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Agilent
Fundamentals of RF and
Microwave Power Measurements
Application Note 64-1C
Classic application note on
power measurements
Newly revised and updated
Table of Contents
I. Introduction
The importance of power.................................................................................................................................5
A brief history of power measurement .........................................................................................................6
A history of peak power measurements........................................................................................................7
II. Power Measurement
Units and definitions........................................................................................................................................9
IEEE video pulse standards adapted for microwave pulses......................................................................13
Peak power waveform definitions ..................................................................................................................14
New power sensors and meters for pulsed and complex modulation......................................................15
Three methods of sensing power ...................................................................................................................15
Key power sensor parameters .......................................................................................................................16
The hierarchy of power measurement, national standards and traceability .........................................17
III. Thermistor Sensors and Instrumentation
Thermistor sensors ..........................................................................................................................................19
Coaxial thermistor sensors . ...........................................................................................................................20
Waveguide thermistor sensors ........................................................................................................................20
Bridges, from Wheatstone to dual-compensated DC types .......................................................................20
Thermistors as power transfer standards.....................................................................................................22
Other DC-substitution meters .........................................................................................................................22
Some measurement considerations for power sensor comparisons.........................................................23
Typical sensor comparison system ................................................................................................................23
Network analyzer source system ....................................................................................................................24
NIST 6-port calibration system.......................................................................................................................25
IV. Thermocouple Sensors and Instrumentation
Principles of thermocouples ..........................................................................................................................26
The thermocouple sensor ................................................................................................................................27
Power meters for thermocouple sensors.......................................................................................................31
Reference oscillator ..........................................................................................................................................33
EPM series power meters ................................................................................................................................33
V. Diode Sensors and Instrumentation
Diode detector principles ................................................................................................................................35
Using diodes for sensing power ......................................................................................................................37
Wide-dynamic-range CW-only power sensors ..............................................................................................39
Wide-dynamic-range average power sensors................................................................................................40
A new versatile power meter to exploit 90 dB range sensors ...................................................................42
Traceable power reference ..............................................................................................................................44
Signal waveform effects on the measurement uncertainty of diode sensors ........................................45
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VI. Peak and Average Diode Sensors and Instrumentation
Pulsed formats ................................................................................................................................................48
Complex modulation wireless signals.........................................................................................................49
Other formats..................................................................................................................................................50
Peak and average power sensing .................................................................................................................51
EPM-P series power meters ..........................................................................................................................53
Computation power........................................................................................................................................55
Bandwidth considerations ............................................................................................................................56
Versatile user interface..................................................................................................................................57
VII. Measurement Uncertainty
An international guide to the expression of uncertainties .....................................................................58
Power transfer, generators and loads ........................................................................................................59
RF circuit descriptions ..................................................................................................................................59
Reflection coefficient ....................................................................................................................................61
Signal flowgraph visualization .....................................................................................................................62
Mismatch uncertainty....................................................................................................................................66
Mismatch loss and mismatch gain...............................................................................................................67
Other sensor uncertainties ...........................................................................................................................67
Calibration factor ..........................................................................................................................................68
Power meter instrumentation uncertainties ............................................................................................69
Calculating total uncertainty........................................................................................................................71
Power measurement equation .....................................................................................................................72
Worst case uncertainty ..................................................................................................................................74
RSS uncertainty..............................................................................................................................................75
New method of combining power meter uncertainties ...........................................................................76
Power measurement model for ISO process ..............................................................................................77
Standard uncertainty of mismatch model .................................................................................................79
Example of calculation of uncertainty using ISO model .........................................................................80
VIII. Power Measurement Instrumentation Compared
Accuracy vs. power level ...............................................................................................................................84
Frequency range and SWR (reflection coefficient) ..................................................................................86
Speed of response ..........................................................................................................................................87
Automated power measurement .................................................................................................................88
Susceptibility to overload..............................................................................................................................89
Signal waveform effects.................................................................................................................................90
An applications overview of Agilent sensors.............................................................................................90
A capabilities overview of Agilent sensors and power meters ...............................................................91
Glossary and List of Symbols .................................................................................................................94
Pulse terms and definitions, figure 2-5, reprinted from IEEE STD 194-1977 and ANSI/IEEE STD 181-1977, Copyright