]
behaves as a double-tuned coupled circuit.
The response maybe doublepeaked or single-peaked, depending on the Q of the resonant iris. The
resonant iris may be made up of a symmetric inductive iris and a capacitive post in the plane of the iris, and the Q of such a structure is pro0.195”
~ y’”-’
FIG, 6.17,—Crystal
mount with iris for broad pass band.
FIG. 6.18.—Admittances of representative crystals in broadhand mount.
portional to the susceptance of the inductive iris at resonance,
Such a
structure can be made to give, for a given crystal, less than about
0.5-db reflection loss in the 12 per cent band, but this structure does not
represent a significant improvement in the bandwidth of the crystal
mount for many crystals.
The tuning and the effective coupling are
[SEC. 6.7
changed if the admittance of a crystal does not match the waveguide
admittance at the center frequency, and the compensation of the iris for
the frequency sensitivity of the crystal is not so good as for a crystal that
It has been found that there is no
is matched at the center frequency.
iris Q that gives significantly improved results with crystals representing
all r-f admittances to be encountered.
A more satisfactory means of improving the bandpass characteristic
of the simple crystal mount was found in the form of a simple inductive
iris. The final design of this crystal mount is shown in Fig. 617.
FIG. 6 19.—Perspective view of 3.3-cm magic-T balanced
using one inverted crystal
average crystal in the mount shown in detail in Fig. 3.6 has, at the center
of the frequency band, a conductance slightly above the line admittance.
The susceptance of the inductive iris, and its position, are such that the
area covered by the admittance plot for representative crystals is centered
at the characteristic admittance of the line at the midband frequency.
The combination of the frequency sensitivities of the line length from
crystal to iris, of the iris susceptance, and of the crystal admittance is
such that the total spread of admittance is reduced from that for a simple
Curves showing the admittances measured at 3.14 cm, 3.33 cm,
and 3.5o cm are given in Fig. 6“18. Almost all of the representative crystals fall within the circle of voltage standing-wave
ratio equal to 2.65
SEC. 6.8]
and, therefore, the
at any wavelength
Figure 6.19isa
for the 12 per cent
crystal mounts in
for the magic
A Double
T, and a variable
for Separate-channel
circuit for a magic-T
of a second
A simple
the local-oscillator
reflection loss for almost all crystals is Iess than ldb
in this band.
perspective viewofa magic-T balanced mixer designed
band centered at 3.33 cm. Included in the figure are
irises, the
opposite polarities, the band-broadening
for the LO coupling
for separate-channel
is simple,
FIG. 620.—Two-channe1
on the high-power
of the
have been made
in Chap.
with a balanced
a simple
of local-oscillator
side of the local-oscillator
is straightforward.
mixer for each channel,
noise is not significant
as an AFC
in the application
of the
A two-channel
One T is used
in Fig.
useful purpose.
for each
the two
their admittances
arm of the center
is not essential,
one mixer
the local-oscillator
in the local-oscillator
all four
to split
in the manner
the fourth
If the attenuator
this reason
is constructed
and the other
a dummy
Iess, no local-oscillator
it does serve
arm is reflectionis coupled
in the same way as if each were connected
into the
to a matched
generator independently.
of this mixer,
at this power
of the center magic T over a simple T-structure
the TR
alike to allow
is sent
not more
to be coupled
is that
an increase
is obtained
of this power
into the mixer,
It M therefore possible to use a
losses will not be large.
Another advantage
the signal-input
arm of the
the local-oscillator
in the
the two
10 per cent
out the local-oscillator
r-f admittances
of such power,
To travel
the AFC mixer this power must be coupled from arm (1) to arm (2) of
the center magic T.
If the reflection
for waves traveling
in arms
(3) and (4) are both
(2)is zero
the dummy
by the amount
no attenuation
a very
in arm (3) is determined
to drive
the signal
as is local-oscillator
differ by as much
6 db
by way of the local-
is obtained.
to have
in the worst
arms (1)
is infinite.
the use of the center
the receiving
losses of the crystals
of 15 db of cross attenuation
in just
(4) can be made
but the reflection
is gained
The signal
is discriminated
in arm
of attenuation
of cross attenuation
zero, the coupling
if the
as 3 db, the [email protected]
Thus a total of at least 31 db of
cross attenuation
can be obtained
with this double
mixer, even with
a local oscillator having just sufficient available power to drive the
four crystals.
With more local-oscillator
power and well-balanced
crystals, the cross attenuation would be very high and an ordinary
leakage signal from the TR switch would certainly not interfere with the
functioning of the AFC circuit.
The balanced AFC mixer ser-ves also to reduce the effect, on the AFC
circuit, of the video pulse produced at the output terminals of a crystal,
when the AFC signal is too large. Such video pulses may contain
frequency components in the intermediate-frequency
region and these
are sometimes large enough, relative to the beat-frequency
signal, to
cause some interference with the AFC action.
With the balanced mixer,
if the rectification efficiencies of the two crystals are equal, the video
pulses produced by the two crystals will also be equal. With an i-f
SEC. 6.8]
input circuit arranged to transmit the beat-frequency signal, the i-f
Video components due to stray
components of the video pulses cancel.
signals or to harmonics of the transmitter signal are similarly canceled.
One difficulty often encountered with an AFC circuit is that the circuit
locks when a harmonic of the beat frequency passes through the i-f
With an intermediate frequency of 30 Me/see, for instance,
the AFC circuit might lock with the local-oscillator frequency only 15
Me/see away from that of the transmitter.
To prevent this, the harmonics of the beat frequency must be kept below the threshold level
of the AFC circuit.
The balanced mixer assists in this because evenorder harmonics, arising from beats between an even-order harmonic of
the local oscillator and a harmonic of the signal of the same order, are
balanced out. This may be shown to occur because a reversal in phase
of a fundamental frequency does not alter the phase of an even-order
harmonic generated from it. The cancellation of such even-order
harmonic voltages is probably not very complete, because the efficiency of generation of harmonics by different crystals probably varies
A further attractive feature of the balanced mixer for the AFC
channel is that the signal-input arm can be provided with a matched
dissipative attenuator without affecting the coupling of the local oscillator.
If such an attenuator is used, the crystals receive signal power
from a matched generator, which is not true if a cutoff attenuator, or
small hole, alone is employed.
From a matched generator, the power
delivered to the crystals is not strongly dependent on their admittances
and, therefore, the range of input power for which the ‘circuit must be
A dissipative attenuator made
made to operate is considerably reduced.
of polyiron, cut with matching transformers at both ends and having
20 or 30 db of attenuation, has been used in the signal-input arm of the
magic T that forms the AFC mixer. This attenuator also reduces the
danger that stray leakage signals may get into the signal circuit at a
Interference with the operation
connector on the signal-arm waveguide.
of the AFC circuit from this source is therefore reduced.
of the AFC signal coming from the transmitter tube are also effectively
attenuated and should therefore cause no trouble.
Thus it is apparent
that the balanced AFC mixer solves practically all of the problems
encountered in the two-channel mixer, and the improved performance is
well worth the added complexity of one extra crystal.
A perspective view of a double balanced mixer used in the 12 per cent
band centered at 3.33 cm is shown in Fig. 6.21.This mixer represents
only one of many possible arrangements of the magic T’s and was chosen
only because it gave the most convenient physical arrangement for the
[SEC, 6,8
A double balanced mixer for the 1.25-cm band is made from a die-cast
block containing all of the waveguides and matching irises. Once the
dies have been made, this part of the mixer can be inexpensively reproduced with very high precision and in large quantities.
The remaining
parts, associated. with the crystal mounts, the i-f attenuator, and the
waveguide choke joints, may be added later or machined into the die-cast
For the block to be die-cast, it has to be made in two halves and
FIG.6.2 1.—A
double balanced
mixer for 3-cm band.
there has to be a small taper in the waveguide heights to allow the pieces
to be pulled off the dies. The mixer is split in a plane through the center
of the broad wall of most of the waveguides so that no current lines are
cut by the split, except in the regions of the junctions of the m~gic T’s,
No difficulties are caused by leakage or poor contacts in this split.
The additional precaution has been taken, however, to have the adjacent
faces of the two halves honed flat. ‘I’he tapers in the wavcguides cause
their heights to change from 0.17 I in. at the center, in the plane of the
SEC. 6.9]
split, to 0.169 in. at the side walls. There isno detectable effect on the
A perspective
standing-wave ratios in the mixer from this small taper.
view of the double balanced mixer, with the two halves separated to
show the internal structure, is shown in Fig. 6“22.
tub+ mo
IN26 crystal m
from bottom
I mounts
Cut away to reduce weight
double balanced mixer for 1.25-cm band.
6s9. Other Special Circuits.-It
is very simple to adapt the double
balanced mixer to satisfy other, special, circuit requirements.
If, for
instance, a separate local oscillator for beacon reception is desired, such
an oscillator maybe connected tothe dummy arm of the center magic T.
The dummy load may be replaced with a variable attenuator and this
arm becomes equivalent to the input arm of the first local oscillator.
Either of the oscillators maybe used, with a switch provided to select the
desired one. For beacon reception, the AFC mixer is not used, but no
harm comes of supplying local-oscillator power to it.
If beacon AFC is desired, a reference cavity and detector crystal
may be added to the LO-tube mount in place of the short circuit normally
used behind the tube antenna.
The same requirements must be met
by the circuit, to avoid frequency discontinuities, as by the circuit
described in Sec. 4.13.
If a resonant TR cavity is used with a mixer for a radar system, it
This device can be
may be desirable to use a beacon-tuning device.
placed, just as in the single mixers, in the signal input arm a half-wave
[SEC. 69
length behind the TR cavity.
Shutters for protection of the crystals
during shutdown and turnon periods can also be added to the signal input
Because the magic-T balanced mixer is especially suited for use with a
broadband nonresonant TR cavity, the 3-cm-band versions have usually
been used in combination with a TR system of that type.
As a consequence beacon tuners have not been required.
In conjunction with
systems using the bandpass TR cavity, inthedesire toeliminate as many
of the manual tuning controls as possible, the electronically controlled
Matched pad
balanced mixer with beacon-AFC cavity and detector.
In this mixer a
single thermally tuned oscillator is used for both radar and beacon reception.
thermally tuned local oscillators have usually been used. In the 3-cm
band, for instance, the 2K45 tube, which can be tuned electronically from
3.13 to 3.53 cm, is useful for this purpose.
With such an oscillator
tube it is not necessary to add a second oscillator for beacon reception.
Instead, the single oscillator is tuned electronically to receive either the
beacon signal or the radar signal depending upon which AFC circuit is
When the AFC circuit is actuated by the balanced AFC
mixer, the oscillator is controlled at the correct frequency to receive
radar echoes.
On the other hand, a beacon reference cavity and detector
crystal may be added and used to control the oscillator at the right
frequency to receive beacon signals. Such a reference cavity may be
thC. 69]
added in place of the short circuit behind the tube antenna in the ordinary
tube mount, as for a separate beacon oscillator,
It is also possible to add
the beacon reference cavity by means of another magic T, as illustrated
symbolically in Fig. 623.
The magic T provides independence between
the two circuits in such a way that reflections in the cavity circuit do not
affect the power delivered to the mixers.
~ pad between the magic T
and the cavity reduces the interaction between the cavity and the
Consequently, the load on the beacon cavity need not be so
heavy as in the application without the input-circuit pad.
In this circuit
the steepness of slope in the transmission characteristic of the cavity is
sacrificed to some extent to gain decoupling in order to reduce pulling
of the resonant frequency of the cavity by the external circuits.
formulas of Sec. 4.11 still apply, since the magic T between the oscillator
and the cavity is equivalent to 3 db of matched-attenuator padding.
In the first chapter (Sec. 12) it was shown that the allowable percentage frequency drift is much smaller in microwave receivers than in those
Furthermore, many microwave oscildesigned for lower frequencies.
lators are inferior in percentage stability.
In some cases radar gear
must be operated by the pilot of a plane, who cannot spare the time to
For these and other reasons, the need
maintain correct tuning manually.
for automatic frequency control (AFC) became apparent early and at
present AFC is used in nearly all equipments.
This chapterl will
consider the causes of frequency drift and methods for minimizing its
ill effects through AFC.
7.1. Sources of Frequency Drift.-In
most microwave receivers, the
pass band of the r-f components is much wider than that of the over-all
receiver. The center frequency of the pass band of the i-f amplifier is
very stable compared with the beat note at intermediate radio frequency.
Consequently, a receiver once tuned will operate at full efficiency as long
as the frequency difference between local oscillator and transmitter has
the correct value.
oscillators of three types are in common use at microwave frequencies:
the magnetron, the velocity-modulation
tube, and the triode lighthouse
tube. Each is governed by a resonant circuit having effective inductance
and capacitance.
Although lumped constants are not used, as in the
case of low-frequency oscillators, the same fundamental criterion for
operating frequency applies, namely, that the over-all impedance around
the feedback loop shall be equal to zero. Changes in resistance produce
changes in amplitude, while changes in reactance cause a shift to a new
frequency at which the net reactance is again zero.
For practical purposes, factors affecting circuit reactance may be
divided into three classes:
1. Geometric factors, in which the effective inductance and capacitance of the oscillatory circuit are changed directly through
mechanical motion.
2. Pulling factors, in which reactance is coupled into the oscillatory
circuit from the load.
1See also Vol. 23, Chap. 3.
3. Pushing or electronic-tuning
factors, in which reactance is introduced by changes in electrical conditions, such as voltage, current,
or magnetic field.
Here we are concerned with geometric factors deliberately introduced
through a tuning mechanism only in so far as the mechanism is affected
by the ambient conditions of temperature, pressure, and vibration.
Magnetrons, whose resonant circuits are carved of solid copper blocks,
are geometrically stable except for a drift of a few megacycles per second
during warmup.
They are, however, affected by both pulling and
The pulling jigw-e of an oscillator (see also 1-o1. 7) is defined as the
maximum change in frequency when a load having a voltage standingwave ratio (VSWR) of 1.5 is presented in all possible phases to the tube.
Pulling figures in the 10- and 3-cm bands range from 10 to 15 NIc/see,
At low frequencies,
while at 1 cm, values lie between 25 and 30 Me/see.
pulling may be avoided by the use of a buffer amplifier.
microwave amplifiers, however, do not exist, and the microwave transmitter is therefore coupled directly to the antenna line. Consequently,
pulling may occur during scanning because of reflections in the line caused
by off-center rotary joints, reflections of energy into the antenna from
radomes or other nearby objects, lobe switches, or variable antennafeed devices such as wobbled feeds or variable-width leaky-waveguide
The last-named antennas are very troublesome because the
standing-wave ratio often suffers large fluctuations when the reflections
from the individual radiating elements all add in phase.
The amount of transmitter pulling is variable.
Low-gain antennas
are particularly troublesome since their diffuse pattern makes reflection
back into the line almost unavoidable.
Thus, in the l-cm band, in
spite of the large pulling figure, pulling is usually negligible because of
the high antenna gains commonly used.
The pushing figure of a magnetron is defined as the frequency shift,
in megacycles per second, per ampere change in magnetron current.
The figure is negligible in the 10-cm band, around 1 Me/see per amp in
the 3-cm band, and 2 Me/see per amp in the l-cm band.
With reasonably well-regulated primary supplies, pushing offers no AFC problems.
The resonant frequency of the catiity of a velocity-modulation
is altered by changes in either the cavity volume (inductance) or the
For our purposes, only the
space between the grids (capacitance).
Geometric changes in grid spacing
capacitance change is significant.
are caused by thermal expansion and, in the case of airborne gear, by
changes in barometric pressure. The magnitude and polarity of thermal
changes depend on the detailed design used; in s“ome cases, excellent
compensation is possible.
Tubes in which the tuning range is covered
ofa thermal strut (see Sec. 7.2) areliiely toshow large drifts
Tubes such as the 2K45 and the 2K50,
caused by temperature changes.
which have built-in triodes to energize the thermal strut, are very sensiThe end efiect here is geometrical, although
tive to triode heater voltage.
the immediate variable is a voltage.
Pulling, in local oscillators, is seldom a problem since the r-f geometry
is fixed. A special difficulty arising from the use of precision reference
cavities as AFC standards has been treated in Chap. 4.
Pushing, in local oscillators, is commonly referred to as electrical or
electronic tuning.
In triodes very little electronic tuning is available
without serious deviation from optimum conditions.
Velocity-modulation tubes, however, may be tuned many megacycles per second by variation of either accelerator or reflector voltage.
This property offers
little difficulty as a source of drift since well-regulated power supplies
may be used. In fact it is a means of tuning well suited to either manual
or automatic control of frequency.
7.2. Properties of Local Oscillators for Frequency Control.-As
pointed out at the beginning of the previous section, control of the
frequency difference between the local oscillator and the transmitter is
sufficient to maintain correct tuning of a microwave receiver.
it is usually far easier to tune a local oscillator than a transmitter, the
former is usually chosen for control purposes.
Corresponding to the three mechanisms for producing frequency
changes, there are three types of control that may be applied to the local
Geometric control may be exercised either by straight
mechanical devices operating through motor-driven tuning mechanisms
Pulling control can be used by lockor by the use of thermal expansion.
ing the oscillator to a stabilizing cavity.
In such a system there is no
AFC per se, but only frequency stabilization.
The use of reactance
tubes, which is common at low frequencies and perhaps possible in the
10-cm region, is a means of utilizing the principle of pulling since the
reactance tube injects reactance across the tuned circuit in much the same
manner as does a reactive load.
Electronic tuning is commonly effected
by control over the reflector voltage of a reflex velocity-modulation
(VM) oscillator.
Typical reflex oscillators may be tuned anywhere
from +30 Me/see to +60 Me/see before the output power is cut in half.
The tuning sensitivity of such tubes ranges from 1 to 4 Me/see per volt
in the higher range of frequencies, with large variations within any
given type.
A complete discussion of electronic tuning will be found
in Vol. 7.
Geometric control is relatively slow whereas response in electronic
tuning is essentially instantaneous.
Control circuits are accordingly
quite different as will be seen in later sections.
SEC. 7.2]
A number of thermally tuned reflex oscillators are now available.
One example of the type is the 2K50, which operates in the 25,000Mc/sec band.
The essential features of the tuning mechanism are shown
in Fig. 7.1. It operates in the following reamer.
When the bias on the
tuner triode grid G is reduced, current flows to the plate P, causing its
temperature to rise.
The resulting expansion of P distorts the triangle
abc, causing the apex a to pivot downward about c. Since the apex is
welded to a metal sleeve S, which, in turn, is welded to the upper plate D of
the resonant cavity, this motion is transmitted to the cavity,
and causes
FIG. 7.1 .—TherllIml-ttll~illg
‘ O;l0:”,,:0’0’
mcclwmism U[the
2K50 oscillator.
upper grid GI to approach the lower grid C2. ‘his reduces the opera.
It will be noted that the reflector R, which is inside
of a ceramic cylinder cemented inside of S, maintains a fixed distance
from G1.
The 2K50 will tune from 1.21 to 1.29 cm (about 2000 Me/see) with
6 watts of triode plate dissipation.
The thermal time constant is about
1.7 sec; consequently the maximum tuning rate at either end of the band
pcr see, and at band center, 650
toward the other end is 1300 Me/see
per sec.
The tuning mechaThe 2K45 operates in the 10, Of)O-IWc/scc
nism is somewhat different from that of the 2K50 but gives the same
results. The tube also covers a 2000-&lc/sec
range with 6 watts of
triode power,
but the time constant
at band
to the triode
the AFC
will oscillate
8 seconds,
that occurs
one wishes
and even
to have
of the
in frequency
for by the AFC.
for instance
the heater
is to
If, how-
(to allow
to regulate
in Sec. 7.10.
volts ge
the electronically
on the triode
it is necessary
is necessary.
of a stable
LO accelerating
this limit
as will be shown
of the frequency
of AFC
of a
of several hundred megacycles
This introduces
the problem
always slow and can be readily
in the event
a range
of thermal
the application
of equilibrium
is turned fully off or fully on when
The new circuits
this “on-off”
a disturbance,
is the dependence
a maximum
of new
second at a single value of reflector
of possible locking to the “wrong
A particularly
grid and the attainment
can follow
is the time delay
of these
is about
of 125 ~?vlc/sec per sec.
these properties
of AFC
are two
and transmitter, and A-F
systems are those which hold the local oscilltitor to a fixed radio frequency.
The conventional AFC of a home broadcast receivcrL ii an example of
a D-F system, since the ~omparison between local oscillator and received
signal is made at the intermediate frequency, and errors in the frequency
of the resultant i-f beat are used to control the local oscilltitor.
The crystal-controlled
fixed-frequency receivers used in commercial
II] microwave
communications are examples of A-F systems.
10cal oscillator
is performed
‘are required.
The type of system required depends on the problem involved.
normal radars, samples of the trmsmitter signal are at hand, and variation in transmitter frequency is expected.
A D-F system is therefore
1 F. IL ‘1’erman, Radio Engineer’s
p. 654.
McGraw-HilI, New York, 1943, %.
SEC. 7.4]
clearly necessary.
On the other hand, for the reception of beacons, no
signal is available until the beacon transmitter has been triggered.
Therefore, the receiver should be always in tune. Tuning can be maintained only by the accurate control of beacon transmitter frequency
coupled with A-F stabilization of the local oscillator.
Again, in home receivers any one of many carriers must be received,
which eliminates the possibility of A-F control; in fixed-frequency
receivers, the signal should not be lost during a fading spell or a noise
burst, so that A-F control is desirable.
In addition to classification according to the frequency to be controlled
(that is, intermediate frequency or radio frequency),
In particular, each of the specific
according to control circuit is useful.
systems mentioned above requires that the local oscillator be tuned
very close to the desired frequency before control is established; that is,
these systems have a small “pull-in”
range. Once locked, a much
larger drift tendency may be overcome; that is, the systems have a large
“ hold-in” range. These, then, are nonhuntz’ng systems.
It is possible in either D-F or A-F systems to cause the local oscillator
to sweep over a large band of frequencies in order to find the correct
operating point.
When the local oscillator is used in such a way, the
system is known as a hunting system, and the pull-in range may approach
or even equal the hold-in range. Hunting systems become useful when
two conditions exist: (1) the expected drifts are large compared with the
receiver bandwidth, and (2) there is no possibility of signal confusion
(locking to wrong transmitter, etc.).
Since both of the conditions
usually apply, most AFC systems developed for radar receivers have the
hunting feature.
The balance of this chapter will treat hunting and nonhunting
systems, and absolute-frequency
hunting systems.
Corresponding to the greater effort spent in their development, emphasis
is placed on D-F hunting systems suitable for pulsed transmitters rather
than on A-F and nonhunting systems for c-w transmitters.
It is recognized, however, that the latter will play an increasingly important role
in postwar work.
7.4.The AFC Feedback Loop.-The
basic operating principles of a
difference-frequency AFC system are illustrated in the block diagram of
Fig. 7“2. Samples of the transmitter signal f, and the local oscillator
signal j~~ are applied to a mixer. The resultant i-f signal is amplified
and applied to a discrz’rninator.
This produces an error voltage whose
depends on whether the intermediate signal frequency is above
[SEC. 7.4
or below the crossover jrequency
and which is zero at crossover, as shown
in Fig. 73.
The error voltage is amplified and applied to a control
suitable for changing
circuit which transforms it into a control
the LO freauencv.
Polarities are such that anydeviation from crossover
produces a correction voltage tending to offset such deviation.
It can
l-f signal
fT ‘f~o
Control circuit
Control voltage
FIG. 7.2.—Block
diagram of AFC loop.
be seen that such a circuit is essentially an inverse feedback loop, and
“therefore, the Nyquist theoremz applies.
In particular, if theloop is broken between thediscrirninato
control circuit, an alternating voltage applied to the control circuit will
reappear, modified in both phase and amplitude, at the discriminator
output terminals.
By Nyquist’s theorem, the system will be stable
provided the over-all gain islessthan unity at each frequency for which
the two voltages are in phase. For
the normal operating frequencies, the
gain will be large for high stability,
and the phases 180° apart corresponding to the negative feedback.
Most of the differences between
hunting and nonhunting systems are
in the control circuits.
The next
sections treat in detail those features
I’IG. 73.-Discriminator
common to both.
Most of the emphasis
is placed on systems with near-by.- uulsed transmitters, partly
because these are more complex than those with remote or c-w transmitters, and partly because much material on the latter systems is already
in the literature.
7.5. The Transmitter
Sample .—When, as in a communications
receiver, the transmitter is remote, the normal received signal must be
1See Sec. 7.7
2 IVyquist
for a more
“ Rcgcncration
Theory, ”
of these terms.
used. It is customary to utilize the main receiver channel, up to and
The simple detector
including the last i-f stage, without modification.
is replaced by a discriminator (Sec. 7“7) which generates the necessary
error voltage.
Normally, no changes in the r-f, mixer, and i-f stages are
required although, occasionally, a separate i-f channel is used to obtain
greater bandwidth.
In a radar set the transmitter is near by.
At first glance this would
seem to simplify the problem since a constant source for sampling is
available. . It proves, however, to add a whole new set of problems
brought about by the excessive power which may reach the receiver unless
special care is taken.
Experience has shown that in pulsed-radar sets an overwhelming
maj m-ity of AFC failures result from improper r-f conditions.
and quality of transmitter
they take the form of an improper quantity
sample reaching the AFC crystal (which may be either the main receiver
crystal or a separate crystal).
When a very large signal is applied to a silicon rectifier, it begins to
pass current in the backward dh-ection. The “back resistance” falls
until it approaches the value of
the “forward resistance. ” Cons&
quently, the rectification efficiency
of the crystal approaches zero. If
we observe the rectified current as
a function of a-c input power we
obtain a curve such as is shown in
~~- t
Fig. 7.4, which has a real maximum,
P (Watts)
with decreasing output current for
FIG. 7.4.—Typical
rectification characvery large input powers.
teristic of a silicon crystal-rectified current
A typical radar pulse is really
~,. input po~,~.
more or less trapezoidal in shape, as
shown in Fig. 7.5a. The effect of impressing such a pulse on the characteristic of Fig. 7“4 is shown as a function of pulse amplitude in Figs.
7.5c, d, and e.
It can be seen from a Fourier analysis that this ti~deo pulse from the
crYstal, even if it has the simple shape shown in Fig. 7.5c, will contain
The amount of
energy components at the intermediate frequency.
energy at this frequency is, however, 30 db or more below the normal
i-f level,
Under overload conditions, the pulse will have the form shown
in curve d or even curve e of Fig. 7,5. In thk case, there will be large
amounts of energy at the intermediate frequency, which in some cases
will exceed the desired energy and result in the continuous generation of
error voltage, even when the local oscillator is completely dead. This
spurious error voltage can be regarded as being produced by a shock
excitation of the i-f circuit.
It hassometimes been referred teas “video
There are also found, in the output voltage from the crystal, components whose frequencies are integral multiples of the difference between
the frequencies of the local oscillator and transmitter.
Such harmonic
signals, or “harmonic hash,” may be generated by the nonlinearity af the
crYstal, or they maybe caused by the beating between
harmonics of the transmitter and the local oscillator.
Spurious control information results when the frequency difference between the two oscillators is a
submultiple of the intermediate frequency.
(a) Transmitter pulse,
positive envelope
If the local-oscillator frequency is swept through
the region around the transmitter frequency, a series
of pulses is obtained.
Figure 76 shows how these
look with and without spurious control signals of each
of the kinds mentioned above.
One may produce
(b) l-f pulse
these characteristics experimentally by applying a
linear sweep voltage to the frequency-control
electrode of the local oscillator and to the horizontal
plates of an oscilloscope, and by applying the discriminator output voltage to the vertical plates
through a suitable amplifier.
The relative importance of each type of spurious
signal increases with increasing transmitter-sample
Experiments with crystals at 10,000 M c/see
Me/see show that they both become
(d) Saturated’’video
troublesome if the r-f power at the crystal exceeds a
few milliwatts.
Also, the desired signal increases but
slowly at these levels. An operating level between
1 and 2 mw is therefore desirable.
The partial saturation at this level makes the signal output voltage
(e) Wideopulse’’under
fairly independent of input power.
On the other
extreme overload
hand, spurious signals are at least 20 db below the
FIQ. 7.5.—Generadesired signal. Furthermore, if one tries to operate
tion of shock excitation.
below 1 mw, the suurious signal decreases but
slowly whereas leakage soon becomes intolerable, and extra i-f gain is
Accurate control of gain up to the error-voltage generator is clearly
If the gain is too low, locking occurs, if at all, near the peak of
the dkcriminator curve, well away from crossover (see Fig. 7’3).Ifitis
too high, spurious signals will cause locking either completely out of the
band (transient response) or at one half, one third, etc., of the intel-medlate frequency (harmonic response).
SEC. 7.6]
Leakage is partiaslarly troublesome in automatic frequency control.
There are two sources: (1) bad joints (choke joints, backs of crystals),
and (2) inadequate cross attenuation, which allows TR leakage power to
reach the AFC crystal through the common coupling provided by the
local oscillator.
Leakage power and the sample power introduced
deliberately are coherent and add vectorially in amplitude.
Thus if
P’ WA‘
Time or frequency
(a) C-w transmitted no spurioussignals
Time or frequency
lb) Pulsed transmitter no spurioussignals
Time or frquency
(c) Pulsed transmittefi shock excitation only
b 11+1 ‘+
Time or frquency _
FIG. 7.6.—Output
(d) Pulsedtransmitter harmonic signal only
signal from a discriminator at radio frequency;
frequency; ji is the intermediate frequency.
J.r is the transmitter
the two are equal, the net power may range from zero to four times the
desired power, according to the phases.
The importance of leakage becomes apparent when one considers
that the power in the main transmitter line may be as high as 1 megawatt, while the amount allowed to reach the crystal through leakage
should be less than ~ mw, a difference of 96 db.
7.6. Mixers, Local Oscillators, and I-f Amplifiers.-In
early radar
sets a single mixer was used, and the transmitter sample was the power
leaking past the TR switch. The first two stages of the mam receiver
served as i-f amplifier, and only three or four additional tubes were
[SEC. 76
needed: one or occasionally two i-f amplifier stages, and two control
A typical AFC chassis circuit of the “d-c amplifier” type is
shown in Fig. 7.15. The use of a gas-discharge-tube control circuit
(Fig. 7“18) was also common.
In its simplest form, single-mixer AFC suffers three serious drawbacks.
First, the power reaching the crystal is much too high (20 mw or more),
giving rise to spurious signals caused by shock excitation.
Second, the
20-mw “flat” is preceded by a short high-energy “spike”
which gets
past the TR tube before it has had a chance to fire. This generates
Moreover any harmonic energy present in the transmitted
signal may be passed by the TR switch in the fired condition.
the system is subject to control by energy reaching the antenna between
transmitter pulses. In practice, this results in echoes from nearby
objects (“ground clutter, ” and so forth) producing cent rol information.
The effective gain of the system therefore depends on whether the antenna
points toward the horizon or toward the sky. Also, the AFC may
lock to the wrong transmitter either accidentally from a friendly system
or as a result of enemy jamming.
By the use of more elaborate devices, some of these difficulties maybe
Bell Telephone Laboratories have developed a “spikeblanking” circuit in which the leading edge of the video pulse at the
primary of the transmitter pulse transformer is differentiated and applied
to the cathode of one of the i-f stages. The positive pulse thus produced cuts off the stage during the time of the TR spike, but allows it to
recover for the balance of the transmitted pulse. Bell Telephone
Laboratories have also used an “enabling”
circuit to reduce the effects
of echoes.
Again the primary video pulse is used, undifferentiated.
is reduced to about +120 volts in amplitude and applied to the screen
and plate of one of the i-f stages. Since this stage has no other source
of d-c power, it is dead except during the transmitted pulse, so that the
signals entering the antenna between pulses are ineffective.
7.15 shows how these triggers are introduced.
With these modifications, reliable operation may be achieved in some
cases. No control over the flat part of the TR leakage power is possible,
however, and many system designers have gone over to double-mixer, or
separate-channel AFC.
In the separate-channel system, a small fraction of the transmitted
pulse is coupled out to a separate crystal which drives a separate i-f
Thus, the power reaching the crystal may be adjusted to the
optimum value and will be “spike-free.”
Because of the high attenuation, signals entering the antenna cannot reach the AFC crystal.
and operation
have already
of the r-f components
been discussed
in Chaps.
A and 6.
in separate-channel
8EC. 7.6]
Further improvement in AFC reliability may be obtained by the use
of a balanced mixer (Sec. 6.8).
Since a balanced mixer is customarily
used in conjunction with a similar mixer for the main receiver, the
resulting unit is commonly called a “four-crystal mixer. ” In the fourcrystal mixer, TR leakage power and the resultant transients, and all
harmonics of even order generated in the crystals are balanced out.
Only stray leakage and harmonics generated by the oscillators remain as
Harmonics of third and higher orders are normally negligibly
The method of obtaining the transmitter sample in a separate-channel
system is importatit.
Usually, a small couphng hole in the side of the
transmitter line is used, although occasionally
directional couplers
(Vol. 11, Chap. 14) are used to make the sample-power level independent
of standing waves in the antenna line. Only part of the necessary 75 to
90 db of attenuation may be thus provided.
Often, from 20 to 40 db
more is obtained from a dissipative pad inserted directly in the mixer.
This pad serves to provide a matched line looking out from the mixer,
and to reduce the effects of leakage into the line in front of the pad.
The coupling hole is a waveguide beyond cutoff and may be a waveThus, a small percentage of
guide m“thin cutoff for harmonic frequencies.
harmonic content in the transmitter output may become a large or even a
dominating fraction of the power in the AFC line. Because this harmonic
energy may be so large as to generate transients, its elimination is most
To attenuate the harmonics, a resistance strip or a polyiron
plug may be inserted in the coupling hole.
Little need be added about local oscillators.
Many of their properties
were discussed in Sec. 7“2, and the problems of coupling them into
mixers are covered elsewhere (Chap. 4). The amount of power that
should be applied to the AFC crystal from the local oscillator is governed
by the fact that it should differ from the power from the transmitter by at
least a factor of 3, in order to reduce the amount of harmonic generation
by the crystal.
It is clear that the local-oscillator power should be the
lesser of the two. First, there is seldom any power to spare in reflex
oscillators; and second, the higher the transmitter power at the crystal,
the less important is a given amount of leakage power.
Thus, in normal
parlance, the transmitter serves as local oscillator, and the real local
oscillator serves as signal.
A local-oscillator power level of about ~ mw is desirable and also
convenient, since it is also the approximate power required for a main
receiver crystal and so the two crystal currents may be set to the same
If a magic T is used to divide the power among the crystals,
as in a four-crystal mixer, a single adjustment will suffice, and all crystals
will receive equal power,
[SEC. 7.7
The i-f output signal of an average crystal operating under the conditions outlined above lies between 0.25 and 0.50 volt rms. Since
this is inadequate for ~ discriminator, one or more stages of i-f amplification are used. The bandwidth requirement of the i-f amplifier is governed by the discriminator bandwidth, which should be slightly less than,
or equal to, the over-all receiver bandwidth.
The receiver bandwidth,
in turn, is governed by the system pulse-length or modulation requirements. Since typical radar bandwidths lie between 1 and 8 Me/see to
the half-power points, the gain per stage is usually low. Furthermore, it
is now considered good practice to make the AFC i-f channel considerably
wider than the. discriminator peak-to-peak separation to remove the
necessity for complete realignment when the discriminator crossover
frequency is shifted.
This makes possible the adjustment of the AFC
locking frequency with a single control.
With the system locked to
AFC, this control may be tuned for maximum performance.
Gain at the intermediate frequency is expensive, whereas gain after
detection is cheap, since, in most cases, the video pulses have been
and hence the video bandwidth requirements are
greatly “stretched,”
low. It does not pay, however, to overwork this idea. The video input
signal should be approximately 1 volt in order to be large compared with
stray pickup.
For pulses longer than 1 or 2 ~sec, a single i-f stage
preceding a conventional
dual-diode discriminator will suffice. For
pulses between ~ ,usec and 1 psec, two stages may be needed, while still
shorter pulses may require three or more. In the latter case, extra bandwidth may be obtained by staggering the center frequencies of the first
two stages (Vol. 18). A voltage ,gain of four or more is possible in the
circuit between the crystal and the first amplifier grid. This extra gain
involves extra alignment problems, however, and a single-tuned circuit
with unity gain may be preferable.
Symmetry in the i-f amplifier is far more important in the AFC
The i-f spectrum of a short pulse
channel than in the signal channel.
contains sideband energy on either side of its center frequency.
If the
amplifier is asymmetrical, the over-all discriminator characteristic will’
likewise be asymmetrical, and the sidebands will not be canceled out at
7.7. Discriminators.-The
characteristic curve of a discriminator
shown in Fig. 7.3 is not of the most general possible type.
For one thing,
the zero referred to may bc at some d-c level other than ground potential.
For the purposes of this chaptm-, the zero to which polarities are referred
is the d-c voltage existing at the output terminals when there is no signal at
the input terminals.
Crossover frequency is that frequency lying between
the two output peaks for which the output voltage is zero. If the i-f
input signal consists of continuous waves, the output voltage will be d-c;
SEC. 7.7]
if it consists of a series of short pulses, the output voltage will consist of
a series of pulses whose amplitude and polarity follow the scheme shown
in Fig. 7.3. In the special case of the beacon AFC described in Sec.7. 18
output (DO)
Video and avc
signal (VO)
Travis circuit
++’~‘; -[‘;
R~ . . CB
R& =~c;
R.f choke
Foster-seeley cwcult
Weiss circuit
FIG. 7.7.—Discriminator
the output voltage varies sinusoidally.
Change of polarity is replaced by
a 180° reversal of phase, but if plus and minus are taken to mean one or
the other phase, Fig. 7.3 still applies.
[SEC. 77
types of i-f discriminators areshown in Fig. 77.1
The Travis circuit depends on the action of two resonant circuits,
one tuned above the desired crossover frequency and one tuned below it.
Detectors across the two circuits are connected back to back. The
individual and sum voltages de~~eloped by the detectors are shown in
Fig. 7.8. It should be noted that the individual resonant elements
Output voltage
of upper detector
of lower detector
is used,
of the
is not
If the peak-to-peak
great for the circuit
Q’s in any of the
a “chair,”
the characteristic
as shown
is too
will have
in Fig. 7.8d.
Three factors must be adjusted:
the crossover frequency, the peakto-peak separation, and the sym(c)
In the Travis discriminator
the crosso;-cr is shifted by tuning the
Over-all output
two resonant elements in the same
direction, ~vhileseparation is changed
:by tuning them in opposite directions. The other circuits, on the
other hand, have separate, independent crossover and separation adjustments.
T h e characteristic
symmetrical if the i-f amplifier pass
band is symmetrical, and if the disCrassover
criminator primary is tuned to the
FIc+. 7. S.—Operation
of Travis discrimiIn addition,
crossover frequency.
the Travis circuit requires that the
The adjustment of the primary
individual circuit bandwidths be equal.
circuit of the discriminateor is commonly called the symmetry control.
It may be used to offset the slight inherent asymmetry which arises from
the unbalance of the discriminator with respect to ground potential (see
Sec. 7.8).
The Foster-Seeley discriminator of Fig. 77b has been well covered
1 D, E. Foster and S. W. Seeley, “Automatic Tuning, Simplified Circuits, and
Design Practice, ” Proc. I. R. E., 25, 289, March 1937.
Hans Roder, “Theory of the Discriminator Circuit for Automatic Frequency
Control, ” Proc. I. R. E., 26, 590, May 1938. Charles Travis, ‘( Automatic Frequency
Control, ” Pmt. I. R. E., 23, 1125, October 1935.
in the literature and will not be treated here beyond noting that the
mutual inductance determines the peak-to-peak separation and that the
crossover frequency is the resonant frequency of the secondary circuit.
At the frequencies commonly used for i-f amplifiers in microwave receivers, little if any lumped capacitance is added.
The distributed capacitances of the diodes, in series, comprise the bulk of the tuning
The Weiss discriminator of Fig. 7“7c was developed at the Radiation
Laboratory in an attempt to reduce the detrimental effect of stray
It is essentially
capacitances by making them serve a useful function.
the capacitance-coupled
analogue of the Foster-Seeley circuit.
It has
been shown experimentally that the two discriminators have substantially identical electrical performance
The Weiss dissusceptibility to stray capacitance, and so forth).
criminator, however, requires accurate control over the small difference
between the coupling condensers required for a narrow-band characteristic.
On the other hand, the
Foster-Seeley discriminator suffers
at large bandwidths from the large
variation in mutual inductance
with small displacements of the . m“”‘O
coils. An analysis of the action +
of the Weiss discriminator is given ‘O
in the next section.
The term “discriminator efficiency” is commonly applied to the
rati-o of the maximum available
video circuit of a
FIG. 7.9,—Equivalent
output voltage (d-c or pulse) to
the peak voltage of the i-f signal
at the input terminals.
Since voltage stepup is possible, resulting in
“efficiencies” greater than unity, such usage is improper.
We shall use
the term “discriminator voltage gain” to express this factor.
As in a conventional detector with transformer coupling, discriminator
gain is affected by a variety of factors, including diode conductance,
transformer design, and video load resistance.
In addition, when one of
the detectors is producing a maximum signal, the other is absorbing
some of the available power, and this power, when rectified, balances
out part of the signal from the first detector.
It can be shown that this
balance causes a 30 per cent reduction in discriminator voltage gain
under optimum adjustment.
[email protected] 7.9 is the equivalent video circuit of a discriminator.
the action of one of the diodes alone. If a step-function i-f signal is
applied to the discriminator, the voltage across the bypass condenser will
[SEC. 77
Rise times of the
rise exponentially with the time constant ~mtCB.l
order of 1 ~sec are common.
When the step function is removed, the
voltage across C~ will immediately start to decay with a time constant
Full voltage is reached, therefore, only if the i-f pulse is long.
In a typical design the amplitude of the output pulse for a~psec input
signal will be about one third that for a long pulse.
Increasing REC. results in a stretching of the pulse. If CB is increased,
there will be a corresponding reduction in amplitude unless the original
l-f pulse
(a) Output voltage of upper detector
(c) Net output voltage
(6)-Outputvoltageof lower detector
FIG. 7,10.—Effect
k-h Swept f-m pulse response
of video unbalance.
pulse is long.
An increase in R, produces
no such loss of
amplitude, but values i; excess of about a megohm should be avoided
because of grid current in the following amplifier and because of increased
hum pickup from the heaters. If the discriminator output pulse is
used to operate a hard-tube reversing multivibrat or or “trigger circuit, ”
as in the systems of Sees. 7.15 and 7.16, it is unnecessary to stretch the
pulse. If it is used to fire a gas-discharge tube (Sec. 7. 11) stretching up to
about 10 ysec reduces the threshold for firing. If it is used to energize a
diode search-stopping rectifier of the type described in Sec. 7.13, its
effectiveness is almost proportional to the amount of stretch.
Discriminators should have good video balance.
The charge and
discharge times of the two bypass condensers should be respectively
1 Rimt is taken to include the effective forward resistance of the diode. This is
variable, depending both on signal amplitude and on the instantaneous voltage acroaa
Since the two generator impedances are equal, the effective
It should be noted that the total
bypass capacitances should be equal.
capacitance across the lower detector includes both the coupling condenser C.of Fig. 7.9 and stray capacitances.
Consequently, the actual
value of condenser CB should be 15 to 20 wf greater than that of C4.
Figure 7.10 shows the effect of a moderate video unbalance.
(a), (b), and (c) show the waveforms observed across the individual
detectors and at the output terminals when a pulse oflength~,
at crossThe capacitance across
over frequency, is applied to the discriminator.
the upper detector is assumed to be 30 per cent too large. Because
of the difference in the time constants for charging, the peak voltage
reached across the upper detector is less than that reached across the
FIG. 7.11.—Foster-SeeleY discriminator with Strandberg detectors.
lower detector.
At the end of the i-f pulse, therefore, the net output
voltage is negative.
Because of the difference in the discharge time
constants, however, the voltage across the lower detector falls toward
zero more rapidly than that across the upper detector.
after a time, the voltage across the upper detector dominates, and the
total output voltage becomes positive.
Finally, all charge leaks off,
and the voltage becomes zero.
If the signal from a pulsed signal generator (see Fig. 7.6), the frequency of which is varied from pulse to pulse, is applied to such a discriminator, the pattern of Fig. 7- 10d will be seen on an oscilloscope
N’ear the crossover frequency every
connected to the output terminals.
pulse will extend on both sides of the axis, and the crossover frequency
will no longer be sharply defined.
Such a broadening of the crossover is
not serious unless the unbalance is severe, in which case the output voltage
A nominal figure of 20 per cent
of one polarity is markedly reduced.
unbalance tolerance is usually stipulated for discriminators that are to
be manufactured in quantity.
This is readily achieved if the original
design is good.
From the foregoing, one might assume that only diodes are used as
Actually, triodes are often used. For instance, Bel! Tele-
[SEC. 73
phone Laboratories have used a pair of plate-circuit or “anode bend”
Since both output voltages are positive, one of them is
A circuit of this
inverted to give the correct over-all characteristic.
type is found in Fig. 7“15. Strandbergl hasused a plate-circuit detector
for one branch and an “infinitei mpedance”
or cathode detector for the
P- E,+
FIG. 7.12. —Gircuit
and equivalent
circuit for Weiss discriminator.
other, the two being coupled by a common cathode connection.
circuit is shown in Fig. 7.11.
The great advantage of these detectors is that they supply the
energy necessary tocharge the bypass condensers from the power supply
Much greater pulse stretching is
instead of from the i-f amplifier.
Thus, in the circuit of the Bell Telephone Laboratories, the
pulse is stretched out until the next pulse arrives, so that almost d-c
smaller bypass condensers,
the rise
output voltage is independent of
pulse length even for pulses less than
simplified theory for approximate
calculationhas been developed forthe
Weiss discriminator.
Figure 7.12
shows the basic circuit of the discriminator, its equivalent circuit, and the
important voltages.
Cl and C, represent the diode capacitances, and
the circuit Q’s are assumed to be infinite. The first step is the transformation of themnetwork Cl – C, –L into its equivalent T-network,
FIG. 7.13.—Equivalent
Weiss discriminator
after into-T transformation.
in Fig. 7.13,
‘M. W. P. Strandberg, “AVideo-Frequency
Modulation Detector,’’ RLInternaI
Group Report 53, Apr. 1, 1945.
1 W. Selove, “FrequencyDiscriminatorA nalysis,”
RL Internal Group Report 61,
Jan. 1, 1945.
SEC. 7.8]
and where
At some angular frequent y u,, Z, will resonate with C, so that all of
the current will flow in the upper branch, making El large, and E’ ze, z
Similarly, at an angular frequency ~’, Ez will be large and El zero.
The frequencies UI and UZ are very close to that of the peak response,
@LC’ -l=
If, for the sake of argument, it is assumed that Cl > C’, then COI> ti2.
For angular frequencies decreasing from a,, the impedance of the upper
branch increases from zero and is inductive.
Similarly, raising the
angular frequency from COZcauses the impedance of the lower branch
to increase capacitively.
Therefore, there exists an angular frequency
ae at which the two impedances are equal in magnitude but opposite in
phase. At this frequency the currents in the branches are equal in
magnitude, so that El = Ez, and the error voltage is zero. This is the
crossover frequency.
Z,+zc = –(Z, +ZJ,
Z,+z, = –2Z..
the values forthcse
impedances given in Eq. (l),
.(&+&) ~.
‘(”’La ““’c’
o.L — —,
Equation (4) shows that the crossover frequency is that frequency at
which L resonates with C’ and C/2, that is, with the total capacitance
across L.
An expression for the peak-to-peak separation can be obtained from
Eqs. (2), (3), and (4):
J=w2%- da
In some cases, a simplified expression is possible.
Eqs. (2), (3), and (4), we have
a;— Cd; C,+c–c,
Cd: =
Starting again from
Now if the percentage peak-to-peak
separation is small, we may write
SEC. 78]
Equating thk to the right-hand side of Eq. (6), we obtain
WI — U2 ~ C(C1 + c,).
The voltage at each peak can easily be calculated.
For example,
at 01 the current in the upper branch is E/Z3 and the voltage across the
diode is E, = (E/ZJA7c.
= –– 1
() z.,
– tOIC’)
_ c1 + C2.
– C,+c
These equations indicate that peaks of equal amplitude are possible
only if Cl + C = C2 + C, for which condition El = E2 for all frequencies,
and the error voltage from the discriminator is zero. The branch having
the smaller coupling condenser will have the larger current, and we have
already seen that this will be the low-frequency branch.
If we make
C, < C,, then E, < E2. We can,
however, by restricting the size of
the bypass condensers of Fig. 7.12,
arrange matters so that not all of the
voltage El in the theoretical expression appears
the upper
the two peaks
as shown
be made
Cl < C2, the
for hum reduction.
characteristic is to have the opposite sense, then for the equality of the
peaks to be maintained, the diodes themselves must be reversed.
In any event, the dissymmetry is usually not serious and approximate
compensation may be sec~u-ed by a slight detuning of the resonant
circuit normally associated ~vith the primary voltage source E of Fig. 7.12.
It may he notccl here that most miniature tubes have a certain amount
of Ieakagc conductance bctwccn heater and cathode resulting in the
appearance of a hllm voltage at the cathode of the upper diode, which
carries the desired signal. ‘llc amount of sllch h~lm is variable from tube
[SEC. 7.9
to tube and depends on the resistance from cathode to ground.
If this
resistance is ~ megohm, a common value, the hum may amount to a large
fraction of a volt.
Fortunately, a bias of either polarity between cathode
and heater will cure the trouble.
Positive bias on the cathode is particularly effective.
If the amount of such bias slightly exceeds the peak
value of the heater voltage, the hum will be completely eliminated.
This condition may be readily attained by the use of a separate negatively
biased heater winding, or by the circuit of Fig. 7“14, which may be
applied to any of the discriminators of Sec. 7.7.
7.9. Control Circuits for Nonhunting Systems.—Control circuits for
nonhunting systems with c-w transmitters are very simple.
Since the
characteristic of a discriminator is linear near crossover, the output
voltage is a pure d-c voltage whose level and polarity are determined
by the frequency error of the local oscillator.
As a rule the only requirement is a direct connection between the discriminator and the frequencUcontrol
that is, the grid of the reactance tube, or the reflector of
the reflex oscillator.
Descriptions of many such circuits are to be found
in the prewar literature. 1 If the frequency-control electrode is insensitive, a d-c amplifier, preferably push-pull, may be required.
When the transmitter output power consists of short pulses separated
by long intervals, as in a radar set, it is necessary to provide only for the
stretching out of the pulses that appear at the discriminator, so that their
peak amplitude is maintained between pulses.
Figure 7.15 shows the circuit used for AFC in a radar set designed at
Bell Telephone Laboratories.
This represents a highly developed
nonhunting, single-mixer system (Sec. 7.5).
It is seen that the output
terminals of a conventional Weiss discriminator (Sees. 77 and 7“8) are
The plate load
connected to a pair of plate or anode-bend detectors.
resistors are very high and are bypassed by large condensers, giving a
time constant of 3.2 X 10–2 sec. Since the interval between pulses in
this set is only 2.5 X 10–2 sec for the lowest pulse recurrence frequency,
most of the charge developed during the pulse will be sustained until the
next pulse. What little ripple remains is filtered out by a large condenser at the reflector of the local oscillator.
The plates of the detectors are connected directly to the grids of a pair
of push-pull d-c amplifiers which have a large common cathode resistor,
Because this resistor is degenerative for everything except signals on
either grid, it increases stability.
Control voltage is taken from one of
the amplifier plates, the operating range being selected by adjustment of
the plate supply voltage.
1 Terman,
+ “Spike- Blanhing” trigger
+ 300 v
Afi capacities are in ~~f
FIG. 7.15.—” D-c-amplifier”
To reflector
[SEC. 7.10
The output voltage of this amplifier will swing at least 25 volts above
or below the no-signal level, and is adequate to control a reflex oscillator.
feature discussed in Sec. 7.5 is
It will be noted that the “enabling”
provided by energizing the first i-f amplifier stage only during the initial
transmitter pulse. The trigger for the screen and plate supply of this
tube is taken from the primary of the transmitter pulse transformer.
Other BTL circuits have also contained the “spike-blanking”
The leading edge of the video pulse at the
already considered (Sec. 7.5).
pulse transformer is differentiated to produce a sharp, very short positive
pulse, which is applied to the cathode of VI, cutting this tube off during
the first part of the transmitter pulse, during the time when the TR
spike comes through.
The point at which such a trigger is introduced is
also shown in Fig. 7.15.
Other nonhunting systems have been used successfully by the British.
An interesting feature of one of their circuits is the “ reflexing” of a parallel pair of output i-f amplifier tubes to serve as push-pull d-c amplifiers.
With reference to Fig. 7.6 (a), if the connections are so chosen that a
positive error voltage tends to reduce the local-oscillator frequency, it is
then clear that lockifig is possible where and only where the discriminator
characteristic has a positive slope. In the main pass bands, there are
three such regions: one near crossover at the low-frequency sideband and
two on the outer skirts of the Klgh-frequency sideband.
The latter pair
In this case, then,
are too far from crossover for satisfactory operation.
the high-frequency sideband is the wrong sideband.
Other types of
operation on the wrong sideband will be noted later. It is also possible to
lock incorrectly at any one of three places on each pair of harmonic
sidebands if the gain is too high. With adequate r-f selectivity, of course,
these dangers could be avoided; in nearly every microwave receiver, however, they must be considered.
7.10. Basic Theory—The
[‘drift-in” theory of operation is illustrated
in the block diagram of Fig. 7.16. During the hunting cycle, only the
slow-sweep generator need be considered.
This generator impresses a
sawtooth voltage on the frequency-control
electrode, which results in
a sawtooth frequency modulation large enough to allow for all possible
tuning errors. At some time during the sweep, the crossover frequency of
the desired sideband will be passed. Information generated at this time
will actuate the search stopper which will halt or reverse, as needed,
the progress of the slow sweep. There is a perpetual tendency for the
frequent y to drift off; this tendency is offset by the search stopper.
“wall” may be thought of as existing at the point A in Fig. 7.17 and
inhibiting the sweep. Note that here too there is a wrong sideband,
SEC. 7.11]
exists at B.
Each harmonic likewise offers a pair
of “walls” for possible locking.
The system is stable, for, if the oscillator frequency tends to drift
to the right, the rising discriminator output voltage will develop extra
since a similar
To local oscillator
FIG. 7. 16.—Drift-in
Wrong sideband
.E .%1
E Zz
Tuning error
Direction of slow sweep
FIG. 7. 17.—Rlght
Tuning error
and wrong sidebands.
power, pulling the frequency back.
Similarly, a shift
to the left results in a diminution of search-stopping
power, and the
normal slow-sweep drift will resume.
at Radiation
of Fig.
first AFC
this circuit
for pulse
has certain
Rz 0.5 M ~2
Discriminator 2050
0.25 M
0.25 M
:’ ‘
FIG. 7,18.—Standard
AFC circuit.
limitations which have necessitated the development of new hard-tube circuits,
it is still in wide
use and is likely
of this, and because
this circuit
will be considered
to remain
no adequate
so for some
on it has yet been
in detail.
VI is a gaseous tetrode having the characteristic that the grid voltage
necessary to cause breakdown is nearly independent of plate voltage e~,.
is so biased
pulse or trigger
to remain nonconducting
V2 is a gaseous
eP, reaches
V2 is
the amplifier
a critical
so biased
in the absence
that follows
200 volts
of a positive
the discriminator.
as to fire whenever
the plate
for a 300-volt
RI and R,, charging Cz until the critical voltage
is reached.
V, then breaks down, discharging C2 abruptly.
of the large number of ions formed in V2 (or later in Vl) during the
FIG. 7.19.—Voltage-time
it to execute
a corresponding
than C2, plays
to the reflector
R? and Rt, is applied
in gm-ditmharge-tube
of the finite
and R9 can recharge Cz
of the reflex local
an insignificant
rate, e,% is
Before R ~
Cl, being
role in modifying
the sweep.
If the range-set control Rs is properly adjusted, the local oscillator will
At first, negative
be swept through the correct operating
as crossover
is reached
SEC. 7.12]
and are replaced by positive pulses. The first pulse of sufficient amplitude will fire the search stopper VI.
When this happens, e~, abruptly
drops to some 11 volts above the cathode potential.
The flow of current
in R2 is reversed, and eP, starts to fall. This causes the local-oscillator
frequency to move back from the threshold, so that one of the next few
pulses to appear will be too small to fire VI, or may even be negative.
Because Cl is small, however, RI and R2 quickly restore the charge, and
the forward sweep resumes until another pulse large enough to fire VI
comes through.
These effeots are shown in Fig. 7.19. The potentials of the two plates
at any one time are shown, one above the other.
The time scale after
locking (to the right) has been expanded manyfold for clarity.
This circuit is an example of the frequency-control
control voltage applied to the reflector is determined by the frequency
with which VI is triggered and is unaffected by the trigger amplitude as
long as it exceeds the threshold determined by the bias on the VI control
grid. Later (Sec. 7.13) we shall consider circuits employing amplitude
control, in which every pulse is effective, the amount of the effect being
proportional to pulse amplitude and thus to the amount of deviation from
the crossover frequency.
7.12. Design Theory for Gas-discharge-tube
Control Circuits.-In
pulsed systems, since control information is available only for short,
widely separated intervals, it is necessary to limit the amount by which
the LO frequency can shift between successive pulses.
This restriction,
in turn, limits the speed with which the control circuit can readjust itself
to meet new conditions.
In Sec. 7.1 the causes of frequency drift were considered.
Of the
effects discussed, pulling during the antenna scan is usually the only one
that takes place so rapidly as to constitute a following-rate problem.
When rapid pulling occurs, the local-oscillator frequency may lag behind
its proper place, resulting in mistuning, or it may drop back so far that
control information is lost, causing the system to become unlocked.
With reference to Fig. 7.17, pulling may be thought of as causing a
displacement of fo to the left or to the right, with the discriminator
characteristics executing a similar shift.
If fO shifts to the right, control
information will disappear and the local-oscillator frequency v.ill start
to drift to the right as the slow sweep resumes.
No matter how great the
shift in ~0 (within the limits of the control range) nor how fast the shift
takes place, the local oscillator will ultimately reach the threshold
frequent y A, and control will be restored.
If, on the other hand, f, shifts to the left, the firing rate of the searchstopping tube (VI of Fig. 7. 1S) will increase Up to the [irnit of one per
transmitter pulse, causing the local-oscillator frequency to shift to the
[SEC. 7.12
left. If the rate of shift of FO is too great, the oscillator will fail to keep
up with it and presently will be so far out of tune that the positive pulse
from the discriminator amplifier will fall below the threshold, and V,
will cease firing. Then the slow sweep to the right will resume and the
system will be unlocked.
This one-sidedness is a characteristic of all
drift-in systems.
It might be mentioned here that the “push-pull”
systems discussed
in Sees. 7.14 to 7.16 can become unlocked as a result of fast shifts in
either direction.
Nonhunting systems may also become unlocked if a
fast frequency shift exceeding the system pull-in range occurs (see
Sec. 7.3).
Maximum following rates determine the ability of a system to follow
fast frequency shifts. They are usually express~ in megacycles per
second per second.
They are functions of the value of the oscillator
frequency within its control range and are, in general, different for the two
directions of frequency shift.
The control circuit determines tbe maximum rate at which the frequency-control electrode (here, the reflector) voltage may be changed.
The corresponding frequency following rate is then determined by the
electronic-tuning sensitivity of the oscillator, that is, by the shift in
frequency in megacycles per second per volt change on the frequencycontrol electrode.
In any pulse-operated hunting type of AFC, there is an inherent
ripple in the local-oscillator frequency.
This is due to the tendency
of the oscillator to resume the hunting sweep during the interval between
successive pulses and can be reduced only at the expense of reduced
following rates. Ripple is usually expressed as the peak-t~peak amplitude of the frequency modulation (in megacycles per second) where the
system is in equilibrium and depends, as do the following rates, upon
the value of the local-oscillator frequency within the control range.
In a practical design, ripple is usually the factor that limits the
following rates. Sometimes, however, it is found that while the hunting,
sweep is traversing the discriminateor characteristic, the cent rol inform ation received is insufficient to stop the sweep although, once the sweep is
stopped, locking is possible.
The speed of the hunting sweep would then
be the limiting factor.
The maximum permissible ripple can be calculated from receiver bandwidth and similar considerations, and from this
the amount of voltage ripple that can be tolerated on the reflector maybe
With these data, the following theory may be applied to
determine optimum circuit constants.
For the rest of this section, following rates and ripple W-n be referred
Two voltage following rates are
to in terms of the reflector voltage.
defined: the maximum”” down-pull” rate, the rate at which the reflector
voltage becomes more negati~’e when the search-stopping
each transmitter pulse; and the maxim(lm “up-pull”
at whichit becomes less rmgativc ~~henthescarch stopper
all. These rates arc cxprcssc(l in ~-olts per second,
referred to as the peak-to-peak amplitude of the ripple
reflector when the system is in equilibrium.
tubeis fired at
rate, the rate
does not fire at
Ripple will be
voltage at the
Basic cwcult
Effective andequ,valent circuits forcharg,ng C,
Effective andequivalent circuits forcharging C2
FIG. 7.20.—Equivalent
circuits for gas-discharge-tube
N. Rochester has developed a theory giving theprecise behavior of
gas-discharge-tube control circuits, from which the following rates and
ripple may be derived.
The only assumption involved is that the time
constant for charging the sweep condenser C’zis much larger than that for
charging the search-stopping condenser Cl. This is always true in practice since the slow sweep must be such that several pulses appear during
the transit of the receiver pass band, whereas the search stopper must be
fully recovered within a few pulses.
1Sylvania Electric Products Co,, Boston, Mass.
[SEC. 7.12
For the notation of this discussion, the reader is referred to Fig. 720.
In this figure capital letters denote fixed quantities; lower-case letters,
variable quantities.
Average values are differentiated from instantaneous values by the presence of a superscribed bar.
VI and V, are represented by switches which close only long enough to discharge their
respective condensers.
To simplify the calculations, all voltages are
referred to the plate voltage of either tube when conducting (about
10 volts above the cathode potential).
The resistance of the potentiomOne can allow for it by
eter from which Ei is derived is neglected.
replacing it with an equivalent voltage and resistance, using Th6venin’s
In practice such a cortheorem, and including the resistance in PTR.
rection is small.
Because of the difference in time constants, ez may be considered
constant during any one firing cycle of T1. Henc e, may be computed
as a function of time. When el has been determined, the instantaneous
current in PR flowing into Ca may be computed for one cycle.
Figure 7.20b shows the circ~it
this, the change in e, may be computed.
— _pEO+~
and resistance
R, = ~
When, after a trigger, the tube V, is momentarily made conducting,
the voltage across Cl will build up exponentially from zero, with a time
constant RdCl, approaching ~.
The equation is
el =
a (1 —
and ~ is the interval between pulses.
When the AFC is in equilibrium, control pulses will be applied to the
grid of T1 at more or less regular intervals so spaced as to maintain the
required value of ~.
Let us assume this interval to be rw. Because
of the linear relation between voltage and current, the average current
flowing in pR may be computed from the difference between the average
voltage e1 across Cl and the voltage et:
A plot of F(z)
nr \ o
vs. z, where z = p/n, is shown in Fig. 721,
To compute the ripple, we observe
current in pR equals the average
slope de2/dt is zero. This is the
excursion downward
between triggers, and the time at
which it occurs may be found by
equating the right-hand sides of F(z)
Eqs. (11) and (13), with the result
that when el = ~, the instantacurrent so that the instantaneous
h = m In ~F-
8 10 12 14 16
We next note that, as shown in
FIG.7.21.—F(x) VS.Z.
Fig. 7.20c, Th6venin’s theorem
can be applied to reduce the influences on the voltage across CZ to that
of a single variable voltage source es with internal resistance R5 where
Now e6 is made up of a steady component
e; and a ripple component
We may obtain Z by replacing e, by~, in the first of Eqs. (15)
1 +-%
The ripple is then given by
7(el – ~).
Taking el and z from Eqs. (11) and (13), we obtain
e2 =1+7
(1 – F – e-:).
The current flowing out of C, is
This may be integrated from zero to the time of the maximum excursion
tl, of Eq. (14), to give the flow of charge.
Dividing by CZ gives the
maximum ezcursion, or peak-to-peak ripple, Ae2n.
AezB =
Eqs. (10), (13), and(16)
for Z,eliminating
[SEC. 713
This gives
P-YFEO + (1 + p)E3
The maximum down-pull rate occurs when T, is fired by every pulse.
This is computed in the same way as the ripple except that the integration
interval is simply r. The result is
(Aez). =
[(1 – F)r + pr(e-~-– l)] = ~,
[F, – F],
F. = ~(~}
= 1 – ~(1 – e-~).
The up-pull rate is simply the free charging rate of C,. Again by
Th6venin’s theorem, we can combine the influences of Eo and Ea on Cz
The circuit is
into a single voltage EB acting through a resistance R6.
similar to that shown in Fig. 7 20c except that el is replaced by EO, and
pR by (1 + p)R. Thus
~, = (~ + P)E3 + PYEa,
The current flowing into C, is
j.— Ee – ez
giving rise to a voltage change per interpulse interval of
~Ae,)u = (1 +
TOE, – (1 +
P +
These equations, although accurate, are inconvenient to use, A
simpler form that is directly related to quantities easily measured in a
practical circuit may be obtained as follows:
v = —,
l?. = ~,
when n = I,
E* = ez,
After prolonged operation with no triggers, e%will equal E., and Ae, will be
From Eq. (25), then,
(1 +
P +
(1 +
SEC, 7 12]
This may be substituted back into Eq. (25), giving
From Eqs. (16) and (13)
For n = 1, this becomes
These quantities may be substituted in Eq. (22) to give
VP y
No such simplification of the expressions for the ripple voltage is possible.
E, and E, may be measured with a vacuum-tube voltmeter at the
plate of Vz by the application of triggers to VI at the pulse recurrence
frequency and by the removal of all triggers from VI, respectively.
may also be computed from Eq. (21) by the substitution of FO and
F- = 1 respectively for F. These values depend on Ea, which is
determined by the range-setting potentiometer.
The general principles that must guide the designer are fairly clear.
The highest possible following rate consistent with allowable ripple
should be sought.
En and ET should be well outside the control limits
between which e, is to operate in order to provide residual following speed
at the limits.
It appears that the choice of p is not critical.
All values between
~ and 2 will give substantially the same ratio between ripple and maximum down-pull rate. A large value of p tends to make the up-pull and
down-pull time constants (not following rates) equal, and provides better
filtering of the sawtooth voltage on Cl by the PRC’: network.
extra filtering is precisely offset, however, by the reduced down-pull
rate and meanwhile Vl will become harder to extinguish.
A similar
The compromise value p = I
effect is observed if p is made small.
should be satisfactory in nearly every case.
The choice of C, should be such as to make Z have its midrange value
for n s 3.5. If n is much smaller, there will be inadequate control range
for down-pull, whereas if it is larger, the ripple will become excessive at
the upper end of the control range, for which n will become greater than
10. Equilibrium at different parts of the range will occur for values of n
between 2 and 10, the range below 2 and above 10 being for extra following
[SEC. 7.12
rate at the ends of the range. At n = 10, the ripple will be almost
exactly twice themaximum down-pull, and this will bethe limiting factor
C*. Ripple isnormally limited toapeak-to-peak
about one fourth of the receiver bandwidth to the half-power points.
The peak current allowable for tubes used for V, is usually 0.5 amp.
This fact makes necessary the use of a limiting resistor of at least 600
ohms (for a 300-volt supply), or a limiting choke in series with Cl and Cj.
With such limiting, V, will not extinguish reliably if R,, the parallel
resistance of R and pR, is less than about 500,000 ohms.
The lowest
value consistent with reliable performance should be used. A common
value is R = pR = 1 megohm.
The current through the bleeder p~R
To reduce
reduces E~, particularly when Es is made large and negative.
this effect, pyR should be as large as possible, consistent with the leakage
Values in excess
and runawayl possibilities of the controlled reflector.
of 6 to 8 megohms are dangerous.
One serious problem faces the designer of a gas-discharge-tube control
It is necessary to ensure proper operation with any tube fulThe specifications for a type 884 gasfilling JAN-1A specifications.
discharge triode, for instance, are such that if the bias is set for nominal
firing at, for example, +200 volts, various tubes may fire anywhere
between 160 and 240 volts.
Added to this variation is an uncertain y
of at least A 10 per cent in the bias if 5 per cent resistors are used. The
tube is required to fire at a plate voltage appreciably less than ET for any
In a reasonable design, with a 300-volt
setting of the range-set control.
supply, ET must be as low as 250 volts when the control is at its most
negative end.
On the other hand, the tube must be capable of covering the entire
sweep demanded by the local-oscillator
When the control
is at its most positive end, the value of ~z at the positive end of the hunting
sweep is fairly high. In fact it has not been found possible to find any
set of constants that will ensure iiring at the end of the sweep with the one
setting and simultaneously ensure non firing within the control range
at the other setting for all JAN-approved
The addition of a
bias adjustment for Vz will cure this difficulty but no simple procedure
exists for making such an adjustment in the field.
It may be pointed out here that the effects of tube variation may be
greatly reduced by feeding back part of the d-c plate voltage to the control
grid. The effect is similar to the use of inverse feedback with highvacuum-tube amplifiers.
If one plots a graph of the grid voltage at
1If the reflectorof a reflexoscillatorbecomespositive,from an accidentallyapplied
potential, it may draw sufficientcurrentto heatup and emit electrons,and secondary
electronswill be produced. In this event, if the externalresistancein the reflector
circuit is too high, the control of the reflectorvoltage may be lost.
SEC. 712]
which the tube will fire as a function of the plate voltage, it will be seen
that a triode such as the 884 has a “gain” of about 10, in that if the
plate potential is increased by 10 volts, thegrid firing potential becomes
more negative by 1 volt. The corresponding curve for a tetrode such
as the 2050 shows a “gain” of around 200, the grid firing potential being
The feedback factor B is the ratio
almost independent of plate voltage.
between RI and RI -t RZ h I% 722.
0.25 M
of Vz
Using these definitions, the usual equations for feedback apply.
effective ‘(gain” is given by
and the improvement
variability with feedback)
_ (Firing-voltage variability without feedback)
1 – Aj3
Using the constants shown in Fig. 7.22, and taking A = 200, we find
that G = 19, and the variability reduction factor is 1/12.5.
It should be
not ed that a fairly large negative supply is required.
If the feedback
is achieved through the use of a cathodebiasing
resistor, the control
range is reduced by the reduction in available cathode-to-plate
Also, the feedback loop draws current and reduces E, in the
same way as did P7R for negative settings of the range-set control.
Much of the benefit of such stabilization is thus offset.
It will also be noted that there is considerable variation (up to 3 to 1)
in the maximum up-pull and down-pull rates, depending on the position
of the range-set control and the position in the sweep, because of the
[SEC. 7.13
exponential nature of the Cz charging curve.
Since the conditions which
limit following rate apply to the maximum case, the following rate is
unpleasantly low in the minimum case. Many of these difficulties are
reduced to tolerable proportions if the supply voltage is increased.
the circuits may be suspended between the – 300-volt and the +105-volt
This results in considerable improvement.
Some workers claim that gas-discharge tubes are not sufficiently
One claim is that the firing conditions
reliable for these applications.
Another claim
are affected by past history, age, and temperature.
is that, in those circuits where the entire control unit is required to
operate at the —2000-volt level, the tubes are subject to erratic firing
caused by electrostatic influences.
Neither of. these claims has been
conclusive y verified, but both add weight to the argument that only
high-vacuum tubes should be used in the control circuit.
The following
sections deal with a circuit that contains only hard tubes and is therefore
free from the above objections, including the one resulting from nonlinear
sweep rates.
7.13. Diode -transition Control Circuits.—The new hard-tube control
circuit is shown in Fig, 7.23. The block diagram of Fig. 7.16 is still
0,5M ~--
discriminator el
I L ‘R’”‘“s
FIG. 7.23.—Diode-tranaitron
R-f 0S6
control circuit.
applicable, the diode detector VI serving as search stopper, and the
transitron oscillator V2 as the slow-sweep generator.
The transitron
oscillator is a modification of a precision ranging circuit used extensively
in radar indicators (Vol. 22). Its operation, which will be explained in
detail below, depends essentially on the negative transconductance
which exists between the suppressor grid Ga and the screen grid GZ of a
As used in the control circuit, it is a frw+running sawtooth
oscillator whose plate voltage sweeps slowly from just below the plate
supply voltage to a point not far from the cathode voltage, after which
SEC. 7.13]
it snaps back rapidly, and starts the downsweep again. The downsweep part of the cycle is used as the hunting sweep. Thus the localoscillator frequency sweeps from low to high frequency, whereas, when
the gas-discharge-tube circuit is used, it sweeps from high to low.
If, during the downsweep, the grid-return resistor is tied to a point
suitably negative with respect to the cathode, the sweep action will
stop, and the tube will act as a normal d-c amplifier with a gain of approximately 50. Such a negative bias, supplied by the diode detector when it
receives control information from the discriminator, is the basis of locking.
Let us consider the sequence of events which takes place in this
circuit, starting at the beginning of a downsweep.
Assume, for the
sake of argument, a plate supply of +150 volts measured from the cathode
The plate voltage e, is about + 140 volts, the plate current
ip being therefore 20 pa. Gs will be at ground or positive potential
(see below, also Fig. 7.24).
As the division of the cathode current between
plate and screen is normally in the ratio of about 4 to 1, the screen
current i., is 5 pa, causing a drop in the screen resistor of only 0.25 volt.
Since the cathode current L is only 25 pa, the control grid G, must be
nearly at cutoff potential, about —10 volts. At the beginning of the
downsweep, the local oscillator is far off tune, and no control information
appears at the output terminals of the discriminator amplifier.
being small, plays no part at this time, nor does the diode, since its plate
will be at —5 volts because of the division between RI and R2. Because
of the 10-volt drop, a current of 5 pa flows along RI and Rz into the
condenser C,. Consequently, the voltage across C,, tvhich is (e,, – e,),
changes at a rate
The grid voltage does not approach ground potential at this rate, for,
as it rises, the plate voltage is approaching ground A times as fast, where
A is the gain of the stage. Thus
t& _
dt –
Substituting in Eq. (33), we have
= (R, + R,)(’1 + A) C,-
There is, therefore, an apparent input capacitance (1 + A) times as
great as the actual feedback capacitance Cz, ‘l’his capacitance ampli-
fication makes possible very slow sweeps with small condensers.
manifestation of the well-known Miller effect. 1
The downward rate of change of the plate voltage is
– (R, + R,) (1 + A)C,
= (R, +
[SEC. 7.13
It is a
since A >> 1. The sweep rate is nearly independent of tube characteristics.
In practice, e., swings from about – 10 to – 8 volts as the plate
covers its sweep. The sweep is therefore linear to within about +10 per
cent, a great improvement over the gas-discharge-tube circuit (Sec. 7. 12).
This then is the picture that we see during the downsweep, up to the
time the discriminator crossover frequency is reached.
As soon as the
crossover frequency is passed, positive pulses appear at the plate of
the discriminator amplifier and are coupled through Cl into the diode
The action of the detector is straightforward.
During the positive
pulse the diode is conducting, and charge flows into Cl. When the pulse
is removed this charge remains, and the potential across the diode
becomes negative.
After a few pulses the average potential across
the diode is sufficiently negative so that the charge leaking off Cl through
RI between pulses equals the charge transferred to Cl by the pulses.
The system will reach a stable equilibrium in which the oscillator rides
far enough up on the discriminator characteristic to supply pulses whose
amplitude is just right to maintain the bias which holds the transitron,
If the oscillator frequency
and thus the reflector, at the correct voltage.
were to increase, the pulse amplitude would increase, causing an increase
This would cause the
in bias and hence of transitron plate voltage.
oscillator frequency to decrease again. Lowering the oscillator frequency
would be compensated for in a similar way.
To complete the picture, we have only to show how the system is
recycled if no control information is received during the sweep or if
the system becomes unlocked.
The effects are illustrated in Fig. 724,
with reference to the circuit of Fig. 7.23. When cent rol information is
lost, the charge on Cl quickly disappears, so that the downward sweep
of the plate is resumed.
This is illustrated in region A.
At first, the voltage drop across the screen-supply resistor Ro, is
negligible both because most of the cathode current reaches the plate and
because of the low value of i?,,. As the plate potential approaches
ground, however, an increasing fraction of the increasing cathode current
1 J. M. Miller, “Dependence
of the Input Impedance of a Three-electrode
Tube Upon the had
in the Plate Circuit, ” Bureau of Standards Scientific Paper
No. 351, Terman, op. cit., Sec. 5, p. 468.
is diverted to the screen Gz whose potential therefore starts to fall.
Because of the condenser C~, this fall is coupled ovor to the suppressor G,.
Soon, the process becomes regenerative, at B. As the suppressor voltage
e~, is carried below ground potential, it diverts current from plate to
screen, causing ePto rise and eo, to fall farther. The rise in ePis coupled
through C2 to G,, causing an increase in cathode current most of which
FIG. 7.24,—Transition
now flows to the screen, further accelerating the process described above.
Since this process involves no change in the charges on Cl and C,, only
interelectrode and stray capacitances slow it down.
The entire transition
actually takes place in a few microseconds.
When e,, has been carried by the plate to a slightly positive voltage,
grid current will be drawn, preventing further rise. At this instant the
cathode current is large, and all of it flows to the screen, the plate being
[SEC. 7.13
cut off by the suppressor.
Consequently, e,, is close.to ground potential,
eo, is far below ground potential, and e= is perhaps 15 volts above its
value at the end of the slow downsweep.
During the next period (region C of Fig. 7.24) C, is charged, with a time
constant RPC’2, toward E,.
Meanwhile, the charge on C3 leaks off
through R,,, so that e,, approaches ground potential with a time constant
RO,CS. Presently, eo, comes close enough to ground potential to allow
some of the current to reach the plate, which by this time is practically at
Ttis flow of plate current, by causing e= to drop, starts the second
regeneration at D, in the following manner.
The downward trend of P, being transmitted by C’2 to GI causes a
reduction in the cathode current, and hence in the screen current.
resultant rise in e,,, because of Ca, causes a similar rise in e,,, which in
turn allows more current to reach the plate.
Thus, the original effect is
accelerated both by the increased drop in e= and by the decreased screen
current. Again there is a fast transition, which stops only when eg,
has been carried so far negative that only a little cathode current flows,
an amount consistent with the plate current flow necessary to maintain
e, some 10 volts below E=. At this point the slow sweep downward
This sawtooth sweep, then, will recur
repeats, starting the new cycle.
until control is again secured.
Before the idea of the diode search stopper was conceived, a circuit
was developed using a gas-discharge tetrode search stopper, as in the
standard gas-discharge-tube AFC, and a transitron control tube.
Essentially, the plate of VI of Fig. 718 was attached to a potential divider
whose lower end was at —300 volts, and the divider tap was connected
through a resistor to the control grid of the transitron.
A new type of miniature tube, the 6AS6, was developed for use in
In that application, a sharp cutoff of plate
transitron ranging circuits.
current by the suppressor was desired.
When this tube was tried in the
circuit described above, it was found that the regeneration at the end of
the downsweep occurred while the plate was still far above ground potential. In order to prevent this, the circuit was modified by coupling only
about one sixth of the screen wave to the suppressor by tying the coupling
condenser Cs of Fig. 7.23 to a tap on the screen-dropping resistor Rg,.
The change is shown by dotted lines.
An examination of the diode-transitron circuit shows a number of
advantages some of which, such as linearity of sweep and the obtaining
of long sweep times with relatively small condensers, have already been
Others include the possibility of using a high-voltage condenser
between the video amplifier and the diode, enabling the circuit to operate
at a voltage far from ground potential.
A further increase in sweep
time may be obtained by the use of high resistances in the grid circuit;
SEC. 7.14]
this is not possible when the charging resistance is in the plate circuit.
Since the output voltage is taken from the plate at relatively low impedance, it impossible to apply voltage to tbe reflector from a divider of lower
impedance than that used in the gas-discharge-tube circuit, without
having the sweep seriously affected by the range-set control.
By proper
choice of constants, the range covered by the sweep may be made nearly
independent of tube selection and resistor tolerances.
One final point
to be noted in connection with reflector circuits is that the control
tubes are often connected between the negative power supply and ground,
since the reflector voltage is usually below ground.
the 2K45
the feedback
in order
on or fully
or even
in which
of the tuning
that fully
in others,
is either
are limited
it is arranged
so that
on frequency
be of primary
by friendly
In peacetime
is the
over a wide range
in enabling
either by the enemy
this prop-
be less important.
A second
point is that, with the advent
to the wrong
of a radar set to escape from jamming,
erty may
to the
will lock
the operator
was applied
of the art, these circuits
of a tunable
of the
In some of the circuits,
in complexity;
the tuner
is, these systems
In the present
the sweep
and following
is inherentl y rej ected;
on either
of the
had to be set at 90 sec.
only by the thermal
sent a considerable
the time
the wrong
there is no wrong
so that
the output
a suitable
a serious
when such a system
of the wide tuning
One of the normal
be used by connecting
to avoid
(Sec. 7.9) became
it was necessary
their frequency.
For instance,
1 the complete
of this kind were used,
to be made
for controlling
(Sec. 7.10)
to the grid of the tuner
the 2K50,
If a system
new circuits
noise in the receiver
was an early
however, the external
power supply
of the balanced
mixer (Chap.
has been practically eliminated, and
used for heating
did not have a tuning
the tuning mechanism
was grid-
the major
for the use of high intermediate
[SEC. 714
trend is toward the use of a 30-Mc/sec intermediate frequency for which
the sidebands are only 60 Me/see apart.
When a 60-Mc/sec receiver
is used, the local oscillator stops oscillating before it reaches the wrong
At 30 Mc/se,c, this is not true, and locking on the wrong
sideband is a problem even with the limited tuning range afforded by the
A final point is that, at least in the mechanically tuned 25,000-Mc/sec
2K33 oscillator, a large ungainly tuning mechanism is required.
the temperature drifts to be expected are so great that a remotely conpoor
Nibbe. Case A. _
Durand { Case B-+
is thereby
Wrong~;deband “
for Whitford AFC
60 fvfc/sec
Heat on
Frequency _
Whitford AFC
The direction of the frequency drift
FIG. 7,25.—Operation of thermal AFC systems.
after a pulse of a given polarity is given at the top of the figure for the various cases. Note
the possibility in the Whitford system of being trapped between the negative trigger wall
In the Nibbe-Durand AFC, Case A repreat C-C’ and the search-reversing point B-B’.
sents the condition existing after a heat-control reversal at A-A’; Case B, that existing
after a reversal at B-B’.
trolled tuning motor is required to enable the operator to select the
operating range for the AFC.
This motor adds considerably to the
weight and volume of the local oscillator.
In spite of their complexity, the circuits about to be described are
reliable, and are not critically dependent on tube selection or component
tolerance for satisfactory operation.
In view of the advantages cited,
therefore, their use is justified for some applications.
The “on-off” feature described at the beginning of the section makes
possible reasonable following rates. This feature is combined with
push-pull operation to obtain Iocklng and wrong-sideband rejection.
In the Whitford AFC system, the operation (see Fig. 7.25) is the following.
If the circuit is arranged in such a way that positive triggers
from the discriminator turn the strut power on, causing the oscillator
SEC. 7.15]
frequency to decrease (move to the left) and negative triggers turn it off,
causing the frequency to increase (move to the right), then it is possible
to lock on frequency at the left-hand sideband, and locking at the other
sideband is excluded.
If, furthermore, provision is made for causing
this cycle to repeat once every few seconds when the system is not locked,
the frequency will hunt back and forth ,over a band whose limits are
shown at A-A’ and B-B’ in the figure, until the desired locking frequency
is reached.
The AFC system as described can be trapped between the
right-hand end of the sweep B-B’ and the negative “trigger wall”
C-C’ at the high-frequency
side of the right-hand sideband.
trapping is overcome by desensitizing the video amplifier during the
heating part of the hunting cycle so that tbe frequency has to sweep all
of the way to the left and start back before any pukes can come through.
In the Nibbe-Durand system described in Sec. 716, a form of” lazy man”
is used,
in essence,
and the tuning-strut-heater
the relation
in such
a way
as to
make it correct for locking to the first sideband encountered during
The next two sections treat in detail the circuits actually used.
7.16. The Whitford AFC.—A block diagram of the control circuit is
shown in Fig. 7.26 and a circuit diagram in Fig. 7.27. The balance of the
coupling circuit
FIG, 726.-Control
circuit for Whitford AFC.
feedback looD is similar to those already discussed in Sees. 7.4 to 7.8
and shown in Fig. 7.2. The only difference is that the discriminator
must be designed to produce a pulse with a short rise time (Sees. 7.7 and
7.8); stretching the pulse is unnecessary.
The circuit operates in the following manner. The power in the
tuning strut of the local oscillator is controlled by a reversing multivibrator, or Eccles-,Jordan “trigger”
circuit ( V1 in Fig. 7.27).
circuit has two stable conditions of equilibrium.
In the first condition,
the left-hand section, V~*j is conducting heavily, with its grid potential
at the grid-current point, while the other section, V4a, is completely
cut off. The plate potential of section a is therefore close to B+, and the
tuner triode grid is close to ground potential.
Strut power is therefore
high, and local-oscillator frequency low or falling.
In the other position,
The plate of section a is now close to
V* is cut off and V46 conducts.
cathode potential, the tuner grid is negative, strut power off, and frequency high or rising.
Hunting is accomplished by switching Vd alternately between these
positions at intervals somewhat longer than the thermal time constant
of the local oscillator (from 2 to 10 see). Locking is accomplished by
- Wdeo
FIQ. 7.27. —Whitford
switching at a rate so high (50 to 200 per see) that thermal inertia keeps
the strut temperature substantially constant.
The average temperature
is determined by the ratio of the time spent at full power to that spent at
zero power.
It was shown in the previous section that a one-to-one relation
between trigger polarity and the application or removal of strut power
was sufficient to provide locking of one sideband and rejection of the
other. A simple capacitance coupling between the video-amplifier plate
and the grid of Vla produces such a relation, but it is unreliable.
small negative pulse is capable of turning an “ on-tube” off, but a large
positive pulse is required to turn an “ off-tube” on. This is because
the grid of an on-tube is held, by grid current, close to cathode potential
where the mutual conductance g- is high, ~vhcrcas, to provide an adequate
margin of safety against tube variations, the grid of an off-tube must be
held far below the point of complete plotc-current cutoff.
The serious
effect of such asymmetry is that if the gain of the system is adequate to
ensure operation on the positive pulses of the fundamental sideband,
it may allow operation on transients or on the negative pulses of a
harmonic sideband (see Sec. 75).
Complete symmetry is assured by using a phase inverter (V,) and
applying the two equal but opposite output voltages to the two grids of
1’,. Thus, positive pulses at the plate of V, result in negative pulses
at the plate of V2, which will turn V4b off if it is o
Similarly, negative
pulses at VI produce negative pulses at the cathode of Vz, which can
turn V4. Off.
In principle, the positive pulses appearing at the plate or cathode d Vz
might be used to aid the negative pulses on the opposite electrode.
such aid is permitted however, another ill effect causing unreliability
may occur.
Suppose two positive pulses appear in sequence at the plate
of V1. The first produces a negative pulse on the grid of V,6, which is
therefore turned off. The second produces, in addition, a positive pulse
which would reach the grid of Vt~ if it were not for the diode Vs.. Since
Vl= is now conducting, with its grid drawing current and acting as a
diode, this fiositive pulse would charge the coupling condenser.
the cathode end of this condenser returned to its quiescent voltage,
This overshoot, caused by differthe grid end would become negative.
entiation of the pulse, would be quite capable of turning Vla off again and
producing an undesired reversal of the heat-control circuit.
Adding the
diodes of V, is a complete cure for this trouble.
This special coupling
circuit gives satisfactory operation independent of tube selection and
component tolerance.
Returning to the main argument, then, we see
that VI through V1 provide precisely the type of coupling between
discriminator output voltage and thermal triode power that was specified
in Sec. 7.14.
Hunting and the desensitizing discussed in the previous section are
accomplished by means of a slow timing multivibrator Vs. The cycle of
the grid potential of a multivibrator is such that during one phase the
grid is very close to ground potential, whereas during the other phase it
is negative and rising. One of the grids of V, is tied directly to the
suppressor grid of the video amplifier V 1. When these grids are close to
When they are negative,
ground potential, VI acts as a normal amplifier.
47 k
22 k
,5 k
470 k
390 k
390 k
470 k
360 k
360 k
22 k
22 k
22 k
470 I
470 k
2.2 M
560 k
30 k
170 k
--300 v
All resistors ~w unless
otherwise noted
FIG. 7.28. —Nibbe-Durand
-—470 k
To triode
gnd of
thermal 470 I
-D Transdron
2,2 M
however, the plate current in VI is completely cut off, providing the
required desensitizing.
Furthermore, the transition between the two
conditions produces a sharp voltage rise at the plate of VI when this tube
is cut off. This abrupt voltage change is differentiated in the coupling
condenser, proceeds through Vz and V3, and acts as a trigger to cut
V,~ off.
The multivibrator that governs strut power is thus reversed,
and the desensitized recovery sweep of the local oscillator is started.
Similarly, when the multi vibrat or switches to the other phase, turning V 1
on again, the negative wavefront thus produced turns V4b on again,
institutes the active hunting sweep.
The only problem remaining is to stop the action of the multivibrator
when the system is locked.
For this purpose, the audio-frequency
square wave at one of the plates of the heat-control multivibrator is
differentiated and rectified by V,.
The negative voltage thus produced is
applied to the grid of Vsb, effectively holding the multivibrator fixed.
7.16. Nibbe-Durand AFC System.—This system, shown in Fig. 728
is arranged to lock on whichever sideband is first encountered after the
heat-control reversal marking the end of a hunting sweep. Both directions of the sweep are active, and the video amplifier is always sensitive.
The heart of the system is a pair of reversing-multivibrator
similar to that used in the Whitford system described in the previous
The coupling into the first circuit and the coupling out of the
second are respectively identical to the input and output couplings of
the reversing-multivibrator
circuit in the Whitford AFC.
In addition,
there is a coupling between the two multivibrators such that whenever
the first one reverses, the second will likewise reverse. Thus, with a given
phase relationship between the two, the system can lock on one sideband
just as it does in the system previously discussed.
The triggered reversals
of the first trigger-sign selector, or TSS, circuit are transmitted to the
If the relative phases are changed,
second heat-control, or HC, circuit.
This is
the system will lock in a similar manner on ~k~
~,.. other sideband.
illustrated in Fig. 7.25.
A transitron oscillator VT that has a period of one to two times the
time constant of the thermal assembly of the local oscillator to be controlled is provided (see Sec. 713).
The transitron generates triggers
The triggers are obtained by
which operate the TSS and HC circuits.
differentiating the voltage wave at the screen grid (see Fig. 7.24c).
The differential output waveform consists of a sharp negative trigger
followed by a sharp positive trigger. These triggers are introduced to
the grid of a triode Vs that is biased beyond cutoff.
The negative trigger
therefore has no effect, but a positive trigger brings the grid into the
conducting region and results in a small positive trigger at the cathode
and a large negative trigger at the plate. Because of a connection from
the cathode of this tube to the cathode of the video amplifier V,, the small
negative trigger is applied to the signal channel leading to the TSS.
It is
equivalent to a negative trigger at the grid of VI and therefore presets the
TSS in such a way as to make it ready to accept only positive triggers from
the discriminator.
Simultaneously, the negative trigger at the plate of l’, is coupled
through small condensers to the grids of the HC and cuts off whichever
section of the HC is conducting at the time. The heat control in the
tuner triode is reversed and a reverse sweeu is started.
To restate, in the absence of control information from the discriminator, the oscillator frequency is swept up and down over the band, the
At each reversal,
reversals occurring at each cycle of the transitron.
provision is made to ensure that the TSS is ready to accept positive
Examination of Fig. 7.25 shows that,
triggers from the discriminator.
after each HC reversal, the first discriminator triggers that are capable
of causing a TSS reversal, and hence a locking reversal of the local oscillator, come only after the crossover frequency has been passed.
Consequently, if control information appears, the frequency will pass crossover,
When the crossover frequency is
and then the drift will be reversed.
again passed, the negative triggers from the discriminator will cause a
second reversal of frequency drift, and so on. The system will be
If the transitron were allowed to continue operation, there would be
an even chance that a given reversing trigger would disturb the phase
relation between the TSS and the HC, making a shift to the other
sideband necessary.
For, although every trigger would cause a reversal
of the HC, reversal of the TSS would occur only if it happened to be
prepared to receive negative triggers at the time, which would be true
on the average only half of the time.
Therefore, the transitron trigger generator must be stopped.
This is
accomplished by a detector, Vg, whose input voltage is the differentiated
waveform at one plate of one of the reversing multivibrators.
pulses that appear every few seconds from the hunting-cycle reversals
are too infrequent to generate appreciable voltage, but when the system
is locked, pulses appear at an audio frequency, and Vg develops a large
negative bias. This bias is applied to the suppressor grid Gs of the
Since the bias does not affect phases A, B, and C of Fig. 7.24,
after due time the transitron screen voltage suffers its abrupt drop.
It does, however, prevent the completion of phase D of the wave on G3
(Fig. 7.24g), with the result that the plate remains completely cut off
and the transitron cycle is stopped.
Application of the stopping bias voltage in this manner permits a
valuable “second chance” feature.
The time required for the voltage
to leak off, should the system become unlocked, is set to be somewhat
greater than the time required for the frequency to sweep from one sideband to the other and back (about ~ sec in a typical case). Suppose that,
because of transmitter sparking, for example, the discriminator output
signal disappears long enough to allow the system to become unlocked.
If, at that time, the oscillator frequency is approaching the transmitter
frequency, it will drift over to the other sideband, where a pulse will
The bias voltage will
appear that sends it back to its original position.
have held the transitron off long enough to allow this to happen and locking will be restored.
If triggers have not been restored when the other
sideband is reached, the frequency will continue to charge for a short time,
at the end of which the bias voltage will leak off, the transitron will
begin to oscillate, and the drift will be reversed by the first trigger. The
If the oscillator frequency
system now will lock on the other sideband.
were moving away from the transmitter frequency at the time of the
original unlocking, it would simply continue until the release of the
trigger generator, at which time it would reverse its direction of frequency
change, move back, and lock to the original sideband.
In a typical case, the interval between unlocking and the secondchance trigger is about ~ sec. Locking is therefore resumed within a
This speed of locking represents a great improvement over the
Whitford AFC in which, with equal probability, locking may be restored
quickly by the pulse from the other sideband, or a complete recycling,
which may take two full t ransitron periods (20 see, in some cases) may be
It may seem that fairly complex methods have been adopted to
secure simple ends. When the circuit was originally conceived, Vz,
Vs, Vb, and VS were not included, yet locking was obtained.
system was unreliable, however; to provide positive action, all of the
above tubes are required.
The necessity for the phase inverter V, and
the dual diode Vt has already been discussed in connection with the
Whitford circuit (Sec. 7.15).
The identical problem exists here.
Originally, the coupling to the HC was taken from a single plate of
the TSS. The negative wavefront of one reversal turned the on-tube off,
and the positive one from the other reversal turned the off-tube on. This
arrangement worked satisfactorily except for the special case where the
input pulse to the TSS was slightly below the voltage necessary to produce
a reversal. With such a trigger, the plate voltage of the on-tube of the
TSS would rise part of the way, reversing the HC, and then fall again,
leaving the TSS unreversed and destroying the correct phase relation.
Under these conditions, the plate potential of the TSS off-tube remained
fixed. The slightest lowering of this voltage sufficed to ensure TSS
reversal. Therefore, the negative triggers from both plates were coupled
to the HC,
each other
the diodes
The main purpose
V5 were
and to eliminate
of the tube
at the
to decouple
of the positive
l’, was to make
of the transitron
the effects
screen wave,
to negative
the plates
the use of the
which provides
to utilize
and used the negative
part of the screen
part of the wave and from the loading
One further
a common
In a second
be noted.
on the negative
N’o troubles
it was
from the transitron
were slowed
be slow enough
yet fast enough
to reduce
be eliminated
the desired
and amplifier:
the so-called
TvIodel 208 oscilloscope.
use of separate
the prob-
may be possi-
if the wavefronts
be found
to a negligible
be possible.
A circuit
One tube
phase inverter
use of a combination
in the Dumont
in the
For instance,
a combination
of course,
the capacitance
to ensure
of circuit
was traced
Other solutions
by an RC circuit,
for the hunt-
a similar,
in that of VI.
of the two sections.
Vs produced
with amplifica-
a second
The trouble
came along;
to the capacitive
the grids
This caused
no net reversal
ing sweep.
of the HC when,
the positive
of the final
were used for T’1 and Vg, which
on the
of the HC by the coupling
a reversal
FIG. 7.29.—Phase
In the first model
of a 6J6 twin triode
the tube
of the HC by the TSS difficult.
the two sections
of the
the second-
Vs was unreliable
of the difficulties
[SEC. 716
for this device
is shown
in Fig. 7.29.
it could
is caused
be reduced
slope at the end of the pulse small.
be possible.
If the capacitance
of the TSS were increased
of the pulse,
The elimination
of the cross-coupling
it may
of V3 might
C (Fig.
pose new problems
in the
SEC. 7.17]
triggering of the TSS), the wave at one of the plates would have the form
shown in Fig. 7.30a. The downward trend of the plate voltage is inhibited
The voltage rise is
only by interelectrode and stray capacitances.
likewise fast until the grid of the opposite section begins to draw current.
After that, it is slow, as the plate load resistor charges the cross-coupling
If this waveform were differentiated by an RC circuit of
very short time constant, the
pulses of Fig. 7.30b ~vould appear.
The sum of these pulses }vould be
a smaller negative pulse which
might be adequate to reverse the
TSS, eliminating the need for V,.
(a) Plate waveform, TSS
It is doubtful if the phase inversion can be eliminated.
The circuit in its present form
is fairly reliable.
It will operate
with any tubes meeting JAN-1A
specifications and with any resistors or condensers within t 10
per cent of design value, including
(6) Differentiated waveform
the most unfavorable
combinaFIG. 7.30.—Effect of waveform on overshoot,
tions, with the exception that the
resistors in the reversing multivibrator circuit should be f 5 per cent if
limit tubes are to be used,
7.17. The Beacon Problem.—The
nature of absolute-frequency,
A-F, AFC systems and their application to the radar-beacon problem
were briefly considered in Sec. 7.3. Beacons are treated extensively
elsewhere in this series, 1 but a brief review of their operation will be
given here.
A radar beacon is a device which enables a radar operator to determine
the range and bearing of the point at which the beacon transponder is
When the operator throws the switch to BEACON,the length
of the transmitter pulse is changed to a value that will allow the pulse to
pass through the beacon receiver and operate the coding circuits.
As a
result, the beacon transmitter issues a series of coded pulses which
identify it from other beacons, and the first of which appears on the radar
indicator at a position that shows the range and bearing of the beacon.
If beacon signals were received continuously, one of the AFC systems
described in the previous section could hunt for and lock to the signals.
But because of antenna scanning, only a few sets of pulses are received
1Volume 3, Radiation Laboratory Series.
at each rotation.
the first b~conpulse
of manually
to the
be in tune when
to a beacon,
is almost
at the instant
a manual
at which
all beacons
the antenna
or AFC
is highly
for a given class of service
fixed frequency.
aid consists
peak differs from
a receiver
be in tune
at a single
The manual
to the operator.
the beacon
[SEC. 7.18
is received.
the receiver
is applied
is read on a milliammeter.
he gets an indication
of a precision
the transmitter
to a crystal,
on the meter,
by an amount
tunes the local oscillator
at which
his receiver
is in
is used, the same type of reference
4, and the circuits
for hunting
for control
of the control
will be treated
for beacon
will be described
and crystal
are used.
in the rest of this
AFC! have had provision
in Sees.
7.18 and 7.19.
discriminator and capable of very precise control is discussed in Vol. 11 Chap. 2,
of this series.
A tunable wavemeter cavity may be used in any of these systems to
provide a stable tunable receiver with a precise calibration.
Such a
combination would be useful for multichannel communication.
7:18. Reflector-modulation
Schemes for Reflector
AFC .—These
systems employ the drift-in control circuits described in Sees. 7.10 to 7.12.
The problem is to convert information coming from the beacon AFC
The block
crystal to a voltage capable of operating the search stopper.
diagram of Fig. 731 shows the method used when a diode transitron
(see Sec. 7“13) is used. When a standard gas-discharge-tube control
circuit (see Sec. 7.11 ) is desired, the coincidence tube itself is the searchstopping tube, the rest of the circuit being as in Fig. 7.18.
The nature of this circuit is such that when the local-oscillator frequency is on one side of the cavity resonance peak, the gas-discharge tube
will not fire, but after the peak is passed (analogous to passing the crossover frequency), the tube starts to fire 1000 times per second.
But this is
precisely what happens when a conventional discriminator is used. On
one side of the crossover frequency, the negative signal from the discriminator amplifier is ignored; on the other side, the positive signal triggers a
gas-discharge tube or operates a diode detector as the case may be.
A nonhunting
d-c amplifier
with a microwave
SEC. 7.18]
Standard diodecontrol circuit
Fm. 7.31 .—lteflector-modulation
Modulation voltage
Low w
Crystaloutput (DC) .s
Input frequency
Generation of a.c output voltage
FTG. 7.32. —W-vefornls
in Coincidence detertion.
LO frequency
AC output voltage
vs. frequency
[SEC. 7°18
It should be noted that when the gas-discharge tube fires, since the voltage
across C cannot change instantaneously,
the first effect is that the
cathode voltage rises toward the plate potential.
Only later, as C is
discharged through the tube and R (a low resistance of about 2000 ohms)
does the plate voltage fall to mark the start of the sawtooth sweep.
This positive pulse at the cathode acts precisely as did the positive signal
from the discriminator in developing a negative search-stopping voltage
across the diode.
All of the explanations of Sees. 7“11 and 7’13 therefore
It remains, then, to analyze the action of coincidence detection, which
is illustrated in Fig. 7.32. A l-kc/see oscillator provides a modulation
voltage (b) of about 0.5-volt peak, which is superimposed on the LO
reflector voltage.
Thk causes a frequency modulation (c) to appear on
the LO output signal. In (d) and (e) are shown the output voltage of the
crystal when the frequency-modulated
signal is applied to the cavity
To show the relative phases, the time at
with the indicated pass band.
which the modulation voltage crosses zero with a positive slope is denoted
by t,.
Figure 7.32a shows the output voltage from the beacon AFC crystal
Since the LO output power
as a function of local-oscillator frequency.
is nearly constant over the narrow range involred, this is essentially the
cavity resonance curve.
It may be noted here that the cavity is loaded
by the local oscillator and the crystal until its bandwidth at the half-power
points approximates the locking accuracy desired; that is, it 1s nearly
equal to the peak-to-peak separation of the discriminator that would be
used were the AFC of the difference-frequency type.
If now the center frequency of the local oscillator is on the low-frequency side of this response curve, the frequency modulation will cause a
voltage component at 1 kc/see to be superimposed on the d-c output
voltage from the crystal.
As is shown in Fig. 7.32d this voltage is 180°
If, on the other hand,
out of phase with the original modulating voltage.
the center frequency is above the resonance peak, the a-c component of
the crystal output voltage ~rill be in phase ~vith the original modulation
voltage, since on this side the slope of the resonance curve is negative.
Figure 7.32f shows this a-c component as a function of frequency and
is drawn so that amplitude is proportional to the magnitude of the
ordinate and phase is indicated by its polarity, a positive ordinate indicating that the crystal voltage is in phase ~~ith the original modulating
It is seen that this curve has the appearance of a conventional
discriminator response curve.
If the amount of frequency modlllation is large, there will be some
been found
with z f’ollr-section
fur the purpose.
only of even harmonics
and can be removed
of second
and higher orders of the l-kc/see
by a suitable
falter if desired.
The crystal output voltage is applied to a high-gain amplifier with
negligible phase shift at the modulation frequency.
Either two stages of
may be used, or a low-impedance
transformer (such as the UTC type 0-14) driving a
single stage.
The output voltage from the amplifier is applied to the control grid
of a gas tetrode (2050 or 2D21) and, simultaneously, a 10-volt peak
signal from the l-kc/see oscillator is coupled to the shield grid. Each
grid has a bias of about – 10 volts with respect to the cathode.
Measurements on gas tetrodes show that if either grid is biased to – 10
volts, the tube will not fire even if as much as +75 volts is applied to the
other grid. Therefore, if the a-c signals on the grids are 180° out of phase
When they are in phase, however,
with each other, firing is impossible.
and of adequate amplitude, the tube will fire once each cycle if the plateThus,
circuit time constant permits adequate recovery between cycles.
the condition stipulated at the beginning of the section is fulfilled,
and the AFC system will lock.
The phases must, of course, be selected
so that during the hunting sweep the phase condition for firing will not be
encountered until the resonance peak has been passed, or else the system
will lock far out on the skirt of the response curve.
Some of the earlier beacon AFC systems used a pentode coincidence
tube in place of the gas-discharge tetrode.
The amplified crystal
output voltage was injected at the control grid and the direct signal from
the audio oscillator at the suppressor grid, both being biased beyond
Under coincidence conditions the pentode put out broad negative
pulses. An additional amplifier was therefore required to obtain the
positive output pulse necessary to fire a gas-discharge tube.
This arrangement operated successfully in conjunction with the
standard gas-discharge-tube AFC, although two more tubes were required
than are used in the circuit described at the beginning of this section.
It was completely unsuccessful in conjunction with the diode-transitron
control circuit, however, and this failure led to the circuit of Fig. 7.31.
The cause of the failure was essentially the enormous variation in the
In addition to the normal factors of tube
effective gain of the system.
variability, LO output power, crystal rectification, and so forth, three
potent effects exist:
1. For constant modulation voltage, the amplitude of the frequency
excursion, and hence of the crystal output voltage, is proportional
to the electronic-tuning
In usual reflex
oscillators this factor varies by a factor of 3 among tubes of a
[SEC. 7.18
given type.
In addition, unless very loose coupling is used, the
pulling effect of the cavity on the local oscillator may cause a
further increase by a factor of 3; that is, tubes with a high normal
dv/dV are readily pulled, and the effect issuch as to increase the
effective dv/dV, but tubes with a low dv/dV are little affected.
These two factors of 3 combine togivean
uncertainty in the gain
of a factor of 9.
2. The bias on the control grid must be enough to ensure cutoff for
every tube.
If it were not, the signal on Gi would give rise to plate
output voltages capable of operating the control circuits even
when no signal was present on G ~. If tube variability is such that
cutoff ranges from —4 to —8 volts, then —10 volts is a reasonable
design figure. If, moreover, one of the tubes whose cutoff is – 4
volts is used, then a signal having a peak amplitude of 7 volts will
cause a l-volt excursion into the conducting region, but an 8-volt
signal (14 per cent larger) will produce a 2-volt excursion.
3. Not only is this excursion twice as large, but the upper half of it
occurs in a region of higher tube G~; the output voltage might
therefore be three or four times as large.
From the foregoing discussion, it can be seen that a mere change of
local oscillator and coincidence tube, may cause a system in which the
maximum available output voltage is barely adequate for the generation
of control voltage to become one in which a slight deviation from the
crossover frequency will produce the maximum effect. In practice the
output voltage of the coincidence tube, under the high-gain condition,
changes, between two successive cycles of the audio oscillator, from zero
or a small value to one so great that a large potential is developed across
the detector of the diode-transitron circuit.
This large potential causes
the local-oscillator frequency to be driven back a long way, so that an
interval of perhaps 10 to 20 cycles will occur before the next crossing of
the resonance peak. It will be found that the ripple in the local-oscillator
frequency will amount to many megacycles per second.
It is felt that this difficulty is inherent; that the cavity-modulation
scheme must always be applied to a control circuit which operates on the
frequency prinziple (Sec. 7. 11), and which is not affected by amplitude
variations as large as 100 to 1.
Another problem peculiar to a circuit of this type should be noted.
Let us ignore, for the moment, the audio-modulation voltage, and consider
only the slow-sweep voltage of the hunting cycle.
As the frequency is
swept through the resonance curve, a positive transient voltage appears at
the crystal output terminals.
A badly distorted reproduction of this
voltage—the distortion depending on the low-frequency amplitude and
phase response of the amplifier-will
appear at the grid of the coincidence
SEC. 7.19]
tube. At the time coincidence information should appear, for instance,
the potential of this grid may be more negative than its fixed bias,
and hence it may be necessary for the local-oscillator frequency to
pass somewhat beyond the resonance peak before the gas-discharge tube
starts to fire. On the other hand, after the gas-discharge tube does fire,
the transient may cause a reduction in bias such that the firing will
continue for several cycles after the reversal of the drift direction.
generation of an excessive search-stopping voltage results, so that the
frequency is pulled back in much the same way as when a pentode
coincidence tube is used. When the output pulses from the coincidence
tube are observed, groups of 5 to 15 consecutive pulses followed by a long
interval without pulses are seen instead of a more or less uniform distribution.
A large ripple appears in the reflector voltage, and a spectrum
analyzer shows large excursions in the oscillator frequency.
This effect can be eliminated by so designing the amplifier that it has
poor response to low frequencies.
On the other hand, its phase shift at
the modulation frequency must be small if firing in the “ anticoincidence”
position is to be avoided.
One solution is to admit the considerable phase
shift in the amplifier which occurs when short-time-constant
net works are used, but to offset it by an equal phase shift in the line
carrying the oscillator signal to the shield grid. In practice, the phases at
the two grids should be compared when the whole system is in place,
including any small bypass condensers at the reflector.
Such a comparison may be easily made with an oscilloscope, and a suitable phasecorrecting circuit may be installed.
This is a design test, and normally
should not have to be made on each individual system.
7.19. Beacon AFC for Thermally Tuned Tubes.—At the time of the
writing of this section, no fully engineered circuit for the absolutefrequency AFC of thermally tuned oscillators has been developed.
circuits to be described have been built and operated but are not yet
known to be fully satisfactory.
The first approach to the problem was a circuit designed by M. W. P.
Strandberg, 1 who, following the lines of development
described in
Sees. 7.14 to 7.16, used push-pull, on-off control with reversing multivibrators.
The circuit is shown in Fig. 7.33.
The r-f part of the circuit is identical with that described in the
previous section.
Since no modulation is applied to the reflector, the
A sweep mechanism which will be
response curve of Fig. 7.32a applies.
described later causes the local oscillator to sweep back and forth across
the band just as it does in the thermal AFC circuits described in Sees.
7.14 to 7.16. The crystal output voltage is applied through an amplifier
1 M. W. P. Strandberg,
RL Report
No, 955.
for Thermally
having very good low-frequency response to a‘( trigger shaper,” TS. The
TS is essentially a reversing multivibrator similar to those previously
described, except that one of the grid-plate crosscoupling resistors is
replaced by the coupling of the common cathode.
The first output voltage from the crystal, as the operating frequency
This voltage actuates the
approaches the cavity resonance, is positive.
TS in such a way as to preset it to a defmit~ position.
The TS signal at
this reversal is ignored by the subsequent circuits.
As soon as the resonance peak is passed, the crystal output voltage
starts to decrease. This negative wave causes the TS to reverse again,
but thk time the reversal is effective in operating the subsequent circuit,
which is a heat-control reversing multivibrator similar to those described
in Sec. 7.15. Thus, immediately after the frequency has passed the peak,
the power switch in the tuning triode is reversed so that the frequency
once more approaches the peak, resulting in a positive output voltage and
the presetting of the TS once more, so that it can again operate from the
Thus, the system
negative signal received on the other side of resonance.
is trapped between the two sides of the response curve.
The preset feature is important for, if it were not present, small
fluctuations due to hum or microphonics would cause two or more successive negative impulses to appear, which would result in an extra
reversal of the heat-control switch that would carxy the oscillator away
from the peak.
On the other hand, the sensitivity of the TS to a presetting signal
must be appreciably greater than its sensitivity to a heat-control signal;
otherwise the frequency might ride back over the “hump”
without the
TS being preset, and the next reversal of the heat-control switch would
not occur. It is this extra sensitivity, apparently, that introduces the
troubles which at this stage make the circuit seem impractical.,
For if,
immediately after receiving the HC signal, the frequency should vary
rapidly, as from hum or microphonics, there is a chance that a small signal
adequate for presetting may be followed by a larger signal adequate
for heat reversal while the oscillator is still on the same side of the peak.
This extra reversal would then send the frequency away, and the system
would be unlocked.
Whether this dMiculty can be overcome without
basic circuit change is not known.
The sweep mechanism referred to in the foregoing material is similar
to that used in the radar AFC circuits.
A transitron (see Sec. 7.16)
simply triggers the heat-control multivibrator at suitable intervals.
A circuit was devised,l which, it was hoped, would not be sensitive to
It is shown in Fig. 7.34. This circuit combines many of
the features discussed in connection with several of the previous circuits.
+150 v
Input terminal
0.82 M
0.2 M
2.2 k
-105 v -3r)o v
0.1 M
to reflector
0.2 M
D.2 M
0.18 M
O.l M
- -.
FIG. 7.34.—Second
form of beacon AFC,
To triode
tuner grid
of thedrift-in type (Sec. 7.10).
scheme of Sec. 7“18 is used to provide the searchstopping information, but control is of the on-off type.
The circuit, up to the gas-discharge-tetrode
coincidence tube, is
identical with that used forreflector beacon AFC (Sec. 7.19).
The plate
voltage of the gas tube is, however, supplied from a multi vibrator V1,
point for both the
which provides the hunting sweep. The “ground”
multi vibrator and the gas-discharge tube is at a negative potential
(usually – 105 volts).
The tuner-triode grid is tied directly to the plate
of the gas-discharge tube, while the plate supply is the real ground (at
The following action occurs.
chassis potential).
During the desensitized or return portion of the sweep, the left-hand
Its plate potential is therefore
section of the multivibrator is conducting.
close to cathode potential, and thus the potential of the tuner-triode
grid is far below ground potential and the strut p~wer is zero. After a
suitable interval, the multi vibrator reverses spontaneous y, initiating the
As a result,
of the sweep.
At this time, the left-hand
its plate load resistor
the strut
sweep downward.
the audio
is cu~ off.
acts as part of the plate load of the gas-
is therefore
at ground
power is high, and the oscillator
starts to
As the frequency
the cavity resonance,
the crystal
(see Sec.
is in the wrong
as resonance
to fire the gas-
is passed,
of the correct phase appears and fires the gas-discharge tube.
plate potential of the gas-discharge tube therefore is brought momentarily
close to the potential of the cathode, cutting off the tuner triode and causThe oscillator consequently sweeps
ing a reversal of the frequency drift.
back over the hump.
Presently, however, the gas-discharge-tube
condenser is recharged through its plate load resistor so that strut power
The strut power causes the frequency to drift back into the
coincidence region, and another firing of the gas-discharge tube ensues.
The circuit is locked.
To stop further action of the multivibrator when the system is locked,
positive pulses developed across a small resistor in the cathode lead of the
gas-discharge tube are impressed on the detector VJ, the left-hand section
of the multivibrator, effectively preventing the completion of its cycle.
This circuit should not be sensitive to microphonics, since microphonics, by producing a few extra firings of the gas-discharge tube would
merely cause the local-oscillator frequency to back away somewhat from
the cavity peak without becoming unlocked.
The one test model of this
circuit that has been built showed some tendency to unlock when the
local oscillator was tapped.
The cause of this unlocking has not yet been
The purpose of this chapter is to outline some of the special measurement techniques that have been used in conjunction with the design and
testing of microwave mixers. There are many microwave and lowfrequency techniques that have had general use in the microwave-radar
development program.
These will not be discussed here because they are
well described elsewhere. For discussions of such subjects as admittance
measurements, power measurements, and the design of signal generators,
power meters, and standing-wave detectors, the reader is referred to
I-O1. 11 of this series. Only those techniques and pieces of apparatus
which have been used primarily for the design and testing of mixers,
because of peculiarities of the problem not encountered in other microwave problems, will be discussed here.
8.1. Production Tests for Losses of Sigmd Power.—A mixer cannot
be tested, in production quantities, for correct dimensions and good
electrical contacts so simply as can many other pieces of microwave
In the design of a mixer, the tuning of the crystal mount,
is one of the most important features, and this is determined by making
measurements for large numbers of crystals.
work is reduced by using crystals representative of the extremes in admittance, selected from a large number of crystals on the basis of admittance
losses due to such causes
As discussed
as poor
in Chap.
it has been
level is applied
for such
can be utilized
a signal;
is a comparison
of a large
be based
if a signal
the fact
at a signal
the mixer
an even simpler
in place.
at the local-
a local-oscillator
a matched
the admittance
of a set of crystals
are to be used
to make
of the
to a simple
to the mixer,
also a detector
in the mixer
of a mixer
r-f components
is almost
for a small signal, with the local oscillator
In practice,
do not
in this way
3, the r-f tuning
of the admittance
and any
are tedious
the extremes
to the optimum
SEC. 8.1]
local-oscillator level, to that produced in a tunable crystal holder by the
same signal when the tunable crystal holder is tuned for maximum
rectified crystal current.
The apparatus used for such a test is illustrated in Fig. 8.1. The signal generator is padded with a matched
variable attenuator and this combination provides a signal source that is
matched to the waveguide and adjusted to deliver power at the required
level. Figure 8. la shows the necessary arrangement of apparatus for
testing a single mixer with an iris-coupled local oscillator designed for
The TR switch must be used in the test
operation with a TR switch.
since it provides some tuning of the mixer and changes the dependence of
the power delivered to the crystal on the r-f admittance of the crystal.
Each of four or five borderline crystals are put into the mixer and the
maximum crystal current obtainable by tuning the TR cavity is noted.
Then the mixer and TR switch are replaced by the tunable crystal holder,
FK~.8 1.—Apparatus
testing for r-f tune and loss in mixer.
for production
and for each crystal the mount is tuned to give maximum crystal current.
At this level (0.5 to 1.0 ma), the crystal current for most crystals is
approximately proportional to the power absorbed and, therefore, the
ratio of the crystal currents produced by the same crystal in the two
mixers shows approximately the transmission loss and reflection loss due
to mismatch in the tested mixer.
Experience shows how much loss can
be expected for a properly constructed mixer. A badly constructed
A poor
mixer will show Up as having a large loss for some of the crystals.
will show
limit of 2 db can usually
the 10SS due
loss for all of the crystals.
be set on the sum of the loss in the TR cavity
to mismatch,
up as a large
be at least 63 per cent
in the tested
of that in the tunable
each crystal.
If the mixer
at each
is to be used
of the band.
a wide
it is well to make
a large
of mixers,
the tunable crystal holder need be used only frequently enough to ensure
that the signal-generator power level has not changed, and that all of the
[SEC. 82
crystals are unchanged in rectification eficienc y. To avoid burnout,
care must be taken, in inserting the crystals, not to allow an electrostatic
discharge to pass through them from the body.
A test of the reflected power alone could be made almost as simply
by means of a directional coupler on the signal-generator waveguide
adjacent to the mixer, so arranged as to couple to the reflected wave only.
This method would eliminate the need for a comparison ~vith the tunable
mixer, but it would not necessarily show a source of loss in the mixer
other than mismatch.
With a mixer designed for use with a tunable TR
cavity, the reflection coefficient that can be tolerated depends upon the
phase, because of the transmission loss of the TR cavity, as shown in
Chap. 3; therefore, a test in which only the reflected power is measured
is not so informative as the one described, which measures both the
reflection loss and the dissipative loss.
8-2. Local-oscillator Coupling.-In
most unbalanced mixers, the LO
coupling circuit has some effect on the transmission of received signals
into the crystal.
It is important to know whether sufficient localoscillator power can be coupled into the crystal without a loss in received
signal strength at the crystal because of interaction of the two circuits.
Such a test can be made with the apparatus just described, by measurement of crystal current only.
The test for local-oscillator coupling, too, must be made with each
One of these crystals is put into
of the selected representative crystals.
the crystal mount of the mixer, and, with the TR cavity tuned for
maximum crystal current at a level of 0.5 to 1.0 ma, the crystal current
is observed as a function of the LO coupling adjustment.
This observation is made with the local oscillator inoperative.
Then the signalgenerator power is attenuated to the extent that the crystal current
produced by this signal is vanishingly small, and the local oscillator is
turned on. The local oscillator must be set at the proper frequency,
relative to the signal generator frequency, to produce the desired intermediate frequency, because when a resonant TR cavity is used, the
The crystal current produced by the
coupling depends on frequency.
local oscillator is observed as a function of the coupling adjustment.
Two curves can be plotted from these two sets of observations as a
function of the same parameter.
If an effect of the LO coupling adjustment on the signal power delivered to the crystal is observed in the first
test, the second test must show that sufficient local-oscillator drive is
obtained when the local oscillator is not coupled too tightly to the
signal circuit.
The test must be repeated for each of the representative
borderline crystals and, if the mixer is to be used in a wide band of frequencies the test must be made at several frequencies in the band.
The local-oscillator tube used for the test should be one that gives, in the
SEC. 8.2]
of four
in a test of this kind on a 3.33-cm
is shown
the crystal
of turns
of this type.
A plot of data taken
of the
in which
in Fig.
it completely
mixer with an
in the
are two
from the local oscillator,
is the
the waveguide.
one representing
and the other representing
Crystal f 1 —
$2 ——
#3 —-—
#4 ----.-
2.5 -
E 2.0
1.0 --- -------
---- “’ >~
-.. .
- -—- —-
Number of screw turns outward from position of deepest insertion
FIG. S.2.—Data
from test of LO interaction
crystal current
the TR
to the crystal.
in the neighborhood
A crystal
and those
the mixer
to allow
the maximum
A very large [email protected]
of resonance
to a length
of 1 ma can be produced
the coupling
in signal power
of the iris, and
of the
to a screw longer
to the right
used was long enough
iris to be tuned
is coupled
with 3.3-cm mixer and four borderline crystels.
of the
to produce
the resonant
any one of the
for either screw length,
the coupling
In practice
1 ma
the screw
of current,
loss in signal
with a signal 10SS of no more than 0.5 db;
iris could
be operated
on either
is cut
off to a length
at maximum
deli vering
[SEC. 8.3
to avoid
to drive
of resonance.
to produce
of a local-
the crystal
a 10-cm
a capacitive
means as a resistor dk.k, for a
matched load for the local-oscillator cable, serious absorption or reflection
of signal power by the local-oscillator circuit can occur. A test of the
same kind as that just described may be used to detect this loss. If,
with the local oscillator inoperative, power from a signal generator enters
the mixer and produces a crystal current about equal to that which would
be produced by local-oscillator power, it is found that the crystal current
falls off when the probe is screwed in for close coupling.
The magnitude
of this effect depends upon the admittance presented to the coupling
probe by the local-oscillator circuit.
If the length of line between the
probe and the loop in the local oscillator is varied, a length can be found
at each signal frequency, for which the effect on the signal circuit is
very large even with a small probe insertion.
This length corresponds to
resonance in the local-oscillator cable. Because the local oscillator is
operated at a different frequency from the signal, the resonance may not
correspondingly enhance the efficiency of the local-oscillator coupling.
Thus a serious loss in received signal strength can occur.
If a resistor
disk is so placed relative to the probe that the local-oscillator line is
matched to a wave traveling toward the mixer, this resonance is prevented
because the admittance at the probe cannot be made smaller than that
of the disk. Such a disk thus serves a double purpose, since its original
purpose was to prevent LO frequency discontinuities.
Even with a
resistor disk, the 10-cm mixer may still be subject to interaction between
the signal circuit and the LO coupling circuit, and any design should
be checked by a test of this kind.
8.3. Over-all Noise-figure Measurements.—One
technique for making over-all noise-figure measurements of receivers requires a very wellshielded c-w signal generator with a calibrated output power, a stable
i-f amplifier of known equivalent noise bandwidth, and a reliable output
power meter for the receiver.
Suitable signal gen~ators -with calibrated output attenuators and
power-measurement apparatus for making an absolute calibration of the
available output power are described in Chap. 4, Vol. 11 of this series.
The i-f amplifier should be designed for the output admittance of the
mixer to be used, and its effective noise figure with this generator admittance must be known.
The output meter need not be calibrated in
and without
by such
SEC. 83]
terms of absolute power, but the law of response should be known, to
allow precise measurement of power ratios. For this purpose a thermocouple and microammeter, or a crystal and microammeter, may be used
as a second detector.
A crystal used for this purpose should be tested
to determine the relation between the rectified current and available i-f
power. If the current meter has a full-scale sensitivity of a few microampere or less and a resistance lesdhan 100 ohms, most crystals will give
a rectified current directly proportional to the square of the impressed
To avoid the
voltage and thus proportional to the available i-f power.
necessity of an output indication of known response, or to allow calibration of the output meter, a calibrated i-f attenuator may be used in the
receiver. Instead of increasing the incident r-f power to change the
LO antenna
C-w signal
FIG. 8.3.—Apparatu.q
for measurement
of the effective
over-all noise figure of a receiver.
output meter reading by a given factor, a known attenuation may be
put into the amplifier and the input power increased to make the meter
read the same value as before.
Figure 8.3 is a block diagram showing the way in which this apparatus
is used. With the local oscillator at the correct frequency and at the
correct power level in the mixer, and with the signal-generator attenuator
set to give no output power, the i-f amplifier gain is set to make noise
from the amplifier give a reading less than half scale on the output-power
meter. Then the signal-generator power is increased until the outputmeter reading is doubled, care being taken that the local oscillator and
TR cavity are tuned to give maximum receiver response.
The effective
over-all noise figure of the receiver is then the ratio of the available
power at this last setting of the attenuator
to kTB,
noise bandwidth
of the i-f amplifier.
where B is the equivalent
[SEC, 8.3
For this measurement to constitute a measurement of the merit of a
In practice the TR cavity
mixer, several other things must be known.
will be connected to a duplexer, which affords effectively a matched
It is, therefore,
waveguide generator for the received signal power.
important that the combination
of signal generator and calibrated
attenuator does represent a generator matched to the waveguide.
a cutoff attenuator is usually used as the variable attenuator of the
signal generator, an additional matched dissipative pad should be used
The i-f admittance of the
in the output line of the cutoff attenuator.
crystals used in the tested mixer must be known to allow the i-f-amplifier
noise figure to be known.
A noise figure larger than expected could result
from an i-f output admittance for the mixer corresponding to a large noise
This could not be considered a fault of the
figure for the i-f amplifier.
mixer, for an amplifier with a different input circuit would correct the
The TR cavity has been included in the diagram to illustrate a point.
The over-all noise figure for a receiver using a mixer and TR cavity
must be measured with the TR cavity in place, since this ccmponent
influences not only the local-oscillator coupling but also the conversion
loss, effective noise temperature, and i-f output admittance of the mixer.
In addition, the transmission 10SSof the TR cavity is affected by the r-f
admittance of the crystal, and consequently the effect of the TR cavity
cannot be taken into account by the assumption of some average transmission loss for a cavity between a matched generator and a load.
If all of these precautions are taken, the test still does not constitute
a test of the mixer unless the noise figures to be expected from the crystals
used are known.
These noise figures may be evaluated by independent
measurements of the crystal conversion loss and noise temperature,
or relative values may be obtained by measurement of the noise figures for
the same crystals in a mixer known to operate properly with these
For this purpose, a mixer that does not require a TR cavity
and that has a tunable crystal mount is useful. Such a mixer may be
substituted for the mixer to be tested, and tuned to give minimum noise
figure for each crystal.
The ratio of the noise figure obtained for this
mixer, to that obtained for the one being tested, does represent a measure
of the operation of the mixer on test, provided that the i-f amplifier
noise figure is known to be the same for the i-f output admittances
associated with each mixer. If it is not the same, one of the sets of
measurements must be corrected to compensate for the difference.
Because of the effect of the reflection of the image frequency and the
filtering of local-oscillator noise by the TR cavity, the noise figures of
the receiver with these two mixers may not differ by an amount to be
accounted for by TR-cavity
loss. The noise figure of a mixer-and-
SEC. 8.3]
amplifier combination, including the TR cavity, is often as small as that
of a mixer without a TR cavity.
When this is so, the fiftering of localoscillator noise and the reflection of the image frequency by the TR cavity
more than make up for the transmission loss of the TR cavity.
It is
apparent that an over-all noise-figure measurement is not the best way
to determine the r-f tuning of a mixer, although it does represent a
measurement of the quantity which is of most direct importance.
better set of quantities to measure would be the conversion loss and
effective noise temperature of the mixer.
The same apparatus, with the addition of an i-f noise diode and an
adjustable capacitance at the input terminals of the i-f amplifier, can
be used to measure the effective noise temperature and the i-f admittance
From these values, in combination with the effective
of the crystal.
over-all noise figure and the effective i-f-amplifier noise figure, associated
with the measured i-f admittance, the conversion loss of the crystal can be
calculated by substitution into the standard formula for the over-all
The noise diode may be
noise figure as a function of these quantities.
added in such a way that the crystal appears as the load admittance at
the plate of the diode, as shown in the circuit of Fig. 2.35. In addition, a
small variable condenser across the output terminals of the mixer allows
the susceptance part of the i-f admittance of the crystal to be tuned out.
The noise diode may be used as follows.
Several resistors, having
covering the range of conductance expected for the i-f
terminals of a mixer (800 to 8000 pmhos, for instance), are put, in turn,
into the crystal holder of the mixer. The effective noise figure of the i-f
amplifier associated with each of these conductance
can be found by
measuring the plate current of the noise diode required to double the
output noise power from the receiver alone. For each resistor the variable condenser is set to minimize this current.
The effective i-f noise
figure is then
where I is the diode plate current and G the conductance of the resistor
It is very important that sufficient plate voltage be used on the
diode to obtain saturation plate-current values, and that the plate
This ensures that
current be regulated by the filament temperature.
there is no space-charge smoothing and that the noise is pure shot-effect
When the values of the i-f noise figure for all values of i-f conductance
are known, the effective noise temperature of the crystal can be found
by a comparison of the output noise power of the receiver when the
crystal is in place, with that when a resistor having the same i-f con-
[SEC. 8.3
ductance is in the circuit.
A measurement of the i-f conductance of the
crystal is required, and for this, too, the noise diode can be used. The
i-f-amplifier gain may be set to give a particular output noise power with a
resistor representing the i-f conductance of an average crystal in the
mixer in place of the crystal.
With this gain setting, the diode current
required to produce a given deflection of the output meter for each of the
The values of diode current obtained
various resistors may be measured.
If the
in this way may be plotted as a function of i-f conductance.
crystal is put into the mixer and the diode current that is required
to give the same increase in output noise power at the same gain is
measured, the i-f conductance of the crystal may be read from the plot.
In each of these operations the susceptance of the output terminals of
Lhe mixer is resonated out by proper setting of the variable capacitance.
The labor of these measurements can be lessened by the use of the
equivalent five-eighth-wavelength-line
input circuit used in the crystal
noise-temperature test sets and described in Sec. 2.18. This method
has the advantage that the noise output power is independent of the i-f
conductance of resistors put into the mixer, and the i-f noise figure is
reasonably constant for the range of conductance
of interest.
addition of an adjustable condenser would allow compensation for the
susceptance part of the i-f admittance of a crystal mixer. Unfortunately,
however, this condenser may not be adjusted by simply maximizing
the receiver response because the equivalent eighth-wavelength
transforms its effect into that of a variable conductance at the first
amplifier grid. If mixers in which the susceptance part of the i-f admittance varies are to be tested, it may be safer to use the simple input
circuit and to take into account the effect of the i-f conductance on the
output noise and on the noise figure.
Measurements that involve the beat frequency between two c-w
oscillators, as in the above example, are often rendered difficult by the
drifting of the relative frequent y of the oscillators.
This is particularly
troublesome at the higher frequencies and with a narrow i-f amplifier
pass band.
Continual adjustment of the local-oscillator frequency must
be made to ensure that the beat frequency is at the peak of the i-f amplifier response.
Sometimes the signal generators may have frequencymodulation components, due to ripple in the power supplies for instance,
sufficient to cause the beat frequency to spread over a band of frequencies
wider than the pass band of the i-f amplifier.
In such a case, the measurements of over-all noise figure and of conversion loss would be in error
because the r-f power measurements would include the power contained
in the whole spectrum of the oscillator.
To reduce these difficulties it is helpful to add to the test apparatus
an AFC circuit arranged to maintain the correct difference frequency
SEC. 8,4]
between the signal generator and the i-f amplifier.
For this purpose a
standard f-m communications
receiver (Hallicrafters-S-27)
has been
used. A small amount of the i-f signal in one of the later stages of the
i-f amplifier is applied to the communications receiver, which is tuned
to the intermediate frequency.
The d-c component of the f-m-discriminator voltage may then be used as an AFC voltage, added in series to the
reflector voltage of the local oscillator.
The only changes that need
be made in the circuit of the communications receiver are the removal
of the ~iscriminator circuit from ground potential, so that the reflector
supply voltage is not short-circuited, and the addition of fairly large
condensers (0.01 ~f) from the reflector lead to ground to prevent oscillation of the AFC circuit.
A reversing switch that inverts the sense of the
discriminator voltage at the reflector lead allows the local oscillator to be
operated either above or below the signal frequency.
This AFC circuit will maintain the correct difference frequency
between the signal and local oscillator even when the signal strength is
sufficient to increase the output power of a l-Me/see-wide
i-f amplifier
by only about 10 per cent. At the level of signals usually used for noisefigure measurements, the control is very good.
The pass band of the i-f
amplifier may be observed on the output meter of the communications
receiver by tuning the receiver through it, since the intermediatee-frequency voltage developed is always almost exactly that read on the dial of
the communications receiver, provided the AFC circuit is locked.
That it
is locked can be confirmed by variation of the reflector supply voltage.
As this voltage is varied there will be an opposing variation in the output
voltage of the discriminator and practically no change in the beat
frequency or in the output voltage of the i-f amplifier of the noise-figure
test apparatus.
8.4. Radio-frequency
Noise Generators.—In
many respects, it is
more convenient to use r-f noise generators for the measurement of
An r-f noise
over-all noise figures than to use c-w signal generators.
generator that has a uniform noise spectrum over a frequency band that is
broad compared with the receiver pass band allows the effective over-all
noise figure to be measured, independently of the shape or width of the
receiver pass band.
R-f noise generators are discussed in some detail
in Chap. 4, lrol. 11 of this series. Only a qualitative description of the
types which have been used and the methods of application to noisefigure measurements will be given here.
A reflex-klystron oscillator can be used as an r-f noise generator if it is
supplied with the usual heater and accelerator voltages, but with a
reflector voltage that does not produce oscillation.
The noise spectrum
in the output line is determined by the resonant cavity of the tube, and
therefore the tube must be one which would ordinarily be used as an
oscillator at the receiver frequency.
To make the tube appear as a
matched generator, a matched dissipative attenuator pad is used between
the tube and the mixer of the receiver.
In the 10-cm band, for instance, a
type 417 reflex Klystron with a flexible output cable having about 10 db
of loss has been used. At 3.2 cm, a 2K25 oscillator, coupled directly to a
waveguide but with a resistance-strip attenuator between the tube and
the output end of the waveguide has been used.
The available noise power from these generators can be defined in
terms of the equivalent noise temperature of the matched termination
formed by the attenuator.
If this temperature is T times room temperature, the effective over-all noise figure of a receiver is simply the value
of (T — 1) that produces twice as great a noise output power from the
receiver as is produced when the noise generator is shut off. With ordinary oscillators, and with receiver bandwidths not exceeding a few megacycles per second, the equivalent noise temperature of the generator can be
regarded as constant throughout the pass band of the receiver.
may be a contribution of noise converted from the image frequency of
the receiver, but an intermediate frequency of 30 Me/see in a receiver for
9000 Me/see is sufficiently high to make the noise temperature of the
generator nearly unity at the image frequency, because of the selectivity
of the oscillator cavity.
Thus, a generator of this kind can be used to
make measurements of the over-all receiver noise figure, if the equivalent
noise temperature of the generator can be measured.
For the purpose of calibrating a noise generator, an apparatus for
measuring crystal noise temperature may be used. A standard mixer
with a local oscillator and a crystal of known conversion loss are required.
With the noise generator connected to the mixer and the generator tuned
to one of the two sensitive frequencies of the test set, the noise temperature of the crystal mixer is measured with the noise generator on
and off. The difference between the noise temperatures of the mixer
measured with the generator turned on and off is directly the required
value of (T — 1) of the r-f noise generator divided by the conversion
loss of the mixer. Values of T up to several hundred, including the
effect of the buffering attenuator pad, can be obtained from reflex
oscillators if sufficient accelerator voltage is used. The effective noise
temperature may be varied by changing the attenuation, or the accelerator or heater voltages of the tube.
A noise generator of another type is a crystal-rectifier unit mounted in
a standard waveguide or coaxial-line crystal holder.
Considerable r-f
noise power is generated by such a crystal if a direct current is forced
through it in the backward (high-resistance) direction.
A current of 5 to
10 ma, which may require a voltage as large as 6 volts, results in a noise
generator having an effective temperature 30 to 100 times room tem-
SEC. 8.4]
Currents lower than 5 ma do not reduce the noise temperature
greatly, and give somewhat more stable operation.
It is well to allow the
current to flow for several hours before calibration is attempted, because
it is observed that the device becomes stable after such a period of operation. A current meter, used with the noise-generating crystal at all
times, allows detection of a change in its d-c characteristic which might
make necessary recalibration of the unit.
The calibration procedure for the crystal noise generator is similar
It is important in this case, however,
to that for the reflex oscillator,
that local-oscillator power from the receiver does not reach the noise
crystal because such local-oscillator power would certainly affect the
All noise components that,
effective noise temperature of the device.
l-f ampljfler
of test set
i’q H ‘:
Local oscillator
for calibration
when mixed
with the local-oscillator
the receiver
pass band
of the
in Fig.
FIG. 8.4.—Apparatus
of crystal noise generators.
to the noise
be used
give components
.4 circuit
as that
perature test set. All of the pieces except the magic T and the noise
generator are parts of the test set and the part labeled “I-f Amplifier”
is meant to include the five-eighth-wavelen gth-equivalent
line, the
preamplifier, and the communications receiver of the test set. The local
oscillator, filter cavity, and buffering attenuators of the test set are
disconnected from the mixer and attached to arm (4) of the magic T.
A matched termination is placed on arm (1), and the crystal of known
conversion loss in the mixer is selected to be matched to the waveguide
at the local-oscillator
Thus no local-oscillator
power is
coupled into the noise crystal,
.kn attenuator is shown as a part of the
noise generator.
This attenuator serves to make the generator appear
matched to the line, both when it is turned on and when it is turned off.
An alternative to this procedure is to select the crystal or to tune the
crystal mount so that the crystal is matched to the waveguide for small
A larger noise power can be obtained
signals when the current is flowing.
in this way, but an attenuator must be inserted when the current is
broken because the crystal is then no longer matched to the waveguide.
In the 1.25-cm band, a dummy load that makes the crystal mount
matched to the waveguide has been inserted in place of the crystal.
The noise crystal develops a noise spectrum that is uniform over a
When the noise crystal is used for
relatively wide frequency band.
measuring receiver noise figures and for calibration, there is an equal
contribution to the converted i-f noise power from the r-f noise in the two
sidebands of the local oscillator.
The desired value of (T – 1) of the
generator connected to the crystal mixer of the test set would, therefore,
be just half the change in mixer noise temperature times the conversion
loss of the mixer. The value of (2’ – 1) of the noise generator connected to the magic T is the whole product of the change in i-f noise
temperature and conversion loss, however, because one-half the available
noise power is lost in the load on arm (1) of the T.
The noise crystal must also be protected from local-oscillator power
when it is used to measure receiver noise figures. The local oscillator
and the noise crystal, therefore, should be coupled to a nonresonant
mixer circuit with a magic T or a similar circuit, as in the calibration
For this reason, an ordinary unbalanced mixer and local
oscillator cannot be tested with the noise crystal unless a resonant
cavity, such as a TR cavity, prevents the leakage of a large amount of
local-oscillator power into the noise crystal.
If such a cavity is used,
filtering of the image-frequency
sideband is also obtained, and the
calculation of the noise figure of the receiver from measurements with the
noise crystal must take into account only a single sideband.
Because of the difficulty of removing local-oscillator power from the
signal circuit of most mixers, the reflex oscillator is a more dependable
noise generator than the noise crystal.
It has the disadvantage, however,
that it must be tuned to the receiver frequency.
On the other hand, its
calibration may be expected to hold under much less restricted conditions
and over a longer time than can that of the noise crystal.
If the output
line of an oscillator ca be made nonreflecting, the equivalent noise
temperature is practically constant over the range of frequencies to
which the tube can be tuned.
For example, a single calibration can be
used for a 417 Klystron, with a matched-cable attenuator, for the wavelength band from 9 to 11 cm.
8.5. Apparatus for Measurement of the Effect of Image Reflection.—
As an example of apparatus of the kind that is useful for experiments
SEC. 8.5]
with converters and mixers, an apparatus developed by E. R. Beringer,
M. C. Waltz, and C. P. Gadsden for experiments with welded-contact
It was desired to measure the
germanium crystals will be described.
convemion loss and noise temperature of the mixer under many conditions
of tuning at both the signal- and image-frequency terminals of the mixer.
The i-f output ad~ttance
of the crystal was known to vary over a very
wide region including negative values of the conductance, and the i-f
input circuit was designed to allow measurement of the mixer parameters
for the whole range of expected i-f admittances.
A circuit diagram showing the essentials of the i-f input circuit used
is given in Fig. 8.5. There is no transformation of the crystal output
admittance, since small conductance values were expected.
The inductance L resonates at the intermediate frequency with the combined
To noise diode
first i-f
FIO. s.5.—I-f
input circuit
used for measuring apparatus for welded-contact
capacitance of the mixer, the tube, and the variable condenser when the
condenser is set at about the middle of its range. The adjustment of the
variable condenser allows compensation for the susceptance component
of the crystal output admittance.
A switch allows a resistor to be
shunted across the crystal output terminals if desired. If the output
conductance becomes negative and has an absolute value exceeding that
of the positive conductance of the input circuit and tube, oscillation at
the intermediate frequency occurs. The added conductance of the resistor allows the total conductance to be kept positive.
The r-f part of the circuit is shown symbolically in Fig. 8.6. The
local oscillator and noise generator are connected independently to the
mixer through the first magic T. A filter cavity is used to remove noise
sidebands from the local-oscillator
signal, and attenuator pads are
provided to make each of the generators appear matched to the waveguide. In the arm attached to the mixer there is a second magic T
with a resonant cavity in one arm and a plunger in another.
plunger is adjusted so that all signals at frequencies other than those in
the region of the cavity resonance are transmitted through to the mixer
crystal. At the resonant frequency of the cavity, the input admittance
of the cavity is a very small conductance and, therefore, waves of this
frequency are reflected from the T. If the cavity is tuned to the image
frequency of the mixer, any imag~frequency
wave developed by the
mixer is reflected back to it from the magic T. The phase of the reflected
wave is determined by the adjustment of the variable length of line
between the T and the mixer crystal.
A sliding-screw tuner in the arm
between the two magic T’s allows tuning of the signal-frequency admittance of the mixer. In this way, independent control of the signal and
image frequencies is obtained,
723 A/B
line length
-It-f circuit for measuring the eKcct of the reflection of the image frequency
the receiver noise figure.
This apparatus is used in the following way. With various dummy
resistors substituted for the mixer crystal a curve of the i-f-amplifier
noise figure, as a function of the i-f conductance of the mixer, can be made
from data taken with the i-f noise diode. Also, by use of the i-f noise
diode and the resistors, a corresponding curve can be plotted of the i-f
amplifier output noise power. The change in output power of the receiver
with a given gain setting is measured as a func~ion of the conductance
of the output terminals of the mixer when the diode current is increased
from zero to a particular value. From these data the i-f conductance
of the crystal, for any condition of the r-f tuning, can be found.
Therefore, the i-f noise figure is known.
The r-f noise source may then be
turned on to determine, from the change of the output noise power from
the receiver, the effective over-all noise figure of the receiver. Since the
available r-f noise power is known from the calibration of the r-f noise
generator, if the available i-f noise power at the crystal due to this r-f
noise power were known, the conversion loss of the crystal would be
SIX” 8.6]
The available converted i-f noise power can be found by comparison with the available noise power from the i-f noise diotle, since the
The i-f noise dio(lc m:ly bc set,at a current
tryst al conduct ante is known,
that produces the same chan~c in the output noise polvcr from the receiver
Tht conversion loss of tl)c mixer is
as does the r-f noise generator.
L = ~;(;~,
where 1 is the noise-diode current, T the effective noise temperature of
the r-f signal generator, and G the i-f output conductance of’ the miser.
From the conversion loss, the effective i-f-amplifier noise figure and the
over-all noise figure, the noise temperature of the mixer can be found from
the usual formula
~;vera,,= I,(I’3 + t – 1)
where t is the desired noise temperature.
Thus, the apparatus can bc used to find the two quantities, L and t,
which are the measures of the merit of the mixer. The apparat~. has
been used in a study of the dependence of 1. and t,for welded-contuct
germanium crystals, upon the various tuning conditions of a mixer,
in the hope that some condition would be found which gives an unusually
small over-all noise figure. NTOsuch tuning conditions were found,
although, as discussed in Chap. 2, the i-f output admittance could be
varied by the r-f tuning elements over a very wide region, including a
If a similar apparatus were to be used
region of negative conductance.
for measurements with ordinary crystals, the shunting resistor in the
i-f input circuit would not be needed, since negative conductance
not occur ~vith most crystals.
Apparatus of this kind would be useful for the measurement of L and t
for ordinary crystals, as a function of the phase of the image reflection.
Some work of this kind has been done, and the indication is that some
improvement in the over-all noise figure of a receiver is to be gained by
proper phasing of the image-frequent y reflection.
The data are insufficient to allow a definite statement to be made about the magnitude of this
effect which could be realized in practice, or about the best phase of the
It does appear that the improvement
resulting from the decrease in conversion loss accompanying
reflection in the best phase is not offset by an increase in the crystal noise
8.6. An Apparatus for Measurement of the Admittance Loss of a
Sec. 2.11, it was shown that a quantity termed the admittance
loss of the mixer can be found by measurement of the dependence of the
signal-frequency admittance of the mixer on the i-f load admittance
presented to it. Since for most silicon crystals the admittance loss is
[SEC. 66
equal to the minimum conversion loss obtainable from the mixer with any
value of signal-generator admittance, the simplicity of this measurement
makes it a good tool for experimentation with mixer circuits.
An apparatus that has been used for measurements of thk kind is
shown symbolically in Fig. 8.7. A magic T is used as an admittance
bridge, in which the admittance of the mixer is compared with that of a
well-matched load on the opposite arm. It is actually the small-signal
admittance that is measured, in the presence of the proper local-oscillator
power supplied from the operating local oscillator of the mixer. The
mixer shown under test is one with an iris-coupled local oscillator and
requiring a TR cavity for proper operation of the couphg
- .-—
4 Tuner
. 2f
– &
Mixer for
FIG. S7.-Brirlge
for measurement
of admittance
loss of a mixer,
The TR cavity is included in the measurement and the measured admittance loss includes the loss of the TR cavity.
A small signal (less than
1 pw) is applied to arm (4) of the magic T through a matched attenuator
pad. On arm (3) is a mixer for detecting the unbalance signal of the
bridge. A matched attenuator pad is also tised, to stabilize the input
admittance of the mixer and to reduce the amount of local-oscillator
power leaking from this mixer to the test mixer. The mixer used for the
detection of the unbalance signal is of the same type as that shown in the
test position, in the diagram.
The TR cavity also decreases the leakage
of local-oscillator signals between the two mixers,
Two slidhg-screw
tuners are used in the circuit.
One between
the attenuator and the magic T, on arm (3), provides sufficient tuning
to make the test w-m, arm (2) of the magic T, nonreflecting to a wave
sent back from the mixer under test, at the signal frequency.
The other
tuner, in the test-mixer arm of the magic T, is used in the test procedure.
An r-f switch, formed of a plate sliding between a pair of choke connectors,
is also placed in this arm of the bridge.
The plate has a rectangular hole
of the dimensions of the inside of the waveguide, and can be adjusted
to make
the waveguide
or can be moved
so that,
the aperture, there is a short-circuiting plate across the waveguide.
This short circuit provides a reflection coefficient of unit magnitude for
calibration of the unbalance detector.
An i-f amplifier and an output power meter are connected to the mixer
for detection of the unbalance signal. An f-m communications receiver,
tuned to the center of the pass band of the i-f amplifier, provides automatic frequency control of the local oscillator of the unbalance detector.
Connected to the i-f output terminals of the mixer under testis a shielding
box containing a shunt-resonant circuit that has an adjustable capacitance and resonates at the beat frequency between the signal and Lhelocal
oscillator of this mixer, when the i-f capacitance of the mixer itself is
The capacitance has sufficient tuning range (at 30 Me/see,
about plus or minus 7 w.tfd) to compensate for any susceptance component
The coil of the resonant circuit is
in the crystal output admittance.
designed to have a small shunt conductance.
Number 12 gauge solid
copper wire, wound on about a l-inch diameter is used, and the turns
The three-position switch
are spaced about one wire diameter apart.
allows the resonant circuit to leave the outtmt terminals of the mixer essentially open-circuited, to provide a load near match for an average crystal
(with a 400-ohm resistor) or to short-circuit the output terminals of the
mixer. The d-c circuit of the mixer is unaffected by the switch, and
crystal current can be read at all times.
The procedure used with this test apparatus is the followhg.
the unbalance-signal mixer and the tuner in am (3) of the bridge are
the tuner
is slid into
is removed
of this arm retracted
a choke-type
of this
the waveguide.
of the
gives a large unbalance signal, and allows alignment of the unbalanceThe
signal mixer, cavity, and l,ocal oscillator as well as the AFC circuit.
tuner in arm (3) is then adjusted until the unbalance signal, read on the
output meter, is not affected by sliding the plunger in and out of arm (2).
This means that the output meter reads the magnitude of the reflected
power in this arm, independently of the phase of the reflection coeficient—a situation that results when arm (2) appears matched to the
reflect ed wave.
With the plunger removed and the mixer to be tested replaced, and
with the local oscillator of this mixer and the TR cavity tuned to the
[SEC. 8.6
proper frequencies, the test may now be made.
These two tuning adjustments are not easy to make with the circuit shown, however, because
there is no indication of their proper adjustment,
To remedy this,
the addition of a second f-m commmications
receiver would be a great
help. A small resistance (about 1 ohm) placed in series between the
shunt-resonant circuit and the first bypass condenser of the crystalcurrent circuit would have little effect on the operation of the test circuit,
even if the resistor were not shorted out in the short-circuiting position
of the switch.
The crystal is an i-f generator of several hundred ohms
internal impedance.
one ohm represents as severe a
reflection for the mystal as does the shunt impedance of the circuit in the
open-circuit position.
A signa~ large enough to excite the communications receiver could be taken off across this l-ohm resistor and the receiver
used as an AFC circuit for the local oscillator of the mixer under test.
The amplitude of the signal into this receiver would be a measure of
the TR-cavity
With the TR cavity tuned to maximize the
signal to the receiver with the switch of the i-f circuit on the load-resistor
position, nearly optimum results should be obtained.
With these adjustments made, the r-f switch in arm (2) of the bridge
circuit is set to the short-circuiting position, and the gain of the i-f
ampLifier of the unbalance-detecting circuit set to make the output meter
read full scale. The fraction of a full-scale deflection obtained with other
terminations on the test arm of the bridge is then equal to the square of the
absolute magnitude of the reflection coefficient, if there is no contribution
to the output-meter reading from receiver noise. The r-f switch is then
opened and the r-f tuner in the test arm of the bridge is adjusted to
balance the bridge with the i-f switch set to short-circuit the i-f terminals.
When this switch is changed to the open-circuit position, the signal
admittance of the mixer changes, and the bridge becomes unbalanced.
If the variable capacitance of the i-f resonant circuit is adjusted to make
the unbalance signal a maximum, the relation between the admittance
loss Lr of the mixer and the voltage standing-wave ratio r is
as shown in Sec. 2.11. Since the bridge reads the square of the absolute
magnitude of the reflection coefficient, the relation between the meter
reading and the admittance loss of the mixer is
(1 – p)}’
1 +
where p is the fraction of full-scale deflection of the meter.
A curve for
this expression, for Lr expressed in decibels for the range from O to 10 db,
is given in Fig. 8.8.
For silicon crystals it is found that the reciprocity condition holds.
The admittance 10SSin this measurement, therefore, represents the actual
conversion loss that would result with the mixer under test if the signal
generator were adjusted to have the internal admittance giving minimum
conversion loss. In practice, there will be some additional loss beoause the
FIG. S.S.—Admittance
the resulting
in the test
the switch
in the
is close
Addmitte.nceloss in db
loss as a function of output-meter
in the
r-f mismatch
be obtained
of the bridge
i-f circuit
the waveguide
in general,
is not
in this
of the incident power reflected, if the amplifier gain is set to make a
complete reflection give a full-scale deflection.
Measurements have been made, with the bridge, of the conversion
loss of many 3-cm mixers, and the results have agreed well with measureAs discussed in Sec. 2.11, the variation
ments made by other methods.
of conversion loss with the distance from the TR cavity to the crystal
has been observed with this apparatus.
Those measurements were
complicated by the fact that the TR-cavity loss was included in the
To prevent variation of this loss with the phase of the
image-frequency reflection, the crystal mount had to be retuned for each
line-length setting.
Better data would probably have been obtained
with a mixer circuit, such as that described in Sec. 8“5, in which the
resonant cavity reflects only the image frequency.
8.7. Tests of the AFC Mixer.—To obtain satisfactory operation of a
separate AFC mixer, the input signal level must be properly set, and care
must be taken to ensure that spurious signals, such as TR leakage power,
and signals at harmonic frequencies are not large enough to mask the
desired i-f signal. The usual procedure in setting the power level is to
design the AFC attenuator for about 30 db less attenuation than the
total amount needed, and then to adjust the diameter of the coupling
hole between the AFC attenuator and the main line of the radar set to
give the desired level of 1 or 2 mw of peak power at the mixer crystal.
If it is known that no spurious signals are present, the power level
can be checked by measurement of the average rectified current with a
Most crystals develop about 1 ma per
low resistance microammeter.
milli]vatt of dissipated r-f power if the resistance of the meter circuit is
less than 100 ohms.
With the local oscillator shut off, a microammeter of
less than 100 ohms resistance may be connected to the output terminals
of the crystal.
With the local transmitter operating, the milliammeter
This is simply the rectified pulse
reads the average rectified current.
current times the fraction of the time during which the transmitter is
turned on. With a pulsed transmitter producing l-~sec rectangular
pulses and a recurrence rate of 1000 cps, an average rectified current of 1
to 2 ~a indicates 1 to 2 ma pulse current.
Some precautions are necessary to make sure that the microammeter
reads the correct current.
Stray radiation picked up in the microammeter or in its lwds can gi~’e rise to a rectified current, because the
crystal is in the microammeter circuit.
Shielding of both the meter and
the leads is usually necessary to prevent this. That no such pickup is
present can be shown by blocking oti the r-f signal from the mixer, where
upon the microammeter reading should go to zero. A microammeter
has a rather large reactance f~ the frequencies involved in a current pulse
of I-psec duration.
This causes the current pulse to be stretched out
Because the
and, therefore, to persist after the r-f pulse has ceased.
crystal response is not linear, the average current is reduced, since the
current must flow through the crystal as well as through the meter.
A bypass condenser should, therefore, be used across the meter to give
It is only under this condition that
the pulse a low-impedance path.
the simple relationship between the average current and the r-f pulse
power holds.
It issometimes informative to observe the video-frequency pulse of
An r-f envelope
rectified current in the AFC crystal on an oscilloscope.
viewer, with the AFC crystal used as a detector, makes this possible.
The impedance, connected to the output terminal .of the crystal should not
be high, however, since a bias voltage would then be developed which
would change the r-f impedance of the mixer crystal and, therefore,
alter the amount of power delivered to it. An instrument of this kind,
calibrated as a current meter, can be used to set the r-f power level, for
the pulse current can be observed directly.
A more informative observation of the operation of the AFC mixer .
With a pulsed r-f
can be made with the help of auxiliary apparatus.
signal generator having the desired available AFC power, and a spectrum
anal yzerj the r-f power level can be set and the presence of any obj actionThese pieces of apparatus are
able spurious signals can be detected.
used in the following way. The crystal to be used in the AFC mixer is
first placed in a simple mixer that has no input attenuator.
This mixer is
Power from
substituted for the regular mixer of the spectrum analyzer.
local oscillator of the spectrum analyzer is introduced into this mixer
at the proper level, or, if a local oscillator is included as an integral part
of the mixer, this local oscillator is connected to the sweeping reflector
If the pulsed signal generator is
voltage of the spectrum analyzer.
connected to the input terminals of the mixer, the spectrum is shown on
the indicator of the spectrum analyzer.
The gain of the analyzer is
then set to show a given amplitude, in the center of the spectrum, with
the desired level of pulses sent into the mixer.
The AFC mixer is then substituted for this mixer in the spectrum
The i-f spectrum coming from the AFC mixer is shown on
the indicator, and if the transmitter sample has the desired amplitude,
the amplitude of the spectrum will be the same as before, with the same
amount of local-oscillator
Blocking off the AFC attenuator
path with a metal plate should cause the spectrum to disappear if the
leakage of signal from the radar mixer through the local-oscillator circuit
is sufficiently small.
Spurious signals leaking into the AFC mixer with enough amplitude
to interfere with the operation of the AFC circuit are made obvious
in a test of this kind. The presence of large pulses of harmonic power,
for instance, can be detected from the appearance of the indicator
of the analyzer.
The presence of the intermediate-frequency components
of the rectified pulse resulting from such harmonic-frequency
pulses is
evidenced by a continuous spectrum that covers the analyzer screen and
is unaffected by the tuning of the local oscillator.
The amplitude of
these components has sometimes been found to be so great as to mask
A signal incident on a
completely the desired beat-frequency spectrum.
crystal mounted in a waveguide far beyond cutoff for the fundamental
frequency, connected to the output terminals of the AFC attenuator
and to the input terminals of the i-f amplifier of the spectrum analyzer,
produced the same pattern on the indicator.
It was a test of this kind
that showed the need for a dissipative attenuator in addition to the
cutoff attenuator for the AFC signal. The addition of the strip of carboncoated Bakelite inside the AFC attenuator completely removed the spurious signal in a 10-cm system, and the desired spectrum of the AFC signal
Excessive leakage of spike
+ was then shown clearly on the indicator.
energy from the TR cavity, through the local-oscillator channel into
the AFC mixer, can be detected in the same way.
Absolute frequency, 294
Admittance, I-f (see I-f admittance)
Admittance, i-f output, 90, 178–185
Admittance bridge, 80, 367-372
Admittance loss, of mixer, apparatus for
measmement of, 367–372
Admittance measurements, 352
Admittance scatter, 134-136, 168
AFC, 5, 190-202, 290-351, 360
absolute-frequency hunting systems,
beacon, 227–231, 234, 244, 287, 341
reflector modulation scheme for,
for thermally tuned tubes, 347–351
d-c amplifier type, 313
diode-transitron, 32&331
double-balanced mixer, 283-287
Bark resistance of crystal, 54, 113, 207
Back rcsistmce mrtcr, 100, 113
Bandwidth, 2, 26, 302
effective noise, 14, 22, 27
optimum, 5
Bandwidth requirements,
5, 302
Barrier capacitance,
53, 92
Beacon, 223, 231, 287, 295
AFC (see AIW,
mixers, 190
stations, 23
43, 83–85,
effect of, on mixer crystal,
Bias voltage, 95, 249, 251
Bridge, 368
thermal hunting systems, 331–341
tunable systems, 33 1–341
AFC feedback
(see AF(’)
115, 300, 307–308, 312, 314
Beringcr, E. R., 83, 365
Bias, d-c, 88
333, 337
nonhunting systems, 3 12–314
Whitford, 332, 333, 337, 33!)
AFC attenuator,
1!W199, 372
AFC difference-frequency
Anti-TR switch, 10
Aperture coupling, 160
cutoff, 196, 374
Beacon tunm-, 225, 234
Bell Telephone
315, 345
design theory,
Amplifier design, 1
Amplitude control, 317
Antenna, temperature of, 12
9G1OO, 118, 172-174
test for crystal,
loop, 295
mixer, tests of, 372–374
AFC systems, classification of, 294
Agitation, thermal, 10
Amplifiers, 291
d-c, 300, 312, 327
i-f, 24
r-f, 2, 23, 43
of contact
i-f, 129
of crystal,
53, 92
Cavity, precision
reaction, 218
reference, 228
53, 92
use of, to reduce
215, 220
for, 155-160
Cole, P. A., 30
i-f, 111, 249, 360
negative, 90, 92
gain, 90
loss, 100, 249, 359, 365
on image-frequency
mination, 75-83
3, 26-28, 44, 119
of, 5%
three - terminal-pair - network
sentation of, 6 1–66
frequency, 24, 56
90, 93
tube, 28
circuit, i-f, 271
Cross attenuation,
Crossbar mount,
194, 195, 284
171, 172
Crossover, 307
296, 302, 304, 310,
314, 328
Crystal burnout, 96-100,
test for, 111–113
testing of, 10&l14
video, 56
cutoff, 301
tunable, 131–134
for 1N26 crystals, 171
for 3-cm bands, 124–128
Controlled reflector, 324
Conversion, frequency, 26
118, 172-174
D-c return, 126
Detection, 20
first, 3
gain of, 20
low-level, 17–19, 47, 54, 111, 115, 124,
regenerative, 45
quality of, 20
video, 115
99, 114
Dickc, R. H., 12n,, 63, 74, 77, 87
Diode mixer, 32–34
Diode transitrrm, 345
Diodes, temperature-lirnitcd,
109, 365
Directional couplers, 14&150, 201, 301
295, 302–308
of, 305
checker, 113
control, 294
Crystal current, 95, 256
Crystal detector, 19
Crystal mixer (see Mixer,
134, 354
of, 100, 114-118
circuit, hard-tube,
voltage, 296
104, 365, 367
noise temperature
of, 58, 93–96, 100,
Control, frequency,
101, 122–126,
for 10-cm bands, 124–128
Crystal rectifier, 47–1 18
Crystals, borderline, 134, 353
tube, 342, 345
for balanced
inverted, 280
d-c, 50, 90
Clutter, ground, 300
Coincidence detection,
gain of, 305
good video balance
hum in, 31]
theory of, 308–312
gain of, 305
with triode detectors, 307
Weiss, 305
Down-pull rate, 318, 322, 325
Drift-in, 314, 318
Drift-in systems, 331
Drifts, 25
Driving power, 34
Duplexer, 6, 96, 199
Gadsden, C. P., 83, 365
Gain, 11, 12, 58, 325
of detector, 20
effective gain of the system,
in, 345
trigger circuit,
tube, 300
General Electric Co., 43, 46, 87, 90
Generator, slow-sweep,
314, 316, 326
Effective noise bandwidth,
14, 22, 27
Electrode, keep-alive,
8, 99, 174, 175
factors, 291, 292
Enabling circuit, 300
circuit is given)
noise, 243–245
Filter cavity, 235
Filtering, 246, 358
197, 300, 335
I-f admittance,
I-f amplifier
Frequency control, 25, 39
of local oscillators, 29*351
electrode, 312, 314
principle, 317
Frequency conversion, 26
Heater voltage, 294
Hold-in range, 295
Hum, 349
Hum pickup, 306
Hunting, 295, 331
Forward resistance, 297
Foster, D. E., 304n.
Flat, 97, 300
Flat power, 173
Following rate, 317, 318
Harmonic response, 298
Harmonic shutters, 174–178
61, 82, 285, 301, 372, 374
Feedback loop, 290
Figure of merit, for receivers, l&17
54, 56
Filter, resonant, to reduce local-oscillator
Harmonic generator, 3–4
hash,” 298
(see component
which equivalent
Error voltage, 295
Enabling feature, 314
Energy level, 48
Envelope viewer, 97, 373
prevented by padding, 219–223
Frequency drift, sources of, 29&292
79, 105, 253, 277,
(see Amplifier,
111, 249, 360
coupling circuit, 271
impedance, 256
I-f output admittance,
90, 178-185
I-f output lead, 128-131
I-f resistance, 115
I-f spectrum, 302
Image, 43
Image frequency,
362, 364, 365
27, 60, 256, 276, 358,
version loss, 75-83
Image reflection, 367
Image response, 26
Image termination,
Impedance, cold, 9
Impedance loss, 66,68, SO, 89
Impurity centers, 49
Incremental method, 103
Input admittance, 66-71, 122
Insulators, 48
Interference, 276
Amplifier, i-f)
Iris, coupling, adjustable, 164
with adjustable choke screw, 165
Jamming, 193,300,331
JAN-lA specifications, 324,341
Johnson, J. B,, 11
Johnson noise, 11,55
‘[Lazy man’’ reversing switch, 333
Leakage, 198, 199
particularly troublesome in AFC, 299
18, 29, 33, 35, 45
triode, 290
Littelfuse, 18
Llewellyn, F. B., 1In.
LO (se. Local oscilbtor)
Load, matched, 200, 206
circuits, 25
circuit elements,
7, 259--262, 363–365
equivalent network of, 264
matching of, 262-264
voltages and currents in, 264-269
Manual tuning aid, 342
Matching, 261
(see quantity
58, 252
frequency control of, 290-351
Locking, 246, 292, 302
LOUp, 168
Loss, 58, 115, 353
conversion (see Conversion 10ss)
66, 68, 80, 89
Keep-alive electrode, 99, 174, ]75
Klystron, 36
reflex, 37-43, 206, 236, 361
Kuper, J.B, H,,237n.
Local OacilIatOrs,
channel, 232
ripple in, 318
Local-oscillator noise (see Noise, localoscillator)
Local-oscillator power, 57, I 15, 2,5
tubes, table of, 40
channel, 150-
for coaxial-line mixers, 142–144
iris for, 160-166
in waveguide mixers, 144–146
i-f, 256
to be meas-
Mechanical shock, 96, 100
Merit, figure of (see Figure of merit)
~lcro wave
Miller, J, M.r 328
Mixer circuit, basic, 120-122
Mixer tubes, 28
Mixers, 3, 119
cavity, 215-218
high-Q, 202-215
with reaction cavity, 213
circuit, 172
coupling, 172, 354-356
capacitive probe, 14&-144
AFC, double-balanced,
balanced, 257-289, 301
crystal mounts for, 276-283
Magic T, 26%279
simple, 257-259
broadband two-channel,
with loop coupling,
complete, drawings of, 180-189
Mixera, crystal, 34,
Noise spectrum,
for, 119-189
double, 194
283, 301
high-loss, 122
for, 392-374
of, 223-234
resonant, 122
for lo-cm band, 188
single, 299
triode, 28–32
on over-all
100, 115
294, 331
Oscillation, 90
Oscillators, beating, 3
phase-shift, 344n.
reflex, 292
Output admittance,
i-f, 90, 178-185
Output lead, i-f, 128-131
Overload, 206, 207
by resonant filters, 243245
reduction by use of a cavity, 245-249
by TR cavity, 241-243
suppression of, 257
random, 10
Noise diode, 109, 254, 359, 367
Noise figure, 10-17, 29
15, 17, 43, 58,
Padding, 219-223
separation, 304, 31o
Phase-shift oscillator, 344n.
Polyiron, 198, 199, 285, 301
Power, 10cal-oscillator,
Precision reference cavity, 342
5, 8, 27, 43, 123
Preselector, 2, 23
Pre-TR switch, 175
as local-oscillator
coupling, 140-144
tests, 352–354
Pull-in range, 295
Pulling, 290, 317
Pulling figure, 203, 206, 213, 291
Pulse radar, 4
measurement of, 15
over-all, 15, 249
effect of local-oscillator
Pulses, 4
stretching of, 306, 312
Pushing, 291
36 1–364
figure, 291
100, 235,
250, 253
measurements of, 356-361
Noise generators, 236
crystal, 363
58, 93-96,
North, H. Q., 46, 87
Nyquist, H., 1in.
Nyquist theorem, 296
of, 235-237
of, 237-239
in cascade, 16
of combination,
effective, 13
of crystal,
247, 270, 273, 275
16, 235, 359
333, 337
Noise, Johnson, 11
effect of, 235-237
Noise suppression,
Noise temperature,
Oilcan tube, 18
“ On-off” principle,
coupling in, 144-146
for 10-cm band, 171–172
velocity, 36
method, 101
pulse, 4
of America,
(see Amplifier,
tube, 292
1, 2
Co., 43
noise figure of (see Noise figure)
3, 24-26,
Receiver unit, complete, 1
of, 4&V
Shutters, harmonic, 174-178
Sideband, wrong, 294, 314, 331, 332
10, 21–24
Spectrum analyzer, 347, 373
Sperry Gyroscope Co., 43
Spike, 8, 97, 98, 300
Spreading resistance, 92
of crystal, 51, 91
frequency, 292
detector, 45
(see component
54, 113, 297
spreading, of crystal, 51, 91
Resistance card, 197, 231, 301
Resistor disk, 141, 149, 206, 356
Resonant stub, 176
Rieke diagram, 203, 211
R-f amplifier, 2, 23, 43
97, 373
Stability, 290
frequency, 212
Static, 10
Static discharge, 115
M. W. P., 308n.,
347, 349n.
receiver, 3, 24–26,
receiver, 45
360, 369
Switch, r-f, 369
Rotary joint, 291
RT switch (anti-TR),
Runaway, 324
RT (anti-TR),
TR, 9, 70, 78, 96, 97, 114, 172, 353
Roberts, S,, 77
Rochester, N., 319
Roder, Hans, 304
H-plane, 260
Terman, F. E., 294, 312
Test mount, 205
Tetrodes, 44
Scaling, 119
Schwinger, J., 155, 201
Search stopper, 314, 317, 326
“Second chance” feature, 338
S. W., 304n.
circuit, 300, 314
Spike energy, 99, 111, 174, 373
efficiency, 207
Rectifier crystal, 47-118
Reflex klystron, 37-43
R-f envelope viewer,
R-f switch, 369
Ripple, peak-to-peak,
304, 310
Sharpless, W. M., 83n.
Shock excitation, 298
Shutdown, 176
Signal, minimum
64, 66, 74, 87, 371
Resistance, back, of crystal,
Resistance, i-f, 115
Signal-input circuit, 166+171
Sink, 204, 206, 208
Slow-sweep generator, 314, 316, 326
Spectrum, i-f, 302
theorem, 63n.
physical description
of mixer crystal,
W,, 308n.
10, 21
Separation, peak-to-peak,
figures of merit of, 54–56
figure of merit of, 1*17
of types of,
Reflex principle,
Reflexing, 314
agitation, 10
strut, 292
time constant,
Th6venin’s theorem, 32o
Time constant, 331
Tolerances, 114
Torrey, H. C., 76, 77, 91, 92, 111
TR-aided tuning, 170, 173, 280
TR cavity, 28,72, 13’3, 157, 162, 166, 174,
179, 224, 256, 276, 358, 364
equivalent circuit for, 167
OUtpUtiOOpOf, 168
reduction of local-oscillator noise hy,
TR leakage, 192, 201
TR leakage power, 173, 372
TR switch, 9,70, 78, 96, 97, 114, 172, 353
Transit-time effects, 17, 34
Transition, capacitance amplification in,
Transmission loss, 169
Transmitter sample, 296-29!), 301
Collpling of, 1’36-199
Travis, Charles, 304
Travis circuit, 304
Trigger circuit, l;ccles-Jordan,
‘rriggcr shaper, 349
Triode, 35, 293
Tube mount, 146
Tuning, 70, 123, 293
electronic, 38
fixed, 123, 134-136
Tuning, TR-aided,
Tuning range, 2
Tuning screws, 132
University of Pennsylvania,
Up-pull rate, 319, 322, 325
Velocity modulation,
tuhc, 290
“ Video hash,” 298
Video pulse, 297
Video unbalance.
Waltz, M. C., 83, 237n., 365
Weiss discriminator,
theory of, 30&312
crystal (see Crystal,
manillm wehlcd-contact)
Wmtcrn Ilcctric
43, 118
Whitford AFC systcm, 332, 333, 337, 33!3
F. C., lln.
wire, 18-19
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