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Agilent
Fundamentals of RF and Microwave
Power Measurements (Part 3)
Power Measurement Uncertainty
per International Guides
For user convenience, Agilent's Fundamentals of RF and Microwave Power
Fundamentals of RF and Microwave
Power Measurements, application
Measurements (Part 1)
note 64-1, literature number Introduction to Power, History, Definitions, International
5965-6330E, has been updated and Standards, and Traceability
segmented into four technical subject AN 1449-1, literature number 5988-9213EN
groupings. The following abstracts
explain how the total field of power Part 1 introduces the historical basis for power measurements, and provides
measurement fundamentals is now definitions for average, peak, and complex modulations. This application note
presented. overviews various sensor technologies needed for the diversity of test signals.
It describes the hierarchy of international power traceability, yielding
comparison to national standards at worldwide National Measurement
Institutes (NMIs) like the U.S. National Institute of Standards and Technology.
Finally, the theory and practice of power sensor comparison procedures are
examined with regard to transferring calibration factors and uncertainties. A
glossary is included which serves all four parts.
Fundamentals of RF and Microwave Power
Measurements (Part 2)
Power Sensors and Instrumentation
AN 1449-2, literature number 5988-9214EN
Part 2 presents all the viable sensor technologies required to exploit the users'
wide range of unknown modulations and signals under test. It explains the
sensor technologies, and how they came to be to meet certain measurement
needs. Sensor choices range from the venerable thermistor to the innovative
thermocouple to more recent improvements in diode sensors. In particular,
clever variations of diode combinations are presented, which achieve ultra-wide
dynamic range and square-law detection for complex modulations. New
instrumentation technologies, which are underpinned with powerful
computational processors, achieve new data performance.
Fundamentals of RF and Microwave Power
Measurements (Part 3)
Power Measurement Uncertainty per International Guides
AN 1449-3, literature number 5988-9215EN
Part 3 discusses the all-important theory and practice of expressing
measurement uncertainty, mismatch considerations, signal flowgraphs, ISO
17025, and examples of typical calculations. Considerable detail is shown on
the ISO 17025, Guide for the Expression of Measurement Uncertainties, has
become the international standard for determining operating specifications.
Agilent has transitioned from ANSI/NCSL Z540-1-1994 to ISO 17025.
Fundamentals of RF and Microwave Power
Measurements (Part 4)
An Overview of Agilent Instrumentation for RF/Microwave
Power Measurements
AN 1449-4, literature number 5988-9216EN
Part 4 overviews various instrumentation for measuring RF and microwave
power, including spectrum analyzers, microwave receivers, network analyzers,
and the most accurate method, power sensors/meters. It begins with the
unknown signal, of arbitrary modulation format, and draws application-oriented
comparisons for selection of the best instrumentation technology and products.
Most of the note is devoted to the most accurate method, power meters and
sensors. It includes comprehensive selection guides, frequency coverages,
contrasting accuracy and dynamic performance to pulsed and complex digital
modulations. These are especially crucial now with the advances in wireless
communications formats and their statistical measurement needs.
2
Table of Contents I. Introduction ........................................................................................................ 4
II. Power Transfer, Signal Flowgraphs...................................... 5
Power transfer, generators and loads .......................................................... 5
RF circuit descriptions ..................................................................................... 5
Reflection coefficient ....................................................................................... 7
Signal flowgraph visualization ....................................................................... 8
III. Measurement Uncertainties .......................................................... 12
Mismatch loss uncertainty ............................................................................. 12
Mismatch loss and mismatch gain ............................................................... 13
Simple techniques to reduce mismatch loss uncertainty ........................ 13
Advanced techniques to improve mismatch uncertainty ......................... 17
Eliminating mismatch uncertainty by measuring source and
load complex reflection coefficients and computer correcting ........... 18
Other sensor uncertainties ............................................................................. 18
Calibration factor .............................................................................................. 19
Power meter instrumentation uncertainties ............................................... 20
IV. Alternative Methods of Combining Power
Measurement Uncertainties .......................................................... 23
Calculating total uncertainty .......................................................................... 23
Power measurement equation....................................................................... 23
Worst-case uncertainty method .................................................................... 25
RSS uncertainty method ................................................................................. 26
A new international guide to the expression of uncertainty in
measurement (ISO GUM) ............................................................................ 27
Power measurement model for ISO process .............................................. 29
Standard uncertainty of mismatch model ................................................... 31
Example of calculation of uncertainty using ISO model ........................... 32
Example of calculation of uncertainty of USB sensor using
ISO model ....................................................................................................... 35
3
I. Introduction The purpose of the new series of Fundamentals of RF and Microwave Power
Measurements application notes, which were leveraged from former note 64-1,
is to
1) Retain tutorial information about historical and fundamental considerations
of RF/microwave power measurements and technology which tend to
remain timeless.
2) Provide current information on new meter and sensor technology.
3) Present the latest modern power measurement techniques and test
equipment that represents the current state-of-the-art.
Part 3 of this series, Power Measurement Uncertainty per International Guides, is
a comprehensive overview of all the contributing factors (there are 12 described in
the International Standards Organization (ISO) example) to power measurement
uncertainty of sensors and instruments. It presents signal flowgraph principles
and a characterization of the many contributors to the total measurement
uncertainty.
Chapter 2 examines the concept of signal flow, the power transfer between
generators and loads. It defines the complex impedance, its effect on signal
reflection and standing waves, and in turn its effect on uncertainty of the power in
the sensor. It introduces signal flowgraphs for better visualizations of signal flow
and reflection.
Chapter 3 breaks down all the various factors that influence measurement
uncertainty. It examines the importance of each and how to minimize each of the
various factors. Most importantly, considerable space is devoted to the largest
component of uncertainty, mismatch uncertainty. It presents many practical tips
for minimizing mismatch effects in typical instrumentation setups.
Chapter 4 begins by presenting two traditional methods of combining the effect of
the multiple uncertainties. These are the "worst-case" method and the "RSS"
method. It then examines in detail the increasingly popular method of combining
uncertainties, based on the ISO Guide to the Expression of Uncertainty in
Measurement, often referred to as the GUM.[1] ISO is the International Standards
Organization, an operating unit of the International Electrotechnical Commission
(IEC). The reason the GUM is becoming more crucial is that the international
standardizing bodies have worked to develop a global consensus among National
Measurement Institutes (such as NIST) and major instrumentation suppliers as
well as the user community to use the same uncertainty standards worldwide.
Note: In this application note, numerous technical references will be made to the
other published parts of the series. For brevity, we will use the format
Fundamentals Part X. This should insure that you can quickly locate the concept
in the other publication. Brief abstracts for the four-part series are provided on the
inside front cover.
[1] "ISO Guide to the Expression of Uncertainty in Measurement," International Organization for Standardization,
Geneva, Switzerland, ISBN 92-67-10188-9, 1995.
4
II. Power Transfer, Power transfer, generators and loads
The goal of an absolute power measurement is to characterize the unknown
Signal Flowgraphs power output from some source (for example a generator, transmitter, or
oscillator). Sometimes the generator is an actual signal generator or oscillator
where the power sensor can be attached directly to that generator. On other
occasions, however, the generator is actually an equivalent generator. For example,
if the power source is separated from the measurement point by such components
as transmission lines, directional couplers, amplifiers, mixers, etc., then all those
components may be considered as parts of the generator. The port that the power
sensor connects to, would be considered the output port of the equivalent
generator.
To analyze the effects of impedance mismatch, this chapter explains mathematical
models that describe loads, including power sensors and generators, which apply
to the RF and microwave frequency ranges. The microwave descriptions begin by
relating back to the equivalent low-frequency concepts for those familiar with
those frequencies. Signal flowgraph concepts aid in analyzing power flow between
an arbitrary generator and load. From that analysis, the terms mismatch loss and
mismatch loss uncertainty are defined.
RF circuit descriptions
At low frequencies, methods for describing a generator include the Thevenin and
Norton equivalent circuits. The Thevenin equivalent circuit of a generator, for
example, has a voltage generator, es, in series with an impedance, Zg , as shown
in Figure 2-1. For a generator, even if composed of many components, es is
defined as the voltage across the output port when the load is an open circuit. Zg
is defined as the impedance seen looking back into the generator when all the
sources inside the generator are reduced to zero.
Figure 2-1. A Thevenin equivalent generator connected to an arbitrary load.
5
The power delivered by a generator to a load is a function of the load impedance.
If the load is a perfect open or short circuit, the power delivered is zero. Analysis
of Figure 2-1 would show that the power delivered to the load is a maximum when
load impedance, Z , is the complex conjugate of the generator impedance, Zg. This
power level is called the "power available from a generator," or "maximum
available power," or "available power." When Z = (R + jX ) and Zg = (Rg + jXg)
are complex conjugates of each other, their resistive parts are equal and their
imaginary parts are identical in magnitude but of opposite sign; thus R = Rg and
X =