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5988-9215EN English _ 2014-08-01 _ PDF 987 KB c20141022 [43]


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Keysight Technologies
Fundamentals of RF and Microwave
Power Measurements (Part 3)



                             Application Note
    For user convenience, the Keysight      Fundamentals of RF and Microwave Power
    Fundamentals of RF and Microwave
    Power Measurements, applica-
                                            Measurements (Part 1)
    tion note 64-1, literature number       Introduction to Power, History, Deinitions, 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      Part 1 introduces the historical basis for power measurements, and provides
    explain how the total field of power    definitions for average, peak, and complex modulations. This application note
    measurement fundamentals is now         overviews various sensor technologies needed for the diversity of test signals. It
    presented.                              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. Sen-
                                            sor 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. Keysight has transitioned from
                                            ANSI/NCSL Z540-1-1994 to ISO 17025.

                                            Fundamentals of RF and Microwave Power
                                            Measurements (Part 4)
                                            An Overview of Keysight 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
2                                           communications formats and their statistical measurement needs.
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 GUM1. 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
    Signal Flowgraphs   The goal of an absolute power measurement is to characterize the unknown
                        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 = 



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