Note for Ham Radio Measurements
A p p l i c a t i o n
N o t e
Compilation of
Application
Notes for
Ham Radio
Measurements 2013
1. Transmitter Trapezoid Test
2. Transmitter Two Tone Test
3. Amplifier Linearity test with Spectrum Analyzer
4. Power Measurements with an Oscilloscope
5. Return Loss Bridge Measurements
6. Station Monitor Selection
7. TDR Transmission line Testing
Precision Ham Radio Measurements
File: Appnote#6 TDR measurements-1
5/20/2013
© 2013 Roger M. Stenbock W1RMS & preciseRF, all rights reserved
2
Application Note #1
Transmitter Trapezoid Test
© Roger Stenbock W1RMS 3/3/2012
How to measure amplifier non-linearity
How can the ham make practical amplifier measurements to check for splatter, IMD
products and unwanted harmonic content? While it is helpful to understand the theory
and math behind amplifier non-linearity’s, all that is required is to make accurate
measurements minimizing splatter and distortion is an understanding of the basic
concepts.
Basically there are three methods to measure non-linearity and IMD products; Spectrum
analyzer, Trapezoid test and the Two Tone test. Each has its advantages and
disadvantages.
Trapezoids station monitor testing
Figure 1. The station monitor
provides all the components to
make accurate transmitter
tests. It includes a
demodulator with separate
level control for the scope’s X
input, an RF sampler for the
scope’s Y input, and a scope
Figure 1 Station monitor
trigger output.
This station monitor allows for precise tuning of the entire transmitter chain with
transceiver output of up to 100 Watts driving linear RF amplifiers. It features a wide band
sampler, a high performance demodulator, a variable base band output, and an
oscilloscope trigger output. A Linear RF amplifier generally amplifies an RF signal from
20-100 Watts by 20dB or more to about 500-1,500 Watts. Its performance and
modulation can be characterized using a low-cost oscilloscope with a trapezoid display.
Figure 2 Block diagram station monitor
Figure 3. The RF signal is
sampled and demodulated by
the station monitor. The outputs
are connected to the scope’s X
and Y inputs and external trigger
input for monitoring the signal
quality.
Figure 3 Station monitor connection
This is done by sampling the amplifier’s output by using an RF sensor. This sensor is
connected to the oscilloscope’s vertical (Y) input. See the Figure 2. block diagram..
The input of the amplifier is driven by a transceiver which usually outputs less than
100W. Its output drives the input to the amplifier and also a wide band demodulator
which extracts the baseband from the modulated carrier. It is this baseband that is
connected to the oscilloscope’s horizontal (X) input. This display yields a trapezoid
pattern. This pattern compares the transceiver’s output to the amplifiers output.
Figure 4. Shown here is the
amplitude of the modulated
RF increasing in a linear
fashion, from minimum at left
to maximum at right. When
the demodulated horizontal
(X) is reversed the trapezoid
will be reversed seen here.
Figure 4 Station monitor display
If the amplifier is linear without any distortion and not overdriven, the trapezoid pattern
will be a linear undistorted triangular waveform. To rely on such a measurement, the
demodulator and signal samples must be linear and free of distortion.
Figure 5. Wave-envelope
patterns; with their
corresponding trapezoidal
patterns. The wave envelope
patterns were obtained with a
linear oscilloscope sweep
having a frequency one-third of
sine-wave audio modulating
frequency, so that three cycles
of the modulation envelope
may be seen.
A. Unmodulated carrier
B. Approximately 50%
modulation
C. 100% modulation
D. Shows modulation in
excess of 100%
E. Modulation improper
transmitter adjustment
F. Indicates improper
modulation, incorrect bias,
and clipping
Figure 5 Oscilloscope patterns showing various
forms of modulation of an RF amplifier
HF amplifier distortion measurements
Linear RF Power Amplifiers are used in a wide variety of ham radio stations. The output
power of these linear amplifiers can range from a few watts to several thousand watts.
FCC regulations limit the maximum power to 1,500 peak envelope power (PEP). When
adjusted properly and operating in their linear region, these amplifiers do exactly that,
they amplify RF energy without adding any significant additional distortion products.
However, if overdriven or not properly tuned, the potential distortion products can cause
severe problems such as unintelligible modulation. RF power being transmitted out of
band, thus causing interference with other radio communications. The interfering signals
are the result of harmonic and intermediation products – sometimes referred to as
“splatter”.
Efficiency
Another byproduct of improper linear amplifier operation is inefficiency. Power that is not
converted to a useful signal is dissipated as heat. Power Amplifiers that have low
efficiency have high levels of heat dissipation, which could be a limiting factor in a
particular design. This can have an adverse effect on the components, particularly the
final output tubes or transistors.
Instability
Another undesirable amplifier phenomenon is instability. Instability in RF amplifiers may
manifest itself as oscillation at almost any frequency, and may damage or destroy the
amplifying device. This unwanted RF energy is called spurious oscillation.
These spurious oscillations can arise at specific or very wide ranging frequencies and
over a particular bias, drive level, temperature or output load impedance.
Responsibility
In the amateur radio service, the control operator (i.e. ham) is responsible for ensuring
that all emitted signals including RF linear power amplifiers are operated in accordance
with those prescribed by their license privileges and do not exceed the maximum
allowed distortion by the FCC.
Some practical theory
In practice and to ensure efficiency, many linear amplifiers operate as Class B. In Class
B the conduction angle for the amplifying device (tube or transistor) is approximately
180°. Thus, the amplifying device conducts only half of the time, either on positive or
negative half cycle of the input signal.
The same as in Class A, the DC bias applied to the amplifying device determines the
Class B operation. Class B amplifiers are more efficient than Class-A amplifiers. The
instantaneous efficiency of a Class-B PA varies with the output voltage and for an ideal
PA reaches π/4 (78.5 %) at PEP. However they are much less linear. Therefore a typical
Class-B amplifier will produce quite a bit of harmonic distortion that must be filtered from
the amplified signal.
PDC = (2*VCC*V) / (Π*R);
PLOAD = V2 / (2*R);
η (Efficiency Class-B) = (Π*V) / (4*VCC)
A common configuration of Class B amplifiers is push-pull. In this configuration, one
amplifying device conducts during positive half cycles of the input signal and the second
transistor conducts during the negative half cycle. In this way, the entire input signal is
reproduced at the output. In the push-pull arrangement, the DC components and even
harmonics cancel, (but odd harmonics add), thus the output contains the fundamental
signal only. Note that the cancellation of odd harmonics is only valid if the amplifier is not
driven hard.
Power amplifier linearity
When two or more signals are input to an amplifier simultaneously, the second, third,
and higher-order intermodulation components (IM) are caused by the sum and
difference products of each of the fundamental input signals and their associated
harmonics. The rated PEP of a Power Amplifier is the maximum envelope power of a
two-tone signal for which the amplifier intermodulation level is -30dBc. When two signals
at frequencies f1 and f2 are input to any nonlinear amplifier, the following output
components will result:
Fundamental: f1, f2
Second order: 2f1, 2f2, f1 + f2, f1 - f2
Third order: 3f1, 3f2, 2f1 ± f2, 2f2 ± f1,
Fourth order: 4f1, 4f2, 2f2 ± 2f1,
Fifth order: 5f1, 5f2, 3f1 ± 2f2, 3f2 ± 2f1, + Higher order
terms
The odd order intermodulation products (2f1-f2, 2f2-f1,
3f1-2f2, 3f2-2f1, etc) are close to the two fundamental
tone frequencies f1 and f2.
The nonlinearity of a Power Amplifier can be measured on the basis of the generated
spectra (i.e with a spectrum analyzer) than on variations of the fundamental waveform
(i.e. oscilloscope). The estimation of the amplitude change (in dB) of the intermodulation
components (IM) versus fundamental level change, is equal to the order of nonlinearity.
For a one dB increase of fundamental level (f1 and f2), the level of IM2 will go up by
2dB, the level of IM3 will go up by 3dB, and so on. As a relation between the degree of
nonlinearity (third, fifth, etc) and the frequency of the side tone (such as IM3, IM5, etc). It
can be mentioned with the IM5 tones are not affected by third-degree nonlinearities, but
IM3 tones are functions of both third- and fifth-degree (and higher) nonlinearities. That
means at low signal amplitudes, where the fifth-order distortion products can be
neglected, the amplitudes of the IM3 tones are proportional to the third power of the
input amplitude (see below).
Figure 6 Spectrum of IMD products
- end -
Application Note #2
Transmitter Two Tone Test
© Roger Stenbock W1RMS 3/3/2012
How to measure amplifier non-linearity
How can the ham make practical amplifier measurements to check for splatter, IMD
products and unwanted harmonic content? While it is helpful to understand the theory
and math behind amplifier non-linearity’s, all that is required is to make accurate
measurements minimizing splatter and distortion is an understanding of the basic
concepts.
Basically there are three methods to measure non-linearity and IMD products; Spectrum
analyzer, Trapezoid test and the Two Tone test. Each has its advantages and
disadvantages.
Two tone signal test using an oscilloscope
The Two Tone, third-order intermodulation distortion (IM) test measures the degree of
nonlinearity of an electronic device with a definable dynamic range, such as an amplifier.
Nonlinear RF Amplifiers may spread signals into adjacent channels, and or frequencies,
which can cause Cross Modulation. This is based on the same phenomena as third
order intermodulation for nonlinear amplifiers with two-tone inputs. Fortunately, when
making a Two Tone test, the signal distortion is relatively easy to spot. Testing ham
radio HF linear amplifiers can be done by injecting a two tone test signal (usually 700 Hz
and 1900Hz) into the amplifier input and observing the modulation envelope with an
oscilloscope.
This test can be done by simply inputting the signal into the transceiver’s mike jack from
the line out of the two tone test generator, or in the alternative, using the speaker output
to drive an external speaker placed close to the microphone. The drawback to using this
technique is that the microphone and speaker performance may impact the test result.
For this reason separate level and balance control are provided.
Fig 1. This Two Tone test
generator provides a standard
2-tone (700 and 1900 Hz)
audio source. This type of
testing is most commonly
used as a measure of
transmitter linearity for
amateur radio equipment.
Figure 1 The TTG1 Two Tone test generator
Results of 2-tone IMD tests can be found in every ARRL review of new transceivers and
power amplifiers.
Figure 2 Scope Two Tone test display
Figure 3 Two Tone test characteristics
Fig. 2 Top trace, note the lack of flat topping and or cross over distortion as
when compared to the example shown in Fig 3.
A & B Properly
adjusted transmitter.
C & D Crossover
distortion resulting in
high IMD products.
E & F Flat topping
over driven
modulation causing
splatter and high IMD
products.
Figure 4 Tow Tone test, left column scope display, right
column spectrum analyzer display
HF amplifier distortion measurements
Linear RF Power Amplifiers are used in a wide variety of ham radio stations. The output
power of these linear amplifiers can range from a few watts to several thousand watts.
FCC regulations limit the maximum power to 1,500 peak envelope power (PEP). When
adjusted properly and operating in their linear region, these amplifiers do exactly that,
they amplify RF energy without adding any significant additional distortion products.
However, if overdriven or not properly tuned, the potential distortion products can cause
severe problems such as unintelligible modulation. RF power being transmitted out of
band, thus causing interference with other radio communications. The interfering signals
are the result of harmonic and intermediation products – sometimes referred to as
“splatter”.
Efficiency
Another byproduct of improper linear amplifier operation is inefficiency. Power that is not
converted to a useful signal is dissipated as heat. Power Amplifiers that have low
efficiency have high levels of heat dissipation, which could be a limiting factor in a
particular design. This can have an adverse effect on the components, particularly the
final output tubes or transistors.
Instability
Another undesirable amplifier phenomenon is instability. Instability in RF amplifiers may
manifest itself as oscillation at almost any frequency, and may damage or destroy the
amplifying device. This unwanted RF energy is called spurious oscillation.
These spurious oscillations can arise at specific or very wide ranging frequencies and
over a particular bias, drive level, temperature or output load impedance.
Responsibility
In the amateur radio service, the control operator (i.e. ham) is responsible for ensuring
that all emitted signals including RF linear power amplifiers are operated in accordance
with those prescribed by their license privileges and do not exceed the maximum
allowed distortion by the FCC.
Some practical theory
In practice and to ensure efficiency, many linear amplifiers operate as Class B. In Class
B the conduction angle for the amplifying device (tube or transistor) is approximately
180°. Thus, the amplifying device conducts only half of the time, either on positive or
negative half cycle of the input signal.
The same as in Class A, the DC bias applied to the amplifying device determines the
Class B operation. Class B amplifiers are more efficient than Class-A amplifiers. The
instantaneous efficiency of a Class-B PA varies with the output voltage and for an ideal
PA reaches π/4 (78.5 %) at PEP. However they are much less linear. Therefore a typical
Class-B amplifier will produce quite a bit of harmonic distortion that must be filtered from
the amplified signal.
PDC = (2*VCC*V) / (Π*R);
PLOAD = V2 / (2*R);
η (Efficiency Class-B) = (Π*V) / (4*VCC)
A common configuration of Class B amplifiers is push-pull. In this configuration, one
amplifying device conducts during positive half cycles of the input signal and the second
transistor conducts during the negative half cycle. In this way, the entire input signal is
reproduced at the output. In the push-pull arrangement, the DC components and even
harmonics cancel, (but odd harmonics add), thus the output contains the fundamental
signal only. Note that the cancellation of odd harmonics is only valid if the amplifier is not
driven hard.
Power amplifier linearity
When two or more signals are input to an amplifier simultaneously, the second, third,
and higher-order intermodulation components (IM) are caused by the sum and
difference products of each of the fundamental input signals and their associated
harmonics. The rated PEP of a Power Amplifier is the maximum envelope power of a
two-tone signal for which the amplifier intermodulation level is -30dBc. When two signals
at frequencies f1 and f2 are input to any nonlinear amplifier, the following output
components will result:
Fundamental: f1, f2
Second order: 2f1, 2f2, f1 + f2, f1 - f2
Third order: 3f1, 3f2, 2f1 ± f2, 2f2 ± f1,
Fourth order: 4f1, 4f2, 2f2 ± 2f1,
Fifth order: 5f1, 5f2, 3f1 ± 2f2, 3f2 ± 2f1, + Higher order
terms
The odd order intermodulation products (2f1-f2, 2f2-f1,
3f1-2f2, 3f2-2f1, etc) are close to the two fundamental
tone frequencies f1 and f2.
The nonlinearity of a Power Amplifier can be measured on the basis of the generated
spectra (i.e with a spectrum analyzer) than on variations of the fundamental waveform
(i.e. oscilloscope). The estimation of the amplitude change (in dB) of the intermodulation
components (IM) versus fundamental level change, is equal to the order of nonlinearity.
For a one dB increase of fundamental level (f1 and f2), the level of IM2 will go up by
2dB, the level of IM3 will go up by 3dB, and so on. As a relation between the degree of
nonlinearity (third, fifth, etc) and the frequency of the side tone (such as IM3, IM5, etc). It
can be mentioned with the IM5 tones are not affected by third-degree nonlinearities, but
IM3 tones are functions of both third- and fifth-degree (and higher) nonlinearities. That
means at low signal amplitudes, where the fifth-order distortion products can be
neglected, the amplitudes of the IM3 tones are proportional to the third power of the
input amplitude (see below).
Figure 5 Spectrum of IMD products
- end -
Application Note #3
Transmitter Spectrum Analyzer Test
© Roger Stenbock W1RMS 3/3/2012
How to measure amplifier non-linearity
How can the ham make practical amplifier measurements to check for splatter, IMD
products and unwanted harmonic content? While it is helpful to understand the theory
and math behind amplifier non-linearity’s, all that is required is to make accurate
measurements minimizing splatter and distortion is an understanding of the basic
concepts.
Basically there are three methods to measure non-linearity and IMD products; Spectrum
analyzer, Trapezoid test and the Two Tone test. Each has its advantages and
disadvantages.
RF spectrum analyzer
The spectrum analyzer method is used to make quantifiable laboratory grade
measurements. The spectrum analyzer test measures the amplifier’s RF spectra
distribution as a function of frequency, generally in MHz (X axis) and magnitude (Y axis).
By comparing the level of the fundamental frequency to the level of any unwanted
harmonic products (spurious) a precise quantifiable results can be obtained. The results
are generally shown in the amount that the spurious products are down compared to the
fundamental frequency and are express in dB. For example if the ratio is -20 dB than the
spurious power is 1/100 that of the fundamental, and if the level was down -30 dB than
the spurious power would be 1/1000 that of the fundamental. It should be noted that the
spurious signals could be multiples of odd and even harmonics.
For convenience, some spectrum analyzer are equipped with a tracking generator. The
tracking generator, by sweeping the amplifier’s frequency, allows for measuring the
performance at more than one frequency.
The frequency range of the spectrum analyzer should be at least five times the highest
fundamental frequency to be measured. In the case of a 50MHz signal (6 meter) test,
that would require a spectrum analyzer with a 250MHz frequency range or higher.
An alternative to the spectrum analyzer is using an oscilloscope that provides a Fast
Fourier Transform (FFT) display. The FFT display is derived from the mathematical
transformation of the signal’s magnitude versus time components and then displayed as
magnitude versus frequency. However, the oscilloscope’s bandwidth needs to also be
at least five times the fundamental frequency.
Either of these methods yields predictable and accurate measurement results. When
comparing spectrum analyzer results to oscilloscope FFT results, and so long that the
signal being measured is with the dynamic and frequency range of the measurement
instrument input, the results are generally within .5dB.
Measurement considerations
While it is relatively straight forward to make these measurements, you need to consider
the transceiver and or amplifier signal levels and the modulation being applied to their
input. One can’t simply just connect the high power RF output from the amplifier or
transceiver directly to the input of the spectrum analyzer. This may result in damage to
the instrument and may even cause injury to people. The power levels of even QRP
transceivers are about 5 Watts and for transceivers can be as high as 200 Watts. Linear
amplifiers can have levels of greater than 1,500 Watts. The levels are way out of the
input range of a typical spectrum analyzer or oscilloscope. One could use attenuators.
These would have to be wideband and high power. That means lots of money. The most
economical way to condition the desired signal level is to use an RF sampler/coupler
(see Figure 2).
While it is possible to just modulate the transmitter by speaking or whistling in to the
microphone and observe the results, it is not recommended. Nonetheless, if such
technique is used, it has been found that repeatable speaking the letter “X” will give the
best results. The “ae” sound produces medium frequency levels for a long enough
duration, and the “ks” sound produces higher frequency components to make some
useful measurements. However, to make repeatable quantifiable measurements, a
precision signal source, such as in Fig 3. below, a Two Tone test generator, is required.
Fig. 1 The DSA1030A series spectrum
analyzer with advanced measurement
capabilities. It uses digital IF technology
which guarantees the reliability and
performance required meeting the most
demanding RF applications for measuring
amplifier no-linearity. This spectrum
analyzer will make virtually all ham radio
Figure 1 3GHz spectrum analyzer
measurements and test. Price is about
$5,000
Fig. 2 This wideband RF sample/coupler
inductively couples a sample of high
power RF (up to 1.5 KW PEP) passing from
the RF IN to the RF OUT connector. This
signal is coupled at -30 dB, a power
reduction of 1000:1. The sampled signal is
very useful for analyzing HF signals on an
Figure 2 HFS-1.5 HF sampler/coupler -30dB
oscilloscope and spectrum analyzer.
Fig . 3 The TTG1 Two Tone test generator
is an excellent oscillator to test SSB
transmitter performance such as Intermodulation Distortion (IMD). The TTG1 was
created to deliver a standard 2-tone (700
and 1900 Hz) audio source for testing of
SSB transceivers and linear amplifiers. This
type of testing is used as a measure of
transmitter linearity for amateur radio
Figure 3 TTG1 Two tone test generator
transmitters.
Figure 4 Spectrum analyzer display
Fig. 4 This example is a typical spectrum analyzer display. The fundamental frequency is
the large spike at the start of the sweep. The harmonic contents are the smaller spikes.
They are down from the fundamental frequency about 70 dB. The FCC minimum levels
for the amateur radio service for unwanted IMD products is around -20dB. So in the
example in Fig.4, this level would be considered excellent performance.
Summery
Using a spectrum analyzer or an oscilloscope with an FFT for amplifier distortion
measurements provides the most accurate and repeatable results. However, there are
always tradeoffs, see Fig. 5 below.
Test Equipment
Spectrum analyzer, RF Sampler/coupler, dummy load,
signal source such as a two tone test generator.
Advantage
Results are displayed in quantifiable units, easy to
duplicate, accurate to a dB or less.
Disadvantage
New laboratory grade spectrum analyzers are expensive.
Figure 5 advantages and disadvantages
Careful shopping on eBay will reveal that affordable used spectrum analyzers are
available. It is recommended if such purchase is contemplated that it is calibrated with
NIST certified equipment.
HF amplifier distortion measurements
Linear RF Power Amplifiers are used in a wide variety of ham radio stations. The output
power of these linear amplifiers can range from a few watts to several thousand watts.
FCC regulations limit the maximum power to 1,500 peak envelope power (PEP). When
adjusted properly and operating in their linear region, these amplifiers do exactly that,
they amplify RF energy without adding any significant additional distortion products.
However, if overdriven or not properly tuned, the potential distortion products can cause
severe problems such as unintelligible modulation. RF power being transmitted out of
band, thus causing interference with other radio communications. The interfering signals
are the result of harmonic and intermediation products – sometimes referred to as
“splatter”.
Efficiency
Another byproduct of improper linear amplifier operation is inefficiency. Power that is not
converted to a useful signal is dissipated as heat. Power Amplifiers that have low
efficiency have high levels of heat dissipation, which could be a limiting factor in a
particular design. This can have an adverse effect on the components, particularly the
final output tubes or transistors.
Instability
Another undesirable amplifier phenomenon is instability. Instability in RF amplifiers may
manifest itself as oscillation at almost any frequency, and may damage or destroy the
amplifying device. This unwanted RF energy is called spurious oscillation.
These spurious oscillations can arise at specific or very wide ranging frequencies and
over a particular bias, drive level, temperature or output load impedance.
Responsibility
In the amateur radio service, the control operator (i.e. ham) is responsible for ensuring
that all emitted signals including RF linear power amplifiers are operated in accordance
with those prescribed by their license privileges and do not exceed the maximum
allowed distortion by the FCC.
Some practical theory
In practice and to ensure efficiency, many linear amplifiers operate as Class B. In Class
B the conduction angle for the amplifying device (tube or transistor) is approximately
180°. Thus, the amplifying device conducts only half of the time, either on positive or
negative half cycle of the input signal.
The same as in Class A, the DC bias applied to the amplifying device determines the
Class B operation. Class B amplifiers are more efficient than Class-A amplifiers. The
instantaneous efficiency of a Class-B PA varies with the output voltage and for an ideal
PA reaches π/4 (78.5 %) at PEP. However they are much less linear. Therefore a typical
Class-B amplifier will produce quite a bit of harmonic distortion that must be filtered from
the amplified signal.
PDC = (2*VCC*V) / (Π*R);
PLOAD = V2 / (2*R);
η (Efficiency Class-B) = (Π*V) / (4*VCC)
A common configuration of Class B amplifiers is push-pull. In this configuration, one
amplifying device conducts during positive half cycles of the input signal and the second
transistor conducts during the negative half cycle. In this way, the entire input signal is
reproduced at the output. In the push-pull arrangement, the DC components and even
harmonics cancel, (but odd harmonics add), thus the output contains the fundamental
signal only. Note that the cancellation of odd harmonics is only valid if the amplifier is not
driven hard.
Power amplifier linearity
When two or more signals are input to an amplifier simultaneously, the second, third,
and higher-order intermodulation components (IM) are caused by the sum and
difference products of each of the fundamental input signals and their associated
harmonics. The rated PEP of a Power Amplifier is the maximum envelope power of a
two-tone signal for which the amplifier intermodulation level is -30dBc. When two signals
at frequencies f1 and f2 are input to any nonlinear amplifier, the following output
components will result:
Fundamental: f1, f2
Second order: 2f1, 2f2, f1 + f2, f1 - f2
Third order: 3f1, 3f2, 2f1 ± f2, 2f2 ± f1,
Fourth order: 4f1, 4f2, 2f2 ± 2f1,
Fifth order: 5f1, 5f2, 3f1 ± 2f2, 3f2 ± 2f1, + Higher order
terms
The odd order intermodulation products (2f1-f2, 2f2-f1,
3f1-2f2, 3f2-2f1, etc) are close to the two fundamental
tone frequencies f1 and f2.
The nonlinearity of a Power Amplifier can be measured on the basis of the generated
spectra (i.e with a spectrum analyzer) than on variations of the fundamental waveform
(i.e. oscilloscope). The estimation of the amplitude change (in dB) of the intermodulation
components (IM) versus fundamental level change, is equal to the order of nonlinearity.
For a one dB increase of fundamental level (f1 and f2), the level of IM2 will go up by
2dB, the level of IM3 will go up by 3dB, and so on. As a relation between the degree of
nonlinearity (third, fifth, etc) and the frequency of the side tone (such as IM3, IM5, etc). It
can be mentioned with the IM5 tones are not affected by third-degree nonlinearities, but
IM3 tones are functions of both third- and fifth-degree (and higher) nonlinearities. That
means at low signal amplitudes, where the fifth-order distortion products can be
neglected, the amplitudes of the IM3 tones are proportional to the third power of the
input amplitude (see below).
Figure 6 Spectrum of IMD products
Application Note #4
Measuring Transmitter Power with the Oscilloscope
© Roger Stenbock W1RMS 4/19/2012
HF Amplifier Power Measurements:
Power is often defined as peak power, carrier power, average power, Peak
Envelope Power (PEP) and sometimes incorrectly as RMS power. In the United States
the Federal Communications Commission uses PEP to set maximum power limits for
amateur radio transmitters. The maximum power allowed on certain frequencies using
SSB modulation is 1,500 Watts PEP. PEP is the average power supplied by the
transmitter/linear RF amplifier to the transmission line and eventually the antenna, during
one radio frequency cycle at the crest of the modulation envelope, under normal
operating conditions.
What is Electric Power
Electric power is the rate at which electric energy is transferred by an electric
circuit. The unit of power is the Watt. Joule heating, is ohmic heating and resistive
heating, it is the process by which the passage of an electric current through
a conductor releases heat. It was initially studied by James Prescott Joule in 1841.There
is potential power (no heating), instantaneous power and average power. When one volt
is applied across a one ohm resistor, one ampere of current flows though the resistor.
Since P=IE then the resistor is dissipating one Watt.
When power is defined over time it is expressed in Joules. One Joule equals one
Watt per second; that is synonymous to one Watt second. When power is referred to as
“instantaneous power”, it is expressed as a fraction of a Joule; for example if the instant
of that power lasts for one Millisecond, that equals one Millijoule or one Milliwatt second.
It should be noted that the power applied to an ideal antenna does not heat the
antenna. The antenna radiates the power (less any losses, which indeed heat the
antenna). This radiated power is eventually absorbed by the atmosphere, natural and
1
manmade objects, and also at the radio receiver’s antenna and receiving circuits;
eventually the energy is transformed either to useful work, or heat.
PEP may be more difficult to measure than CW power. Nonetheless, PEP is the
average power during one radio frequency cycle at the crest of the modulation envelope
and continuous wave (CW) power is also an average power, thus they are equal.
All power measurements rely on these formulas:
For DC power measurements, use:
2
P= E /R
For AC, PEP measurements, use:
2
P= (Eavg) /R
Peak Power
Measuring peak voltage with an oscilloscope is not difficult, and generally, the
load impedance (R) in amateur radio transmitters and transmission lines equals 50 ohms
(sometimes 300 ohms). Making a peak power measurement is straightforward by
measuring the peak voltage. Some users find it simpler to measure the peak-peak
voltage. In that case, divide the results by 2 to get peak voltage.
Figure 1, Oscilloscope display
2
See figure 1. Note, the Max (peak) voltage is 70 volts, which is half of the Pk-Pk
voltage. To solve for peak power, square the peak voltage (E) and divide by 50 (the load
impedance) So:
2
(70) =4900/50=98 watts Peak Power
Average Power
Let’s dispel the myth of RMS power. There is no such thing as RMS power. RMS
is an abbreviation of Root Mean Squared. The term “Mean” is just another word for
average. With respect to power calculations, the AC RMS voltage is the equivalent to the
DC voltage. For example, 25V RMS or 25V DC across a non-inductive 50ohm load
results in identical power dissipation of 12.5 watts in either case.
The RMS value by itself is not the comparable heating power and it doesn’t
correspond to any useful physical quantity; no heat, no power. Recall P=IE, and I=E/R.
Voltage (E), nor current (I) by themselves generate power. The power is only produced
when a current is induced by a voltage across a load R. Finally, RMS and average
values of nearly all waveforms are different. One exception is a steady DC waveform, for
which the average, RMS, and peak values are identical.
Figure 2 sampled sine wave
See figure 2. If one were to sample a waveform at regularly spaced times, and
then add up their values and divide that total by the number of samples taken, one would
3
have approximately the average value of whatever the waveform represents; this could
be voltage, current or power. The less the time intervals between samples, the more
accurate the average will be. The mathematical integration is a method to find what the
value would be if we could minimize the time interval really close to zero. That’s
important if we want to calculate the exact average value of some waveforms. The
corresponding formula for a continuous function (or waveform) f(t) defined over the
interval
Thus substitution volts for f we arrive at the familiar equation:
Fortunately this mathematical integration can be reduced to the RMS values. And
for an ideal sine wave that happens to be the peak waveform value multiplied by .707.
So power is still power, whether PEP or average. The correct way to express average
AC power is Pavg. as a result:
2
Pavg=(ERMS) /R
We know that oscilloscopes are great tools to measure voltages of AC
waveforms. For a perfect sine wave, multiplying peak voltage times .707 will give us
RMS voltage. Some of the newer scopes make this step easy and calculate the RMS
voltage directly. These calculations are quite accurate even for non-sinusoidal
waveforms. See Figure 1, what is the average power if the peak voltage is 70 volts?
Step one: Calculate the RMS voltage (70 x .707 = 49.5 volts). You’ll note that in
Figure 1, the calculated RMS voltage is 50 volts not 49.5 volts. That is because the
oscilloscope measurement was done on a somewhat imperfect sine wave, thus giving a
slightly higher reading.
4
Step two: Square the voltage, and divide by 50 (the load impedance):
2
(49.5) =2450/50=49 watts Avg.
A common error some make calculating average power is they multiply PEP by
.707, i.e. 98 watts times .707. This results in an incorrect answer of 69.3 watts. Power is
always calculated by squaring the voltage and dividing the result by the load impedance.
PEP Power
The International Telecommunication Union (ITU) Radio Regulations define the
terms Peak Envelope Power (PEP) as:
“PEP means the average power supplied to the antenna transmission line by a
transmitter during one radio frequency cycle at the crest of the modulation envelope
taken under normal operating conditions.”
Figure 3 SSB Modulation
Understanding the definition of PEP, the question then arises what is meant by
“radio frequency cycle at the crest of the modulation envelope”?
See figure 3. The crest of the modulation envelope is the peak value; this
oscilloscope labels it as “Max”. It is 197 volts. Note, that the scope calculated the RMS
voltage as 86.6 volts which would be correct for a steady RF carrier. However, here the
modulation is not a steady carrier, but instead represents the minimum and maximum
modulation levels as an envelope.
5
The modulation envelope duration is 25mS over the entire display duration. At
7.3 MHz, this duration contains 182,500 individual radio frequency cycles. Since the
scope calculates RMS voltage over all these cycles, we cannot rely on that calculation.
So how do we obtain the RMS voltage for one radio frequency cycle? We know by
examining the scope display that there must be at least one radio frequency cycle at the
crest of the modulation envelope. The peak value of that cycle 197 volts. We also know
that RMS voltage equals .707 times the peak voltage; so 197 x .707=139.3 volts. To
calculate PEP power we again use this formula:
2
Pavg=(ERMS) /R
PEP means the average power. So we can substitute PEP for Pavg. Thus:
2
PEP=(ERMS) /R
Accordingly, applying this formula yields:
2
PEP = (139.3) =19,404/50=388 watts.
Amplitude Modulation (AM) Power
Figure 4 Approximately 90% AM modulation
6
See Figure 4, the PEP output of an AM transmitter at full modulation is four times
its carrier PEP; in other words, a 100-watt amateur transceiver is usually rated for no
more than 25 watts carrier output when operating in AM mode.
RF Power Meters
Absent a PEP function, virtually all analog power meters measure average
power. Many low cost power meters are notoriously inaccurate as they are generally not
calibrated to a known power standard. The Bird model 43®, and Heathkit® HM-102 are
an exception. Their accuracy is guaranteed to better than 5% of full scale. The HM-102
employs an internal accurate calibration standard to which the meter is calibrated. The
Bird® 43 slugs are individually calibrated at the factory against an accurate RF power
source.
As a result, these two analog power meters are generally much more accurate
than 5%. The accuracy of any meter can be verified to better 2% (the scope vertical
amplifier specification) when an oscilloscope is used to measure the power and
comparing that result to an unknown power meter.
PEP RF Power Meters
You may notice that your oscilloscope PEP measurements are consistently
higher than that obtained by most RF watt meters. There is nothing wrong. That is
because the oscilloscope, with its very fast rise time, can measure PEP based on peak
voltages.
Most commercially available watt meters display average power only. Some RF
meters employ a “PEP” function. They do this with a sample and hold circuit. This circuit
needs to have a fast rise time, i.e. considerably faster than the PEP envelope
components. Even then, some of these meters may not accurately measure the true
PEP power. As a result, their PEP reading can be significantly lower.
One of the most reliable ways to confirm the accuracy of any analog or digital
power meter is by using an oscilloscope with a calibrated vertical amplifier and sufficient
bandwidth (normally twice the measured frequency).
Direct sampling power measurements with the Oscilloscope
Most modern oscilloscopes have a maximum calibrated vertical amplifier
deflection factor of about 5 volts/division. With an accurate X10 voltage probe, the
7
vertical amplifier can display up to 50 volts/division. Given the 8 vertical divisions
normally found on an oscilloscope display, the maximum voltage measurement with a
10x probe is 400 volts peak to peak. That is the equivalent of 141.4 volts RMS, which in
turn calculates to 400 watts into 50 ohms. Any measurement of greater power requires
an RF sampler (discussed below).
The method used to make the power measurements is called direct sampling.
Set the scope to the appropriate volts/division setting, sample the voltage applied to the
center conductor of transmission line with an accurate 10x probe which in turn is
connected to the scope’s vertical input. This can be done with a “T” connection. For HF
frequencies, the measured voltage will be quite accurate. The closer the sampling point
is to the transmitter the better.
Figure 5 direct power measurement
The primary errors will be the result of the combined uncertainty of the
specifications of the vertical amplifier and the 10x probe. However, these can be
checked with an accurate signal generator such as a Tektronix® SG 503 constant
amplitude calibration generator. My experience has been that the accuracy achieved is
better than 2% and correlates with a Bird 43 ® power meter. In figure 5 the scope
measured 63.6 volts RMS which equals 80.89 watts, and the Bird 43® indicates 80
watts. That’s within +/- 1% well within the specifications of either instrument.
8
Problems with Direct Voltage Measurements
While it is possible to make direct high power measurements with an
oscilloscope, such as 1500 watts, it is rarely done. For example, at 1500 watts, the RMS
voltage is 274 volts, 388 volts peak, and 775.1 volts peak to peak. These levels can
result in damaged equipment and potential injury or death to the operator. It is possible
to use high power attenuators to reduce the voltage levels to a practical level. However,
these attenuators must be able to take the full brunt of the maximum power to be
measured.
The RF Sampler or Coupler (sampler)
Fortunately using an oscilloscope with an appropriate sampler is uncomplicated
and provides accurate results of better than 1 db. One way is to measure the power is to
load the amplifier directly into an antenna capable of radiating the maximum applied
power. The preferred and most practical way, is to load the amplifier in a “dummy load”,
which is usually 50ohms. These dummy loads are inexpensive and simple to connect.
But how do you measure the high voltage input to the dummy load? The best way to do
this is with an RF sampler. The sampler reduces the power to a manageable level. The
most common power reduction is a 1000 to 1. This equals -30 dB of the RF being
sampled.
Figure 6 The HFS-1.5 HF sampler/coupler covers 2MHz to 50MHz.
Employing a wideband transformer; it samples the high power RF (up to
1.5 KW PEP) from 2MHz to 50MHz.
Figure 6, The HFS-1.5 HF sampler allows for a maximum input of 1.5 KW, at HF
frequencies from 2MHz to 50MHz with a sample transfer coefficient of - 30dB or a
1000:1 reduction in power. Most samplers, including this example, provide a “Sample”
9
port which requires a 50ohm termination. Nearly all scopes have 1 Meg ohm vertical
input impedance and do not have the necessary 50ohm input impedance. As a result,
they require a 50ohm pass-through terminator at the scope’s vertical input. However,
when connecting the sampler to a spectrum analyzer, a pass-through terminator is not
required since most spectrum analyzers have a 50ohm input impedance.
Using the Sampler to Measure Power
An ideal sampler with a -30 dB power reduction (1000:1) has a voltage gain/loss
of 31.62. Therefore, to find the equivalent voltage (peak, pk-pk, or RMS) for -30dB,
multiply the sampled voltage times 31.62. Using peak voltage allows for calculating
power at any instant in time. If the peak voltage at the sampler port equals 2.83 volts,
than the actual RMS voltage is 2.00 volts (2.83 x .707). Multiplying the RMS voltage by
the gain/loss ratio 2.00×31.62 which we get 63.3 volts RMS. Calculate power using:
2
P= E /R equals 80.05 watts
When comparing that measurement using a calibrated -30 dB sampler to the
direct measurement in figure 5, (80.05 watts) correlates well with the previous direct
measurement of 80.89 watts, and the Bird 43® indication of 80 watts.
Here is a sampler with a -20 dB power reduction (100:1) it has a voltage
gain/loss of 10. To find the equivalent voltage (peak, pk-pk, or RMS) for -20 dB, multiply
the sampled voltage times 10. For instance, if the peak voltage at the sampler equals 5
volts, that equals 3.54 volts RMS. The voltage at the sampler input is 3.54×10 which
equals 35.4 volts RMS. Calculate power using:
2
P= E /R equals 25.06 watts
A much quicker way to obtain PEP and average power measurement is to refer
to Table 2 below. Connect the output of sampler port to the oscilloscope input (use a 50
ohm terminator at the scope input) and note the peak voltage. Move to the right and read
the peak and average power in watts, or power expressed in dBm.
10
Other handy formulas
To obtain the voltage ratio from a given dB, use this formula, where A=dB
V2/V1=10(A20)
To obtain the RMS voltage for any power use:
V= √ (PxR)
So for a 100 watts and 50 ohms than the RMS voltage is calculated thus:
V= √ (100x50)=70.71 volts RMS
What are dB
Decibels state a power ratio, not an amount. They tell how many times more
(positive dB) or less (negative dB) but not how much more or less in absolute terms.
Decibels are logarithmic, not linear. For example, 20 dB is not twice the power ratio of 10
dB. Use this equation to find decibels: A = 10*log10 (P2/P1) (dB) where P1 is the power
being measured, and P1 is the reference to which P2 is being compared. To convert
from decibel measure back to power ratio: P2/P1=10^(A/10). Voltage is more easily
measured than power, making it generally more convenient to use: A = 20*log10(V2/V1),
Where A=voltage ratio. The equation for obtaining voltage ratio from dB is V2/V1 =
10^(A/20).
What are dBm
dBm is an abbreviation for the power ratio in decibels (dB) of the measured
power referenced to one milliwatt (mW). It is used in radio and microwave equipment as
a convenient measure of absolute power because of its capability to express both very
large and very small values in a short form.
Compare dBW, which is referenced to one watt (1000 mW). Since it is
referenced to the watt, it is an absolute unit, used when measuring absolute power. By
comparison, the decibel (dB) is a dimensionless unit, used for quantifying the ratio
between two values, such as signal-to-noise ratio.
Zero dBm equals one milliwatt. A 3 dB increase represents roughly doubling the
power, which means that 3 dBm equals roughly 2 mW. For a 3 dB decrease, the power
11
is reduced by about one half, making −3 dBm equal to about 0.5 milliwatt. To express an
arbitrary power P as x dBm, or vice versa, the following equations may be used:
X=10log10(100P) or x=10log10P+30 and
P=10(x/10)/1000 or P=10(x-30)/10
Table 1. Relationship of dBm to power and application
dBm level
Power
Application
80 dBm
100 kW
Typical transmission power of FM and TV radio station with about a
31 mile range.
60 dBm
1 kW
Typical combined radiated RF power of microwave oven elements.
Approximate maximum RF output power from a ham
radio transceiver allowed.
50 dBm
100 W
Typical thermal radiation emitted by a human body. Typical
maximum output RF power from a ham radio HF transceiver.
40 dBm
10 W
Typical PLC (Power Line Carrier) Transmit Power.
37 dBm
5W
Typical maximum output RF power from a handheld ham radio
VHF/UHF transceiver.
36 dBm
4W
Typical maximum output power for a Citizens' band radio station
(27 MHz) in many countries.
33 dBm
2W
Maximum output from a UMTS/3G mobile phone (Power class 1
mobiles). Maximum output from a GSM850/900 mobile phone.
27 dBm
500 mW
Typical cellular phone transmission power. Maximum output from a
UMTS/3G mobile phone (Power class 2 mobiles).
20 dBm
100 mW
Bluetooth Class 1 radio. Maximum output power from
unlicensed AM transmitter per U.S. Federal Communications
Commission (FCC) rules.
−73 dBm
50.12 pW
"S9" signal strength, a strong signal, on the S-meter of a
typical ham or shortwave radio receiver.
−127.5 dBm
0.178 fW
Typical received signal power from a GPS satellite
−174 dBm
0.004 aW
Thermal noise floor for 1 Hz bandwidth at room temperature (20 °C)
12
See Table 1 for typical power levels. It provides an insight into the relationship of dBm
to power and application. Note the very wide power range in dBm that can be easily
expressed
Making Precision RF Power Measurements
Table 2. It shows calculations for power measurements using an ideal -30dB
sampler. Affordable samplers usually have a specification of -30dB +/- 1 db. A 1dB
error could have an effect on the measurement accuracy.
Table 2. Sine wave peak and average watts and dBm power, with a -30db sampler
Peak volts at
sampler In/Out
Peak volts at
sample port
(-30db)
Peak Power
Watts
Avg. Power
Watts
Power in
dBm
16
0.50
5
3
37.10
32
1.00
20
10
43.11
47
1.50
44
22
46.45
63
2.00
79
40
48.10
79
2.50
125
62
50.16
95
3.00
181
90
52.56
111
3.50
246
123
53.92
126
4.00
318
159
55.02
142
4.50
403
202
56.06
158
5.00
499
250
56.98
174
5.50
606
303
57.82
190
6.00
722
361
58.59
206
6.50
849
424
59.23
221
7.00
977
488
59.90
237
7.50
1123
562
50.51
253
8.00
1280
640
61.07
269
8.50
1447
723
61.61
285
9.00
1625
812
62.11
300
9.50
1800
900
62.55
316
10.00
1997
998
63.00
332
10.50
2204
1102
63.43
348
11.00
2422
1211
63.84
364
11.50
2650
1325
64.23
379
12.00
2873
1436
64.58
395
12.50
3121
1560
64.94
13
Consider an ideal sampler with a sample coefficient -30dB. That equates to a
voltage gain/loss of 31.62. Then consider a sampler that has a sample coefficient of
-31dB. That equates to voltage gain/loss of 35.48. Now consider a sampler with a
sample coefficient of -29dB. That equates to a voltage gain/loss of 29.18.
Table 3. Calculates power for each of these examples based only on the voltage
gain/loss, results in the following measurement uncertainty:
Table 3 Measurement uncertainty
-29dB
Ideal -30dB
-31dB
Voltage gain/loss
29.18
31.62
35.48
Calculated power
17.03 watts
20.00 watts
25.18 watts
Approximate Error
17%
0%
21%
For all practical purposes, a 1dB gain or loss in transmitted and or received
signals is insignificant and difficult to notice. However, when checking the accuracy of a
component in the transmitter chain or using the device as a “ham shack” standard,
measurement uncertainty is important. A 1dB error may be significant.
How to improve measurement accuracy
There are three practical ways to improve the accuracy. One expensive way is to
compare your power measurement to a laboratory standard. Another, lower cost
alternative is to purchase a sampler which was calibrated with NIST traceable
equipment. These samplers have the measured transfer coefficient i.e. -30dB stamped
on their enclosure. The third, and least expensive alternative, is to calibrate the sampler
yourself. You can do this assuming that your oscilloscope has accurately calibrated
vertical amplifiers.
See figure 7, a precise method to improve measurement accuracy is to measure
the sampler’s RF input voltage (usually with a 10X probe) and compare that
measurement to the sampler port output voltage (terminated into 50 ohms). The yellow
(top) trace is the sampler port output, and the blue (bottom) trace is sampler RF input.
To calculate the voltage gain/loss, using the Pk-Pk voltages will give greater resolution
14
than RMS voltage. That is because Pk-Pk voltages are greater. In our example, we
divide 152V/4.52V equals a measured voltage gain/loss of 33.62. From this we
determine that the sampler coefficient is -30.53dB, well within the samplers published
specification.
Figure 7 Sampler coefficient
Multiply the sampler port voltage by the sampling gain/loss value and plug it into
VRMS. In this case the sampler port voltage Pk-Pk is 4.52V. (The equivalent voltage on
the sampler RF input equals 4.52x33.62=152volts). This equals Pk-Pk volts, so we need
to calculate RMS:
(152×.707)/2 = 54.08 volts RMS
That’s pretty close to the measurement (54.7 volts) on our scope in figure 7. The
minor difference is attributed to the scope’s resolution and specification limits. Finally, to
calculate the power we use:
2
Pavg=(ERMS) /R resulting in
(54.08)2/50=58.5 wattsavg.
These types of calculations/measurement will be well within +/- 1% of the scope’s
specifications. This accuracy is better than that obtained by the +/- 1dB uncertainty.
15
Figure 8, Calibrated Sampler
See figure 8, attach a calibration label on the sampler “-30.01 dB, & 31.67 VRatio”. Now when you use the “calibrated” sampler, you’ll get accurate and consistent
results. Table 4, provides a quick way to look-up voltage gain/loss ratios given a sample
coefficient from 29dB to 31dB.
Table 4, dB versus voltage gain/loss
Coefficient (dB)
29.0
29.1
29.2
29.3
29.4
29.5
29.6
29.7
29.8
29.9
30.0
30.1
30.2
30.3
30.4
30.5
30.6
30.7
30.8
30.9
31.0
Voltage gain/loss
28.13
28.51
28.84
29.17
29.51
29.85
30.20
30.55
30.90
31.26
31.62
31.99
32.36
32.73
33.11
33.50
33.88
34.28
34.67
35.08
35.48
- end -
16
Application Note #5!
Return Loss Measurements
Measuring Return Loss with an oscilloscope and a Return Loss Bridge (RLB)
© Roger Stenbock W1RMS, revised 1/8/2013
An RF return loss bridge (RLB) is a wide band bridge which can be used to check the
impedance of antennas, coaxial cables, and filters, etc. The ARRL Handbook defines
return loss as:
“a measure of how closely one impedance matches a reference impedance in
phase angle and magnitude. If the reference impedance equals the measured impedance level with a 0°phase difference, it has a return loss of infinity.”
For Ham radio applications This impedance is usually 50-ohms. The INPUT port is normally connected to a test frequency (an RF oscillator or tracking generator from a spectrum analyzer). The DET (detector) is usually connected to an oscilloscope or spectrum
analyzer. A RLB is ideal for measuring filter response because return loss measurements are a more sensitive measure of pass band response than insertion-loss measurements.
Figure 1. Return Loss Bridge
An RF Return-Loss Bridge
Figure 1. The RLB-I (internal reference – three ports) is a high performance RLB. It is
carefully designed specifically for Ham radio applications. It uses a wide band 1:1 minia-
5-1
Application Note #5!
Return Loss Measurements
ture SMD 750 MHz transformer. The bridge reference resistors are precision 50 ohm
SMD devices. The circuit board employs computer optimized 50-ohm strip line technology.
How to measure return loss with an oscilloscope
There are a number of ways to measure return loss. The method described below relies
only on the accuracy of a low-cost step attenuator and removes the scope and signal
generator accuracy uncertainty.
Note: For maximum accuracy, the oscilloscope input impedance should be 50-ohms
(this may require an external 50-ohm feedthrough terminator) the step attenuator
should be 50-ohms and the signal generator should be 50-ohms as well.
Figure 2. Return loss measurement setup
5-2
Application Note #5!
Return Loss Measurements
1. See Figure 2 above. Apply the output of the signal generator to the RF INPUT
port of the RLB. It may be necessary to attenuate the generator output to avoid
overloading the device under test.
2. Connect the bridge DETECTOR port to an oscilloscope through a step attenuator
and leave the (DUT) port of the bridge open circuited.
3. Set the step attenuator for a relatively high level of attenuation of approximately
40 dB, and note the oscilloscope deflection.
4. Adjust the signal generator level and the oscilloscope vertical VOLTS/DIV setting
for a convenient six divisions of amplitude as observed on the oscilloscope display.
5. Now connect the unknown impedance of the device under test to the bridge DUT
port. The scope reading will decrease.
6. Adjust the step attenuator to produce the same reading obtained when the DUT
port was open circuit. The difference between the two measurements is the return loss, measured in dB (as taken from the attenuator setting).
Example: Assume the step attenuator initial setting was 40 dB with six divisions of
vertical signal displayed. After connecting the device under test to the DUT port, the
step attenuator has to be adjusted to 10 dB of attenuation in order to get as close to
six divisions of vertical deflection as possible. The difference between 40 dB and 10
dB is 30 dB. The return loss in this example is 30dB.
Accuracy Limitation
Since most low cost step attenuators have only 1dB of resolution, you may not be able
top exactly match the initial divisions of the displayed signal. Thus, the accuracy is limited to about 1 dB. If greater accuracy is required, a spectrum analyzer and or precision
RF power meter, or a very high accuracy oscilloscope may have to be employed.
5-3
Application Note #5!
Return Loss Measurements
Bridge Operation
By way of operation, the reference internal impedance (50-ohm) is compared to the
DUT impedance. If the impedances are exactly equal, than the detector output will be
essential zero (0). In practice this never happens. Most bridges have residual return
loss from 30-40 dB (1000-1 to about 10,000-1).
The unknown impedance measured by this technique is not limited to amplifier inputs.
Coax cables attached to a load, an antenna, a filter, or any other fixed impedance device can be characterized by return loss.
What is return loss
You may want to skip reading this section if all that interests you is the practical aspects
of measuring return loss. Thanks to feedback from our customers, clarification as to the
exact definition of return loss, particularly whether it should be expressed as a positive
or negative quantity is useful.
I believe that return loss when expressed as a relative quantity, such as a dB, is a positive quantity, and when expressed as power as in dBm, it can be either positive or negative regardless whether or not it is measuring an active or passive device.
Notwithstanding the foregoing, there are a number of experts such as Dr. Trevor S. Bird,
editor of the IEEE Antennas and Propagation Transactions, who have published articles
addressing the science behind return loss measurements. Yet confusion still prevails.
The internet provides a great deal of information, some of it questionable, so, for those
interested, I suggest they research this issue on their own and draw their own conclusion.
Nonetheless, Wikipedia defines return loss as follows:
“..In telecommunications, return loss is the loss of signal power resulting from the
reflection caused at a discontinuity in a transmission line or optical fiber. This discontinuity can be a mismatch with the terminating load or with a device inserted in the
line. It is usually expressed as a ratio in decibels (dB);
5-4
Application Note #5!
Return Loss Measurements
where RL(dB) is the return loss in dB, Pi is the incident power and Pr is the reflected
power. Return loss is related to both standing wave ratio (SWR) and reflection coefficient (Γ). Increasing return loss corresponds to lower SWR. Return loss is a measure of how well devices or lines are matched. A match is good if the return loss is
high. A high return loss is desirable and results in a lower insertion loss. Return loss
is used in modern practice in preference to SWR because it has better resolution for
small values of reflected wave.
Sign
Properly, loss quantities, when expressed in decibels, should be positive numbers.
However, return loss has historically been expressed as a negative number, and this
convention is still widely found in the literature. Taking the ratio of reflected to incident power results in a negative sign for return loss;
where RL'(dB) is the negative of RL(dB). Return loss is identical to the magnitude of
Γ when expressed in decibels but of opposite sign. That is, return loss with a negative sign is more properly called reflection coefficient. The S-parameter S11 from twoport network theory is frequently also called return loss, but is actually equal to Γ.
Caution is required when discussing increasing or decreasing return loss since these
terms strictly have the opposite meaning when return loss is defined as a negative
quantity...”
See figure 3 below. Remember, a dB is a relative value and dBm are actual power levels. dBM can be either positive or negative. When using a return loss bridge, the detector port displays the reflected power from a device under test. When displaying this
value on a spectrum analyzer, assuming the reference level is set to zero dBM, the reflected power from a device as measured from the detector port can very well be less
5-5
Application Note #5!
Return Loss Measurements
than zero dBm. As a result, negative values may be shown if the output power is less
than zero dBm. Remember, zero dBm is not zero power.
Figure 3. Reflected power expressed in dBm
You don’t have have to make these calculation manually. At the time of this writing
there were a number of online SWR and Return loss calculators available free on the
Internet. See below:
http://www.microwaves101.com/encyclopedia/calvswr.cfm
http://cgi.www.telestrian.co.uk/cgi-bin/www.telestrian.co.uk/vswr.pl
http://chemandy.com/calculators/return-loss-and-mismatch-calculator.htm
5-6
Application Note #5!
Return Loss Measurements
5-7
This is done by sampling the amplifier’s output
by using an RF sensor such as a sampler or
coupler.
Application Note #6
This
sensor
is
connected
to
the oscilloscope’s vertical (Y) input.
Ham Radio Station Monitor
The input of the amplifier is driven by a
Performance and Selection
transceiver which usually outputs less than
100W. Its output drives the input to the amplifier
© Roger Stenbock W1RMS 3/3/2012
and also a wide band demodulator which
The SMT Station Monitor and SMT-Pro Station
extracts the baseband from the modulated RF.
Monitor are ideal for monitoring the performance
of the entire transmitter chain for both AM and
It is this baseband that is connected to the
SSB operations. Selecting which SMT Station
oscilloscope’s horizontal (X) input. This display
monitor depends on your measurements needs.
yields
For basic monitoring of high power RF (QRO)
compares the
only,
is
amplifiers output. If the amplifier is linear without
recommended. If you want to monitor both high
any distortion and not overdriven, the trapezoid
power (CRO) and low power (QRP) with higher
pattern will be a linear undistorted triangular
precision than the SMT-Pro is recommend. This
waveform see Fig1. To rely on such a
discussion will give you some insight to help you
measurement, the demodulator and signal
make a more informed selection.
samplers must be linear and free of distortion.
than
the
SMT
Station
Monitor
a
trapezoid
pattern.
This
transceiver’s output
pattern
to
the
One of the best methods to monitor your station
is by observing the demodulated RF being
transmitted and or comparing the amplified RF
to the un-amplified RF from the transceiver. This
can be done with a trapezoid monitor and or two
tone tests.
The station monitor consists of a wide band
sampler, a high performance demodulator, a
variable base band output and an oscilloscope
Fig. 1 Trapezoid test pattern
trigger output, A linear RF amplifier generally
Most passive wide band demodulators employ
amplifies an RF signal from .5 – 5 Watts by
an envelope detector. This detector is an
30dB or more to about 500-1,500 Watts. Its
performance
and
modulation
characterized
using
a
spectrum
can
electronic circuit that takes a high-frequency
be
signal as input and provides an output which is
analyzer
the “envelope” of the original signal. Generally a
(expensive) or a low cost oscilloscope using a
diode rectifies the incoming signal, allowing
trapezoid display.
current flow in only one direction.
1
Most practical envelope detectors use either
maximum modulation depth of the carrier
half-wave or full-wave rectification of the signal
Unique diode bias circuit
to convert the AC audio input into a pulsed DC
One
signals. Filtering is then used to smooth the final
way
to
mitigate
this
undesirable
phenomena is to bias the diode such that it is
result. This filtering is rarely perfect and some
conducting throughout the 100% modulation
“ripple” is likely to remain on the envelope
envelope.
follower output, particularly for low frequencies.
The
SMT-Pro
Station
Monitor
incorporates such a bias currents source. See
More filtering gives a smoother result, but
Fig 3. This provides exceptional baseband
decreases the responsiveness; thus, real-world
linearity over a wide input range for precise
designs must be optimized for the application.
transmitter amplifier linearity measurements.
Low level detection
This discussion focuses on the trapezoid test
Another undesirable artifact is non-linearity of
technique. The RF sampler or RF coupler and
the detected baseband. This is caused by the
demodulator performance can impact the quality
diode’s conduction voltage drop ranging from .2
of the test
volt to .8 volt depending on the diode type
Note the clipping at low modulation levels (upper
and current. The diode does not linearly detect
trace) especially evident during the modulation
in this diminished conduction region. For high
trough. This phenomenon is caused by the
level RF envelopes this small region usually
inherent lack of the detector level bias current.
represents only a small percentage of the
envelope
and
can
be
ignored.
Fig. 3 Modulation envelope with bias
See Fig. 3 Note the demodulated product (upper
Fig. 2 Demodulator clipping no bias
waveform) clearly shows the improvement at the
See Fig 2. However, in low level RF envelopes
trough modulation level resulting from the
encountered with QRP operation, this region
represents
a
considerable
portion
of
addition of the detector level bias current option.
the
modulation envelope. As a result, the baseband
will exhibit significant non-linearity near the
2
Fig. 4 Demodulated sine wave without bias
Fig. 6 THD without bias
Fig. 4 Note the RF envelope (top waveform),
Fig. 6 Note the significant harmonic distortion
detected product (bottom waveform) without
(-24.4 db) levels resulting from modulation
bias current option. This is caused by the
through clipping without the detector bias option.
intrinsic lack of detector bias current at the
This is especially noticeable at low power level
modulation trough.
such QRP operation. At higher levels this effect
is significantly reduced.
Fig. 5 Sine wave modulation with bias
Fig. 7 THD with bias
Fig. 5 Note the lack of clipping at low modulation
levels
is
especially
evident
during
the
Fig. 7 Note the significantly reduced harmonic
modulation trough. This is the result of adding
distortion levels as a result of eliminating
low level detector bias current available on the
modulation through clipping with the detector
SMT-Pro option.
bias option. This is especially noticeable at low
power
level
such
QRP
operation.
At
higher levels this effect is significantly reduced.
The second harmonic distortion is down -31.2
dB.
At higher modulation levels of > 5watts,
second order harmonic distortion is -45 dB. All
other
modulation
eliminated.
3
products
are
virtually
power being measured, and P1 is the reference
to which P2 is being compared. To convert from
decibel
measure
P2/P1=10^(A/10).
back
Voltage
to
is
power
ratio:
more
easily
measured than power, making it generally more
convenient to use: A = 20*log10(V2/V1). Where
A=voltage ratio. The equation for obtaining
voltage ratio from dB is V2/V1 = 10^(A/20).
Thus, to obtain the equivalent voltage (Peak, PFig. 8 Pulse response
P, or RMS) for -30dB multiply the sampled
Fig. 8 This graph shows the modulated RF
voltage times 31.63. For example if the RMS
envelope
the
voltage at the sampler = 5 volts, than the actual
demodulated signal (upper trace). Note that the
RF RMS voltage at the sampler input would be
transition times easily meet the bandwidth
5×31.63=158.15. The power (P=E^2/R) would
specifications (10-30,000
be 500.2 Watts.
(lower
trace)
along
Hz)
with
there is no
spurious distortion ringing, overshoot present.
Fig. 10 The wideband graph of the sampler
output is shown here. While the nominal sampler
output equals is -30dB of the RF being sampled.
Fig. 9 Sampler bandwidth
Fig. 9 The nominal sampler output equals -30dB
of the RF being sampled. This is a power ratio
Fig. 10 2-150 MHZ bandwidth
reduction of 1000:1. This also equals a voltage
Here at 4MHz it is -30.75dB, and 21.91 dB at
ratio reduction of 31.623. Decibels state a power
144.53 MHz Again, the equation for obtaining
ratio, not an amount. They tell how many times
voltage ratio from dB is V2/V1 = 10^(A/20).
more (positive dB) or less (negative dB) a signal
Thus, -21 dB equals a voltage-ratio of 11.22 and
is but not how much more or less in absolute
the power ratio equals 125.89. To obtain the
terms.
Decibels
equivalent voltage (Peak, P-P, or RMS) for -21
For
dB, multiply the sampled voltage times 11.22.
example, 20 dB is not twice the power ratio of 10
For example, if the RMS voltage at the sampler
dB.
= 5 volts, than the actual RF RMS voltage at the
Use
are
this
logarithmic,
equation
not
to
linear.
find
decibels:
A = 10*log10 (P2/P1) (dB) where P1 is the
4
sampler input would be 5×11.22=56.1. The
power passing through the sampler is delivered
power (P=E^2/R) would be 62.9 Watts.
to the load.
Fig 11 Insertion loss with bias
Fig. 13 Spurious emissions
Fig. 11 Station monitor insertion loss without
Fig. 13 The graph of spurious emission of a
detector bias current option is show here. The
typical linear amplifier (Ameritron AL811H)
insertion loss (-.03dB at HF frequencies) is
passing through the SMT & SMT-Pro station
barely
current
monitor. Note, the worst case harmonic spurious
consumed by the detector only (a few micro
emission is -63.15 dB from the fundamental
amps). For practical purposes this loss can be
frequency of 14MHz. This is the residual
ignored since it equals a power radio of
spurious emission of the AL811H amplifier.
1.00693:1, so again, virtually all the power
Remarkably, when not overdriven, the AL811H
passing through the sampler is delivered to the
despite its ancient design, exhibits excellent
load.
spurious emission characteristics. The additional
measurable.
This
is
the
spurious emissions contributed by the station
monitor
measurements were
negligible.
It
should be noted that the power of these
spurious emission are at least 100 times (20dB)
better than the minimum allowed by the FCC:
§97.307 Emission standards (d) For transmitters installed after
January 1, 2003, the mean power of any spurious emission
from a station transmitter or external RF amplifier transmitting
Fig. 12 Insertion loss with bias
on a frequency below 30 MHz must be at least 43 dB below
Fig. 12 Station monitor insertion loss with
the mean power of the fundamental emission.
detector bias current option is show here. The
Most, if not, all of the foregoing oscilloscope
insertion loss (-.25dB at HF and 1dB at 200MHz)
measurements
is barely measurable. This is the current
can
be
made
with
an
inexpensive 30MHz oscilloscope. By using
consumed by the detector and its biasing current
appropriate accessories and techniques, the
supply (a few micro amps). For practical
ham radio operator can maximize the RF
purposes this loss can be ignored since it equals
transmitted signal performance.
a power radio of 1.059:1. Here, virtually all the
5
A p p l i c a t i o n
N o t e
Using TDR for
Measuring
Transmission
Lines in Ham
Radio
Installations
This application note reviews the elements of transmission line measurement in the ham radio
environment. It demonstrates how you can measure line impedance, return loss, SWR, velocity factor, distance to fault and line losses using pulse interrogation techniques. It focuses on the new preciseRF TDR-CableScout® pulse generator as a companion accessory to an oscilloscope.
Precision Ham Radio Measurements
File: Appnote#6 TDR measurements-1
5/20/2013
© 2013 Roger M. Stenbock W1RMS & preciseRF, all rights reserved
A p p l i c a t i o n
TDR Transmission Line Measurements
1. Transmission Lines!
N o t e
4
Ideal Transmission Line!
4
Line Losses!
4
2. TDR Basics!
5
Properly Terminated Line!
5
Open Line!
5
Shorted Line!
5
TDR Sensitivity!
6
Incident Pulse!
6
Reflected Pulse!
6
3. TDR Equipment!
7
Equipment Choices!
7
4. The TDR-CableScout ®!
8
TDR for Ham Radio!
8
TDR-CableScout ® Method!
9
Rise Time!
9
Effects of Rise Time on TDR Resolution!
10
5. TDR-CableScout ® Controls!
11
Display!
12
Step TDR Output!
12
Pulse TDR Output!
12
6. TDR Concepts and Terms!
13
The Reflection Coefficient!
13
Transmission Line and Load Impedance!
13
Return Loss of the Transmission Line!
13
VSWR of the Transmission Line!
13
Cable Losses of the Transmission Line!
14
2
A p p l i c a t i o n
TDR Transmission Line Measurements
N o t e
Gaussian Pulse Loss Measurements!
14
Summary!
15
7. Step-by-step TDR Measurements!
16
Reflection Coefficient, Return Loss, SWR and Zo Measurements!
16
Distanced to Fault (DTF) Measurements!
19
Velocity Factor Measurements!
21
Line Loss Measurements!
23
8. Common Transmission Line Faults!
26
TDR Sensitivities!
26
Ideal Line!
26
Inductive Fault!
26
Capacitive Fault!
26
Impedance Mismatch ZL > Zo!
27
Impedance Mismatch ZL < Zo!
27
ECB Trace Impedance Variations!
28
High Resolution Pulse TDR!
28
9. Zo Measurement by ZL Substitution!
29
The VZ500 Variable Terminator!
29
Adjust for Minimum Reflections!
29
Reading the RL Resistance!
29
10. Additional Information!
30
3
A p p l i c a t i o n
TDR Transmission Line Measurements
N o t e
1. Transmission Lines
Virtually all ham radio installations require
ter, transmission line and antenna (or resistive
some type of transmission line. The purpose of
load) quality. Their main disadvantage is that
a transmission line is to efficiently transfer RF
they do not provide information as to where the
energy from the transmitter to the transmitting
fault is located, nor do they indicate the fault
antenna, or conversely, efficiently transfer RF
type, such as defective cables loose, connec-
energy from the receiving antenna to the re-
tors or other problems. Fortunately, time do-
ceiver.
main reflectometry (TDR) provides more information. Wikipedia defines a transmission line
Ideal Transmission Line
as:
The ideal transmission line matches the
transmitter and antenna impedance precisely
“In communications and electronic en-
and delivers all input energy without losses.
gineering, a transmission line is a spe-
This usually occurs when all the power is
cialized cable designed to carry alter-
transmitted without reflections and or resistive
nating current of radio frequency, that
losses. Real-world transmission lines always
is, currents with a frequency high
have losses because either the source imped-
enough that their wave nature must be
ance (Zs) of the transmitter, the load imped-
taken into account. Transmission lines
ance (ZL) of the device receiving the energy
are used for purposes such as connect-
(usually the antenna) or the line impedance
ing radio transmitters and receivers with
(Zo) of the transmission lines are not matched.
their antennas, distributing cable sig-
Line Losses
nals, and computer network connec-
There are other losses such dielectric, re-
tions.”
sistive and reactive losses which affect the performance of the transmission line. Many times
these losses are due to manufacturing defects,
poor quality, inferior connectors, environmental
damage to the line such as UV radiation, moisture, physically kinked or broken cables, missmatched cable types or excessive cable length.
The goal is to insure that the transmission
line meets the expected performance requirements. In the ham radio applications, overall
transmission lines performance is usually
measured with SWR meters, return loss
bridges or RF samplers with station monitors.
These techniques work well and are low cost.
They provide an overall check of the transmit4
A p p l i c a t i o n
TDR Transmission Line Measurements
2. TDR Basics
N o t e
Since the pulse in transmission lines travels
at a certain speed (.66 to .90 times the speed
of light) depending on the cable type, it is possible to locate the reflection (fault) by measuring the round trip time and thus, locate the distance to the fault.
Open Line
See figure 3. The scope displays the inci-
Figure 1. Simple TDR set-up
dent pulse and any reflections. With an open
See figure 1. TDR principles are fairly easy
to master. Think of it as cable radar. A pulse
generator is connected via a “T” connection to
an oscilloscope’s high impedance input and a
pulse or step is injected (incident pulse) into the
cable. The pulse and any reflections are then
displayed on the oscilloscope for analysis.
Properly Terminated Line
Figure 3. Open cable
See figure 2. If the conductor is of a uniform impedance and is properly terminated, the
cable for example, which is a very high imped-
entire transmitted pulse will be absorbed in the
ance, increases in the impedance create a re-
far-end termination and no signal will be re-
flection that reinforces the original pulse.
flected toward the TDR. Any impedance dis-
Shorted Line
continuities will cause some of the incident signal to be sent back towards the source. This is
similar in principle to radar.
Figure 4. Shorted cable
See figure 4. A shorted cable, for example,
Figure 2. Terminated line
has very low impedance, it creates a reflection
that opposes the original pulse.
5
A p p l i c a t i o n
TDR Transmission Line Measurements
N o t e
TDR Sensitivity
Because of TDR’s sensitivity to impedance
variations, it may be used to verify cable impedance characteristics, splice and connector
locations, associated losses, and measure cable lengths.
Figure 6. The incident pulse
Reflected Pulse
The reflected signal, also called the reflected pulse, contains signals which are made
of reflections caused by the line impedance
(Zo) not matching the pulse generator source
impedance (Zs). The amplitude is measured as
Figure 5. Reflections
a deviation from the most positive level of the
See figure 5. By analyzing the pulse ampli-
incident pulse. This level can be either positive
tude, shape, and time, one can analyze the
or negative.
likely cause of the fault. In this example, the
See figure 7. This multiple exposure wave-
first reflection is negative going, indicating a
form shows the incident pulse (the first half of
decrease in impedance (most likely caused by
the screen), and the reflected signal of positive
a kinked cable). The second reflection is posi-
and negative values.
tive going, indicating an increase in impedance
(most likely caused by a defective connector or
braided shield failure).
Incident Pulse
See figure 6. The incident pulse is the
pulse applied to the device under test (DUT).
The amplitude is measured from the most
negative level (generally ground) to the most
positive level (excluding any aberrations not
Figure 7. Multiple exposure of Zo
variations
caused by reflections from the DUT).
6
A p p l i c a t i o n
TDR Transmission Line Measurements
3. TDR Equipment
N o t e
compromise and use an ordinary oscilloscope
and pulse generator and accept the limitations
The commercial communications industry
has long adopted TDR techniques to analyze
provided by this solution.
transmission lines. A TDR measurement of a
Equipment Choices
transmission line provides precise quantitative
The electronic practitioner who wishes to
data of the line performance and identifies any
make TDR transmission line measurements
faults.
basically has these options:
Specifically, TDR measurements provide
1.
information such as distance to fault (DTF),
If you have the money, buy a new TDR system such as the Mohr CT100, a Tektronix
TDR scope or Angilent TDR scope. Starting
at $18,000, these solutions are expensive,
but they have the latest software and work
well and have factory support.
reflection coefficient (p), transmission line impedance (Zo), return loss (RL), voltage standing wave ratio (VSWR), line length, line velocity
factor (Vf), cable dielectric and resistive losses
2.
at specific frequency and cable length. While
Buy a used TDR system from eBay. Good
price, but they may be difficult to get calibrated or serviced.
the measurement capability is impressive, the
3.
equipment costs are high and generally beyond
the reach of ham radio operators.
Compromise and use your scope, pulse
generator and your trusty calculator. This
works pretty well depending on your pulse
generator performance. This choice is low
cost, uses “T” connection, but has no low
impedance scope input capability (needed
for speed). All calculations must be done
manually.
Up until now, ham radio operators wanting
to make TDR measurements either had to
spend considerable money on a commercial
TDR oscilloscope and pulse generator with integrated samplers and TDR computers, or
7
A p p l i c a t i o n
TDR Transmission Line Measurements
N o t e
4. The TDR-CableScout ®
Recognizing the cost and performance limitations of the available choices, we created the
TDR-CableScout ®. It was designed to be affordable, yet provide laboratory level accuracy and
utility. TDR-CableScout ® takes
advantage of the fact that low
cost, high performance oscilloscopes are available from many
sources. When used with an oscilloscope of sufficient bandwidth,
measurements can be made rivaling those of commercial TDR sys-
features isolated high speed samplers and separate device
tems at a fraction of the cost.
under test (DUT) outputs. This design allows a direct, fast Tr
The TDR-CableScout ® in-
50 Ω connection to the oscilloscope for accurate TDR meas-
cludes a TDR computer because
urements without the inconvenience and lower performance
these scopes, while high enough
that the “T” connector solution offers.
in bandwidth (about 200MHz) do
A transmission line library is included. It contains data for
not have a TDR computer. This
velocity factor (Vf), line impedance (Zo) and line loss data.
requires the user to make all the
The integrated TDR measurement computer takes the work
calculations manually. While not
out of TDR measurements, such as time to fault (TTF), re-
difficult to do, they are neverthe-
flection coefficient (p), cable length, velocity factor (VF), line
less tedious. Conventional pulse
impedance (Zo), return loss (RL), SWR and cable loss.
generators do not have the very
fast rise time, selectable Zs and
duration rates best suited for TDR
work.
TDR for Ham Radio
The TDR-CableScout ® gives
hams the means to analyze
transmission lines and circuit
board strip lines. Line impedance
from 50 Ω to 600 Ω can be
measured with 25 ps resolution. It
The TDR-CableScout ® features both pulse and step
TDR. The step TDR has a maximum range of 15 KM and
time resolution of better than 1 ns. The pulse TDR features a
≤ 400 ps pulse width and ≤ 150 ps Tr.
The resolution is under 5mm, which is well suited for
analyzing circuit board strip lines. A dedicated trigger output
features a 100 ns pre-trigger to allow viewing of the TDR
pulse leading edge when using sampling scopes without a
delay line such as the 7S11 and 7T11 installed in legacy Tektronix 7000 scopes.
8
Application Note #6-1!
TDR Transmission Line Measurements
TDR-CableScout ® Method
The TDR measurement
set-up consists of the TDRCableScout ® pulse generator
and an oscilloscope. The pulse
generator provides all required
TDR pulses with the proper
amplitude and transition time
(Tr) and source impedance
(Zs). The scope displays the
resultant TDR waveform and
provides a means of measuring time and amplitude of these
pulses.
The user inputs voltage
The TDR-CableScout ® with scope option
and time values observed on
the scope, and the pulse generator computer provides
measurement results. The scope option shown above includes a 200 MHz Hantek DSO oscilloscope especially
selected for TDR measurements.
Rise Time
The scope should have a calibrated vertical amplifier
and calibrated time base. See figure 8. Three bandwidths
displays created with a bandwidth limiter are shown. The
scope bandwidth should be sufficiently high to identify reflections at the resolution needed for the application.
For short line distances and circuit board TDR, finer
time resolution is required. Resolution is a function of the
scope’s rise time (Tr). Bandwidth is directly related to Tr
and the commonly accepted mathematical relationship is
BW=.35/Tr. While some users have used scopes with
bandwidth as low 20 MHz, 100-200 MHz bandwidth
scopes will work for most ham radio applications.
Figure 8. Tr displays of 20, 100 and 200
MHz BW scopes
9
Application Note #6-1!
TDR Transmission Line Measurements
Effects of Rise Time on TDR Resolution
The scope’s rise time has a significant effect on TDR measurements are shown in figure 9. The
example is a TDR measurements of a 12 foot piece of RG 58 coax with a published velocity factor
(Vf) of .66 with the end open.
It demonstrates that this is about the shortest cable that can be tested with a 20 MHz scope. Note
that impedance variations are clearly visible in the 100 MHz and 200 MHz scope.
Figure 9. Scope rise time and bandwidth effects on TDR Measurement resolution
10
A p p l i c a t i o n
TDR Transmission Line Measurements
N o t e
5. TDR-CableScout ® Controls
See figure 10. Here is a depiction
of the TDR-CableScout ® pulse generator front panel and controls. Black is
used for labels, blue is for outputs and
green is for trigger functions. Green
LEDs indicate the state of the current
TDR mode and output impedance. The
controls are grouped into five sections,
Figure 10. The TDR-CableScout ® front panel
see tables 1 and 2.
Button
CABLE/Vf
Table 1. Key Description
Provides a cable selection from the library. Each cable includes the nomenclature, cable loss per 100 feet at 100 MHz,
cable impedance (Zo) and velocity factor (Vf). A selection of a
cable is used as a preset value for calculations performed by
the TDR computer.
Zo
Sets the source impedance Zs and step or pulse TDR selection. Zs impedance is 50 Ω, 75 Ω and 300 Ω suitable for line
impedance measurements ranging from 50 Ω to 600 Ω.
RANGE/
Selects TDR range and duration ranging from 15 KM (100 us
pulse width) to 75 Meter (500 ns pulse duration) in four
ranges. Maximum resolution is 10 ps (using pulse TDR).
DURATIO
N
CALC
Selects calculation of distance to fault (DTF), cable length,
velocity factor (Vf), reflection coefficient (p), return loss (RL),
SWR, and line loss per 100 ft at 100 MHz.
UP
Use the UP and DOWN key to scroll increasing or decreasing
numerical data or selectable items.
DOWN
Use the UP and DOWN key scroll increasing or decreasing
numerical data or selectable items. Also used to display additional calculation results.
ENTER
Completes a data entry or sub calculation or function.
Table 2 Displayed Prompt Convention
Whenever prompted by the return symbol press the ENTER
key to advance.
Whenever prompted by the down arrow, press the DOWN key
for additional measurement results.
11
Application Note #6-1!
TDR Transmission Line Measurements
Display
The display is a high contrast two line sixteen digit
backlit LCD display. See figure 11. It provides the state of
the current TDR function and shows various input and output conditions. It also indicates TDR measurement results.
Step TDR Output
Figure 11. LCD display
Pulse TDR Output
See figure 12. The Step TDR output con-
See figure 13. The DUT pulse output. The
sists of the DUT output and the scope output.
very fast pulse TDR is used to measure circuit
The pulse waveform duration and frequency is
board traces and line losses.
settable from 5 KHz to 1 MHz. They are accu-
The SMA outputs a pulse to the device un-
rately set by a crystal oscillator timebase.
der test (DUT) with a 400 ps pulse width, a Tr
of ≤ 150 ps and an amplitude of 2 V Pk-Pk.
When PULSE TDR is enabled the green LED
next to the DUT connector illuminates. The
maximum range is 1.5 KM, pulse width is 10 us
and the frequency is 50 KHz.
When using pulse TDR, the SMA connector
is intended for the DUT and the BNC connector
for the scope’s vertical input. To preserve the
high frequency detail, the scope vertical should
be terminated into 50 Ω.
Figure 12. Step TDR
This allows for TDR range measurements
from a few centimeters to 15 KM. Step TDR is
most useful for measuring reflection coefficient,
cable impedance (Zo), return loss (RL), voltage
standing wave ratio (VSWR) and distance to
fault. The source impedance (Zs) is calibrated
and selectable from 50 Ω, 75 Ω and 300 Ω,
using high speed SMA microwave relays set by
the on-board microprocessor.
Figure 13. Pulse TDR
12
A p p l i c a t i o n
TDR Transmission Line Measurements
6. TDR Concepts and Terms
N o t e
A ZL reading of zero (0) implies a short cir-
There are a number of primary TDR meas-
cuit. The reflected wave is equal to the incident
urements concepts terms. These are the reflec-
wave, but opposite in polarity. As seen below,
tion coefficient (p), distance to fault (DTF), ve-
the reflected wave negates part of the incident
locity factor (Vf) and line loss or cable loss.
wave. The ρ value is -1.
Some of these measurements also provide return loss (RL), line impedance (Z0), VSWR and
ρ = V reflected ÷ V incident
other parameters. What follows are the mathe-
= -V ÷ V = -1
matical relationships governing these meas-
When ZL is infinite, an open circuit is im-
urements:
plied. The reflected wave is equal to the inci-
The Reflection Coefficient
dent wave and of the same polarity. The reflected wave reinforces part of the incident
TDR measurements are based on a series
of impedance ratios. TDR measurements are
wave. The ρ value is +1.
described in terms of a reflection coefficient, ρ
Transmission Line and Load Impedance
(rho). The coefficient ρ is the ratio of the re-
The characteristic impedance Z0, or the
flected pulse amplitude to the incident pulse
load impedance Z0 can be calculated with the
amplitude:
value of ρ:
ρ = V reflected ÷ V incident
ZL = Z0 * (1+ ρ)÷(1-ρ)
For a fixed termination ZL, ρ can also be
Return Loss of the Transmission Line
expressed in terms of the transmission line
The return loss (RL) of a transmission line
characteristic impedance, ZO and the load im-
is a conversion of the reflection coefficient (ρ) to
pedance ZL.
dB. Return loss is expressed as a positive
ρ = V reflected ÷ V incident
number and can be calculated by the equation
as follows:
= (ZL -Z0) ÷ (ZL + Z0)
RL = -20 log 10 (ρ)
Representing a matched load, a short circuit and an open load, ρ has a range of values
VSWR of the Transmission Line
from +1 to —1, with 0 representing a matched
The voltage standing wave ratio (VSWR)
load. When ZL is equal to Zo, the load is
represents the ratio between the maximum and
matched. V reflected, the reflected wave, is
minimum amplitude of the standing wave.
equal to 0 and ρ is 0. There are no reflections:
VSWR can be calculated by the equation as
ρ = V reflected ÷ V incident
follows:
= 0 ÷V = 0
VSWR = (V max ÷ V min)
= 1+ ρ ÷ 1 - ρ
13
Application Note #6-1!
TDR Transmission Line Measurements
Cable Losses of the Transmission Line
tenuation per unit length is known for a particular frequency f1, the loss of any other frequency
Cable losses in the ham radio installation
are caused by several factors. While both con-
f2 can be calculated from the following equa-
ductor loss and dielectric loss occur, conductor
tion:
loss usually dominates. Conductor loss is
ƒ2 =
caused by the finite resistance of the metal
conductors in the cable which, due to the skin
where
effect, increases with frequency. The result of
this incremental series resistance is an appar-
ƒ1 (√ ƒ2÷ƒ1)
is loss in dB
Since the TDR-CableScout ® makes loss
ent increase in impedance as you look further
measurements using a very fast gaussian
into the cable. So, with long test cables, the
pulse, we can apply the above equation using a
DUT impedance looks higher than it actually is.
200 MHz scope for our measurements.
The second problem is that the rise time
See figure 14. The TDR-CableScout ® gen-
and settling of the incident pulse is degraded by
erates a pulse with a Tr of ≤ 150 ps and a pulse
the time it reaches the end of the cable. This
width of ≤ 400 ps. When the pulse is displayed
affects resolution and accuracy since the effec-
on a Tektronix 6 GHz DSO, the incident pulse
tive amplitude of the incident step is different
Tr of ≤ 150 ps Tr is clearly evident.
than expected. This amplitude inaccuracy does
not cause much error when the DUT impedance is close to 50 Ω, but for a larger or smaller
impedance, the error can be significant.
Loss per unit of length is generally provided
by the manufacturers. For example, RG 58
might be specified as 4.1 dB/100 feet. Given a
constant amplitude sine wave generator and a
known length of transmission line, one can
measure the actual loss per unit of length and
compare that to a specified cable length usually
given as dB/100 feet.
Figure 14. Gaussian pulse displayed on 6
GHz DSO
Gaussian Pulse Loss Measurements
One can make loss measurements using a
Given the relationship of BW=.35/Tr, we
TDR pulse generator with a fast enough pulse
see that .35 ÷ 150ps = 2.3 GHz. The maximum
Tr output by comparing the incident pulse am-
FFT frequency is about 2.3 GHz.
plitude to the reflected pulse amplitude.
See figure 15. When the same pulse is
Losses in a transmission line due to
viewed on a 200 MHz scope, the displayed
changes in frequency are proportional to the
pulse Tr and pulse width will be stretched and
square root of the frequency. Thus, if the at14
Application Note #6-1!
TDR Transmission Line Measurements
the amplitude is decreased. However, the gen-
erator measurement. This holds true as long as
erated Tr, width and amplitude are unchanged,
the measurement scope’s bandwidth is ≥ 2
it’s just that the scopes lower BW limit can’t
times the measurement parameter (loss @ 100
display them.
MHz). So, a 200 MHz scope will give reliable
results.
Not all secondary factors affecting cable
loss are taken into account using the gaussian
pulse cable loss measurement method. For this
reason, when making cable loss measurements
a normalized cable length gives the most accurate result. Sample cable lengths of 25-50 feet
give the best accuracy. However, for comparative cable loss testing, cables with identical
Figure 15. Gaussian pulse displayed
on 200 MHz DSO
length of just a few feet can be tested and high
measurement certainty can be achieved.
According to the ARRL on-line calculator,
the Tandy RG 58 coax is specified to have a
cable loss of 4.068 dB/100 feet, and at 2.2 GHz
the calculated loss is 26.66 dB /100 feet.
Using a Rigol DSA1030 laboratory spectrum analyzer, we measured an actual cable
loss of 5.2 dB/100 feet. At 2.2 GHz the measured loss was 21.3 dB /100 feet. The calculated
results are pretty close when compared to realworld cables measurements.
Fundamentally, the TDR-CableScout ®
makes the loss measurement at 2.2 GHz and
then calculates the loss at 100 MHz, using the
equation previously discussed:
ƒ2 =
where
ƒ1 (√ ƒ2÷ƒ1)
is loss in dB
Summary
Understanding the frequency contents of
gaussian pulses allows for measurements of
cable losses using pulses with equivalent results as a constant amplitude sine wave gen-
15
A p p l i c a t i o n
TDR Transmission Line Measurements
N o t e
7. Step-by-step TDR Measurements
This section explains how to make TDR measurements using the TDR-CableScout ® measurement computer (accessible by using the CALC key). In each example you will be shown how to connect the scope and the DUT to the TDR-CableScout ®. Examples of the TDR-CableScout ® display
and scope display are shown. Since the DUT transmission lines and cables you will be using are
most likely different than the examples shown, your measurement results will reflect the actual cables
you will be testing. The following examples are covered:
1. Reflection Coefficient, Return Loss, SWR and Zo Measurements.
2. Distanced to Fault (DTF) Measurements.
3. Velocity Factor Measurements.
4. Line Loss Measurements.
Reflection Coefficient, Return Loss, SWR and Zo Measurements
Hams worry about VSWR, and for good reason. Most transmitters do not tolerate a mismatched
load with a VSWR > 2:1, and power that is supposed to go to the antenna is lost as heat. As previously discussed, VSWR is directly related to the reflection coefficient (ρ), return loss (RL), and line
impedance (Zo). Using TDR to measure ρ, we get all four parameters in one measurement. See the
step-by-step instructions below:
Reflection Coefficient
Measurements Steps
Scope Display
1. Using the Zs key, set the
TDR-CableScout ® to STEP
TDR and the appropriate Zs
(Usually 50 Ω).
16
Application Note #6-1!
TDR Transmission Line Measurements
Reflection Coefficient
Measurements Steps
Scope Display
2. Connect the Step TDR
SCOPE OUT to the scope
input, use a 50 Ω
feedthrough terminator. Set
the scope for the display
shown.
3. Using the CALC key, select the Calc. Reflection Coefficient (p) function.
4. Connect the cable to be
tested to the DUT output.
Adjust the scope to show
both the incident pulse and
the reflected pulse.
5. Adjust your scope for
about 6 divisions amplitude.
Measure the incident pulse
Pk-Pk amplitude.
17
Application Note #6-1!
TDR Transmission Line Measurements
Reflection Coefficient
Measurements Steps
Scope Display
6. Measure the reflected
pulse Pk-Pk amplitude.
7. Press the ENTER key.
The reflection coefficient will
be displayed. Press the
down key for additional results.
8. Results for Zo, return loss
and SWR will be displayed.
18
Application Note #6-1!
TDR Transmission Line Measurements
Distanced to Fault (DTF) Measurements
While it is good to know the reflection coefficient, return loss and VSWR, if there is a problem, it
would be helpful to know where in the line the problem is located. Fortunately, if we know the cable
type and its velocity factor (Vf), we can locate the fault quite easily. The Vf is a part of the cable specification. If you don’t know the Vf, it can also be measured with the TDR-CableScout ®. See the stepby-step instructions below:
Distance to Fault
Measurements Steps
Scope Display
1. Using the Zs key, set the
output to STEP TDR and the
appropriate Zs (usually
50 Ω).
2. Select the cable from the
cable library using the
CABLE/Vf key. If the cable is
not found, set the Vf during
the DTF measurement.
3. Using the CALC key, select
the Calc. Reflection Coefficient (p) function.
4. Confirm the Vf of your cable or set the desired value.
19
Application Note #6-1!
TDR Transmission Line Measurements
Distance to Fault
Measurements Steps
Scope Display
5. Connect the cable to be
tested to the DUT output.
Adjust the scope to show both
the incident pulse and the
reflected pulse.
6. If the reflected pulse is not
displayed, change the range
with the RANGE/DURATION
key.
7. Press the ENTER Key.
Measure the delta time from
the incident to the reflected
pulse. Enter this value into
TDR-CableScout ®.
8. The distance to fault is
displayed
20
Application Note #6-1!
TDR Transmission Line Measurements
Velocity Factor Measurements
The velocity factor (Vf), also called wave propagation speed or velocity of propagation (VoP) of a
transmission medium is the speed at which a wavefront of an electromagnetic signal or a change of
the voltage on a wire passes through the medium, relative to the speed of light.
See table 3. The speed of radio signals in a vacuum, for example, is the speed of light and so the
velocity factor of a radio wave in a vacuum is unity (1) , or 100%. In electrical cables, the velocity factor mainly depends on the insulating material.
Vf
Transmission line
0.95 0.99
Open-wire “ladder” line
0.80
Belden 9085 twin lead
0.82
RG-8X Belden 9258 coaxial cable (foamed polyethylene dielectric)
0.66
RG-213 RG-58 coaxial cable (solid polyethylene
dielectric)
Table 3. Typical velocity factors (Vf) of transmission lines
The use of the terms velocity of propagation and wave propagation is confined to transmission
lines and cables. In a ham radio and engineering context, these terms would be understood to mean
a true speed or velocity in units of distance per time. Since Vf affects the accuracy of distance to fault
measurements, a means to measure Vf is provided. See the step-by-step instructions below:
Velocity Factor
Measurements Steps
Scope Display
1. Using the Zs key, set the
TDR-CableScout ® to STEP
TDR and the appropriate Zs
(usually 50 Ω).
2. Select the measurement
choice for Vf using the CALC
key.
21
Application Note #6-1!
TDR Transmission Line Measurements
Velocity Factor
Measurements Steps
Scope Display
3. Select Units, Meters or
Feet.
4. Set the known cable
length using the up and
down keys.
5. Connect the cable to be
tested to the DUT output.
Make sure the cable is open
at the other end.
Adjust the scope to display
both the incident pulse and
the reflected pulse.
6. Measure the delta time
from the incident to the reflected pulse. Enter this
value into the TDR-
CableScout ®
7. Press ENTER. The velocity factor (Vf) is displayed - in
this case it is .675. That’s
pretty close to the published
value of .66.
22
Application Note #6-1!
TDR Transmission Line Measurements
Line Loss Measurements
Line loss or cable loss is a function of frequency and the length of the cable. It is expressed in dB
loss for a given length at a specific frequency. Doubling the length doubles the loss in dB. However,
doubling the frequency does not double the loss as the losses in a transmission line due to changes
in frequency are proportional to the square root of the frequency. The greater the frequency and
length, the greater the loss.
Line loss is a published specification provided by the cable manufacturer. A fundamental contributor to line loss is the dielectric. Dielectric quality and condition can change over time due to environmental conditions such as moisture and mechanical stress. It is not uncommon for cables that have
been in service a number of years to have increased line losses. If you want to transfer the maximum
power from your transmitter to the antenna, a measurement of line loss is important. See the step-bystep instructions below:
Line Loss Measurement
Steps
Scope Display
1. Using the Zs key, set the
TDR-CableScout ® to pulse
TDR.
2. Using the CALC key, select Cable Loss measurement.
3. Connect the PULSE TDR
SCOPE OUT to the scope
input using a 50 Ω
feedthrough terminator. Set
the scope for the display
shown.
23
Application Note #6-1!
TDR Transmission Line Measurements
Line Loss Measurement
Steps
Scope Display
4. Select Units, Meters or
Feet.
6. Set the Cable Length.
5. Connect the cable to be
tested to the PULSE TDR
DUT OUT. Adjust the scope
to show both the incident
pulse and the reflected
pulse.
7. Using your scope cursors,
measure the incident pulse
Pk-Pk amplitude. Enter this
value into the TDRCableScout ®.
24
Application Note #6-1!
TDR Transmission Line Measurements
Line Loss Measurement
Steps
Scope Display
8. Using your scope cursors,
measure the reflected pulse
Pk-Pk amplitude. Enter this
value into the TDRCableScout ®.
9. The cable loss is shown
on the display.
25
A p p l i c a t i o n
TDR Transmission Line Measurements
8. Common Transmission Line Faults
N o t e
The ideal line does not exist in reality.
There are always some faults; they may be
In this section we’ll take a look at common
line faults and what they look like on the oscil-
small but they are there. In the following exam-
loscope. This will help you pin-point the source
ples, I have purposely induced larger errors to
of the problem and how to fix it.
better illustrate the concept.
Common transmission line problems are:
Inductive Fault
1. Defective shield
See figure 17. In this example, there is an
2. Pinched cable
inductive component in part of the line. This
3. Line mismatches
may occur when the shield has been compromised or a connector is defective.
4. Faulty connectors
5. Circuit board trace mismatches
TDR Sensitivities
We know that TDR basically measures only
two parameters, impedance and time. They are
changes in impedances at a given time in the
line.
Ideal Line
See figure 16. Assume the ideal condition
where Zs = Zo = ZL. Here, all the energy is absorbed by ZL and there are no reflections.
Figure 17. Faulty transmission line
Zo contains an inductive
component in series
Capacitive Fault
See figure 18. In this example, there is a
capacitive component in part of the line. This
may occur when the shield has been pinched
close to the center conductor in a coaxial
transmission line or the line is defective or the
loss is due to the dielectric having a localized
defect.
Figure 16. Ideal Transmission Line
Zs=Zo =ZL
26
A p p l i c a t i o n
TDR Transmission Line Measurements
N o t e
nected to a section of RG 59 75 Ω coax and
then further connected to a section of RG 58.
This problem is quite common and can result in
unexpectedly high VSWR conditions.
Impedance Mismatch ZL < Zo
See figures 20 and 21. In this example,
there is an impedance mismatch in part of the
line.
Figure 18. Faulty transmission line
Zo contains a capacitive
component to ground.
Impedance Mismatch ZL > Zo
See figure 19. In this example, there is
an impedance mismatch in part of the line.
Figure 20. Mismatched transmission Line Zo<ZL=Zs
This may occur when line impedances with
differing Zo are connected in series. I purposely
set Zs to 75 Ω. In this case, a piece of RG 59
50 Ω coax was connected
to a section of RG 58 75
Ω coax and then further
connected to a section of
RG 59. This problem is
quite common and can
Figure 19. Mismatched transmission Line Zo>ZL=Zs
result in unexpectedly
high VSWR conditions.
This may occur when line impedances with
differing Zo are connected in series. In this
case, a piece of RG 58 50 Ω coax was con-
27
Figure 21. Zs set
to 75 Ω
A p p l i c a t i o n
TDR Transmission Line Measurements
N o t e
ECB Trace Impedance Variations
See figure 22. In the following example, a
circuit board trace was examined for correct
strip line design. The scope display clearly
shows the impedance variations. The positive
going Zo indicates trace width over a ground
plane which is narrow (higher impedance)
and the negative going variations indicate
trace width which are wider (lower impedance).
As a starting point, some microwave engineers use .125” trace width over a ground
plane to achieve a Zo of 50 Ω over Fiber Re-
Figure 22. ECB strip line impedance variations
inforced Plastic (FRP-4) PCB material.
High Resolution Pulse TDR
See figure 23. The fast Tr ≤ 150 ps pulse
allows for very high resolution measurements.
The length of an SMA connector clearly reveals itself. A TDR measurement of an SMA
cable with a Vf of .66 with one end open displays a major reflection at 9.88 ns.
This cable is 38.5 inches in length. The
aberrations on the trailing edge are the reflections caused by the connector. Note a cable
loss of 10 dB at the 2.2 GHz (the equivalent
FFT frequency of the incident pulse). It has
been my experience that when displayed on a
high bandwidth scope, Zo changes in distance of just a few millimeters are clearly ob-
Figure 23. Detail of high resolution
TDR measurement when viewed on a
Tektronix TDS 820 6 GHz DSO
servable.
28
A p p l i c a t i o n
TDR Transmission Line Measurements
N o t e
9. Zo Measurement by ZL Substitution
See figure 24. We know that if ZL = Zo
there will be no reflections. So, if we could
somehow measure ZL, we would know the line
impedance Zo.
Figure 24. Zo terminated with
variable ZL
Figure 26. RG 59 cable
connected to variable ZL
Reading the RL Resistance
The VZ500 Variable Terminator
See figure 27. After confirming that RL
See figure 25. An adjustable ZL VZ500 is
VZ500 resistor has been adjusted for minimum
nothing more than a 500 Ω variable resistor
which can be adjusted to match the line Zo.
The only requirement is that it have low series
inductance and low shunt capacitance.
Figure 27. Measurement
results of RG 59 cable
Figure 25. VZ500 variable
terminator
reflections, remove it from the cable end and
measure the DC resistance with an ordinary
Adjust for Minimum Reflections
ohm meter. In this example, we see that it
reads 74 Ω. That is very close to the line’s 75 Ω
See figure 26. We have connected the
impedance.
VZ500 variable resistor to a length of RG 59
75 Ω cable and adjusted VZ500 for minimum
reflections as observed on the oscilloscope
display.
29
A p p l i c a t i o n
TDR Transmission Line Measurements
N o t e
10. Additional Information
James A. Strickland, Allen Zimmerman, Gordon Long and George Frye, all from Tektronix at the
time, wrote a comprehensive Measurement Concepts paper, “TIME-DOMAIN REFLECTOMETER
MEASUREMENTS” in the late 1960’s. It is still considered the authoritative reference despite it being
more than 40 years old. Of all the papers and information I researched in preparation of this application note, I found it to be most enlightening and fairly easy to read and understand.
http://www.davmar.org/TE/TekConcepts/TekTDRMeas.pdf
If you are into home-brewing circuit board level projects, this application note entitled, “Time Domain Methods for Measuring Crosstalk on PCB Quality Verification” will help you layout your circuit
board traces for best-high frequency performance.
http://www.coe.montana.edu/ee/lameres/courses/eele461_spring12/information/TDR_AppNote_T
ektronix_Xtalk_11499_EN.pdf
A detailed discussion is also available at the ARRL website:
http://www.arrl.org/files/file/Technology/tis/info/pdf/q1106037.pdf
http://www.arrl.org/files/file/Technology/tis/info/pdf/9706057.pdf
CPU and firmware: Rob Kirkpatrick KI6HNA
Microwave & Analog design: Roger Stenbock W1RMS
Precision Ham Radio Measurements
22781 Airport Rd NE Suite D-1
Aurora, Oregon 97002 Phone: (503) 915-2490
www.preciserf.com Email: [email protected]
See www.preciseRF “Calibration” page for more info. Specifications and prices subject to change without notice (c) 2013 preciseRF all rights reserved. file: 2013 PRICELIST
30
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