Voltage and Power Measurement - Fundamentals, Definitions, Products

Voltage and Power Measurements
Fundamentals, Definitions, Products
60 Years of Competence in
Voltage and Power Measurements
RF measurements go hand in hand
with the name of Rohde & Schwarz.
This company was one of the founders
of this discipline in the thirties and has
ever since been strongly influencing it.
Voltmeters and power meters have
been an integral part of the
company‘s product line right from the
very early days and are setting standards worldwide to this day.
Rohde & Schwarz produces voltmeters
and power meters for all relevant frequency bands and power classes covering a wide range of applications.
This brochure presents the current line
WF 40802-2
of products and explains associated
fundamentals and definitions.
Contents
RF Voltage and Power Measurements
using Rohde & Schwarz Instruments
3
RF Millivoltmeters
6
Terminating Power Meters
7
Power Sensors for URV/NRV Family
8
Voltage Sensors for URV/NRV Family
9
Directional Power Meters
10
RMS/Peak Voltmeters
11
Application:
PEP Measurement
12
Peak Power Sensors for
Digital Mobile Radio
13
Fundamentals of RF Power
Measurement
14
Definitions of Voltage
2
Voltage and Power Measurements
and Power Measurements
34
References
38
RF Voltage and Power Measurements
The main quality characteristics of a
parison with another instrument is
The frequency range extends from DC
voltmeter or power meter are high
hampered by the effect of mismatch.
to 40 GHz. Several sensors with differ-
measurement accuracy and short
Rohde & Schwarz resorts to a series of
ent frequency and power ratings are
measurement time. Both can be
measures to ensure that the user can
required to cover the entire measure-
achieved through utmost care in the
fully rely on the voltmeters and power
ment range. The Rohde & Schwarz
design of the probe or sensor and
meters supplied:
sensors feature built-in calibration
data memories and temperature sen-
through the use of microprocessors for
computed correction of frequency
– Preaging of basic units and sensors in
sors to ensure that the measuring
response, temperature effect and line-
temperature tests lasting several days
instruments are calibrated and ready
arity errors.
with monitoring of the drift and aging
for use immediately after the sensor is
to identify unstable components
plugged in. Manual calibration, a
– High-quality RF connectors to ensure a
Measurement accuracy
Two factors are decisive for the accuracy of power measurements: the pre-
potential error source, is thus avoided.
constantly low SWR
– In-depth self-testing upon switch-on
and during measurements
The calibration-data memory contains
all the relevant information required to
produce accurate results, plus the sen-
cision of sensor calibration and the
sor-specific data like serial number,
degree of sensor matching to the
device under test. A great amount of
Operation
type and calibration date as well as
hardware and software is involved
In many applications, operating the
the permissible measurement and fre-
especially in calibration. To ensure
Rohde & Schwarz voltmeters and
quency ranges. It is merely the fre-
that the calibration standards for the
power meters just means connecting
quency of the current measurement
URV/NRV sensors (see pages 8/9)
the DUT and selecting the display
that has to be entered on the meter
comply with the stringent require-
mode for the result. Fast autoranging
which will then automatically scan the
ments, many of them are compared
and a digital averaging filter matched
data memory for the relevant calibra-
directly with the primary standards at
to the measurement range ensure opti-
tion factors and perform any required
the German Standards Laboratory
mally worked out results. Individual
interpolation (see also page 21).
(PTB).
settings can be made either via the
menu or by direct key entry. All infor-
Each sensor can be used with any of
Measurement errors due to mismatch
mation required on the instrument sta-
the basic units of the URV/NRV series,
are in practice the main source of
tus (range hold, zero, etc) is displayed
ie voltage and power measurements
error (see page17 ff). Therefore the
in plain text or using easy-to-under-
are possible with one and the same
power sensors of the NRV-Z series are
stand symbols.
instrument – with equally high accuracy.
not only carefully calibrated but also
optimized for minimum SWR.
The displays with digital reading feature in addition a quasi-analog bargraph indicator with selectable scale
Reliability
to immediately show the user instanta-
Even a top-quality measuring instru-
neously the trend in signal variations.
ment may fail, either due to obvious
Level Meter URV 35 combines a
functional faults or – with severe con-
pointer instrument with an LCD scale.
sequences – out-of-tolerance conditions that remain unnoticed. An
increase in the measurement uncer-
Individually calibrated and sensors
tainty is very difficult to detect in par-
The sensors of the URV5/NRV-Z family
ticular with power meters, since there
permit direct measurement of voltages
are no reference instruments which
between 200 µV and 1000 V and of
are much more accurate and any com-
powers between 100 pW and 30 W.
Voltage and Power Measurements
3
Power Meters
Depending on the application, there
Diode sensors feature a higher sensi-
are two types of power meters:
tivity; their power measurement range
Directional power meters
starts at about 100 pW. Since they
... are inserted into an RF line and
are able to measure true RMS power
measure the magnitude of the forward
nected to the output of a source,
down to 10 µW, they may even be
and reverse wave separately with the
absorb the wave incident on the
used for signals with harmonic con-
aid of a directional coupler. Direc-
sensor and indicate the power of
tents, noisy or modulated signals.
tional Power Meters NRT and NAS
– Terminating power meters are con-
can then be used to determine the
this wave.
Diode sensors with an integral 20 dB
transmitter output power and the
nected between source and load
attenuator fill the gap between pure
antenna or load matching in all stand-
and measure − practically with no
diode sensors and thermal sensors.
ard communication bands up to
loss − the power of the forward and
They provide true RMS measurements
4 GHz and for transmitter powers up
reflected wave.
in a range up to 1 mW and satisfy the
to the kilowatt range. Due to the low
most exacting requirements on meas-
insertion loss of the sensors, the power
urement speed even for levels between
meter can remain connected to the
10 and 100 µW, where the use of
transmitter for continuous monitoring.
thermal sensors is limited.
Special sensors with peak weighting
– Directional power meters are con-
Terminating power meters
Depending on the principle of opera-
are available for measuring pulsed
tion, the RF power is either converted
Peak power sensors contain a peak
signals such as in modern digital radio
into heat or measured with the aid of
hold circuit for measuring the peak
networks (see page 10).
diode rectifiers.
envelope power (PEP). They enable
direct measurement of pulsed signals
NRT-Z43 and NRT-Z44 take a special
The thermal sensors from R&S open up
with a pulse width from 2 µs, eg of the
place among the directional power
a wide power range from 1 µW to
TV sync pulse peak power or the
sensors from Rohde & Schwarz. These
30 W. Irrespective of the waveform,
power of TDMA radio signals. In the
sensors can be operated even without
they measure with extremely high
range from 1 µW to 20 W these sen-
basic power meter on any PC under a
accuracy the RMS value over the full
sors are a value-for-money alternative
Windows user interface. They can be
range and are thus easy to use. Sig-
to special peak power meters.
connected via a standard serial (RS-
nals with harmonic contents or modu-
232) or PC Card interface adapter.
lated and complex signals do not
cause any additional measurement
errors. Moreover, the R&S models
feature an unrivalled linearity.
Evolution in power measurements:
Directional Power Sensor NRT-Z44
as a self-contained measuring
instrument that can be connected
to every PC
WF 42665
4
Voltage and Power Measurements
Voltmeters
The sensors for the RF voltmeters from
Rohde & Schwarz function similarly
Which is the best?
like diode power sensors. A diode
Both methods – RF voltage and power
rectifier in the sensors changes the
measurement – have their merits and
unknown AC voltage into DC voltage.
drawbacks. Users of Rohde &
This DC voltage is processed in the
Schwarz Voltmeters URV 35 and
basic unit (the rectifier characteristic
URV 55 or Terminating Power Meters
being linearized by the microproces-
NRVS and NRVD however do not
sor through correction) and indicated.
have to make a decision: as pointed
Voltmeters operating on this principle
out before, all voltage and power sen-
use the square weighting of the diode
sors of the URV5-Z and NRV series can
rectifier to measure the RMS value of
be connected to any of the available
small voltages up to about 30 mV (or
meters with no loss in accuracy. This
higher with divider) and the peak or –
unique concept allows universal use of
if a full-wave rectifier is used – the
any model for the whole range of RF
peak-to-peak value of voltages above
measurements.
WF 39821
1 V. Due to linearization the meter
reads the RMS value of a sinewave in
the entire measurement range.
The RF probe is indispensable for
measurements on non-coaxial circuits
and components. Small input capacitance and low losses enable low-load
measurements directly in the circuit.
Dividers increase the voltage measurement range and minimize the loading
Probes and insertion units being used in RF
voltage measurements
of the DUT.
RF insertion units are used for voltage
measurements in coaxial circuits. They
incorporate a diode rectifier connected to the inner conductor or to a
coaxial divider and permit broadband
measurements to be made up to
3 GHz with low reflection coefficient.
Given matched conditions, these insertion units can also be used for practically no-loss measurements of RF
power. To avoid confusion with the
insertion units of directional power
meters, they are also referred to as
coaxial voltage probes.
WF 43230
Voltage
and
Power
Measurements
Voltage
and
Power
Measurements
5 5
WF 43229
RF Millivoltmeters
Level Meter
URV 35
RF Millivoltmeter
URV 55
The name of the URV 35 already
RF Millivoltmeter URV 55 fitted with
implies its dual use as a versatile volt-
IEC/IEEE bus is intended for use in labs
meter and power meter. It is suitable
or in test systems. All parameters like
for mobile applications (battery-
averaging filter, display resolution and
powered model), system-compatible
measurement rate can be set manually
via the RS-232-C interface and it fea-
with a minimum of effort. Fully auto-
tures a unique combination of analog
matic measurement is of course possi-
and digital display, the scale of the
ble.
moving-coil meter being superimposed on an LCD display – with the
URV 55 features a wide range of sen-
appropriate indication range automat-
sors for all fields of RF voltage and
ically selected, of course.
power measurement and has a twin
brother in power measurements, ie
• DC to 40 GHz
Power Meter NRVS.
• Voltages from µV to kV
• Powers from pW to kW
• DC to 40 GHz
• AC-supply or battery powering
• Voltages from µV to kV
• Menu-guided operation
• Powers from pW to kW
• Selectable scaling
• IEC/IEEE bus
• Frequency-response correction
• Frequency-response correction
• Attenuation correction
• Attenuation correction
• Analog output
• Averaging filter, automatic/manual
• Test generator 1 mW/50 MHz
• Analog output
(optional)
• Test generator 1 mW/50 MHz
(optional)
6
Voltage and Power Measurements
WF 43224
Terminating Power Meters
Power Meter
NRVS
Dual-Channel Power Meter
NRVD
A high-precision test generator is fitted
Power Meter NRVS – the twin brother
NRVD is the high-end instrument
add-on devices.
of RF Millivoltmeter URV 55 – is the
among the Rohde & Schwarz power
standard instrument for RF power
meters and voltmeters. Two fully inde-
• DC to 40 GHz
measurements in laboratory and sys-
pendent channels, the simultaneously
• Powers from pW to kW
tem applications.
measured values of which can be ref-
• Voltages from µV to kV
erenced to each other, enable the
• Two independent channels
• DC to 40 GHz
NRVD to perform many relative meas-
• IEC/IEEE bus to SCPI
• Powers from pW to kW
urements eg of attenuation and reflec-
• Frequency-response correction
• Voltages from µV to kV
tion (with the aid of a directional cou-
• Attenuation correction
• IEC/IEEE bus
pler or SWR bridge).
• Averaging filter, automatic/manual
• Frequency-response correction
as standard for checking the sensors
as well as for measuring and adjusting
• Test generator 1 mW/50 MHz
• Attenuation correction
The IEC/IEEE-bus command set of the
• Averaging filter, automatic/manual
NRVD is in line with the SCPI stand-
• Analog output
ard. Additional inputs/outputs
log outputs, trigger input and
• Test generator 1 mW/50 MHz
enhance the range of system applica-
ready output
(optional)
fitted as standard
• Optional DC frequency input, ana-
tions.
Voltage and Power Measurements
7
Power Sensors for the URV/NRV Family
100 W
10 W
1W
100 GHz
100 mW
10 GHz
10 mW
1 GHz
1 mW
100 MHz
100 µW
10 MHz
10 µW
1 MHz
1 µW
100 kHz
100 nW
10 kHz
10 nW
1 kHz
1 nW
100 pW
DC
NRV-Z1
NRV-Z1
NRV-Z2
NRV-Z3
NRV-Z4
NRV-Z5
NRV-Z6
NRV-Z15
NRV-Z31
NRV-Z32
NRV-Z33
NRV-Z51
NRV-Z52
NRV-Z53
NRV-Z54
NRV-Z55
8
-Z2
-Z3
-Z4
-Z5
Diode Power Sensor 50 Ω
200 pW to 20 mW, 10 MHz to 18 GHz
Diode Power Sensor 50 Ω
20 nW to 500 mW, 10 MHz to 18 GHz
Diode Power Sensor 75 Ω
100 pW to 13 mW, 1 MHz to 2.5 GHz
Diode Power Sensor 50 Ω
100 pW to 20 mW, 100 kHz to 6 GHz
Diode Power Sensor 50 Ω
10 nW to 500 mW, 100 kHz to 6 GHz
Diode Power Sensor 50 Ω
400 pW to 20 mW, 50 MHz to 26.5 GHz
Diode Power Sensor 50 Ω
400 pW to 20 mW, 50 MHz to 40 GHz
Peak Power Sensor 50 Ω
1 µW to 20 mW, 30 MHz to 6 GHz
Peak Power Sensor 50 Ω
100 µW to 2 W, 30 MHz to 6 GHz
Peak Power Sensor 50 Ω
1 mW to 20 W, 30 MHz to 6 GHz
Thermal Power Sensor 50 Ω
1 µW to 100 mW, DC to 18 GHz
Thermal Power Sensor 50 Ω
1 µW to 100 mW, DC to 26.5 GHz
Thermal Power Sensor 50 Ω
100 µW to 10 W, DC to 18 GHz
Thermal Power Sensor 50 Ω
300 µW to 30 W, DC to 18 GHz
Thermal Power Sensor 50 Ω
1 µW to 100 mW, DC to 40 GHz
Voltage and Power Measurements
-Z6
-Z15
-Z31
-Z32
-Z33
-Z51
-Z52
-Z53
-Z54
-Z55
Power measurements of highest sensitivity up to
18 GHz in 50 Ω systems
Power measurements with minimum mismatch, for
high powers in 50 Ω systems
Power measurements in 75 Ω systems
Power measurements of highest sensitivity and with
extremely large dynamic range
Same as NRV-Z4, but for higher powers and
minimum mismatch
Power measurements up to 26.5 GHz with high sensitivity and large dynamic range, PC 3.5 connector
Power measurements up to 40 GHz with high sensitivity and large dynamic range, K connector
Measurement of peak envelope power of modulated
RF; three models, also for GSM (see page 13)
Same as NRV-Z31; two models, model 05 additionally for PDC and NADC (see page 13)
Same as NRV-Z31, but for direct power measurements
on transmitters; two models (see page 13)
High-precision power measurement even of nonsinusoidal signals, N connector
Same as NRV-Z51, but with PC 3.5 connector for
measurements up to 26.5 GHz
High-precision measurement of high powers
Same as NRV-Z53, but up to 30 W
Same as NRV-Z51, but with K connector for measurements up to 40 GHz
WF 40121
Voltage Sensors for the URV/NRV Family
1 kV
100 V
10 GHz
10 V
1 GHz
1V
100 MHz
100 mV
10 MHz
10 mV
1 MHz
1 mV
100 kHz
100 µV
10 kHz
10 µV
1 µV
DC
URV5 -Z2
-Z4
-Z7
+20 dB +40 dB with -Z50with -Z3 URV5-Z1
URV5-Z2
10 V Insertion Unit 50 Ω
200 µV to 10 V, 9 kHz to 3 GHz
Low-load RF voltage measurements and low-loss
power measurements in well matched 50 Ω RF
lines
URV5-Z4
100 V Insertion Unit 50 Ω
2 mV to 100 V, 100 kHz to 3 GHz
Virtually no-load RF voltage measurements on
coaxial lines, even at high voltages. Due to minimum insertion loss and reflection coefficient, this
unit leaves the RF line practically unaffected
URV5-Z7
RF Probe
200 µV to 10 V, 20 kHz to 1 GHz
For voltage measurements in non-coaxial RF circuits with low capacitive and resistive loading
WF 39821
…with 20 dB 2 mV to 100 V, 1 to 500 MHz
divider
The 20 dB and 40 dB dividers enhance the
measurement range of the RF probe; the high Q
factor of the capacitive divider makes the resistive loading negligible and reduces the capaci…with 40 dB 20 mV to 1000 V, 500 kHz to 500 MHz
tive loading to 0.5 pF (40 dB divider)
divider
…with 50 Ω 200 µV to 10 V, 20 kHz to 1 GHz
Adapter
URV-Z50
With built-in termination for power or level measurements up to 1 GHz on DUTs with 50 Ω source
impedance
…with 75 Ω 200 µV to 10 V, 20 kHz to 500 MHz
Adapter
URV-Z3
With built-in termination for power or level measurements in 75 Ω systems such as antenna or
video systems
URV5-Z1
DC Probe
1 mV to 400 V, 9 MΩ 3 pF
DC voltage measurements in RF circuits with minimum capacitive loading
WF 43230
Voltage
and
Power
Measurements
Voltage
and
Power
Measurements
9 9
WF 43221
Directional Power Meters
• Simultaneous display of forward
Directional Power Meter
NAS
Power Reflection Meter
NRT
Directional Power Meter NAS is a
Power Reflection Meter NRT is used for
(AVG) irrespective of modulation
favourably priced versatile instrument
high-precision measurement of power
mode
for use in the service and as a meas-
and reflection. Its menu-guided opera-
urement device for the installation of
tion is extremely user-friendly, with the
mobile and stationary transmitter sys-
main functions being selected at a key-
tems. Its main application is the meas-
stroke. For the first time a processor
urement of transmit power and match-
has been integrated in the sensor and
standards, eg GSM, DECT, PHS,
ing of digital mobile radio base sta-
a standard digital interface used
NADC, PDC, DAB, IS-95 CDMA,
tions and of mobile phones in vehicles.
between basic unit and sensor. This
power and reflection
• Measurement of average power
age burst power
• Compatible with all main digital
W-CDMA, etc
directly controlled from a PC. The large
directly to a PC
otelephony (including digital
choice of sensors makes this instrument
• IEC/IEEE-bus and RS-232 interface
mobile radio)
suitable for any applications in analog
• Sensors of predecessor model
• Simultaneous indication of forward
NAP can be connected
and digital radiocommunications.
• AC supply or battery operation
power and SWR
(optional)
• Battery operation
Sensors
for NAS
NAS-Z1
Meas. range
Frequency range
Sensors
for NRT
Meas. range AVG
Meas. range PEP
Frequency range
10
power (PEP), crest factor and aver-
• NRT-Z sensors can be connected
interface allows the sensor to be
• Insertion units for all areas of radi-
• Measurement of peak envelope
NAS-Z2
NAS-Z3
NAS-Z5
NAS-Z6
for GSM 900
0.01 to 120 W 0.1 to 1200 W 0.01 to 120 W 0.01 to 120 W 0.01 to 120 W
25 to 200 MHz 70 to 1000 MHz 890 to 960 MHz
NAS-Z7
for GSM 900/
1800/1900
0.01 to 30 W
1 to 30 MHz
NAP-Z3
NAP-Z4
NAP-Z5
NAP-Z6
NAP-Z7
NAP-Z8
0.01 to 35 W
—
0.03 to 110 W
—
0.1 to 350 W
—
0.3 to 1100 W
—
0.05 to 200 W
0.5 to 200 W
0.5 to 2000 W
5 to 2000 W
0.4 to 80 MHz
0.2 to 80 MHz
Voltage and Power Measurements
NRT-Z43
(can be connected to a PC)
NRT-Z44
(can be connected to a PC)
Meas. range AVG 0.007 to 30 W 0.03 to 120 W
Meas. range PEP
0.1 to 75 W
0.4 to 300 W
890 to 960 MHz
Frequency range
1710 to 1990 MHz
1 to 30 MHz
25 to 1000 MHz
Sensors
for NRT
NAP-Z9
0.4 to 4 GHz
0.2 to 4 GHz
NAP-Z10
NAP-Z11
(model 04 for GSM 900)
0.3 mW to 1.1 W 0.005 to 20 W 0.05 to 200 W
—
0.05 to 20 W
0.5 to 200 W
0.1 to 1 GHz
35 MHz to 1 GHz (model 02)
890 to 960 MHz (model 04)
WF 43226
RMS/Peak Voltmeters
These voltmeters feature a broadband
RMS Voltmeter
URE 2
RMS/Peak Voltmeter
URE 3
ers. A high-impedance input circuit
The URE 2 measures DC voltages and
In addition to all the advantages of
allows low-load measurements on the
the RMS value of AC and AC+DC volt-
URE 2, the URE 3 features a frequency
device under test. Commercial oscillo-
ages. Measurement speeds of up to
counter up to 30 MHz and a fast peak-
scope probes (1 : 1, 10 : 1, 100 : 1)
30 measurements per second make
responding rectifier. The frequency
may be connected for measurements
the URE 2 an extremely efficient instru-
counter allows an automatic fre-
in open circuits. The built-in amplifier
ment in automatic test systems for use
quency-response correction. Digital
has a bandwidth from DC to over 30
in production. Thanks to its high accu-
signal processing extends the fre-
MHz. In contrast to customary thermal
racy, great ease of operation and
quency range to the lower frequencies
methods, an RMS-responding rectifier
large variety of settings, it is the ideal
down to 0.02 Hz (RMS only). The
circuit patented by Rohde & Schwarz
instrument for the development lab.
measurement time can be exactly
amplifier which boosts the test signal
virtually without any noise to the
appropriate level for the built-in rectifi-
allows high measurement speed with-
matched to the period of the test signal
out any reduction in bandwidth and
• DC, 10 Hz to 25 MHz
to achieve the shortest possible meas-
accuracy.
• 50 µV to 300 V RMS (AC,
urement time of one signal period.
AC+DC)
• 20 µV to 300 V DC
• DC, 0.02 Hz to 30 MHz
• IEC/IEEE bus
• 50 µV to 300 V RMS (AC,
AC+DC)
• 100 µV to 500 V ±PEAK (AC,
AC+DC)
• 20 µV to 300 V DC
• Frequency measurement
• IEC/IEEE bus
• Analog outputs, TTL frequency input, trigger input, ready output
(optional)
Voltage and Power Measurements
11
Application: PEP Measurement
modulation mode determines whether
the envelope within the timeslot is flat
(eg with GMSK and GFSK) or whether
it varies with the symbol rate as with
π/4
DQPSK.
GSM specifications prescribe GMSK
modulation. Eight timeslots of 577 µs
duration each form a 4.615 ms wide
frame. Mobile stations occupy one
time slot only and therefore send RF
bursts of 577 µs duration and a repetition rate of 216.7 Hz.
The specifications allow overshoots at
the beginning of the transmission of up
to 4 dB above the otherwise flat envelope of the burst. All sensors from
Rohde & Schwarz with PEP function
are able to measure the quasi-stationary power of a mobile station in the
timeslot, ie its transmit power. With
most sensors, overshoots are supWF 41894
pressed for measurement.
Depending on radio traffic density,
GSM base stations occupy up to eight
Modern digital radio networks make
(crest factor CF), the complementary
timeslots. Since, with a normal power
high demands when it comes to power
cumulative distribution function
meter, it is not possible to select a cer-
measurement. Rohde & Schwarz is tak-
(CCDF) or the average power over a
tain timeslot, the power of the timeslot
ing account of this by continuously
defined time interval is required to an
in which the highest power is transmit-
adding new sensors to its range of
increasing extent in addition to pre-
ted is usually indicated if sensors with
voltmeters and power meters. Each
cise measurement of the simple aver-
PEP function are used.
family of these instruments is fully
age power (AVG) using thermal sen-
GSM-compatible and provides meas-
sor or special diode sensors. Take for
TDMA radio sets using π/4 DQPSK
urement capabilities for many other
instance modern digital radio net-
modulation (eg to NADC, PDC or TFTS
digital communication standards.
works with TDMA structure. The infor-
standards) also send the information
mation for the individual voice and
in the form of RF bursts, but the power
Precision power measurements are
data channels is compressed and sent
transmitted within the burst varies with
indispensable in the development and
in narrow timeslots. Several consecu-
the symbol rate. The fluctuations about
production of radiotelephones as well
tive timeslots form a frame, and after
to about +2/−10 dB referred to the
as in the installation of complete trans-
this frame has been sent, the first times-
average value.
mitter systems.
lot is normally used again.
NRV-Z31 (model 02), NRV-Z32
For modulated or pulsed signals,
What one wants to measure is the
(model 05) and Power Sensors
measurement of the peak envelope
power within the time slot and, possi-
NRT-Z43 and -Z44 determine the PEP
power (PEP), the PEAK/AVG ratio
bly, the peak and average power. The
of such signals.
12
Voltage and Power Measurements
Peak Power Sensors for Digital Mobile Radio
Type
Frequency range
Power range
Function
Burst
width
Burst repetition rate
Uses
NRV-Z31
Model 02
Model 03
Model 04
30 MHz to 6 GHz
30 MHz to 6 GHz
30 MHz to 6 GHz
1 µW to 20 mW
1 µW to 20 mW
1 µW to 20 mW
PEP
PEP
PEP
≥2 µs
≥2 µs
≥200 µs
≥10 Hz
≥100 Hz
≥100 Hz
NADC, PDC, TFTS, INMARSAT M, TV, general
NADC, PDC, TFTS, INMARSAT M, TV, general
GSM 900/1800/1900, DECT
NRV-Z32
Model 04
Model 05
30 MHz to 6 GHz
30 MHz to 6 GHz
100 µW to 2 W
100 µW to 4 W
PEP
PEP
≥200 µs
≥2 µs
≥100 Hz
≥25 Hz
GSM 900/1800/1900, DECT,
GSM 900/1800/1900, NADC, PDC
NRV-Z33
Model 03
Model 04
30 MHz to 6 GHz
30 MHz to 6 GHz
1 mW to 20 W
1 mW to 20 W
PEP
PEP
≥2 µs
≥200 µs
≥100 Hz
≥100 Hz
TV, general
GSM 900/1800/1900
NAS-Z6
890 MHz to 960 MHz
0.01 W to 120 W
PEP
577 µs
217 Hz
GSM 900/1800/1900
NAS-Z7
890 MHz to 960 MHz
1710 MHz to 1990 MHz
0.01 W to 30 W
PEP
577 µs
217 Hz
GSM 900/1800/1900
NAP-Z10
Model 02
Model 04
35 MHz to 1000 MHz
890 MHz to 960 MHz
0.05 (0.005) W to 20 W
0.02 (0.005) W to 20 W
AVG, PEP
AVG, PEP
≥4.5 µs
577 µs
≥50 Hz
217 Hz
TV, NADC, PDC, general
GSM 900
NAP-Z11
Model 02
Model 04
35 MHz to 1000 MHz
890 MHz to 960 MHz
0.5 (0.05) W to 200 W
0.2 (0.05) W to 200 W
AVG, PEP
AVG, PEP
≥4.5 µs
577 µs
≥50 Hz
217 Hz
TV, NADC, PDC, general
GSM 900
NRT-Z43
400 MHz to 4 GHz
0.1 (0.007) W to 75 W
≥ 0.2 µs
≥10 Hz
NRT-Z44
200 MHz to 4 GHz
0.4 (0.03) W to 300 W
AVG, PEP,
CF, BRST.AV,
CCDF
GSM 900/1800/1900, NADC, PDC,
DECT, TETRA, DAB, IS95-CDMA, W-CDMA
Power sensors compatible with digital mobile radio are available for all power meter families
Power Sensors NRT-Z43 and -Z44
CDMA and W-CDMA communication
components involved in signal genera-
additionally allow measurement of the
standards. Due to the modulation
tion is of great importance. The peak-
average power within the active time-
method used very high signal peaks of
to-average power ratio is an essential
slot based on the duty cycle.
10 dB or more above the average
quality criterion of the transmitted sig-
power value may occur. Since signal
nal. This parameter as well as the aver-
Measurement of the peak envelope
distortion due to amplitude limiting
age power can easily and precisely be
power (PEP) and of the PEP/AVG ratio
may also cause crosstalk in adjacent
measured with the two Power Sensors
is particularly important for the IS-95
channels, the linear response of all
NRT-Z43 and -Z44.
Power to be measured
P
0
N−1
N
N+1
N
Nos of time slots
PEP
Average power in time slot
= Pavg · T/tp
Pavg
0
tp
T
Envelope power of TDMA mobile station using GMSK or GFSK modulation
(top) and π/4DQPSK modulation (bottom)
Voltage and Power Measurements
13
Fundamentals of RF Power Measurement
The measurement of electrical power
in RF and microwave applications has
1 Fundamentals
the transfer of energy. Only the rate of
energy flow, power, is an absolute
measure of wave intensity. In the RF
the same significance as voltage
1.1 Power
and microwave ranges, the wave
used for a wide variety of tasks and
The development of carrier-based tele-
play an important role because the
are indispensable in the lab and test
communications at the beginning of
dimensions of the lines and subassem-
department. In comparison with spec-
this century saw a parallel develop-
blies used are of the same order of
trum or network analyzers, they are
ment in the field of RF voltage, current
magnitude as the wavelength used.
relatively unsophisticated instruments.
and power measurements. The majori-
This fact has to be taken into account
However, the great progress that has
ty of methods were based on convert-
when the quantity to be measured is
been made in devising refined proce-
ing electrical energy into heat. For a
selected. Voltage and current are less
dures for correcting probe errors over
long time, this was the only way of
appropriate because they depend on
the last ten years is largely over-
making accurate measurements at
the physical characteristics of the
looked. In spite of this, the application
practically any frequency. In the mean-
transmission medium (dimensions, die-
of probes is limited on account of the
time, direct voltage and current meas-
lectric constant, permeability) and
inherent physical factors. Selecting an
urements can be made up into the
field strength. Consider, for example,
unsuitable probe is still the most fre-
GHz range without having to convert
two matched coaxial cables with char-
quent cause of errors in the measure-
electrical energy into heat. Neverthe-
acteristic impedances of 50 Ω and
ment of RF power. This refresher topic
less, the intensity of RF and microwave
75 Ω. For the same transmitted power,
will give an in-depth description of fun-
signals is still given in terms of power.
the voltage and current for the two
damental measurement principles
Apart from the high accuracy of ther-
impedances differ by a factor of 1.22.
which will help the reader select the
mal power meters, there are other im-
most appropriate measurement equip-
portant reasons for using power.
measurements in electronics or in electrical engineering. Power meters are
properties of the electromagnetic field
There are further reasons for selecting
power as the quantity to be measured.
ment.
A second major source of error is the
Any signal transmission by waves, for
There is no direct way of measuring
example sound propagation, involves
voltage and current in waveguides,
loading effect of the measuring equipment on the circuit under test. Effects of
this kind can even occur at standard
line interfaces where they mostly go
undetected. When a power measurement is carried out correctly these
errors become evident because the
measurement errors themselves are
Fig. 1:
Power measurement on TV transmitter
using Power Meter NRVS
14
Voltage and Power Measurements
WF 40103
considerably smaller.
Definition of Power
and when standing waves occur, there
average power can be measured in
peak or envelope power meters which
are large measurement errors. And of
practice and is referred to as power P.
use fast diode sensors.
course power handling capacity is a
P is related to the RMS voltage V, the
crucial factor that determines system
RMS current I and the phase ϕ by the
or equipment design. All the compo-
following equation
nents in a power transmitter or ampliP = V ⋅ I ⋅ cos ϕ
fier, from the AC line connector,
(2)
through cooling system to the coaxial
v (t),
E (t)
t
RF output, depend on the magnitude
To avoid confusion with other power
of the RF power.
definitions, P is referred to as the true
or active power.
The commercial aspects of measuring
very high powers, say in a TV transmit-
When modulated sinusoidal signals
ter (Fig. 1), are also worth mentioning.
are considered, other definitions of
Every percent of measurement error
power are more appropriate (Fig. 3).
represents a relatively large power
p (t)
P
PEP
Pe (t)
Pavg
which has to be paid for. A manufac-
t
turer of a transmitter with a specified
i (t)
power of 10 kW may have to build in
an extra 100 W of RF power for every
1 % measurement error to cover him-
Fig. 3: Envelope of a modulated microwave signal
top: voltage/field strength
bottom: instantaneous power p(t), envelope
power Pe (t), peak envelope power PEP and
average power Pavg
Z
v (t)
v, i, p
p (t)
v (t)
self on acceptance.
P
0
i (t)
2π
2πft
ϕ
Fig. 2: Power absorbed by passive two-port with
a sinusoidal signal applied (v, i, p = instantaneous values of voltage, current and power,
P = average power)
1.2 Definition of Electrical
Power
A different approach may be used for
RF bursts. If the duty factor tp/T is
known, the peak power can be calculated from the average power Pavg
(Fig. 4). To distinguish it from the peak
envelope power it is also referred to
Power is usually defined as the rate of
as the pulse power Pp.
transfer or absorption of energy in a
system per unit time. The power trans-
The average of P over the modulation
mitted across an interface is then the
period is called the average power
product of the instantaneous values of
Pavg. This is what would be indicated
current and voltage at that interface
by a thermal power meter.
P avg
P p = --------------( tp ⁄ T )
(3)
(Fig. 2):
The power averaged over the period
p(t) = v(t) ⋅ i(t)
(1)
of a carrier is referred to as the envelope power Pe(t). It varies in time with
P
In the case of the sinusoidal signals
the modulation frequency. The maxi-
encountered in RF and microwave
mum envelope power is referred to as
engineering, the instantaneous power
the peak envelope power or PEP. PEP
Pavg
p(t) oscillates about the average
is an important parameter for specify-
0
power at a frequency that is twice that
ing transmitters. PEP and the envelope
of the original waveform. Only the
power can only be measured with
PEP
Pp
Pe(t)
tp
T
t
Fig. 4: Pulse power Pp (dashed line)
Voltage and Power Measurements
15
Power Transmission
1.3 Units and Power Level
RF and microwave ranges. The whole
one flowing from the source to the
complexity of matching can thus be
load and the other one in reverse di-
Electrical power is measured in watts
made very transparent without too
rection from the load to the source.
(W). Because of the large power rang-
many theoretical considerations.
The two waves carry the incident pow-
es that have to be measured, values
Therefore the main parameters and
er Pi and the reflected power Pr which
are usually expressed as the log of a
their relations are to be explained on
is usually smaller. The ratio Pr /Pi only
power ratio. A relative power level L r
this basis. Expressions in terms of volt-
depends on the matching of the load
is expressed in terms of the log of the
age and current in coaxial systems will
to the line and is zero in the case of
ratio of a power P to an arbitrary refer-
be presented at the end of the chapter.
ideal matching.
ence power P0 ; the units are dB:
P
L r = 10 log 10  --------- dB
 P 0
(4)
Absolute power level Labs is referred to
1 mW and measured in dBm:
P
L abs = 10 log 10  -------------------------- dBm
 1 mW
P = 1 ⋅ 10 Labs ⁄ 10 dBm mW
Pr
2
------- = r L
Pi
(5)
(6)
(7)
r L is the magnitude of the reflection co-
2.1 Source and Load
efficient of the load. For the majority of
Any kind of RF power measurement
power measurements it is sufficient to
takes place between a source and a
consider the magnitude. Otherwise
load. In a terminating power measure-
the phase angle Φ L has to be specified
ment, the measuring instrument itself is
as well. Magnitude r L and phase Φ L
the load. In contrast to high-imped-
can be combined in a complex quanti-
ance, virtually no-load voltage meas-
ty, the complex reflection coefficient
urements, the effects of the load on the
ΓL:
source usually cannot be neglected
A list of corresponding absolute and
and are therefore to be examined in
relative power levels is given below
more detail.
with a range of values of 1018:
r L = Γ L , Φ L = arg ( Γ L )
The log of the power ratio 10 log10Pi /Pr
Let us assume that source and load are
(in dB) is referred to as the return loss
Power P
Level L abs /dBm
connected to a standard transmission
ar and, like the reflection coefficient r
1 pW
–90
line, for example a piece of coaxial
and the SWR, used as a measure for
1 nW
–60
line with the characteristic impedance
matching (Fig. 6).
1 µW
–30
Z0 (Fig. 5). The source is to supply a si-
1 mW
0
nusoidal signal of constant amplitude.
The net difference between incident
1W
+30
The line is assumed to be free of loss-
and reflected power is dissipated by
1 kW
+60
es. As the transients die away, there
the load; it is usually referred to as net
1 MW
+90
will be two stationary waves formed,
power or absorbed power Pd:
Pd = Pi – Pr
Pd
2 Power Transmission and
Matching
The electromagnetic wave is an
extremely useful concept for describing the transmission of energy in the
16
Voltage and Power Measurements
Pi
(9)
Pr
G
Source
P d = P i ( 1 – r L2 )
(8)
The log of the power ratio 10 log10 Pi/Pd
Z0
Line
Load
L
Fig. 5: Power flow between source and load
(in dB) is referred to as mismatch loss
ad. It expresses the relative power loss
caused by reflection. For reflection
Nominal Power
coefficients smaller than 0.1 (10 %)
while the phases are in opposition:
The two powers are equal only in the
the power loss is smaller than 1 %,
rL = rG, ΦL = −ΦG (index G referring to
case of matched source (rG = 0), other-
meaning that incident power and
source of generator). Since the maxi-
wise PG max is always greater than PGZ0.
absorbed power are more or less
mum available power is independent
equal.
of the line used, it can be measured
with high accuracy. The conjugate
PGZ0
matching via a tuner (Fig. 7) is however
Pi = PGZ0
time-consuming and not acceptable for
dB ad
1.0
8
10
s
r
8
dB ar
0
many sources, for instance power out-
3
put stages with low output impedance.
0.5
5
3
0.3
2
0.5
0.2
1.5
0.10
0.05
30
0.03
0.02
1.2
1.1
0.05
0.02
0.01
0.002
50
0.01
1.02
0.005
1.01
0.003
0.002
60
0.001
G (arbitrary)
Terminating
power meter
Fig. 8: Measurement of source power delivered
to Z0 load
0.2
0.001
40
L=0
Pi
Pr = Pi · rG2
PGmax
G
Pd
0.005
1.05
Pi
1
0.1
20
Pr = 0
G
*
G
G
*
| G | = | G | = rG
Tuner
(loss-free)
Terminating
power meter
arg G* = −arg G = − φG
Fig. 7: Measurement of maximum available
source power with conjugate matching via tuner
2.3 Power with
Mismatched Load
1.005
With a matched source (Fig. 9a) the
absorbed power decreases with
1.002
Fig. 6 Nomogram for reflection coefficient r,
SWR, return loss ar and mismatch loss ad
A more practical definition of nominal
increasing magnitude of the reflection
source power is the power that can be
coefficient rL irrespective of the phase:
absorbed with the output being terminated with the specified characteristic
P d = P GZ0 ( 1 – r L2 )
for rG = 0
(11)
impedance. It is also referred to as the
power PGZ0 delivered to Z0 load. This
The power reduction is solely attribut-
is the definition commonly used in RF
able to the reflection losses at the
2.2 Available Source Power
and microwave measurements. To
load. The incident power remains
measure this power, a calibrated ter-
unchanged, as shown by a compari-
So far, power ratios as a function of
minating power meter must be con-
son with equation (9).
load mismatch have been considered
nected to the source (Fig. 8). The accu-
only. Absolute power levels on the
racy that can be attained is somewhat
other hand strongly depend on the
limited by the mismatch uncertainty
nominal power of the source. There
(see further below).
P i = P GZ0
for rG = 0
(12)
With a matched source, the incident
power is always equal to the power
are two definitions:
The maximum available power and
delivered to Z0 load. Load mismatch
Theoretically, the maximum available
the power at Z0 are related to each
has no effect.
net power PG max is defined as the nom-
other by the reflection coefficient of the
inal power of the source. To absorb
source (rG):
With a mismatched source (Figs. 9b/c),
this power, conjugate matching of the
the absorbed power is dependent on
load to the source is required. This
means that the magnitudes of the
reflection coefficients must be equal
P Gmax
P GZ0
= ----------------2
1 – rG
the magnitude and phase of the two
(10)
reflection coefficients rL and rG. If, for
instance, the magnitude of the reflec-
Voltage and Power Measurements
17
Mismatch
tion coefficient of the load is kept conP
stant while only its phase is varied, the
Fig. 9: Net power of a source,
plotted versus the plane of the
complex load reflection coefficient ΓL. The grid lines of the 3-D
surface are obtained by projection of the circles rL = const. and
the straight lines ΦL = const.
d
power varies periodically about an
average value. If the reflection coeffi-
P
GZ0
=P
0,2
0,3
Gmax
cients are small, this average value is
0,4
0,5
equal to the power delivered to Z0
+j
0,6
load. With matching degrading, the
−1
average value decreases due to the
0,7
∗=
G
0,8
losses caused by reflection and the
span of variation increases.
G
=0
°
0,9
+1
a) matched source (rG = 0)
rL=1
−j
The effect of the load can be
explained by the fact that the reflected
L
wave is reflected again by the mismatched source (secondary reflection)
and superimposed on the forward
Pd
wave. Depending on the phase, there
PGZ0
is either a gain or a loss. With a
matched source, the reflected wave
however is fully absorbed, so that the
PGmax
0,3
0,4
incident power remains constant.
0,5
+j
0,6
−1
0,7
˚
The power levels can only be calcu-
0,8
lated if magnitude and phase of the
*
G= G
reflection coefficient of the source and
0
0,9
load at the reference plain are known.
+1
r =1
L
−j
The incident power can then be calculated as follows:
P GZ0
P i = -------------------------------1 – ΓG ⋅ ΓL 2
b) mismatched source,
rG = 0.3
(SWR = 2; ΦG = 180°)
L
(13)
Pd
PGmax
Absorbed and reflected power can
then be derived using equations (7)
and (9). With source or load match-
P
GZ0
ing, the special case Pi = PGZ0 applies.
0,3
+j
0,4
−1
*
˚
0,5
G
0,6
0
0,7
0,9
˚
0,8
+1
G
rL=1
−j
L
18
Voltage and Power Measurements
c) mismatched source,
rG = 0.5
(SWR = 3; ΦG = −90°)
Voltage and Current
thus only possible to determine the
spread of the transmitted power. The
incident power can be determined
from the following relationship:
P GZ0
P GZ0
---------------------------- ≤ P i ≤ ------------------------2( 1 + rG rL ) 2
( 1 –rG rL )
Load mismatch
1.2
1.1
0.05
1.05
1.02
spective of the place of measurement,
5%
instance by means of an adapter. It is
s
0.1
phase shift ϕ has to be considered. Irre-
V ⋅ I ⋅ cos ϕ = P d
5%
0.
alteration of the line length, as for
0.2
(19)
2%
0.
1%
0.
ticularly since it changes with any
1.5
at the same place. Moreover, the
1%
and load is not useful to consider, par-
rL
2%
reflection coefficients of the source
0.5
2
%
10
In practice, the phase angle of the
3
%
20
2.4 Mismatch Uncertainty
0.02
0.01
0.01 0.02
Equiv.
SWR 1.02
0.05
1.05 1.1
0.1
1.2
V (x)
0.2 rG 0.5
1.5
2
3
Source mismatch
V
I
ϕ
V (x) · I (x) · cos ϕ (x) = const. = Pd
Vmax
I (x)
Imax
Vmin
Imin
ϕ (x)
Fig. 10: Maximum measurement error due to
mismatch
λ/2
Position x
Load end
Fig. 11: Voltage and current on a line with
mismatched load (rL = 0.5; ΦL = 0°); λ = line
wavelength, ϕ = phase shift between V and I
(14)
This relationship expresses a measure
of uncertainty for the power determination. It implies that a terminating
power meter cannot accurately meas-
2.5 Voltage, Current and
Power
In the microwave range neither current
ure the power of a mismatched source
In coaxial systems, voltage and cur-
nor phase shift can be accurately
delivered to Z0 load unless it is ideally
rent may be used for measuring the
measured, whereas the voltage can
power. With matching (rL = 0), these
be determined with high accuracy
two parameters remain constant all
using coaxial voltage probes. With a
The maximum relative error εm
along the line and are related with
matched load or less demanding
between Pi and PGZ0 is determined by
each other via the (real) characteristic
requirements on measurement accu-
way of approximation (Fig. 10):
impedance Z0:
racy, the power can be calculated
matched itself.
from equation (18). To estimate the
V = I ⋅ Z0
ε m % ≈ 200 % r G ⋅ r L
for r L = 0
(17)
error in the case of mismatch, V2/Z0
was plotted versus the line length in
(15)
Fig. 12, in other words the power that
ε m dB ≈ 8.7 dB r G ⋅ r L
(16)
The approximation is sufficiently accurate for εm % <20% and εm dB <1 dB.
The absorbed power can be calcu-
would be expected in case of match-
lated from the RMS values:
ing. A sineshaped curve is obtained,
V2
P d = P i = ------ = I 2 Z 0
Z0
the average value of which is approx(18)
imately equal to the incident power Pi.
for rL = 0
Example: A terminating power meter
measures an incident power
With a mismatched load, the value of
Pi = 10.0 mW. With rG = 0.22 and
voltage and current depends on where
rL = 0.10, the maximum measurement
the measurement is made along the line
error may amount to ±4.4%
(Fig. 11) and is shifted in phase with
(0.19 dB). The source power deliv-
respect to each other. If the transmitted
ered to Z0 is then in a range between
power is to be accurately determined,
9.56 mW and 10.44 mW.
the two parameters must be measured
2(x)
V____
Z0
ΦL1
ΦL2
ΦL3
1.21 Pi
Pi
0.81 Pi
0
Position x
Fig. 12: Power indicated when measured with a
voltage probe (rL = 0.1; at different values of ΦL
Voltage and Power Measurements
19
Power Meters
Maxima and minima are obtained at
can be easily derived as a function of
ing measurements of high accuracy in
Pi (1 ± rL)2. Fig. 13 shows the measure-
load reflection coefficient:
particular in conjunction with thermal
sensors. The Rohde & Schwarz Power
ment error to be expected for the inciV max
I max
1 + r (20)
SWR = ------------------- = --------------- = ---------------------LV min
I min
1 – rL
dent power.
are typical examples. Connected to
the output of a source, they measure
±20
Measurement error in %
Meters NRVS and NRVD (see page 7)
±10
With matching, SWR = 1; with total
the available power (Figs. 7 and 8). In
reflection, SWR = ∞.
conjunction with directional couplers,
power splitters and SWR bridges they
±5
±3
±2
±1
0.005
0.01
1.01
1.02
0.02 0.03 0.05
1.03 1.05
1.1
0.1 rL
s
1.22
Mismatch of load
Fig. 13: Maximum measurement error for the incident power measured with a voltage probe
The terms standing wave ratio (SWR)
are also suitable for directional power
and voltage standing wave ratio
measurements, attenuation and SWR
(VSWR) are both used for the above
measurements and they can be used
ratio. They have found wide accept-
as calibration standards. Usually, the
ance to the extent that they are even
power absorbed in the termination is
used to describe source matching. It
measured with the aid of a thermocou-
should however be borne in mind that
ple or diode sensor. In this way, the
substituting rL for rG in equation (20) is
average power and, using appropri-
merely a definition and does not
ate diode sensors, the peak power
reflect the real SWR of the line.
can be measured.
Peak power or envelope analyzers
with power sensors based on fast
diode sensors enable measurement of
the envelope power. They are ideal
for in-depth analysis of modulated sig-
2.6 Standing Wave Ratio
3 Power Meters
nals as can be found with radar equip-
The interference pattern obtained
RF power meters have to satisfy a
radio equipment etc. Comparable
through the combination of forward
large variety of requirements. In addi-
with a digital oscilloscope, they are
and reflected wave is referred to as
tion to a wide frequency and power
able to detect single and periodical
standing wave. It is periodical at half
range, low measurement uncertainty is
changes of the envelope power. They
a line wavelength. Maxima and
above all a desired factor. With the
feature a large variety of trigger facili-
minima are obtained at the points
introduction of digital radio networks
ties, screen display of the results,
where voltage and current of the two
there is an increasing demand for
cursor readouts and the like (Fig. 14).
waves are of equal or of opposite
measurements of modulated signals,
phase. Their distance from the line end
from the simple determination of the
is determined by the phase angle ΦL.
peak value through to detailed analy-
ment, nuclear spin tomographs, TDMA
PEAK PWR.=6.93 mW
CURS. ∇ . =5.52 mW 130 ns
CURS + =0.74 mW 123 ns
sis of the envelope. Moreover, moniThe ratio of the maximum to the mini-
toring of the incident and reflected
mum values is a measure of the mag-
power should be possible as well as
nitude of the reflection coefficient at
determination of the power available
the load. It is referred to as standing
from any kind of sources. Different
6.0
wave ratio SWR and can be deter-
types of power meters are available to
4.0
mined to very high accuracy on trans-
cover all these requirements.
2.0
mission lines. Considering that voltage
Terminating or absorption power
wave are in a ratio of 1: r L , the SWR
meters are versatile instruments allow-
Voltage and Power Measurements
50 ns/div
∇
+
and current of forward and reflected
20
10.0
mW
8.0
0.0
Fig. 14: Screen display of envelope power
Sensors
absorbed by the load. Unlike the inci-
parameters (Fig. 17). A large variety
dent and reflected power, it is not
of sensors is available to suit a wide
dependent on the characteristic
frequency and power range. Terminat-
impedance of the directional power
ing sensors can be used to cover the
meter and is therefore even correctly
entire microwave range up to
measured when the characteristic
330 GHz. The sensitivity is deter-
impedance of the test setup is different
mined to a large extent by the meas-
from that of the power meter or there
urement principle. Thermocouple sen-
is no defined reference at all.
sors can be used from about 1 µW,
diode sensors from 100 pW. The
upper measurement limit can be
extended into the kW or MW range
WF 40541
3.1 RF Interface
by connecting attenuators or directional couplers.
Except for a few handheld units, the RF
Fig. 15: Directional Power Meter NAS used
for measuring the power and SWR of a GSM
mobile phone
Pi
Pr
signal is processed in a detached sen-
Power meters are as a rule hooked up
sor. For automatic correction of sys-
to defined interfaces. These are stand-
tematic measurement errors (linearity,
ardized transmission lines, either coax-
frequency response, temperature
ial lines with a characteristic imped-
effect) modern sensors contain a dig-
ance of 50 Ω (75 Ω) or waveguides of
ital memory with the sensor-specific
various types. The frequency ranges
data and a temperature sensor for cor-
listed in the table below are typical for
rection of the temperature-dependent
power sensors. Due to their small band-
50 Ω
G
Z
Radio equipment
Pi
Matching unit
Pr
Insertion unit
NAS-Z
Transfer characteristic at 23 °C
Fig. 17: Intelligent power sensor with
integrated calibration data memory
Directional power meter
Transducer
Fig. 16: Block diagram of directional power
measurement as shown in Fig. 15
Temperature sensor
Directional power meters or feed-
Temperature effect
through power meters are available
for in-service measurements on antennas, radio equipment or other highpower RF generators (Figs. 15 and
16). The built-in dual directional coupler (reflectometer) enables monitoring of incident and reflected power
Frequency response
and hence SWR measurements under
WF 37902
operating conditions. The difference
between incident and reflected power
is always equal to the power
Voltage and Power Measurements
21
Thermal Measurement Methods
Frequency range
Type of line/Z0/connector
0.1 MHz to 4 (6) GHz
coax/50 Ω/N
10 MHz to 18 GHz
coax/50 Ω/N, PC 7
50 MHz to 26.5 GHz
coax/50 Ω/PC 3.5
50 MHz to 40 GHz
coax/50 Ω/K
50 MHz to 50 GHz
coax/50 Ω/2.4 mm
0.1 (1) MHz to 2.5 GHz
coax/75 Ω/N
12.4 to 330 GHz
waveguide,
15 frequency bands
Frequency ranges of commercial power sensors
according to the magnitude of their
sensors (Fig. 18). Calorimetric meas-
power and there are no linearity
urements are still employed for very
errors with envelope-modulated sig-
high powers in the kW and MW
nals.
range as well as for calibration.
The various measurement principles
The smallest measurable power is
differ in the way the generated heat is
determined by the sensitivity of the
measured. Depending on the state-of-
temperature sensor and the immunity
the-art, different methods emerged as
of the test setup to ambient tempera-
favourites in the course of develop-
ture fluctuations. The maximum permis-
ment. At the end of the sixties, for
sible power is largely influenced by
instance, the Thermal Power Meter
the heat resistance of the materials
NRS from Rohde & Schwarz set new
used. Under favourable circum-
width, waveguides are superseded by
standards for precision power meas-
stances, a measurement range of
coaxial systems to an increasing extent.
urements. The power sensors operates
30 dB to 50 dB can be achieved.
as a bolometric detector with two sensors in a self-balancing bridge. This
3.1.1.1 Thermocouple Sensors
With a few exceptions, power meters
instrument is still used as a secondary
Thermocouple power sensors are
are of broadband design. Therefore
standard by the German Calibration
being offered nowadays for the entire
they are less sensitive than selective
Service and the German Standards
microwave range. Although thermo-
test receivers or spectrum analyzers,
Laboratory. At present, thermocouple
couples were used in the past for tem-
but more accurate thanks to their sim-
sensors are dominating in the indus-
perature measurements, it was only
ple design.
trial field, since they are superior as
through the combination of semicon-
regards ruggedness, dynamic range
ductor and thin-film technology that
and zero stability to all other types of
fast, sensitive and yet rugged sensors
3.1.1 Thermal Measurement
Methods
Fig. 18: Dual-Channel Power Meter NRVD with thermal power sensors for the frequency range from DC
to 18 GHz
Thermal power meters are generally
regarded to have little measurement
uncertainty. One reason for the high
accuracy is the high stability of calorimetric and related measurement methods, where the RF power is substituted
by DC current or low-frequency AC
current. Another reason is that with all
thermal methods there are no weighting errors when power is converted
into heat. In contrast to diode sensors,
power, irrespective of the waveform of
the signal. Harmonics are weighted
22
Voltage and Power Measurements
WF 43223-2
thermal sensors measure the average
Thermocouple Sensors
Output
8
1 mm
+
WF 39268-1
11
10
2
Fig. 19: Thermocouple of Power Sensors
NRV-Z51 to -Z54
7
Fig. 20: Sectional view of measurement cell:
1
2
3
4
5
Silicon substrate
6
Membrane
7
RF feed
Termination
8
Thermocouple
9
(hot junction)
10
11
Metal contact
Highly-doped silicon
layer
Cold junction
Insulating layer (SiO2)
Metallized ground
Bump
6
Input
4
5
3
1
9
could be produced (Fig. 19). The
In the measurement cell developed for
also important factors. However, a
measurement cell is based on a silicon
the Rohde & Schwarz Power Sensors
slight degradation resulting from hold-
substrate (Fig. 20). The termination is a
NRV-Z51 to -Z55 the termination and
ing the sensor in the hand for some
thin layer of tantalum nitride or chro-
the thermocouple are DC-isolated. This
time or screwing it to a hot RF junction
mium nickel, and a metal semiconduc-
eliminates the need for a coupling
cannot be avoided altogether.
tor contact in the immediate vicinity
capacitor and a single sensor can be
Because heat is supplied at one end,
generates the thermoelectric voltage
used to cover the entire frequency
there will be a temperature gradient
which is proportional to the converted
range from 0 to 18 GHz (N connec-
across the measurement cell which
RF power (approx. 200 µV/mW). The
tor), 0 to 26.5 GHz (PC 3.5 connector)
produces additional thermoelectric
rated power is 100 mW.
or 0 to 40 GHz (K connector). The
voltages. The magnitude of these volt-
smallest measurable power is about
1 µW and at least ten times lower than
simple, termination and thermocouple
with other thermal methods. This was
are usually DC-coupled. A coupling
made possible through a special
capacitor is used for DC isolation from
design of the measurement cell which
%
the measuring circuit. Large capaci-
in conjunction with the poor heat con-
+5
tors (high capacitance) needed for
ductivity of silicon makes for a good
low frequency operation not only
thermal insulation of the termination.
degrade matching but also reduce the
The high thermal EMF of the metal
upper frequency limit. Wide fre-
semiconductor contact (approx.
quency bands can therefore be cov-
700 µV/K) and the relative insensitiv-
ered only with several sensors.
ity of the thermoelectric effect to fluctuations of the ambient temperature are
Linearity error
To keep the manufacturing technique
0
0.1
1
10 mW 30 100
P
Fig. 21: Typical linearity error of thermoelectric
cell (red: after numerical correction). The nonlinearity is mainly caused by the temperaturedependent heat conductivity of silicon
Voltage and Power Measurements
23
Bolometers, Calorimeters
ages does not depend on the power,
types, the best known of which are
Barretters make use of the positive tem-
resulting in a zero shift of the transfer
thermistors and barretters.
perature coefficient of metals. Common models have a thin platinum-wire
characteristic.
In the thermistor power meter, two
filament to act as an RF absorber and
The ratio of thermoelectric voltage to
semiconductor resistors with high neg-
temperature sensor. They feature a rel-
RF power is also influenced by the
ative temperature coefficient (thermis-
atively low sensitivity and are easily
magnitude of the input power. From
tors) combine the function of termina-
damaged when the rated power is
about 10 mW, the transfer character-
tion and temperature sensor all in one.
exceeded. Once widely used, they
istic therefore becomes pronouncedly
They absorb at the same time the RF
are nowadays obsolete and employed
nonlinear (Fig. 21). With the sensors
power to be measured and a DC power
for very special applications only.
previously available on the market,
(Fig. 22). In a bridge circuit, the DC
this effect was compensated by ana-
resistance is measured and kept con-
3.1.1.3 Calorimeters
log means, resulting in residual errors
stant by varying the DC power. Any
Calorimeters in the original sense are
up to about ±5 % at the high end of the
instruments for measuring quantities of
measurement range. Through individ-
heat, ie energy/power is calculated
from the temperature increase of a
ual calibration and numerical correction the linearity error of the NRV-Z
material of known specific heat capac-
Coaxial
RF connector
thermal sensors can be kept below
0.5 %.
P
Vdif
measurement accuracy, commercial
+
−
IRF
T
calorimeters operate on the substitution
IDC
The small mass of the sensor makes for
Vref
a small thermal capacity and hence
T
temperature coefficient of the output
voltage is either compensated by analog means or corrected numerically.
principle. Due to their high stability,
they are used as primary standards.
They are also used for the direct meas-
for a fast response (thermal time constant is of the order of ms or less). The
ity such as water. To enhance the
Fig. 22: Principle of thermistor power meter. the
absorbed RF power can be calculated from the
measured voltage difference Vdif. With the RF
power switched off, Vref is adjusted to give no
voltage difference (zero adjustment)
urement of very high powers without
attenuators or directional couplers connected ahead. For such applications,
flow calorimeters are used (Fig. 23),
To minimize microphonic effects and
partly with direct absorption of the RF
effects of thermoelectric voltages at the
energy in the cooling medium water.
connectors of the connecting cable,
the output signal of the sensor is
boosted before it is taken to the power
increase of the RF power is thus
meter. Thermoelectric cells have an
always compensated by an appropri-
excellent long-term stability if they are
ate reduction of the DC power and
used within their rated power range.
vice versa. The DC power can easily
A calibration generator is thus no
be measured. Due to the substitution
longer required; it is only needed for
principle employed, thermistor power
sensors which do not have the numeri-
meters feature an extremely high long-
cal correction facility.
term stability and their effective effi-
Inlet
Flow
volume
control
measured with a very low uncertainty.
The term bolometer is used to describe
For general applications, these instru-
power meters which are based on the
ments have however become of little
variation of the electrical conductivity
interest because of their narrow meas-
as heat is absorbed by the termina-
urement range from 10 µW to
tion. There is a variety of bolometer
10 mW.
24
Voltage and Power Measurements
Circulation pump
∆T
Temperaturemeasurement
points
ciency (see further below) can be
3.1.1.2 Bolometers
Outlet
RF power
AF source
A
V
~
Substitution circuit
Fig. 23: Flow calorimeter using substitution
method. The measured temperature difference is
proportional to the absorbed power P. Calibration is made via the substitution circuit
Diode Sensors
3.1.2 Diode Sensors
In addition to the termination, the sen-
against the inner conductor or second
sor contains a half-wave or full-wave
rectifier so that the superimposed DC
In the early days of semiconductor
rectifier and a matching network for
voltage is suppressed.
technology, diodes were already used
compensation of the junction capaci-
for power measurements in the RF and
tance and lead inductance of the
Even with DC coupling to the measure-
microwave bands, since their sensitiv-
diode (Figs. 24 and 25). Due to the
ment circuit, the diode sensors cannot
ity was much better than that of ther-
parasitic circuit elements, matching is
be used at very low frequencies. The
mal sensors. For such applications,
somewhat poorer than that of a com-
frequency range is always limited by
germanium point-contact diodes had
parable thermocouple sensor.
the charging capacitor which in conjunction with the DC resistance of the
both a sufficiently low junction capacitance and a low dynamic resistance
WF 41133
diode forms a highpass filter for the
(video impedance) to enable low-
tapped RF voltage. Due to the unfavour-
noise measurement of the rectified volt-
able RF characteristics of high capaci-
age. Because of the fabrication tech-
tances, very large frequency ranges
nique involved, these detectors exhib-
can only be covered by several sen-
ited however large spreads in their
sors. The measurement accuracy of a
electrical characteristics and instabil-
diode sensor is not only determined by
ity so that for a long time diode power
the quality of calibration and matching,
meters were regarded to be inaccu-
but to a considerable extent also by the
rate.
magnitude of the power applied.
Today, zero bias Schottky diodes pro-
3.1.2.1 Square-Law Region
duced on a silicon substrate or GaAs
At very low powers, diodes behave
diodes are being mostly used. Their
very much like thermal power sensors.
They measure the true RMS power and
electrical characteristics are similar to
those of the germanium point-contact
Fig. 24: Diode sensor of Power Sensor NRV-Z4
indicate neither dynamic nor fre-
diodes, but their long-term stability is
quency-dependent linearity errors.
as high as that of thermocouples.
Harmonics are weighted according to
Diode power sensors cover the power
their power, and the average power is
range from below 10 µW down to
indicated in the case of envelope mod-
about 100 pW. They are indispensa-
To improve it, the coupling capacitor
ulation. In this range the diode
ble for measuring the peak or enve-
between RF connector and termination
behaves like a weakly nonlinear resist-
lope power of modulated signals.
is sometimes omitted. The output volt-
ance (Fig. 26). In addition to the lin-
Where a very high measurement
age is then not referred to ground but
ear component (video impedance),
speed is required, they are used
the current-voltage characteristic also
instead of thermocouple sensors even
has a square term which causes RMS
in the power range from 10 µW to
100 mW. The measurement uncertainties occurring in this range must be
rectification. This section of the transV1
RF Input
P
R3
traded off in each case against the
measurement speed and zero stabil-
Vout
C3
}
}
Termination
(50 Ω)
The output DC voltage is approximately proportional to the input power
C1 C2
}
powers and for improved matching.
R6
R2
}
with plug-on attenuators for higher
referred to as the square-law region.
V2
R1
fer characteristic is therefore also
R4
ity. Diode sensors are made for frequencies up to about 110 GHz, often
R5
Rectifier Charging Decoupling
capacitors
Fig. 25: Simplified block diagram of sensor
(about 800 µV/µW) and the temperature coefficient is constant, its order of
magnitude being the same as of thermocouple sensors.
Voltage and Power Measurements
25
Square-Law Region
value is referred to as the crest factor.
10
Output voltage
I
V, I
1
In the RF and microwave bands, meas-
V
urement errors are mainly caused by
broadband noise and signals with
harmonics (Fig. 28). Measurement
10−3
errors can be positive or negative
depending on the phase of the har-
−1
1
10−6
V/VT
monics.
−60
−30
dBm
0
+20
Power level
Fig. 27: Static transfer characteristics of a diode
sensor with no-load output (full-wave circuit)
The harmonic effect is almost exclusively dependent on the waveform
and measured power. Contrary to
Fig. 26: Current-voltage characteristic of a
Schottky diode in the square-law region (blue);
dotted: square approximation; dashed: I = V/R0,
where R0 is the video impedance without external
bias; VT = temperature voltage (25 to 35 mV)
nonlinear and the temperature coeffi-
Half-wave rectification
%
temperature, power measurements outThere is no fixed upper limit for the
side the square-law region are not pos-
square-law region. With sinusoidal
sible with older type power meters.
signals, the upper limit is usually
Modern sensors can be appropriately
drawn at a crest value of 30 mV,
calibrated so that residual measure-
corresponding to 10 µW PEP in 50 Ω
ment errors become negligible. Prob-
systems. At the lower measurement
lems may be caused by effects which
limit, with input powers between
cannot be corrected subsequently,
100 pW and 1 nW, diode sensors
such as dynamic and frequency-
output a very small DC voltage of a
dependent linearity errors as well as
few hundreds of nV only. Superim-
the effect of harmonics.
Measurement error
cient a complex function of power and
±0.1
−30
0 dBm +10
%
3.1.2.2 Peak weighing
the square-law region. While with low
With increasing power level, the diode
power levels applied to the sensor,
sensor changes from RMS weighting to
there is a fixed relationship between
peak weighting of the RF voltage,
output voltage and input power, out-
exhibiting the well-known behaviour of
side the square-law region each wave-
a diode rectifier. Highly stable, noise-
form has its own transfer characteris-
free measurements are possible due to
tic. Since sinusoidal voltages are used
the relatively high output voltages of
for calibration, other waveforms cause
about 10 mV to a few V outside the
measurement errors which increase in
square-law region. The measurement
proportion to the deviation of the crest
speed is extremely high. Since the
factor of the voltage to be measured
static transfer characteristic (Fig. 27) is
from
2 . The ratio of peak to RMS
Measurement error
Harmonics
With non-sinusoidal signals, major
Voltage and Power Measurements
−10
Power level
3.1.2.3 Measurement Errors Due to
measurement errors may occur outside
26
−60 dBc
−20
Full-wave rectification
set a limit to the practical use of the
diode.
−40 dBc
±1
posed thermal noise and zero drift
caused by local heating of the sensor
−20 dBc
±10
−20 dBc
±10
−20 dBc
−40 dBc
±1
−30 dBc
±0.1
−30
−60 dBc
−20
−10
0 dBm +10
Power level
Fig. 28: Maximum measurement error of diode
sensors in case of sinewave signals with harmonics (red: 2nd harmonic, blue: 3rd harmonic).
Parameter: harmonics. Half-wave rectification
shown in upper diagram, full-wave rectification in
lower diagram
Linearity Errors
popular opinion, it cannot be reduced
3.1.2.4 Dynamic Linearity Errors
by a low-impedance load of the recti-
Dynamic linearity errors occur in the
fier. An improvement can be achieved
measurement of the average power of
with full-wave rectifiers. They derive
modulated signals (Fig. 30). In the
the average value from the positive
square-law region the charging and
and negative voltage peaks, thus elim-
discharging time constants of the sen-
inating the effect of even-numbered
sor are equal and the output voltage
harmonics, in particular that of 2nd
corresponds to the average power
order (Fig. 29). As shown in Fig. 28,
level. With increasing power level, the
elin
20 mW
P
2 mW
5%
200 µW
20 µW
4
8
12
16 18 GHz
f
Fig. 32: Measured linearity error eLin due to varactor effect of a 18 GHz detector
rise time decreases and the fall time
increases because of the non-conduct-
+
3.1.2.5 Frequency-Dependent
Linearity Errors
u
Even with numerically linearized
2 ⋅ f0
Output
voltage
diode sensors linearity errors may
occur outside the square-law region.
t
They are caused by the voltagef0
dependent junction capacitance
−
(varactor effect) and become evident
when the diode starts affecting the RF
Fig. 29: Waveform distortion caused by
2nd harmonic; f0 = fundamental frequency
behaviour of the sensor (as a rule of
Envelope power
considerable measurement errors may
occur with half-wave rectification even
within the square-law region.
Fig. 31: Dynamic transfer characteristic of a
diode sensor outside the square-law region with
low-frequency (red) and high-frequency (blue)
amplitude modulation (static characteristic in
black)
thumb: from 1/4 of the upper frequency limit). Since the junction
capacitance decreases with increasing input power, there is normally an
increase in the frequency response, ie
the linearity error is positive (Fig. 32).
3.1.2.6 Peak Power Measurement
t
Output
voltage
Envelope
power
With high modulation frequencies and
t
Fig. 30: Transfer characteristic of a diode sensor
with pulse-modulated input signal within (blue)
and outside (red) the square-law region; average
values are dash-dotted
ing diode. The output voltage is thus
a voltage crest value of at least 1 V,
greater than the average power level.
any diode sensor can be used for
In the transfer characteristic, this is
measuring the peak power as can be
shown as a kind of hysteresis loop.
seen from Fig. 31. However, it will be
Depending on the modulation fre-
used for this purpose in exceptional
quency, the power and the discharge
cases only, since the measurement
time constant of the sensor, the hyster-
error very much depends on the wave-
esis loop lies somewhat above the
form and power. For universal appli-
transfer characteristic (Fig. 31). For
cations, there are special peak power
modulation frequencies in the audio
sensors. They consist of a fast diode
range, a fairly acceptable characteris-
sensor followed by an amplifier and
tic can be achieved by choosing a sen-
peak hold circuit. This principle is for
sor with a very high lower cutoff fre-
instance employed with Peak Power
quency (small time constant).
Sensor NRV-Z31 from
Voltage and Power Measurements
27
Directional Power Sensors
Rohde & Schwarz. The charging time
pressed on transmitter keying so that
The sensors can be coupled to the
constant in the square-law region
the power at the flat pulse top is indi-
main line so that either the square-law
determines the lower cutoff frequency
cated (Fig. 33).
region or the entire characteristic is
used. There are no strong pros or con-
and rise time of the output voltage. To
avoid dynamic measurement errors,
3.1.2.7 Envelope Power Measurement
tras for the two possible designs. The
the pulse width must be clearly greater
Diode sensors for envelope power
main advantage of the square-law
than the specified rise time. Due to the
measurements must not only be able to
region is the absence of dynamic line-
relationship with the rise time, the
trace the leading edge, but the entire
arity errors. Appropriately designed
lower cutoff frequency is still relatively
envelope of the test signal. For this pur-
sensors are ideal for measuring the
high compared to that of normal diode
pose it is not sufficient to simply reduce
average power of envelope-modu-
sensors.
the charging capacity. Additional
lated signals. If on the other hand the
measures are a low-impedance load
entire characteristic is used, a much
The rectified output voltage has a
connected to the sensor output or the
greater power range can be meas-
large noise component due to its wide
output short-circuited. The short-circuit
ured. This may be of advantage for
bandwidth. Therefore it is not possible
current is converted to a broadband
SWR measurements where only little
to measure powers that are considera-
output voltage by a current-to-voltage
power is available. Accurate measure-
bly smaller than 1 µW with high accu-
transducer. Pulse rise times in the
ments are also possible with well-
racy. Peak power sensors are mainly
range of a few ns require the entire
matched loads and therefore low
signal path from the sensor through to
reflected power.
Level
the A/D converter to be designed for
high frequencies. Since the short-cir-
Harmonics are of minor importance,
cuit current is an exponential function
at least in radiocommunications, since
of temperature, measurement errors
a high degree of harmonic suppres-
−6
greater than that of normal sensors are
sion is prescribed by regulations.
dB
to be expected.
Some sensors can measure the peak
+4
+1
−1
−30
power, the output signal of the sensors
being boosted and applied to a peak
−70
10
8 10
542.8
10
hold circuit before it is transferred to
8 10 µs
the power meter.
Fig. 33: GSM burst specifications and possible
power envelope
3.1.3 Directional Power
Sensors
Pr
Pi
Directional sensors are connected
used outside the square-law region.
between source and load to measure
Such sensors are designed as full-
the power flow in both directions.
wave circuits to minimize weighting
They are fitted with a double direc-
errors with non-sinusoidal waveforms.
tional coupler (reflectometer) to pro-
Moreover, with modern sensors the
vide for separation between forward
frequency dependence of the linearity
and reflected wave. The signals cou-
error is calibrated. Special sensors are
pled out are measured by separate
available for TDMA radio networks.
diodes for the incident and for the
With these designs, the output signal
reflected power. Fig. 34 shows the
of the rectifier is lowpass-filtered
block diagram of a sensor for the
ahead of the peak hold circuit. Over-
Power Reflection Meter NAP from
shoots of the RF burst can thus be sup-
Rohde & Schwarz.
28
Voltage and Power Measurements
Reflectometer
Secondaryline terminations and
frequencyresponse compensation
Rectifier
V~Pi To power meter
V~Pr
Fig. 34: Block diagram of sensor for use with
Power Reflection Meter NAP in the frequency
range 25 to 1000 MHz
Directional Couplers
Pd
2
˚
G=0.3/180°
∆P
˚
rL=0.5
1
+j
−1
L
WF 42665
P1
+1
Fig. 36:
The insertion of a directional
sensor may cause considerable power changes (1 → 2)
if source and load are
mismatched
∆∅L
Fig. 35: Directional Power Sensor NRT-Z44 for
the frequency range 200 MHz to 4 GHz
3.1.3.1 Directional Couplers
negligible. This holds true at least for
3.1.3.2 Directivity
The main features of a directional
the lower band limit, where there is
The directivity of the coupler, ie its
power sensor, such as measurement
only a loose coupling between main
ability to separate incident and reflect-
accuracy, matching, frequency and
line and secondary line. Depending on
ed power, has a decisive influence on
power range are determined by the
the type of coupler, the coupling coef-
the measurement accuracy. The direc-
directional coupler. Due to rather
ficient may increase with the fre-
tivity aD is used to describe the level
small dimensions, line couplers with
quency, resulting in more power being
difference between indicated incident
short secondary line, directional cou-
taken from the main line and an
power Pi‘ and indicated reflected pow-
plers with lumped components or simi-
increase in the insertion loss. With
er Pr‘ for a reflection-free matched load
lar designs are suitable for use with
broadband sensors of low rated
(Fig. 37):
directional power meters. For the fre-
power, insertion losses up to about
quency range up to 100 MHz, the
0.5 dB may thus occur at the upper fre-
lumped coupler designed by
quency limit.
P’
i
a D =10 dB log 10 ----- for r L = 0 (21)
P’
r
Buschbeck is mostly used.
Even with a loss-free and ideally
Due to the directional coupler, direc-
matched directional sensor the inser-
tional power sensors are always some-
tion into the test circuit may cause a
what more narrowband than the termi-
change to the power flow (Fig. 36).
nating power sensors, covering a
The cause lies in a change of the
bandwidth between one octave and
phase between source and load
little more than two decades. The rated
reflection coefficient due to the line
power ranges from a few W to some
being extended by the inserted sensor.
kW. It can relatively easily be influ-
In the worst case, deviations attain
enced by the coupling coefficient, with
twice the mismatch uncertainty. This
hardly any change to the power
effect need not be considered at the
absorbed by the directional sensor.
output of level-controlled sources,
Reflection coefficient and insertion loss
since the incident power is stabilized.
of the directional coupler are usually
Pr=0
L=0
Pi
k2Pi
G
Pi
Incident
power
Pr
(kD)2Pi
Reflected
power
Directional power meter
Fig. 37: Measurement of directivity (k = coupling
coefficient; D = directivity factor)
Voltage and Power Measurements
29
Coaxial Voltage Probes
The greater the difference, the better the
From this follows that the matching of
+6
directivity. Standard values for direc-
loads, whose reflection coefficient is
dB
tional sensors lie between 25 dB and
smaller than the directivity factor, can-
35 dB.
not be reasonably measured. To put it
least be as high as the expected return
ity expression, the linear directivity
loss. Equations 24 and 25 only take into
factor D is also used:
account the effect of the directivity on
+2
Inadequate directivity is clearly shown
The measurement error for the incident
in the indicated reflected power Pr‘,
power (εD) can be derived from a
but it also influences the measured
formula analogous to the mismatch
incident power Pi‘. Due to the
uncertainty. In place of the reflection
unknown phase relationship between
coefficient rG, the directivity factor D is
the forward and reflected wave, nei-
used to obtain the following approxi-
ther magnitude nor sign of the result-
mations
ing measurement errors are predictable. There are measurement uncertain-
ε D% ≈ 200 % D ⋅ r L
(26)
ε DdB ≈ 8.7 dB D ⋅ r L
(27)
ties which the manufacturer is not able
to specify and which the user has to
s'
40
0.01
1.02
30
30
0.02
1.05
20
0.05
1.1
0.1
1.2
10
0.2
1.5
2
±20
%
±10
dB
0
0.5
1
3 5
20
25
±5
30
35
±2
40
±1
±0.5
±0.2
estimate.
±0.1
rL 0.01 0.02
with a validity range of about 20 % or
The measurement uncertainty for the
35
Fig. 38: Maximum measurement uncertainty for
return loss due to insufficient directivity; ar‘, rL‘,
SWR‘ = measured return loss, reflection coefficient and SWR
Measurement error
the return loss is given in Fig. 38.
r
r'L
must also be considered. The corredirectivity).
40
−6
a'
cated incident power (see further below)
sponding measurement uncertainty for
20
−4
load. Generally, the effect on the indi-
D is between 0 (ideal case) and 1 (no
25
Directivity/dB
−2
sufficient in case of a well-matched
(22)
20
1 dB (Fig. 39).
SWR
1.02
1.05
Directivity/dB
0.05
0.1
0.2
1.1
1.2
1.5
0.5
2
3 5
1
8
D =
25
0
the indicated reflected power and this is
aD
– ---------------10 20 dB
30
8
In addition to the logarithmic directiv-
35
+4
Measurement uncertainty
another way, the directivity should at
40
reflection coefficient is very easy to
determine. Based on the measured val-
The relative measurement error for the
ues Pr‘ and Pi‘, the reflection coefficient
absorbed power, which is calculated
of the load is derived from the follow-
from the difference between indicated
ing relationship or read out directly:
incident and reflected power, can be
Fig. 39: Maximum measurement error for
incident power due to insufficient directivity
looked up in Fig. 40.
±20
P’
r
----P’
i
(23)
The true value may be greater or
smaller by the directivity factor D:
3.1.4 Coaxial Voltage Probes
Coaxial voltage probes with diode
rL´ − D ≤ rL ≤ rL´ + D
for D ≤ rL´ (24)
0 ≤ rL ≤ rL´ + D
for D > rL´ (25)
rectifiers (see photo on page 9 bottom)
may also be used for power measurements. They are available for frequencies up to about 3 GHz and a very
30
Voltage and Power Measurements
Directivity/dB 20
25
30
35 40 50
±16
±14
±12
±10
±8
±6
±4
±2
0
rL 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
s
1.0 1.2 1.5 2.0 2.5 3
4
6 10 20
8
rr’
LL´ =
Measurement error
±18
Fig. 40: Maximum measurement error for
absorbed power due to insufficient directivity
Basic Units
Sensor
Fig. 41: Power meter with numerical correction of
sensor-specific parameters (NRVS and NRVD)
Basic unit
Frequency
entry
A
ϑ
D
Correction data
Temperature
compensation
P
Linearization
000
f
Calibration
factor
favourably priced alternative for
specific data. The frequency has to be
mal voltages are produced by expos-
measuring the incident power with
entered by the user. The corrected
ing the junctions of different materials
well-matched loads or when require-
results can be output on the display or
to temperature gradients. The offset
ments on the measurement accuracy
via a remote-control interface.
and thermal voltages shift the transfer
are not high. Modern probes provide
characteristic of the sensor from the ori-
all facilities of intelligent error correc-
gin by an amount independent of the
tion. The rectifier is connected to the
measured power (Fig. 42). The result-
inner conductor either directly or via a
ing zero offset is the greater, the
capacitive 10:1 attenuator. The atten-
3.2.1 Zeroing
smaller the measured power.
pling of the rectifier. Therefore, such
With all power meters, there are addi-
This effect can be corrected for all
probes exhibit an excellent matching
tional measurement errors at the lower
power meters by zeroing. For this pur-
and low insertion loss over the entire
measurement limit due to superim-
pose, the power to be measured must
posed interference. Thermocouple
be disconnected first. One should also
sensors and diode sensors are mainly
avoid to touch the sensor so that no
uator allows almost complete decou-
useful frequency range.
additional thermal voltages will be
produced. The residual offset after
zeroing and the display noise determine the sensitivity of the power meter.
3.2 Basic Units
Reading
The basic power meters have the task
of processing the output signal from the
sensor (Fig. 41). With the exception of
envelope sensors, the sensor signals
are usually low DC voltages with
superimposed residual low-frequency
modulation. They are boosted in a low-
3.2.2 Display Noise and
Measurement Speed
+
−
Power
to a level where they can be digitized.
Display noise causes jitter of a meter
pointer or flickering of a digital read-
noise and low-drift chopper amplifier
Fig. 42: Zero offset
out. Like the zero offset, display noise
The AC component is suppressed by
is an additive error independent of the
lowpass filters or the A/D converter
measured power. By reducing the
measurement bandwidth, display
itself. Modern instruments feature an
extensive numerical correction of the
affected by thermal voltages and offset
noise can be traded off for measure-
measured values based on the sensor-
voltages in the chopper amplifier. Ther-
ment speed (Fig. 43). Usually, the
Voltage and Power Measurements
31
Calibration
100
s
t
Setting time
Power
2.8%
1.5%
10
Diode (NRV-Z4)
Thermocouple (NRV-Z51)
4σ
1
Reading
t
te
0.1
−60
−40
−20
4σ
Reading
te
0
+20 dBm
Power level
t
Fig. 43: Display noise and dynamic behaviour of
a power meter without (center) and with display
filter (bottom)
Fig. 44: Settling time as a function of measured power. The display filter is set so that the relative noise
component (2σ) remains within 0.1%. Only with the filter set to maximum, the noise component rises to
the specified value with the measured power further decreasing
3.2.3 Envelope Analyzers
means of calibration. The determina-
tering. Depending on the measuring
The basic units are similar in design to
proportionality factor is sufficient in
instrument, filtering can either be
digital oscilloscopes. Broadband
few cases only. With modern sensors,
selected by the user or set automati-
amplification of the sensor signal is fol-
the calibration data are stored in a
cally. The smaller the power, the more
lowed by digitization with a fast A/D
digital memory connected with the
effective must be filtering.
converter. Periodical signals can be
sensor and numerically processed in
displayed with high time resolution by
the basic unit.
measurement results are numerically
averaged, partly using analog prefil-
A meaningful indication of the mini-
random sampling. As with average-
mum power specified for a sensor is as
weighting power meters, the display
a rule only possible with high noise fil-
noise can be reduced by limiting the
tering, settling times from 10 s to 30 s
bandwidth, which may cause smooth-
being not unusual (Fig. 44). Short
ing of the pulse edges. For correcting
measuring times of about 0.1 s can
sensor-specific characteristics, the
only be achieved at higher power lev-
same methods are used as with aver-
els, with thermocouple sensors in the
age-weighting power meters.
tion of a single, frequency-dependent
3.3.1 Terminating Power
Sensors
Terminating sensors can be calibrated
relatively narrow range from 1 mWto
so that either the power Pd absorbed at
100 mW. Diode detectors, which can
the reference plane or the incident
be operated beyond the rectifier
power Pi is indicated (Fig. 45). Usually,
square-law region, have the advantage
indication of the incident power is cal-
that they allow a power range of 40 dB
to be measured at maximum speed.
3.3 Calibration
ibrated. The power PGZ0 of the source
delivered to Z0 load can then be meas-
They are therefore ideal for use in auto-
The output signal of high-frequency
ured. With older power meters, the
matic test systems. Since the display
power sensors is a complex function of
calibration parameter is referred to as
noise causes random measurement
measured power, frequency and tem-
the calibration factor. For ease of
errors, it has to be described as a statis-
perature. Since an adjustment of the
understanding, one should assume
tical error. It is usually specified as
high-frequency sensor is not possible
that the power delivered to Z0 load is
twice the standard deviation (2σ) corre-
for practical reasons, the individual
to be measured in the special case of
sponding to a confidence level of 95 %.
characteristics must be determined by
a matched source (Fig. 46). After con-
32
Voltage and Power Measurements
Calibration
cients and usually differs from the
power delivered to Z0 load. This meas-
Parasitic losses
(frequency-dependent)
is entered into the measurement result
Pr1
Pi2
2
Pr2
Pr1
as a mismatch uncertainty (see
T
Fig. 10). Since the source is given, the
V
Thermocouple
sensor
Reflected
power
(frequencydependent)
Pi2
1
urement error cannot be corrected and
Usable thermal
power
Incident power
Pi1
G
mismatch can only be influenced by
the sensor. The better the sensor
Directional power meter
Fig. 47: Calibration of directional power meters
matching, the lower is the measure-
Termination plane
ment uncertainty.
Reference plane of sensor
A considerably higher accuracy can
Fig. 45: Power distribution in a thermocouple sensor. The absorbed power is equal to the sum of
usable thermal power and parasitic losses
be obtained when measuring the maximum available power PG max of the
source instead of the power delivered
3.3.2 Directional Power
Sensors
to Z0 load. For this purpose, the sensor
Directional sensors are usually cali-
must be conjugate matched to the
brated for indication of the outgoing
source via a tuner and calibrated for
power (Fig. 47). This means that the
nection of the sensor, the incident
indication of the power absorbed at
power incident to the load is indi-
power will be of the value PGZ0 (equa-
the reference plane (see Fig. 7). This
cated, as desired, but unfortunately
tion 12), whereas the power absorbed
method of calibration is used for high-
also the reflected power referred to the
at the reference plane will be smaller
precision standards with thermistors.
source connector of the power sensor.
by the mismatch loss of the sensor. To
The calibration parameter is the ratio
For SWR measurements, the resulting
ensure that the power indication is
of the thermal power Ptherm to the
measurement error is negligible even
independent of the reflection coeffi-
absorbed power Pd at the reference
if the sensor exhibits a somewhat
cient of the sensor, the sensor must be
plane. It is referred to as the effective
higher insertion loss. Considerable
calibrated for the incident power.
efficiency ηe and always smaller than
measurement errors may however
1 due to the parasitic losses between
occur if the power absorbed by the
RF connector and termination.
load is to be measured with incident
and reflected power being approxi-
Pi = PGZ0
rL2 ⋅ Pi
PGZ0 (1− rL2)
P therm
η e = -------------Pd
mately equal. In this case, the indi(28)
cated reflected power must be
increased by the amount of the inser-
G
tion loss of the directional power
L
G=0
Fig. 46: Power measurement on matched source
It may at times be necessary to meas-
sensor.
ure the absorbed power with a power
meter calibrated for incident power. If
the reflection coefficient rL of the sensor is known, the equation
P d = P i ( 1 – r L2 )
3.3.3 Coaxial Voltage Probes
Coaxial voltage probes are calibrated
Despite correct calibration, measurement errors may occur if both ends,
(29)
can be used for conversion.
for indication of the incoming or outgo-
that is source and sensor, are mis-
ing power. Details can be taken from
matched. In this case, the incident
the manufacturer‘s documentation.
power is dependent on the magnitude
and phase of the two reflection coeffi-
Thomas Reichel
Voltage and Power Measurements
33
Definitions of Voltage and Power Measurements
Adjustment
operator’s errors cannot be excluded.
Adjustment means to set or adjust a
operator has to rush through the meas-
Directional power meters are able to
measuring instrument so as to minimize
urement. Moreover, this calibration
measure the power flow on a coaxial
measurement errors or to ensure that the
method does not take account of the
line separately for the forward and the
measurement errors do not exceed the
nonlinearity of the sensor and its
reflected wave. For this purpose they
error limits. Adjustment requires an
response to temperature variations.
are fitted with a dual directional cou-
Errors often arise especially if the
action which usually causes a perma-
Directivity
pler (reflectometer) of symmetrical
nent change to the measuring instru-
To eliminate all these error sources, all
design with two test outputs. Each of
ment.
sensors of the URV5-Z, NRV-Z and
the two test outputs is assigned one of
NRT-Z series are absolutely calibrated.
the two power flow directions in the
An integrated ROM contains all the
main line. In the ideal case, the power
relevant data: individual sensitivity for
is coupled out from the wave in the
a large number of frequencies, nonlin-
preferred direction only, which how-
Calibration
earity, temperature effect and general
ever is not possible in practice. The
data such as date of calibration, etc.
selectivity of the directional coupler is
Calibration is used to determine the
Whenever a sensor is connected to the
expressed in terms of its directivity.
response of a measuring instrument
meter, these calibration data are read
The directivity is a logarithmic meas-
relative to a reference instrument of
out and used for calculating the meas-
ure in dB stating the amount of change
higher accuracy. Although the calibra-
urement result. Operator’s errors are
of the power coupled out when the
tion process itself is error-prone,
excluded and the accuracy of the
power flow direction is reversed. The
systematic measurement deviations
results is considerably increased.
higher the directivity, the better the
can be numerically determined and
matching of the load can be deter-
taken into account in subsequent
mined by a directional power meter. A
measurements.
high directivity also reduces the measurement uncertainty for the incident
For the majority of power meters, only
the frequency response of the sensor is
Crest Factor
power in the case of a load with poor
matching.
calibrated, ie the variation of the ratio
The crest factor is the ratio of peak to
between output voltage of the RF sen-
RMS value of an AC voltage and an
sor and input power relative to a refer-
essential criterion in the measurement
ence frequency. This kind of calibra-
of non-sinusoidal AC voltages with an
tion makes it necessary that prior to a
RMS voltmeter.
Frequency Response
subjected to an absolute calibration
This term is used similarly in power
The frequency response of a measuring
with the aid of a precise power refer-
measurements where it is defined as
instrument is defined as the measure-
ence (usually 1 mW, 50 MHz). Apart
the ratio of peak envelope power to
ment error being a function of fre-
from the inconvenience of this proce-
average power.
quency, relative to a reference fre-
measurement each sensor has to be
dure, incorrect manual calibration or
34
Voltage and Power Measurements
quency.
Definitions
German Calibration Service
(DKD)
voltmeters an input impedance of
rated. Only with a well-matched sen-
about 1 MΩ  40 pF can be assumed.
sor can this effect be kept low since the
At 10 MHz the parallel capacitance
measurement errors caused by mis-
Roof organization of industrial calibra-
gives an input impedance of as low as
match are determined by the product
tion laboratories in the Federal Repub-
500 Ω. A connected coaxial cable
of the reflection coefficient of source
lic of Germany. The German calibra-
makes the input impedance even low-
and sensor and the matching of the
tion laboratories can offer calibration
er. The input impedance can be in-
source – that is the DUT – can usually
services for a variety of important
creased by using a voltage divider
not be changed. All URV5 and NRV
physical parameters approved by the
probe (10:1, 100:1) or an active
sensors therefore feature very low
German Standards Laboratory (PTB).
probe.
reflection coefficients. If several,
equally good sensors are available for
With diode probes the AC voltage to
a measurement, the one with the low-
be measured is applied to a diode rec-
est reflection coefficient should be cho-
tifier without input amplifier. At the
sen. Usually, it also has the lowest cal-
IEC/IEE Bus
lower frequencies, the diode probes
ibration uncertainty.
The standard remote-control interface
100 kΩ) as voltmeters with an input
in electronic measurements. It is an
amplifier. Due to their low input
addressable parallel data interface
capacitance of approx. 2 pF, the input
allowing simultaneous control of
impedance is much higher at a few
several instruments. Usually it is pro-
MHz. Using plug-in dividers, the
vided on a separate interface card
capacitance can be reduced to about
The measurement error is defined as
and requires additional programs for
0.5 pF at the sacrifice of sensitivity
the difference between a measured
the process controller used. With the
and the input impedance thus further
value and a reference value that is usu-
international standardization of the
increased. Diode probes permit high-
ally furnished by a high-precision
command syntax for the SCPI stand-
impedance measurements up to fre-
measuring instrument. In the ideal
ard (Standard Commands for Pro-
quencies of 1 GHz.
case the reference value is the "true"
are not as high-impedance (approx.
Measurement Error
grammable Instruments) the standardi-
value of the measurand that cannot be
zation work has come to an end for
measured however. Error limits are the
the time being.
maximum permissible measurement
errors specified by the manufacturer of
Matching
the measuring instrument. If these error
For a quantitative description of this
instrument is considered to be faulty.
limits are exceeded, the measuring
Input Impedance
term the parameters reflection coefficient, return loss and SWR are used.
The accuracy of power meters is usu-
In electronic voltmeters with an input
Extremely low reflection coefficient or
ally not specified in terms of error
amplifier, the input impedance is gen-
an SWR with an ideal value of 1 or
limits. Manufacturers rather state the
erally high and can be represented by
very high return loss are basic require-
measurement uncertainty for the deter-
an ohmic resistance and a lossy ca-
ments. The effect of mismatch on the
mination of the calibration factors
pacitance in parallel. For broadband
measurement accuracy is often under-
(calibration uncertainty).
Voltage and Power Measurements
35
Definitions
Measurement Uncertainty
National Laboratory
Peak Power
Measurement uncertainty is a parame-
National authority responsible for
Amplitude modulation (AM) and many
ter that characterizes the accuracy of a
establishing, maintaining and dissemi-
digital modulation methods cause a
measurement and is associated with
nating standards for physical quanti-
modulation of the envelope of the car-
the result of a measurement or calibra-
ties (eg power) with lowest possible
rier signal. The peak power is defined
tion. More precisely, the measurement
uncertainty. In the Federal Republic of
as the power at the modulation maxi-
uncertainty characterizes the range of
Germany this task is performed by the
mum averaged over one cycle of the
values that can reasonably be attrib-
German Standards Laboratory (PTB)
carrier signal. To avoid confusion with
uted to the measurand.
and in the United States by the
the peak value of the instantaneous
National Institute of Standards and
power, the term peak envelope power
Technology (NIST, formerly NBS).
(PEP) should rather be used instead of
According to international practice,
the specification of measurement
peak power.
uncertainty limits (worst case) has
meanwhile been replaced by the
socalled expanded uncertainty with a
coverage factor of 2. With normal distribution of the measurement errors, it
Nonlinearity
Peak-Responding
Rectification
can be assumed that the measurement
Nonlinearity or linearity error of a
result is with 95% probability within
measuring instrument is the deviation
the interval defined by the expanded
from a linear relationship between
Voltmeters with peak-responding recti-
uncertainty.
measured quantity and displayed
fication measure the peak value of a
value.
periodic signal. They have a storage
The expanded measurement uncer-
capacitor which holds the peak value.
tainty is determined statistically taking
Distinction is made between positive
into account all parameters influenc-
peak (Vp+), negative peak (Vp−) and
ing the measurement. The method is
described in detail for instance in the
Official Calibration
"Guide to the Expression of Uncer-
Testing of a measuring instrument by a
tainty in Measurement" published by
calibration authority in line with cer-
the International Organization for
tain calibration standards. A stamped
Standardization (ISO).
label certifies that at the time of testing
the measuring instrument has com-
The acronym PEP stands for peak
and that due to the nature of such
envelope power which is the carrier
instrument it can be expected that with
power at the highest crest of the enve-
proper handling it will adhere to spec-
lope averaged over one cycle (peak
ifications until the next recalibration
power).
ments subject to official calibration are
governed by legal provisions.
Voltage and Power Measurements
PEP
plied with the calibration standards
becomes due. The measuring instru-
36
peak-to-peak rectification (Vpp).
Definitions
RMS-Responding
Rectification
Sensitivity
Testing
The sensitivity of a measuring instru-
Checking the device under test for
The RMS value is the most widely used
ment is defined as the ratio of the
compliance with one or several given
parameter to determine the magnitude
response of an output quantity (the dis-
conditions. A measuring instrument for
of an AC voltage. It is defined so that a
played value) to the variation of the
instance can be tested for compliance
DC voltage of this magnitude produces
measured quantity. If the sensitivity
with the specified error limits.
the same heat dissipation at an ohmic
depends on the magnitude of the
resistance as the AC voltage meas-
measured quantity, the response is
ured. The mathematical expression
referred to as nonlinear.
(where Ti is the integration time) is:
Thermal Power
Measurement
Ti
V rms =
1
------ ⋅ v 2 (t) dt
Ti
∫
Square-Law Region
Thermal power meters allow an almost
Squaring of the measured voltage
The square-law region of diode detec-
a quantity that can be measured more
may – in line with the definition – be
tors is the range of the input voltage or
easily, eg the temperature rise in a ter-
made thermally by means of nonlinear
input power within which the output
minating resistor.
electronic components or numerically
DC voltage is proportional to the
following a sampling process. Rohde
square of the input voltage or – being
Earlier designs of this type of power
& Schwarz uses a patented circuit in
equivalent – the input power (RMS-
meters usually had the disadvantage
the RMS Voltmeters URE 2 and URE 3
responding rectification).
of a low measurement speed, since
0
error-free conversion of RF power into
whose benefits are great accuracy,
the thermal time constant of the termi-
high crest factor, wide frequency
nation and of the thermal sensor was
range and short settling time.
not small enough. However, semiconductor technology has now made it
Standard deviation
possible to achieve an effective time
Standard deviation is a measure of the
in the Power Sensor NRV-Z55. For this
RS-232 Interface
average deviation of a discrete ran-
sensor, a new method has been
dom variable from its average value.
adopted which allows DC coupling of
A serial data interface, one or several
This term is also used in measurement
the signal, so that a single sensor can
of which are fitted as standard in most
technology to characterize noise sig-
cover the entire frequency range from
of the PCs. A mouse or a plotter can
nals. It can be shown that the standard
DC to 40 GHz.
for instance be connected to the
deviation of a sequence of sampling
RS-232 interface – or a Level Meter
values of a noise voltage (without DC
URV 35 remote-controlled. The inter-
voltage content) is equal to the RMS
face is bidirectional, that means that
value of this voltage.
constant of a few milliseconds only, eg
data can be sent or received. Each
data word is sent as a bit stream, with
start and one or two stop bits, at a
fixed clock rate, ie the transfer rate.
The usual data format consists of
8 data bits, one start and one stop bit,
ie 10 bits per character.
Voltage and Power Measurements
37
References
Barnard, D.L. et al.: Automatic Calibration for
Easy and Accurate Power Measurements.
Hewlett-Packard Journal, Vol. 43 (April 1992),
pp. 95-100.
Blankenburg, K.H.: Waveform weighting for RF
voltage measurements using RF-DC Millivoltmeter
URV. News from Rohde & Schwarz No. 75
(1976), pp. 22-24.
Bailey, A.E et al.: Microwave measurement.
Peter Peregrinus Ltd., London, UK 1985.
Browne, J.: SNA Sensors Trigger on Fast Pulses.
Microwaves & RF, July 1990, pp. 132-137.
Betz, T.: New mobile-radio technology, new test
equipment: Directional Power Meter NAS with
GSM insertion unit NAS-Z6. News from Rohde &
Schwarz No. 139 (1992), pp. 32-33.
Buschbeck, W.: Hochfrequenz-Wattmeter und
Fehlanpassungsmesser mit direkter Anzeige.
Hochfrequenz und Elektroakustik 61 (1943)
No. 4, S. 93.
Betz, T.: Directional Power Meter NAS for any
radio system. News from Rohde & Schwarz
No. 134 (1991), pp. 29-30.
Burns, J.G.: Vector Analyzer speeds Power Sensor Calibration Results. Microwaves & RF,
Aug. 1987, pp. 91-96.
Betz, T.: Power sensors for NRV now up to
26.5 GHz. News from Rohde & Schwarz
No. 133 (1991), pp. 34-35.
Cordes, H.: Messung der Spitzenleistung bei
Mikrowellen. Elektronik, Vol. 34 (1985),
No. 24, pp. 126-127.
Betz, T.: URE 2 and URE 3 – evolution and revolution in RMS voltmeters. News from Rohde &
Schwarz No. 127 (1989), pp. 8-11.
Daw, E.: Determine the Accuracy of loss measurements. Microwaves & RF, Jan. 1984,
pp. 73-79.
Betz, T.: HF-Spannung und HF-Leistung perfekt
gemessen. Elektronik, Vo. 35 (1986), No. 13,
pp. 171-174.
DIN 1319, Part 1, June 1985: Grundbegriffe
der Meßtechnik – Allgemeine Grundbegriffe.
Betz, T.; Köhler, D.; Reichel, T.: RF Millivoltmeter
URV 5 – voltage and power measurement into
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Voltage and Power Measurements
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