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Fundamentals of RF and Microwave Power Measurements (Part 3)

Application Notes

Table of Contents

  • I. Introduction
  • II. Power Transfer, Signal Flowgraphs
    • Power transfer, generators, and loads
    • RF circuit descriptions
    • Reflection coefficient
    • Signal flowgraph visualization
  • III. Measurement Uncertainties
    • Mismatch loss uncertainty
    • Mismatch loss and mismatch gain
    • Simple techniques to reduce mismatch loss uncertainty
    • Advanced techniques to improve mismatch uncertainty
    • Eliminating mismatch uncertainty by measuring source and load complex reflection coefficients and computer correcting
    • Other sensor uncertainties
    • Calibration factor
    • Power meter instrumentation uncertainties
  • IV. Alternative Methods of Combining Power Measurement Uncertainties
    • Calculating total uncertainty
    • Power measurement equation
    • Worst-case uncertainty method
    • RSS uncertainty method
    • A new international guide to the expression of uncertainty in measurement (ISO GUM)
    • Power measurement model for ISO process
    • Standard uncertainty of mismatch model
    • Example of calculation of uncertainty using ISO model
    • Example of calculation of uncertainty of USB sensor using ISO model

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.

II. Power Transfer, Signal Flowgraphs

Power transfer, generators and loads

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.


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