NfST

PUBLICATIONS

e. .T <7 NIST TECHNICAL NOTE 1310

A111D3 DDHDET

NATL INST OF STANDARDS & TECH R.I.C.

A1 11 03004029

Livingston, E. M/Performance evaluation QC100 .U5753 NO.1310 1988 V198 C.I NISTCOMMERCE/ National Institute of Standards and Technology
NATIONAL INSTITUTE OF STANDARDS

TECHNOLOGY

Reeearch Informatioa Center

Gattbersburg, MD 20899
, /J. /J/o

Performance Evaluation of /^^^

Radiofrequency, Microwave, and ^^

IVIillimeter Wave Power IVIeters

Eleanor M. Livingston

Robert T. Adair

Electromagnetic Fields Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Institute of Standards and Technology

Boulder, Colorado 80303-3328

Stimulating Amefica s Progress

1 9 1 3 - 1 988

U.S. DEPARTMENT OF COMMERCE, C. William Verity. Secretary

Ernest Annbler, Acting Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY. Raymond G. Kammer. Acting Director

Issued December 1988
National Institute of Standards and Technology

Technical Note 1310, 158 pages (Dec. 1988)

CODEN:NTNOEF

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1988

For sale by the Superintendent of Docunnents, U.S. Governnnent Printing Office, Washington, DC 20402-9325
FOREWORD

The purpose of this performance evaluation procedure is to provide recommended

test methods for verifying conformance with typical performance criteria of

power meters that are commercially available for use in the radiofrequency

,

microwave, and millimeter wave regions. These methods are not necessarily the

sole means of measuring conformance with the suggested tyoical specifications,

but they represent current procedures which use commercially available test

equipment and which reflect the professional level and impartial viewpoint of

the Institute of Standards and Technology (NIST) (formerly the National Bureau

of Standards (NBS)).

iii

1.0

CONTENTS

FOREWORD

FIQJRES

TABU^S

ABSTRACT

Introduction

1 .

Importance of Power Measurements

1.2 What Power Measurements Indicate About a Device or System ,

Page

iii

ix

xiii

xvii

1-1

1-1

2.0 Background

2.1 Definitions of Relevant Terms. 2-1

2.1 1 2.1 2

2.1 3

2.1. H 2.1 5

2.1 6

2.1 7

2.1 8

2.1 9

2.1 .10

2.1 11 2.1 12

2.1 13

2.1 14

2.1 15

2.1 16

2.1 17

2.1 18

2.1 19

2.1 20

2.1 21 2.1 .22

Energy , Power

Transmission Line

Characteristi c Impedance

Accuracy

Ambient Temperature Time Constant

Bolometer Mount

Bolometer Unit

Bolomet ri c Detector

Bolometric Power Meter

Calibration Factor

Effective Efficiency

Feedthrough Power Meter

Precision

Random Uncertainty

Reflection Coefficient

Resolution

Response Time

Substitution Power

Systematic Uncertainty

Uncertainty

Zero Carryover

2.2 General Methods of Measuring Power.

2.2.1

2.2.3

Direct Methods

Need for Alternate Methods at Radiofrequencies

and Above

Indirect Methods

2-1

2-1

2-2

2-2

2-3

2-3

2-3

2-3

2-3

2-3

2-3

2-3

2-3

2-4

2-1]

2-4

2-4

2-4

2-4

2-4

2-4

2-5

2-5

2-5

2-5

2-5

3.0 Theory of Measurement

3.1 Conversion of Radiof requency Energy to Heat

3.2 Calorimeter as National Reference Standard of Power,

3-1

3-1
CONTEM'S (cont.)

4.0 Measurement Devices

5.2.1 Part 1 5.2.2 Part 2

5.2.3 Part 3

6.3.1 .1 Part 1 6.3.1.2 Part 2

6.3.1.3- Part 3

Page

4.1 Power Sensors 4-1

4.Impedance Bri dges 4-5

5.0 System Calibration

5.1 Reference Standard Calibration System 5-1

5.2 System Calibration Method 5-3

(10-100 MHz) 5-3

(0.1-18.0 GHz) 5-6

(18.0-26.5 GHz) 5-12

6.0 Evaluation of Power Measurement Capabilities

6.General 6-1

6.

Initial Conditions 6-4

6.2.1 Unit Under Test (UUT) 6-4

6.2.2 Signal Source 6-5

6.

Performance Tests 6-6

6.3.1 Frequency Range and Power Range 6-6

(10-100 ^^Hz) 6-6

(0.1-18.0 GHz) 6-9

(18.0-26.5 GHz) 6-12

6.3.2 Pov/er Sensor Calibration Factor 6-14

6.3.3 Operating Temperature Effects 6-19

6.3.4 Response Time 6-21

6.3.5 Long-Term Instability (Drift) 6-21

6.3.6 Display Functions 6-26

6.3.6.1 Automatic Zero 6-27

6.3.6.2 Zero Carryover 6-27

6.3.6.3 Autoranging 6-28

6.3.6.4 Display 6-3O

6.3.6.5 Annunciators 6-3I

6.3.7 Internal Power Reference Source 6-32

6.3.7.1 Oscillator Frequency 6-33

6.3.7.2 Internal Reference Power 6-33

6.3.7.3 Internal Power Stability 6-37

6.3.7.4 Internal Source Impedance 6-38

v1
CONTENTS (cont.)

Page

6.3.8 Power Sensors S-'M?

6.3-8.1 Sensor Voltage Standing Wave Ratio

(VSWR

)

6-42

6.3.8.1.1 Part 1 6.3.8.1 .2 Part 2

6.3.8.1.3 Part 3

(10-100 MHz) 6-il2

(0.1-18.0 GHz) 6-M7

(7.0-26.5 GHz) 6-52

6.3.8.2 Sensor Operating Resistance 6-56

6.3.9 Extended Pov/er Measurement Capability 6-58

6.3.10 Meter Overload Protection 6-6I

7.0 Calculation of Results 7-1

,0 Estimation of Measurement Uncertainty

8.1 Uncertainties Due to Impedance Mismatches 8-1

8.2 Uncertainties Due to Power Sensor 8-4

8.3 Uncertainties Due to Power Meter Instrumentation 8-6

8.4 Uncertainties Due to Internal Reference Oscillator 8-7

8.5 Thermocouple Effects at Lead-Sensor Interface 8-7

8.6 Digital Readout 8-8

8.7 Offset Voltage Uncertainty 8-8

8.8 Zero Carryover Uncertainty 8-8

8.9 Short-Term Instability 8-8

8.10 Long-Term Instability 8-9

8.11 Total Measurement Uncertainty 8-9

8.11.1 Worst Case Uncertainty 8-10

8.11.2 Root -Sum-Square (RSS) Uncertainty 8-11

8.11.3 Calculation of Total Measurement Uncertainty... 8-11

8.12 Uncertainty Analysis of Power Measurements for

known VSWR values 8-12

9.0 Surmary 9-1

10.0 Conclusions 10-1

11.0 Acknowledgments 11-1

12.0 References 12-1

vi1
CONTENTS (cont.)

13.0

14.0

Suggested Additional Reading,

Page

13-1

Appendices

Appendix 14.1

Appendix 14.2

Appendix 14.3

Calibration Results for Typical Coaxial

Dual Directional Couplers

Calibration Factors for a Typical Refer- ence Power Standard ,

14.2.1 K,: (0.01-0.10 GHz)

14.2.2 K,: (0.10-18.0 GHz)

14.2.3 K3: (18.0-26.5 GHz)

Tuner Settings for a Typical Waveguide

Rf Power Transfer Standard

14-1

14-3

14-3

14-3

14-3

14-4

vii1
FIGURES

Page

4.1.1 Resistance vs dissipated power, at various ambient

temperatures, in (a) typical wire barretter,

(b) typical bead thermistor 4-2

4.1.2 Experimentally determined dependence of resistivity on temperature for an arsenic-doped n-type sample

of germanium 4-3

4.1.3 Resistivity at approximately 300 K of MiO doped with 4-4

Ga'+ or Li-*"

4.1.4 Zero-power resistance vs body temperature for a typical

thermistor, showing standard reference temperature 4-6

4.2.1 Basic circuit diagram of a bolometer bridge 4-7

4.2.2 Single thermistor bridge showing inductances required

to keep rf current from dc circuit 4-8

4.2.3 Diagram of two- thermistor bridge 4-9

4.2.4 Unbalanced thermistor bridge 4-11

4.2.5 Dual-element thermistor mount.

(a) Actual circuit, (b) Dc and low-frequency equivalent

circuit, (c) Rf and hi^i- frequency equivalent circuit... 4-12

4.2.6 Simplified diagram of a self-balancing Wheatstone

bridge 4-13

4.2.7 Simplified diagram of a temperature-compensated bridge

circuit in which a second bridge provides temperature

compensation 4-15

4.2.8 Simplified diagram of an automatic power meter showing

bridge, feedback mechanism, and metering system 4-16

5.1 Basic power measurement system showing thermistor bridge

and digital voltmeter 5-2

5.1.1 Typical calibration system for a reference standard 5-4

5.2.1 Typical test setup for a system calibration procedure

for the frequency range of 10 to 1 00 Mhz 5-5

5.2.2 Typical test setup for a calibration procedure for the

frequency range of 0.1 to 18.0 GHz 5-7

5.2.3 Typical test setup for a system calibration procedure

for the frequency range of 18.0 to 26.5 GHz 5-13

1x
FIGURES (cont.)

Page

6.1.1 Block diagram of a power meter illustrating the

subsystems 6-2

6.1.2 Simplified diagram of a temperature- compensated power

meter illustrating the subsystems 6-3

6.3.1.1 Typical test setup for measurement of frequency range

and power range (of the Unit Under Test (UUT) from 10

to 100 MHz 6-7

6.3.1.2 Typical test setup for measurement of frequency range

and power range of the Unit Under Test (UUT) fron

0.1 to 18.0 GHz 6-10

6.3.1.3 Typical test setup for measurement of frequency range

and power range of the Unit Under Test (UUT) frcm I8.O

to 26.5 GHz 6-13

6.3.3 Typical test setup for measurement of operating temperature effects on the Unit Under Test (UUT) 6-20

6.3.4 Typical test setup for measurement of response time of

the Unit Under Test (UUT) 6-22

6.3.5 Typical test setup for measurement of long-term

instability (drift) of the Unit Under Test (UUT) 6-25

6.3.6.3 Typical test setup for testing of the autoranging,

display and annunciator capabilities of the Unit Under

Test (UUT) 6-29

6.3.7.1 Typical test setup for measurement of the frequency of

the internal pov/er reference source of the Unit Under

Test (UUT) 6-34

6.3.7.2 Typical test setup for measurement of the output power

level of the internal power reference source of the

Unit Under Test (UUT) 6-35

6.3.8.1.1 Typical test setup for measurement of power sensor

VSWR of the Unit Under Test (UUT) for the frequency

range from 10 to 100 MHz 6-43

6.3.8.1.2 Typical test setup for measurement of power sensor VSWR

of the Unit Under Test (UUT) for the frequency range

from 0.1 to 18.0 GHz 6-48
FIGURES (cont.)

Page

6.3.3.1.3 Typical test setup for measiirement of pov/er sensor VSWR

of the Unit Under Test (UIJT) for the frequency range

from 7.0 to 26.5 GHz 6-54

6.3.8.2 Relationship of VSWR to impedance at microwave

frequencies for a value of VSV/R of 1.05 6-57

6.3.9 Typical test setup for measurement of extended power

capability of the Unit Under Test (UUT) 6-59

6.3.10 Typical test setup for measurement of overload protection capability of the Unit Under Test (UUT) 6-62

14.1. a Plots of forward and reflected coupling factors of a typical coaxial dual directional coupler in dB with

respect to the OUTPUT Port for the frequency range of

0.05 to 2.0 GHz 14-2

I4.1.b Plots of forward and reflected coupling factors of a typical coaxial dual directional coupler in dB with

respect to the OUTPUT Port for the frequency range of

2.0 to 18.0 GHz 14-2

x1

TABLES

Page

3.2.1 Types and capabilities of calorimeters developed at

the National Institute of Standards and Technology 3~2

5.2.1 System calibration data for the frequency range from

10 to 100 MHz 5-6

5.2.2 System calibration data for the frequency range from

0.1 to 18.0 GHz 5-10

5.2.3 System calibration data for the frequency range from

18.0 to 26.5 GHz 5-l4

6.3.1.1 Data for determining frequency range and power range

of the Unit Under Test (UUT) from 10 to 100 MHz 6-8

6.3.1.2 Data for determining frequency range and power range of

the Unit Under Test (UUT) from 0.1 to I8.0 GHz 6-11

6.3.1.3 Data for determining frequency range and power range

of the Unit Under Test (UUT) from I8.O to 26.5 GHz 6-14

6.3.2.1 Power sensor calibration factors of the Unit Under

Test (UUT) for the frequency range from 10 to 100

MHz 6-16

6.3.2.2 Power sensor calibration factors of the Unit Under

Test (UUT) for the frequency range from 0.1 to 18.

GHz 6-17

6.3.2.3 Power sensor calibration factors of the Unit Under

Test (UUT) for the frequency range from I8.O to 26.5

GHz 6-18

6.3.3 Data for determining the operating temperature

effects on the Unit Under Test (UUT) 6-19

6.3.4 Data for determining the response time of the Unit

Under Test (UUT) 6-23

6.3.5 Data for determining the long-term instability (drift)

of the Unit Under Test (UUT) 6-26

6.3.6.1 Data for testing the automatic zero of the Unit Under

Test (UUT) 6-27

6.3.6.2 Data for determining the zero carryover of the Unit

Under Test (UUT) 6-28

6.3.6.3 Data for determining the autoranging capability

of the Unit Under Test (UUT) 6-3O

XT 1 1
TABLES (cont.)

Page

6.3.6.4 Data for testing the display of the Unit Under Test

(UUT) 6-31

6.3.6.5 Data for testing the annunciators of the Unit Under

Test (UUT) 6-32

6.3.7.1 Data for determining oscillator frequency of the internal pov/er reference source of the Unit Under Test

(UUT) 6-33

6.3.7.2 Data for determining the output power of the internal

power reference source of the Unit Under Test

(UUT) 6-37

6.3.7.3 Data for determining the output power stability of

the internal power reference source of the Unit Under

Test (UUT) 6-38

6.3.7.4 Data for determining the impedance limits of the internal

power reference source of the Unit Under Test (UUT).... 6-42

6.3.8.1.1 Data for determining the power sensor VSWR of the

Unit Under Test (UUT) for the frequency range from

10 to 100 MHz 6-47

6.3.8.1.2 Data for determining the power sensor VSWR of the

Unit Under Test (UUT) for the frequency range from

0.1 to 18.0 GHz 6-51

6.3.8.1.3 Data for determining the power sensor VSW of the

Unit Under Test (UUT) for the frequency range from

7.0 to 26.5 GHz 6-55

6.3.8.2 Data for determining the sensor operating resistance

of the Unit Under Test (UUT) 6-58

6.3.9 Extended pov/er measurement data from the Unit Under

Test (UUT) 6-60

6.3.10 Overload protection data from the Unit Under Test

(UUT) 6-64

8.11.1 Total measurement uncertainty 8-1

3

8.12.1 Calculated values of percent uncertainty in measured

VSviR of a load 8-1

6

XIV
TABLKS (cont.)

Page

14.2.1 Values of calibration factor K^ for a typical reference

power standard for the frequency range from 0.01 to 3.6

GHz 14-3

14.2.2 Values of calibration factor Kj for a typical reference pov/er standard for the frequency range from 0.10

to 18.0 GHz 14-3

14.2.3 Calibration data for a typical reference power standard

measured by the National Institute of Standards and

Technology for the frequency range from 18.0 to

26.5 GHz 14-4

14.3 Tuner settings for a typical waveguide rf power transfer standard for the frequency range from 18.0 to

26.5 GHz 14-5

XV

PERFORMANCE EVALUATION OF RADIOFREQUENCY, MICROWAVE AND

MILLIMETER WAVE PO'^R METERS

Eleanor M. Livingston

Robert T. Adair

Measurement techniques for evaluation of the electrical performance of

commercially available power meters are described. The type of power meter of

interest uses bolometric power sensors and operates in the range from 10 MHz

to 26.5 GHz with an average power of 10 yW to 10 mW with appropriate

attenuation for hi^er power ranges.

Power measurements at dc and low frequencies are relatively strai^tforward since voltage, current, and impedance are discrete entities from which

values of power may be calculated through the use of Ohm's law. For rf, yw,

and mmw frequencies, however, these become complex, interactive, distributed

parameters. Impedance mismatch, leakage, and nonlinear responses must also be

considered. The principle of the bolometric method of measurement of rf, mw

and mmw power is presented.

Techniques are described for analysis of: ranges of frequency and power,

operating temperature, stability, response time, calibration factor, extended

power measurement, overload protection, and characteristics of the internal

power reference source. Some automated methods are discussed. Block diagrams

of test setups are presented. Some typical measurement results are included.

Sources of uncertainty in the bolometric method are analyzed.

Key words: bolometer; dc substitution; microwave power; millimeter wave

power; power measurement; radiofrequency power; temperature compensation;

thermistor; uncertainty.

XVI 1

1.0 Introduction

1 .

1

Importance of Power Measurements

Operating power level is frequently critical in the design and performance of almost all radiofrequency (rf), microwave (uw) and millimeter wave

(mmw) equipment. It is equally significant for each component within the

equipment. Power measurements on devices and systems are frequently required

and are often monitored continuously.

1.2 What Power Measurements Indicate About a Device or System

The term "power" is the rate at v-/hich energy is used to do work. In

rf, uw and mmw systems, power measurement is an indication of the work

capability of the equipment used to transmit information at these ranges of

frequencies [1], To determine whether a device or system is performing as designed, it must be tested. At rf, yw and mmw frequencies, pov;er flow is

easier to measure and more useful than other parameters as an indication of

the ability of the equipment to transmit information [2].

1-1

2.0 Background

2.1 Definitions of Relevant Terms

2.1.1 Energy ; Energy is the capability of doing work. In a system or device, energy is a basic value which may be expressed as the product of

instantaneous power (p) and time (t). For a specified time interval (0 to T)

the total energy (E-p) in a system may be expressed as:

^T

T

pdt (2.1)

V = IR (2.2)

2.1.2 Power ;

a. Low frequency or dc : Ohm's law applies here:

where V = voltage

I = current

R = resistance

Then low frequency or dc power, P, is:

P = VI COS9 (2.3)

where (p is the angle of phase between the voltage vector and the current

vector.

b. High frequency :

1) Instantaneous power (p) is related to instantaneous voltage (v) and

instantaneous current (i) from Ohm's law as follows:

p = vi. (2.4)

2) Average power (P) is average energy or work done in a specific time

interval (0 to T):

2-1
1 '^

p = l vidt. (2.5)

Average power is more closely related to work done by a device or system than

is instantaneous power. Hence, energy per unit time is a definition of

average power, or the time rate of doing work.

Power is often expressed in decibels (dB). This unit is defined as 10

times the common logarithm of the ratio of a measured value of power, P, to a specified reference value of power, P^ef 1^2]. Thus,

dB = 10 log (P/Ppef). (2.6)

P and Ppef i^i^st be expressed in the same units. The ratio is dimensionless

because the decibel unit always indicates a relationship between two

parameters. If P^^ef ^^ 0.001 W (1 mW), then the ratio may be expressed in dBm

which indicates a value of P relative to 1 mV\f. The ratio may be positive or negative whenever P is greater than or less than P^ef' '"espectively.

The decibel, neper and other logarithmic units are acceptable in the

International System of Units.

2.1.3 Transmission line : Any structure which guides the flow of energy

from one point to another is a transmission line [3]. The cross section of

this line may take many forms, such as coaxial cable for frequencies up to

approximately 26.5 GHz (the upper limit considered in this report), and

waveguide configurations for frequencies above a few GHz.

2.1.4 Characteristic impedance : "The ratio V/I is called the characteristic

impedance Zq of the transmission line. Zq is the ratio of the voltage to the

current traveling in a particular direction. This means that Zq is the ratio

of voltage to current traveling together in one direction or the other on the

line. By this definition it can be seen that any change in voltage and

current on a transmission line has a constant of proportionality which is the

characteristic impedance Zq of the line. This also indicates that regardless

of the initial current and voltage conditions, if a wave of voltage and

current is sent down the line, the voltage and current waves still travel at

2-2
the velocity determined by the line parameters, and the ratio of the voltage

to current is still Zq because the transmission line is a linear device" [3].

In addition, the following lEEK standard definitions [4,5] are inclixied here.

2.1.5 Accuracy ; The quality of freedom from mistake or error; that is,

conformity to truth or to a rule.

2.1.6 Ambient temperature time constant : At a constant operating

resistance, the time required for the change in (bolometer unit) bias power to

reach 63 percent of the total change in bias power after an abrupt change in

ambient temperature.

2.1.7 Bolometer mount : A waveguide or transmission-line termination that

houses a bolometer element (s).

2.1.8 Bolometer unit : An assembly consisting of a bolometer element or elements and a bolometer mount in which they are supported.

2.1.9 Bolometric detector (bolometer element) : The primary detector in a bolometric instrument for measuring power or current, consisting of a small

resistor, the resistance of which is strongly dependent on its temperature.

2.1.10 Bolometric power meter : A complete power measuring instrument

that consists of a bolometer unit and a bolometer bridge.

2.1.11 Calibration factor (of bolometer unit) : The ratio of the do substitution power to the rf power incident upon the bolometer unit.

2.1.12 Effective efficiency ; For bolometer units only, the ratio of the

dc substitution power to the total rf power dissipated within the bolometer

unit.

2.1.13 Feedthrough power meter : A power -measuring system in which the

detector structure is inserted or incorporated in a waveguide or coaxial

2-3
transmission line to provide a means for measuring (monitoring) the power flow

through or beyond the system.

2.1.14 Precision : (of a measurement process) The quality of coherence or

repeatability of measurement data [5].

2.1.15 Random uncertainty : That uncertainty which can be predicted only

on a statistical basis.

2.1.16 Reflection coefficient : At a given frequency, at a given point,

and for a given mode of propagation, the ratio of some quantity associated

with the reflected wave to the corresponding quantity in the incident wave.

Note: The reflection coefficient may be different for different associated

quantities, and the chosen quantity must be specified. The voltage reflection

coefficient is most commonly used and is defined as the ratio of the complex

electrical field strength (or voltage) of the reflected wave to that of the

incident wave [5].

2.1.17 Resolution : The smallest discrete or discernible change in power

that can be measured. NOTE: In [4] resolution includes the estimated uncer- tainty with which the power change can be determined on the readout scale.

2.1.18 Response time : The time required for the bolometric power meter

indication to reach 90 percent of its final value after a fixed amount of rf

power is applied to the bolometer unit.

2.1.19 Substitution power : The difference in bias power required to maintain the resistance of a bolometer at the same value before and after

radiofrequency power is applied.

2.1.20 Systematic uncertainty : The inherent bias (offset) of a measurement

process or one of its components.

2.1.21 Uncertainty : The assigned allowance for the systematic uncertainty,

together with the random uncertainty attributed to the imprecision of the

measurement process.

2-4
2.1.22 Zero carryover : A characteristic of multirange direct-reading

bolometer bridges that is a measure of the ability of the meter to maintain a zero setting from range to range without readjustment after initially being

set to zero on the most sensitive range.

2.2 General Methods of Measuring Power

2.2.1 Direct Methods

Power is usually measured in terms of voltage, impedance, and current

at dc and low frequencies, where discrete values for these parameters may be

measured with facility and with acceptable levels of accuracy, precision and

reproducibility. The values of power are derived from the relationships of

these basic parameters in Ohm's lav;.

2.2.2 Need for Alternate Methods at Radiofrequencies and Above

At rf, \ivj and mmw frequencies, however, power values obtained as described in Section 2.2.1 lose identity because the basic parameters no longer may be observed as discrete terms. They become distributed throughout

the circuitry and system. Waves reflected from any impedance mismatch between

source and load can introduce interference, which produces ambiguity in

voltage and current measurements whose values change with positions along the

line. This may occur in either coaxial or waveguide transmission lines.

However, average power remains independent of position within a transmission

medium and therefore is the parameter of interest.

2.2.3 Indirect Methods

For the reasons stated in Section 2.2.2, an alternate form of power

measurement has been developed for rf, yw, and mmw frequencies. This is done

through the conversion of rf energy to heat in a thermally sensitive element

which in turn experiences changes in resistance. These changes are nonlinear

in relation to the heating effect and hence to the power dissipated in the

element. They are also functions of the material in the element and of the

2-5
operating temperature of the device, as shown in the curves discussed in

Section 4. Values of these nonlinear temperature coefficients form a family

of curves for a set of operating temperature values. These are correlated to

values of average power, since most power-measuring devices indicate average

power, rather than peak power. With proper construction of the thermallysensitive element, the heating effect of dc and low frequency power may be

considered an equivalent substitute for the heat energy generated by rf , uw and mmw power.

2-6
3.0 Theory of Measurement

3.1 Conversion of Radiofrequency Energy to Heat

Radiofrequency energy can be detected by changes in the electrical characteristics of thermally sensitive devices. Four general types of thermally

sensitive devices used for high-frequency power measurements are: (1) calorimeters; (2) bolometers; (3) thermocouples and (4) diodes. Types 3 and 4 are

not discussed in this Technical Mote. Average microwave power up to about 10

mWis usually measured by bolometric methods [1]. Changes in bolometer

resis-tance caused by heat absorbed in the sensing element from an rf , yw, or mmw system can be measured and calibrated in terms of the equivalent heating

effect from a dc source of power.

The most accurate microwave power measurements are based on the principle

of dc substitution, in which an input of radiant power to a thermoelectric

detecting device is assumed to be equivalent to the input dc power required to

generate the same response of the device. The uncertainty in the equivalence

of these two parameters is determined by: (1) the effective efficiency of the

detecting device, which by definition does not include effects of impedance

mismatch errors of the system but only the efficiency of the sensing device

[6]; (2) the power losses in the bolometer mount [7].

3.2 Calorimeter as National Reference Standard of Power

A calorimetric method for determination of the combined effect of these

two sources of uncertainty was described by Macpherson and Kerns at the

National Institute of Standards and Technology (NIST), in 1955 [8]. The

technique has been further refined at NIST but retains the original objective

of an adjustment factor for power measurements that are determined by the

bolometer mount technique. "In the microcalorimeter technique the bolometer

mount serves as the calorimetric body or object in which the power is

dissipated and whose temperature rise is measured by means of a suitable

thermopile". Calibration is effected by observing the thermopile response to

dc power dissipated in the bolometer element [7].

Calorimeters for calibrating sensors in both coaxial and waveguide

connectors have been developed at NIST. Table 3.2.1 lists some of the

3-1
calorimeters reported in the NIST literature, with their respective reference

numbers

.

Sensor

Table 3.2.1 Types and capabilities of calorimeters developed

at the National Institute of Standards and

Technology

System Frequency Output Uncert. Year Ref.

bolometer

resistor

bolometer

bolometer

ultrasonic

bolometer

waveguide

coaxial

waveguide

waveguide

coaxial

waveguide

5.2-10.9 GHz

0-300 MHz

9.315 GHz

50-75 GHz

1-15 MHz

95 GHz

- 10 mW <0.2lo

20 mW-12 W ±0.%

- 10 mW <1f.

±0.23^

1 mW-10 V/ <±1.Q%

±0.83/«

1959 [7]

1958 [9]

1955 [8]

1972 [10]

1976 [11]

1981 [12]

3-2
^.0 Measurement Devices

4.1 Power Sensors

Tlie bolometer may be either a: (1) barretter, or (2) thermistor.

The barretter is a short length of metal, in the form of either a fine wire or metal film, with suitable encapsulation and support. The thermistor is a small bead of metallic oxides, such as manganese, nickel, cobalt, or other

similar materials [13], with either intrinsic or added impurities [1^]. The

family of curves of resistance vs. power of the barretter follows a positive

nonlinear slope, shown in figure 4.1.1 (a), while that of the thermistor is

negative and also nonlinear, shown in figure 4.1.1 (b). For small changes in

temperature the barretter experiences small changes in resistance, whereas the

changes in resistance of the thermistor can be considerably larger for similar

small changes in temperature. It is possible for some types of thermistors to

double their resistance with a temperature change of 17°C [13]. Figure 4.1.2

indicates the changes in resistivity of germanium due to temperature changes,

for a temperature range from below 20 K to over 400 K; there are regions of

positive as well as negative temperature coefficients within the temperature

range. However, the operating region of interest for power-meter thermistors

occurs in the neighborhood of 400 K where a change in temperature of very few

degrees will exert a change in resistivity of several hundred ohm-centimeters.

For example, an operating temperature of 60°C or 333 K [14] could produce a resistivity in the neighborhood of 0.06 Q-cm; at an operating temperature of

27°C (300 K), the resistivity for this material could be approximately 0.08

fi'cm.

The resolution of a thermistor's negative temperature coefficient (OTC)

response can be enhanced by addition of extrinsic semiconductor doping materials

Figure 4.1.3 indicates not only a typical NTC sensitivity and resolution

(steep linear slope) but also demonstrates the effect of extrinsic additives

to increase p-type (hole) or n-type (electron) conductivity. The valence and

polarity of the additive determine the type of conductivity while the

concentration of additive determines the extent of change in resistivity of

the thermistor element. A change of less than +1 mole percent can alter the

resistivity of this particular semiconductor material at 300 K by a factor of

several hundred [15]. For the range of operating temperatures shown in figure

4-1
200

(0 180

E

jCo. 160

Q)O

r

CO 140

(0

CO 120

100

4 6 8 10 12 14 13 18

Power (milliwatts)

1000

COE

o

c

CO

^-^ CO

CO

4 6 8 10 12 14 16 18

Power (milliwatts)

b

Figure 4,1.1 Resistance vs dissipated power in (a) typical wire barretter

(b) typical bead thermistor, at various ambient temperatures.

4-2
E

o

>

(0

"(0 (D CC

10.0

Temperature (K)

Figure 4.1.2 Experimentally determined dependence of

resistivity on temperature for an arsenic-doped

n-type sample of germanium.

(After Hemenway, Henry and Carlton).

4-3
10« = ^^"^^1 1 E

10^ 1 1

E

10^

1 ' E

10^

E I i

= \ i

103

E \ 1

102

3 Vi

10 1

1 2 1 + mole % Gafij(a)

iCr^OjXb)

NiO

+ mole % LijO

Figure U.I. 3 Resistivity at approximately 300 K of NiO doped

with Ga^"^ or Li"^. riiO with Ni^"^ vacancies has an equivalent

concentration of Ni^"*" to establish electroneutrality

resulting in p conduction, (a) Li"^ doping increases Ni^"^

concentration, thus increasing p conductivity, (b) Cr^"^ (or

Ga'"^) doping decreases Ni'"*" concentration with resulting

decrease in p conductivity. Each Ni+ eliminates one Ni^+

corresponding to one hole.

4-4
4.1.1 (b), the number of electrons excited from the valence band to the

conduction band exceeds the number of electrons excited from the donor atoms

into the conduction band [14]. This provides rapid changes in conductivity

and hence a sensitive response to small changes in temperature for these

operating temperatures. Figure 4.1.1 (b) shows that the temperature

coefficient curves of the bolometer are fairly close together and most nearly

linear for a thermistor resistance in the region of 200 Q. This is also the

region of "zero- power resistance of the thermistor," which is that region

where little or no self-heating of the thermistor occurs. This thermistor

temperature is measured by special techniques, and is defined as the

Thermistor Standard Reference Temperature. This is shown in figure 4.1.4, at

25°C for a typical thermistor [13] and a zero-power resistance of approximately 450 ii.

4.2 Impedance Bridges

In the bolanetric method of power measurement a bolometer is placed in one arm of a Wheatstone bridge circuit. A basic circuit of this type is shown

in figure 4.2.1. This method is useful to measure levels of average power up

to about 10 mW. In the absence of the rf, yw, or mmw source, the bridge is

balanced by adjustment of the dc power level supplied by the bias source. This reference level of dc voltage is recorded. When the bolometer, T in

figure 4.2.1, is exposed to rf, yw, or mmw power, the bridge again becomes

unbalanced by the change in resistance of the bolometer. The value of dc

power that is required to rebalance the bridge is deemed equivalent to the rf

power sensed by the bolometer and is a measurement of this power [3]. The

difference between the power readings (the difference between the squared

value of each voltage measurement divided by the resistance of the element)

represents the hi^ frequency power applied to, or absorbed by, the sensor.

A single-thermistor bridge, however, requires inductances to keep rf

current out of the dc circuit, as shown in figure 4.2.2, whereas a two- thermistor bridge, in figure 4.2.3, or dual-element bolometer mount, has no rf voltage across the dc circuit, thus eliminating the need for inductances. Radiofrequency chokes in the single-thermistor bridge reduce errors caused by incidental rectification of rf voltages entering the dc circuit, at the same time

reducing loading effects of the bridge on the rf source. However, these induc4-5
1000

100 200

Thermistor Body Temperature (°C)

Figure 4.1.4 Zero-power resistance vs body temperature for

a typical thermistor, showing standard reference temperature,

4-6
SIGNAL

GENERRTOR

Figure 4.2.1 Basic circuit diagram of a bolometer bridge.

4-7
5IGNRL

GENERRTOR

Figure 4.2.2 Single-thermistor bridge showing inductances

required to keep rf current from dc circuit.

4-8
SIGNRL

GENERATOR

Figure 4.2.3 Diagram of two-thermistor bridge.

4-9
tances must 'oe properly installed and shielded, must be stable, and must have

sufficiently high impedance over the frequency range of operation. Because of

these difficulties, the two-thermistor bridge has been the device of choice

[16].

Since the bolometer temperature coefficient varies v^7ith the rf, yw or mmw v/ave power it absorbs, power measurements will experience drift as the

bridge detector circuit approaches equilibrium. Compensation for this may be

provided by including an additional matching thermistor, to balance the drift

such as Ry in figure 4.2.4. The heat accumulated in R^ thermistor is

dissipated to the environment. This temperature compensation significantly

enhances the bolometer response in the microwatt region [1]. The efficiency

of this compensation depends on the degree of similarity between the two

thermistors R^ and R5.

Uncertainties can occur in measurements v;ith dual-element bolometer

mounts if the division of resistance between the two thermistors is unequal.

Figure 4.2.5 (a) shows the basic circuit of a coaxial mount. Rji and R'Y2 are

the detection thermistors. If only dc power is applied to the bolometer

mount, the two thermistors appear to be in series. The equivalent dc circuit

of figure 4.2.5 (b) shows these two thermistors in series. With the rf source

in the circuit and the proper coupling capacitors for ac coupling, the

thermistors appear to the rf source to be in a parallel circuit into the power

meter. The equivalent circuit for this appears in figure 4.2.5 (c). If the

values of R-pi and R-pz slvb unequal, more power is dissipated in the largest

resistor in the series configuration, in which the currents are equal. On the

other hand, the rf voltages across the two parallel elements are equal, and as

a result, more rf power is dissipated in the smaller resistance which carries

the larger amount of current. This source of uncertainty increases as power

increases, but for power levels of 10 mW or less, it is less than 1 percent

for bolometer mourits with well-matched thermistors [1, 1?].

The indicating instrument may have a zero-centered scale, so that either an increase or decrease in the temperature of one thermistor with respect

to the other can be detected. The sensitivity of the bridge detection circuit

thus determines the smallest detectable temperature change. Sensitivity of

the detection device may, however, be enhanced with amplification. For

example, a bridge circuit with a hi^-gain amplifier connected to the output

could measure temperature differentials of 0.0005°C (0.001 °F) [13]. Feedback

4-10
METER

ZERO SET

O

REGULRTED

DC SUPPLY

o

Figure 4.2.^ Unbalanced thermistor bridge. Initial

balance is obtained with meter set at zero. Temperature

compensation is achieved with external thermistor R7.

4-11
a

RF

aRTl

R T2

^

POWER

O METER

POWER METER

O

R T2

Rti

O

(b)

(a)

o

RF

OR TK^T2

(c)

Figure ^.2.5 Dual-element thermistor mount:

(a) Actual circuit.

(b) Dc and low-frequency

equivalent circuit.

(c) Rf and hi^-frequency

equivalent circuit.

4-12
Bins

RF POWER

Figure 4.2.6 Simplified diagram of a self-balancing

Wheatstone bridge.

4-13
from the amplifier provides self-balancing as shown in figure 4.2.6 [2].

Figure 4.2.7 is a simplified diagram of a bridge circuit in which a second

bolometer bridge provides temperature compensation. Both bridges are self-balanced through amplified feedback [2].

Although linearity of the thermistor response is relatively greater at

levels of rf , mw and mmw power above 4 mW, sensitivity decreases in this

region, especially at higher operating temperatures, as seen in figure 4.1.1

(b). Changes in resistance per milliwatt are smaller than those at

pov/er levels below approximately 4 mW.

Mismatch uncertainties occur when values of line and load impedances

become dissimilar. These impedance mismatches reduce the power absorbed by

the sensor and, in an unbalanced bridge, a 2:1 resistance change can cause an uncertainty of up to 0.5 dB [1].

Manually balanced bridges provide excellent sensitivity for the

measurement of low power (less than 2 mW) but require considerable time for

the frequent adjustments necessary to balance the bridge. They have, however,

long been used in standards laboratories where high accuracy is important.

Characteristics of manually balanced bolometer bridges are:

(1) bolometer operation at a single value of resistance, which provides

a dynamic range of about 20 dB and presents closely matching

impedances to rf, mw, and mmw power sources;

(2) measurement of substituted dc power with suitable accuracy and

correlation directly with known voltage and resistance standards;

and

(3) slow measurement, which also requires calculation of the results of

each pov/er measurement [1].

Automatically balanced bridges eliminate all operations required for

the manually balanced bridges, except for the zero adjustment for initial

balance. A diagram of this type of bridge is shown in figure 4.2.8. Positive

feedback, from a differential amplifier placed across the bridge, is

temperature-sensitive , depending on the resistance of the thermistor.

Negative feedback, across the other side of the bridge which contains a tuned

circuit, is frequency- sensitive and reaches a minimum value at the resonant

4-14
SENSOR

RF

BRIDGE

RF POWER

TEMPERRTURE

COMPENSRTION

BRIDGE

POHER

METER

Figure 4.2.7 Simplified diagram of a temperature-compensated

bridge circuit in which a second bridge provides temperature

compensation.

4-15
1^^

DIGITAL

VOLTMETER

METER

BIR5

Figure U.2.8 Simplified diagram of an automatic power meter

showing bridge, tuned circuit, feedback mechanism, and metering

system.

^-16
frequency of the tuned circuit. Characteristics of the automatically balanced

bolometer bridge are:

(1) rapid measurement with no need for auxiliary instruments;

(2) constant value of bolometer operating resistance, which provides a suitable impedance match at all power levels within the dynamic

range of the instrument; and

(3) lack of temperature compensation, which may obscure measurements on

the low-scale setting due to interference from ambient temperature

changes

.

Bolometer mounts for manual and automatic bridges may be: (1) tunable,

(2) fixed and tuned, or (3) broadband and untuned. They are typically coaxial

for frequencies up to 18 GHz, and waveguide structures for frequencies above

18 GHz. The coaxial mounts are untuned, and their bolometer elements usually

present 200 Q to the bridge. The tunable waveguide bolometer mounts are typically tuned manually for each frequency of interest.

4-17

5.0 System Calibration

Reference Standard Calibration System

The Unit Under Test (UUT) must be measured against a reference standard

power measurement system. The following procedure for setting up and calibrating the reference system must be performed prior to testing any parameters of

the UUT. The procedure spans the range of power levels from 0.5 to 10 mW and

typically has three parts, one for each of three consecutive frequency bands

within the frequency range of interest. Part 1 covers the calibration procedure

for the frequency range from 10 to 100 MHz. Part 2 contains the calibration

procedure for the power level range from 0.5 to 10 rrM and the frequency range

from 100 MHz to 18.0 GHz and Part 3 is the calibration procedure for the

frequency range from 18.0 to 26.5 GHz.

The power measurement system basically consists of two units: a Wheatstone bridge which contains a bolometer sensing element and external instrumentation. Two equal resistors form two arms of the bridge and a third resistor

is equal to the operating resistance of the bolometer. Only the bolometer

sensor is external to the meter, but it functions as the fourth arm of the

bridge within the power measurement system.

The theory of power measurement presented in Section 4.2 is based on

the principle of dc substitution. There are two steps. Initially, a single

source of dc voltage is applied to the bridge from a regulated voltage source,

(see figure 4.2.1). This is the total power on the bridge at this time. No

rf power is allowed to impinge on the thermistor sensor in this step. Since

this power is dc rather than rf power, Ohm's law may be used to calculate the

dc value by measuring the dc voltage, Vj, as shown in figure 5.1, and dividing

the voltage by the operating resistance, R^, of the thermistor.

In the second step, rf power is allowed to impinge on the thermistor

with no other changes in the circuit. As rf power is applied to the

bolometer, its resistance decreases (if the element is a thermistor). The

bridge circuit detects this unbalanced condition and increases the dc bridge

current. The new voltage, V2, increases to restore a balance of bridge power.

This change in dc power is equal (ideally) to the rf power dissipated in the

bolometer element. (In practice they are not equal because of dc-rf

substitution errors [6]). The equivalent value of rf pov;er is calculated

5-1
RF POWER

DIGITRL

VOLTMETER

Figure 5.1 Basic power measurement system showing

thermistor bridge and digital voltmeter.

5-2
using the value of the substituted dc power and the appropriate boloneter

calibration factor for the frequency of interest.

System calibration may be obtained with several types of equipment

specifically designed for this purpose. A typical configuration is shown in

figure 5.1.1. This system^ is based on the assumption that power levels about

the measurement reference plane are equal across this plane. A calibration

factor from an NlST-calibrated reference standard is transferred to an internal power sensor with a typical loss of 0.5-1.0 percent in transfer.

This is done for 109 NIST- traceable frequencies [18]. The output power level

of this standard equals the input power level to the reference power sensor

across the measurement reference plane.

This system is used to determine the accuracy of the internal power

sensor. The latter then becomes the standard for evaluating the calibration

factor of the bolometer sensor in a UUT.

5.2 System Calibration Method

5.2.1 Part 1 : (10-100 MHz)

The system is connected as shown in figure 5.2.1. The signal source is

set at the lowest frequency, 10 MHz, with a minimum rf output level. A bias

dc voltage, Vj, in millivolts, (as read on the DVM) is placed on the reference

sensor to establish an operating point within its linear response region with

no rf input from the signal source to the pov/er measurement system. When rf

power is applied to the reference sensor from the signal source at a level of zero dBm (1 mW), the bridge becomes unbalanced and the DVM indicates a new dc

voltage, \/2, in millivolts. The values of V^ and V2 are read and recorded.

These two voltage values are squared and the difference between

these squared terms is divided by the operating resistance (Section 4.1) of

the sensor. The result is the dc-substituted power, P,jq, measured by the

reference sensor of the standard. P^q is the value of P(jq for Part 1,

where

H/hen manufacturers' trade names are used to specify certain types of equipment, this does not imply endorsement by the National Institute of Standards

and Technology. Similar products by other manufacturers may have equal or better quality.

5-3
r MEnSURElCNT | REFERENCE , (Roplace with UUT) 1

S2GNRL

SajRCE

PUjfC 1

1 '

1

'

0I6ITR.

VOLT>€TER

1 [

1

A

RF

OQNTRCX.

IMIT 1

i

RETGRENCE

POCR

METEK

i i

1 r

1 y

a

IHWRtn.

POHER

SENSOR

HLMlHLNGE

POCR

OUT 1 IN SENSOR

L

1 >s

1 '^

' 1 REFERENCE | STRNDRRD 1

Figure 5.1.1 Typical calibration system for a reference standard.

5-4
SIGNRL

SOURCE

REFERENCE STflNDflRD r

-

1 REFERENCE POWER fCTER

Figure 5.2.1 Typical test setup for a system calibration procedure for

the frequency range of 10 to 100 MHz.

5-5
^dc =^H^o^^ ^ ^0' ^^W],

when Vj and V2 are in millivolts.

(5.1)

A further calculation converts the dc substituted power to rf

pov;er, P^f , through the use of the bolometer calibration factor, Ki, where

Ki is the calibration factor of the reference standard bolometer sensor at the

frequency of interest. It is provided by the manufacturer of the sensor.

^dc

Prf

1 =-jr'^i (5.2)

The values of P^q and P^f are recorded. Table 5.2.1 presents the

recorded data in a useful format. This procedure is repeated at typical

frequencies of 50 MHz and 100 MHz.

Table 5.2.1 System calibration data for the frequency range from

10 to 100 MHz

Signal Source Ref. Standard

CAL Factor

(KJ

DVM Calculated Values

Frequency

(MHz) (mV) (mV)

Pdc,

(mW)

Prf,

(mW)

10

50

100

5.2.2 Part 2: (O.I-I8.O GHz)

An rf transfer standard with its own control unit is used for this frequency range. This control unit contains the bolometer bridge and controlledtemperature source for stabilizing the bolometer mount. The control unit is

5-6
SIGNRL

SOURCE

flMPLiriER

nr &1ITIX

PIN RT

CONTROL

UNIT

CQKTROL

BIAS MOKT

REFERENCE STFNDRRD

HT i>#vr

J? RF

Ji TRRNSFER test STFMDflRD

rCUNT KFTCRS

McxNT sans

vm N

REFERENCE

POWER

SENSOR

Xt^KJT

REFERENCE

POWER

METER

DIGITR.

VOLTMETER

REFERENCE

VOLTAGE

GENERFTTOR

Figure 5.2.2 Typical test setup for a calibration procedure for the

frequency range of 0.1 to 18.0 GHz.

5-7
connected to the rf transfer standard as figure 5.2.2 indicates. The rf con- trol unit is maintained in the frequency-locked condition by supplying sufficient rf output power level from the signal source. The voltage applied to the rf transfer standard by the reference

voltage generator, through the reference standard, is measured on the DVM

first with the rf control unit turned off, Vj, and then with the control unit

turned on, V2. The dc-substituted power, P^q, measured by the rf transfer

standard is calculated by taking the difference between the squares of these

voltage values and dividing by the operating resistance (Section ^\.^). For

this frequency range, or Part 2, P^jq is designated as P(jq and is calculated

as follows:

^dc, —2*"-- ^ '°' t"« • (5.3)

P(jQ is linearly related to the calibration factor, K2, of the internal power sensor of the transfer standard and to the value, P(jq , of the

reference standard measured in Part 1. A value of K^ is given by the manufacturer, but the actual calibrated value of K2, is

dc 1

which is recorded together with the value of K2 given by the manufacturer,

K, ^ . A useful format for recording these values is given in table

^mfr ^ ^ 5.2.2. P(2 -, is determined for each frequency of interest and

represents the new calibration (CAL) factor to be used for the rf power

transfer standard. If these new CAL factors agree with those given by the

manufacturer, no change is necessary. If the CAL factors differ from those

given by the manufacturer, the newly determined values must be used.

Dc-substituted power is provided in this frequency range by the rf con- trol unit at 0.5 mW and for 1 mW to 10 mW in 1-mW steps. The rf control ixiit

provides stability of these power levels with an accuracy of ±0.1 percent. In

order to do this the output power level of the rf signal source at the rf

5-8
input of the rf transfer standard must be sufficient to drive a PIN diode

attenuator in the rf transfer standard. This controls the signal level

stability by holding this level in a locked condition. The bridge balance

meter on the control unit will initially deflect to the local oscillator (LO)

region but will return to the center position at zero. This zero position is an indication of the locked condition and therefore signifies that the output

level of the rf signal source is sufficient to maintain a stable power level

of 10 mW at the rf output of the rf transfer standard [18]. Nominal values of

10 yW, 0.5 mW, 1 mW and 10 mW are useful levels of P(jc at each frequency

for determining the calibration factor. The PIN attenuator allows for nominal

values of 10 yW.

To maintain this stable level, the output power level of the signal

source must be greater than +10 dBm (10 mW) at the rf input to the rf transfer

standard to counteract a loss of several decibels in rf power level which

occurs within the rf transfer standard. A nominal value for the level of

output power at the signal source could be +13 dBm (20 mW). This requires the use of a hit;^ quality amplifier.

An amplifier gain of 40 dB is typically used for the signal source in

this frequency range from 0.1 to 1.0 GHz. The output level of the signal source

should be -20 dBm for this frequency range in order to provide an input to the

rf power transfer standard (through the amplifier) of approximately +20 dBm

(100 mW). However, the maximum power input to the rf transfer standard must

not exceed +23 dBm (200 mW). Once this output level has been set on the signal source, no change should be necessary for this frequency range. The

proper level of operation is indicated by the return to the locked position

for each selected value of dc substituted power on the rf control unit.

An amplifier gain of 20 dB is used for the signal source frequency

range from 2 to 18 Qiz. The output level of the signal source should therefore be set at zero dBm for this frequency range to provide an input to the rf

power transfer standard (through the amplifier) of approximately +20 dBm (100

mVO.

Repeat the above procedure for a useful range of frequencies such as

0.5, 1.0, 2.0, 4.0, 7.0, 8.2, 10.0, 12.4, 15.0 and 18.0 GHz.

5-9
Table 5.2.2 System calibration data for the frequency range from

0.1 to 18.0 GHz

Nominal

Signal Source Ref. Standard

GAL Factor

(K,)

DVM Value Calculated Values

Frequency

(GHz)

(mV) (mV)

Pdc,

(mW)

Pdc,

(mW)

Prf

(mW)

0.1 0.01

0.5

1.0

5.0

10.0

0.5

1.0

2.0

4.0

7.0

8.2

5-10
Table 5.2.2. (Cont.)

Nominal

Signal Source

Frequency

(GHz)

Ref. Standard

CAL Factor

(KJ

DVM Value Calculated Values

(mV) fmV)

Pdc,

(mW)

Pdc,

(mW)

Prf

(mW)

10.0

12.4

15.0

18.0

5-11
5.2.3 System Calibration Method, Part 3: (18.0-26.5 GHz)

The system is connected as shown in figure 5.2.3. For frequencies

above 18 GHz, a waveguide transmission line is used rather than a coaxial line.

The reference-power transfer standard is inserted into the waveguide

structure, which is then manually tuned for each frequency of interest during

calibration. Settings for tuners Tj, T2, T3 and T^, for each frequency of

interest, are provided by the manufacturer of the power meter measurement

system. Tuner settings for a typical waveguide power transfer standard are given in Appendix 14.3.

The bias voltage, Vi, in millivolts, which is applied to the referencepower transfer standard from the reference power meter (indicated in figure

5.2.1), establishes an operating point for the linear response of the internal

pov;er sensor of the transfer standard.

The voltage, V2, in millivolts, from the signal source is then measured,

and the dc substituted power for this frequency range, P^q , is determined

by the difference between Vj squared and V2 squared, divided by the sensor's

operating resistance (Section 4.1), where

Values of the calibration factor, K3, of the reference- power standard

for each frequency of interest are provided. These are determined at a standards laboratory.

The rf power, P^f, is then calculated by dividing P^^ by the

calibration factor, K3, for each frequency of interest as follows:

PdC3

rf = K

(5.6)

All values are recorded, as formatted in table 5.2.3, and this procedure is repeated for suggested additional frequencies, at suitable intervals,

such as 20, 22, 24, 25 and 26.5 GHz.

5-12
REFERENCE STFINDflRD

5IGNRL

SOURCE

w 5CN50R ori.— r-n(—

k

^ i/^f- 1 POWER

METER

REFERENCE

POWER

TRANSFER

STANDARD

V

DIGITAL

VOLTMETER

T2 T4

WRVEGUIDE SECTION TERMINATION

Tl T3

l_

Figure 5.2.3 Typical test setup for a system calibration procedure for

the frequency range of 18.0 to 26.5 GHz.

5-13
Table 5.2.3 System calibration data for the frequency range from

13.0 GHz to 26.5 GHz

Signal Source

Frequency

(GHz)

Ref. Standard

CAL Factor

(K3)

DVM Calculated Values

(mV) (mV)

PdC3

(mU)

?rf

(mW)

13.0

20.0

22.0

24.0

25.0

26.5

5-14
6.0 Evaluation of Power Measurement Capabilities

6

.

1 General

The measurement parameter of interest is rf, yw, or mmw power. The

power range of interest commonly used for many industrial and military

applications is 10 yV/ to 10 mW. It is necessary not only to determine whether

a power meter can measure these powers accurately, but also to verify that

these measurements are obtainable throughout the frequency ranges for which

the instrumentation is required. They must also be obtainable within

specified limits of long-term stability, operating temperature, and response

time. Extension of the power measurement capability to 5 W and overload

protection for the power meter are also of interest. In addition, other

characteristics of the total instrumentation must be considered if the final

measurement results are to contain validity. Characteristics of subsystems of

the total instrumentation which contribute to the precision and reliability of

final results must also be studied. These subsystems are: (1) the metering

subsystem; (2) the internal power reference; and (3) the power sensor. Figures 6.1.1 [3] and 6.1.2 (after [2]) are block diagrams of power meters

showing types of power meter subsystems.

Evaluation of power meter performance must include such characteristics

as: (1) ranges of frequency and power; (2) operating temperature; (3)

stability; (4) response time; (5) power sensor calibration factor; (6)

extended power measurement; (7) overload protection; (8) parameters of the

internal power reference, and (9) parameters of the power sensor. Summaries

of techniques are described and block diagrams illustrating these procedures

are presented here, together with some typical measurement results. All

measurement procedures must be preceded by the system calibrations described

in Section 5.

6-1
SELF BRLFMCING BRIDGE <- VOLTMETER

BOLOMETER

INPUT

DC BIBS

NETWORK

BRIDGE

OSCILLATOR

VOLTAGE

DIVIDER

POWER

SUPPLY

VOLTMETER

AMPLIFIER

METER

Figure 6.1.1 Block diagram of a power meter illustrating the

subsystems.

6-2
RF

bridge:

TEMPOWTURE

COMPENSRTION

BRIDGE

Figure 6.1.2 Simplified diagram of a temperature-compensated power

meter illustrating the subsystems.

6-3
6.2 Initial Conditions

The controls of the UIJT and the signal source must be set to the

appropriate positions prior to conducting the performance tests.

6.2.1 Unit Under Test

Perform the following typical settings for each of the controls on the

UUT in this order:

SENSOR INPUT

ON/OFF SWITCH

RANGE

ZERO

POWER REF

CAL FACTOR

CAL ADJUST

SENSOR INPUT

CAL FACTOR

Connect sensor cable to SENSOR INPUT port

Set to ON

(Allow one hour warm-up)

Set to AUTORANGE

Press to zero the meter display

Connect sensor cable to REF OSCILLATOR port

Enter into power meter the CAL Factor for 50

MHz

Adjust until meter reads 1.000 mW

Connect sensor cable to SENSOR INPUT port

Enter into power meter the CAL Factor for

frequency of interest

6-4
6.2.2 Signal Source

Set the controls on the typical signal source as follows

ON/OFF SWITCH

FREQUENCY

AM

FM

PM

AUTOMATIC U^VEL CONTROL

OUTPUT RANGE ATTENUATOR

OUTPUT RANGE VERNIER

RE OUTPUT SWITCH

LEVEL MODE SELECTOR

FREQUENCY REFERENCE

ON

To frequency of interest

OFF

OFF

OFF

Internal

Maximum attenuation

Maximum attenuation

OFF

LEVEL

Internal

6-5
6.3 Performance Tests

6.3.1 Frequency Range and Power Range

The ranges of frequency and power are measured initially before any

other performance tests. The typical frequency range is specified as 10 MHz

to 26.5 GHz and the power range is 10 yVJ to 10 mW.

6.3.1.1 Part 1 : (10-100 MHz)

After the system calibration of Section 5.2.1 for the frequency range

10 MHz to 100 MHz is performed and the initial conditions of Section 6.2 are

met, the UUT is connected as shown in the test setup of figure 6. 3. 1.1 to

measure the frequency range from 10 to 100 MHz and the power range from 10 uW

to 10 mW at each frequency of interest.

The values of frequency, dc-substituted power, ?^q » ^^'^ ^^^ factor,

Ki, of the reference sensor, determined in the calibration of Section 5.1,

Part 1, are recorded in table 6. 3. 1.1 in both watts and decibels.

A frequency of 10 MHz and an rf output pov^er (RFOP) of 1 rrM are selected on the signal source. Attenuation of 20 dB applied to the signal

source output provides an input power level of 10 yW to the UUT. A set of

calibrated attenuators is required here. (These are calibrated by the

manufacturer or a calibration laboratory such as NIST.)

The appropriate value of K^ must be entered into the UUT for each frequency of interest. This must be recorded together with the power indicated

on the UUT, PuuT* ^ useful tabular format is given in table 6.3.1.1.

Actual values of attenuation at the power meter input may vary slightly

from, the nominal value of 20 dB and these data are provided by the manufacturer for each attenuator. The attenuator should be calibrated by a calibration

laboratory such as NIST, prior to use in this test. Therefore, each power

measurement made by the UUT must be corrected for any variations in the

calibrated results from the nominal value. These corrected measurements,

PuuTq, are recorded in table 6.3.1.1. The correction factor is the result

when the difference between calibrated and nominal attenuation values is

divided by the nominal attenuation value.

6-6
1 REFER!ENCE STflNDflRD

5IGNRL

SOURCE

REFERENCE

POWER

SENSOR

REFERENCE

POWER

METER

- >

1

1

1

1L

Y

DIGITAL

VOLTMETER

UNIT

UNDER

TEST

Figure 6.3.1.1 Typical test setup for measurement of frequency range

and power range of the Unit Under Test (UUT) from 10 to 100 MHz.

6-7
-1^ CO

(D

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:=)

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,

u. ^

6-8
The bolometer calibration factor of the UUT, Kyu-p, is determined as follows:

pUUT

KuuT= K. [p--^]. (6.1)

dCi

This value is also recorded in the table, and the procedure is repeated for

each frequency of interest while maintaining the input power level of the UUT

at 10 yW.

For a power input to the UUT of 100 yVJ the signal source output level

is increased to 10 mW.

Upon removal of the attenuator the signal source output levels of 1 mW

and 10 mW equal the input power levels to the UUT. Each of these changes in

power level input to the UUT are followed by the measurement sequence

described above at each frequency of interest.

6.3.1.2 Part 2:(0. 1-18.0 GHz)

The system calibration described in Section 5.2.2 for the frequency

range from 0.1 to 18.0 GHz must be performed and the initial conditions of

Section 6.2 must be met. The UUT is then connected in the test configuration

of figure 6.3.1.2 to measure this frequency range over the power range from 10

yV/ to 10 mW at each frequency of interest. Conparison of figures 5.2.2 and

6.3.1.2 shows that the measurement configuration differs from the calibration

configuration only where the UUT and its level- setting attenuator replace the

reference standard of the former configuration.

The values of frequency and the CAL factor of the reference power sensor of the calibration procedure, Kj, and the calibration factor of the rf

transfer standard, K2, determined in the calibration of Section 5.2.2, are

read from table 5.2.2 and recorded in table 6.3.1.2 at this time. The values

of dc substituted power, P(j(3 , of the rf control unit, are also recorded

from Section 5.2.2 in watts or decibels. The sensor CAL factor of the UUT

from the manufacturer, KyuT ^ , is also entered in table 6.3-1.2. The

power of 10 yW applied to the UUT is obtained by insertion of a calibrated

6-9
SIGNRL

SOURCE

QMOI TC"Tt-o w rTTrT_ir ILr\

1 UNIT UNDER TEST

1

1

1

POWER

METER

r ik

HF *ITCH

PIN RF

CONTROL

UNIT

CONTROL ^

RF lr#vr

J2 RF

Ji TRRNSFER TCST STf=iNDFIRD PCRT

MOUNT hCflTERS

1

h RTTENURTOR

1 POWER

SENSOR

1 ^

^

1 W _l

Figure 6.3.1.2 Typical test setup for measurement of frequency range

and power range of the Unit Under Test (UUT) from 0.1 to 18.0 GHz.

6-10
<D J=

*->

4-. O

<1) bO§

S^

C4

0)5oa

N

tc o a c

CC o

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Unit

Dc

Subst

Power '

Rf

Power

Transfer Standard CAL

Factor

Ref Power

Sensor

Source

Generator

Frequency (GHz) 0.1 0.5 1.0 2.0

Gen

#1

2.0

Gen

#2

4.0 8.2

10.0 12.4 15.0 18.0

6-11
20-dB attenuator between the rf transfer standard and the UUT and then setting

the power output from the transfer standard at 1 mW.

Any variations in attenuation from the nominal 20-dB value are given by

the manufacturer of the attenuator or the calibration laboratory and must be

incorporated into the final power measurement, Ptjut , as discussed in meas Section 6.3. 1 .1

•

After each frequency of interest has been selected and the power measured

and recorded as described above, the power input to the UUT is brought to 100

liV\f v^/ith an output of 10 mW from the signal source. The procedure is repeated

through the same range of frequencies.

The 20-dB attenuator is removed and power levels of 1 mW and then of 10

mW are applied to the UUT for measurement through the same frequency ranges

given above.

6.3.1.3 Part 3: (18.0-26.5 GHz)

After the system calibration described in Section 5.2.3 for the frequency range from IS.O to 26.5 GHz is performed, and the initial conditions of

Section 6.2 are completed, the UUT is connected in the test configuration

shown in figure 6.3.1.3. Measurements on the UUT can then be performed over

this frequency range and over the power range from 10 yV/ to 10 mW at each

frequency of interest. The values of frequency, equivalent dc power, P^q , and sensor GAL factor, Kj, from table 5.2.3 are recorded in table 6.3.1.3 at

this time. A frequency of 18.0 GHz is selected on the signal source at an output power level of 1 mW. The calibrated 20-dB attenuator is inserted

between the source output and the UUT to provide a calibrated input to the UUT

of 10 yW. The waveguide tuners Tj, Tj, T3 and T^ are adjusted for maximum

power transfer to the UUT. The value of K3 is entered into the UUT for each

frequency of interest. The power level displayed on the UUT (Puut) ^^ read

and recorded in table 6. 3. 1.3- The calculated value of the UUT power sensor

calibration factor, Kijut 1 > is obtained as follows: caxc ^, ^KJ;M1). (6.2)

calc dc.

6-12
SIGNRL

SOURCE

REFERENCE STflNDPRD

SENSOR

INPUT REFERENCE

POWER

METER

REFERENCE

POWER

TRRN5FER

STRNDRRD

T

T2

DIGITRL

VOLTMETER

T4

WAVEGUIDE SECTION TERMINATION

Tl T3

RDRPTER

UNIT UNDER TEST

POWER

SENSOR

POWER

METER

Figure 6.3.1 .3 Typical test setup for measurement of frequency range

and power range of the Unit Under Test (UUT) from 18.0 to 26.5 GHz.

6-13
This value of Ktjut i is recorded in table 6.3.1.3. The actual power

caJ-C

levels of the UUT, Pyux, are recorded for each input power level of interest;

useful levels are approximately 10 yW, 0.5 mW, 1 mW and 10 mW. The stepsare

repeated for each frequency and power of interest.

Table 6.3.1.3 Data for determining frequency range and power range

of the (UTJT) from 18.0 to 26.5 GHz

Source Generator

Frequency

(GHz)

Ref Sensor UUT

CAL Factor KuUTj^fp

(K3) PdC3 PUUT ^UUT^^l^

18.0

20.0

22.0

24.0

25.0

26.5

6.3.2 Power Sensor Calibration Factor

The calibration factor KuuT f ^^ the UUT power sensor, given

by the manufacturer, is a nominal value, but an exact value Kuy-p ., caj-C

must be calculated, with the system reference standard and the power

measurements of the UUT, PnuT o' over the specified ranges of

frequency and power.

A typical specification for the calibration factor of the UUT would

require a value between 85 Jo and 100 % within ± 1^, or between +1 and -1 dBm,

within ±0.01 dB.

The system calibration is performed as given in Section 5, and the

initial conditions of the UUT, signal generator and all other required

equipment are set.

The frequency and power ranges of the UUT are verified according to the

performance tests for these parameters. Figures 6.3.1-1, 6.3.1.2 and 6.3.1.3

shov; the test configurations for their respective frequency ranges.

The calibration procedures of Section 5 yield the values of the dc-sub6-14
stituted pov/er of the reference standard, P(jq , for n = 1, 2 and 3 for three

frequency ranges, as well as the values of the reference standard power sensor

calibration factors, K^,. The power sensor calibration factor of the UUT may

be calculated as shown below by use of an algebraic ratio of power measured by

the UUT to that of the dc substituted power of the reference power sensor. This ratio is then multiplied by the calibration factor of the reference power

sensor to give the calculated value of KyuT* Since the system for each

frequency range used for the calibration of the reference standard is the same

as that used for the power measurement of the UUT, then KuuT i holds

the same relationshipto PyUT ^^ that between K^ ^j^^ P(jq . This

is calculated as follows:

p UUT

calc dc

n

which is expressed as a percent if the units of K^^ are in percent. The final

step is the calculation of the difference in percent between K^juT -i ^'^'^

KuUTj^fp. as follows:

^UUT , ~ ^UUT „ AK.,.^ {%) = j^^^ "^^-"^ X (100). (6.4) UUT K^^

calc

A value of 100 percent is assigned to the highest positive value of Kyy-p

^ and the lesser values are obtained in percent v/ith magnitudes scaled accordingly,

If K|ju7 ^ is expressed in decibels, then it is desirable to

convert Knuj -, (in percent) to decibels, and the following

caJ-C

conversion can be applied:

^UUT , t-^^) - 1° l°8f=UUT <?'. (6.5) calc calc

All readings must be recorded. A useful format is given for each frequency

range in tables 6.3-2.1, 6.3.2.2 and 6.3.2.3-

6-15
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6-16
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6-17
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6-18
6.3-3 Operating Temperature Effects

It is important to verify the behavior of the power meter and sensor

under specified environmental conditions. There are several parameters of the

environm.ent which could affect power measurement, but the only significant

effect is that from temperature. A typical specification is the requirement

that the power meter and power sensor meet all other operating requirements

over the temperature range from 0°C to 55 °C.

The internal initial conditions of the UUT are set and the test

configuration of figure 6.3-3 is used. This setup is contained within the

environmental test chamber. The power meter's internal reference oscillator

is used as the signal source. Since this test is independent of frequency,

the single frequency of 50 MHz of the reference oscillator provides sufficient

stability to observe any changes in performance.

The output level of 1 mW of the reference oscillator is attenuated by

20 dB before entering the sensor in order to observe any changes in power

measurement down to 10 nVJ on the 10 ijV/ scale.

Power measurements are made at suitable temperature increments. Any

changes in readings within 10 nW are recorded, along with the percent of

change, in a format such as that shown in table 6.3.3.

Table 6.3.3 Data for determining the operating temperature

effects on the Unit Under Test (UUT)

CAL

Factor Power Power

Frequency Temp for 50 MHz Level Change Percent

(MHz) (°C) (Kuut) (liW) (nW) Change

23 10

37

45

50

55

6-19
ENVIRONMENTAL TEST CHRMBER

UNIT

SENSOR

IM=UT

UNDER TEST

WJ- osc

OUTPUT

i I

y

POWER

SENSOR

Rl lENURTOR

Figure 6.3.3 Typical test setup for measurement of operating

temperature effects on the Unit Under Test (UUT).

6-20
6.3-^ Response Time

Response time of the power meter is defined as the time required for

the indication to reach 90 percent of its final or steady state value (Section

2.1.16). The reading must begin at zero, and arrive at 90 percent of the

final value in a specified time interval. The specified response time is

typically 10 s or less on the most sensitive scale, and 2 s or less on any

other scale setting.

The internal initial conditions of the UUT are set. The test con- figuration of figure 6.3-4 is used. A signal source frequency of 100 MHz is

convenient although this test is independent of frequency. The UUT power

sensor is connected to the rf output of the signal source which is set at -20

dBm, and the most sensitive setting of the UUT indication is selected. A

suitable timing device with a range of 0-60 s is required.

The power readings of the UUT are recorded in a format such as that

shown in table 6.3.4. The rf power of the signal source is turned off. Then

both this rf output and the timing device are turned on simultaneously.

At t = 1 s the power level on the UUT, ^UUT^ , is read and recorded, in both

decibels and watts. At t = 60 s the final power level of the UUT, ^UUTf, is

read and recorded in table 6.3.4 in both decibels and watts.

The values of 90 percent of the final power levels are calculated and

recorded in decibels and watts. The differences in 90 percent of the final

power readings and the associated readings at the appropriate time intervals

are calculated and recorded in the A Reading column. These values are calculated as (0.9 ^UUTf - ^UUT^) both in dB and mW. These A readings can be

compared with the values expected to meet the response time specifications.

A similar procedure is followed with rf power output levels of -10, 0,

and +10 dBm, with timed intervals of 2 s. These tests may be performed at additional frequencies of 1.0 and

10.0 GHz (or other frequencies as desired).

6.3.5 Long-Term Instability (Drift)

Power meter response time is measured in seconds or smaller units and

is indicative of the UUT's short-term characteristics. The long-term

stability [4] (or long-term instability or drift) of the steady-state value is

6-21
TIMING

DEVICE

SIGNRL

SOURCE

UNIT UNDER TEST

PONER

METER

POWER

SENSOR

Figure 6.3.4 Typical test setup for measurement of response time of

the Unit Under Test (UUT).

6-22
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6-23
defined as the maximum acceptable change in a power measurement in 1 h for a constant input rf power, constant ambient temperature, and constant line

voltage [4].

Since this test is independent of frequency, the 50 MHz frequency of

the UUT reference oscillator can be used as a constant signal source for testing long-term instability.

The temperature compensation function built into bolcmeter mounts is designed to eliminate drift in the power sensor due to ambient temperature

changes. This test also includes a preliminary waiting period of 15 min to

further protect the power sensor from ambient temperature changes.

The initial internal calibration of the UUT is completed first. The

CAL factor for 50 MHz of the UUT power sensor, Kyuj, is calculated from

eq (6.3) and recorded in table 6.3.2.1. It is included here. However, since

drift is indicated solely by a change in power level, this may be determined

as a difference in the indicated values rather than in the calculated values.

Then the UUT is inserted into the test configuration shown in figure 6.3.5. A

20-dB attenuator between the reference oscillator and the power sensor

attenuates the 1-mW power output from the reference oscillator to 10 yW.

A series of six power readings are taken at 10-min intervals and

re-corded in a format such as that presented in table 6.3.5. The units of any

changes in power indication are usually nanowatts. The change in power can be

calculated in percent for the various time intervals. These power changes can be recorded and compared with the allowable values as stated by the UUT drift

specification.

6-24
TIMING

DEVICE

UNIT UNDER TEST

SENSOR

INPUT

REP OSC

OUTPUT

I

PONER

SENSOR

±

RTTENUniOR

Figure 6.3.5 Typical test setup for measurement of long-term

instability (drift) of the Unit Under Test (UUT).

6-25
Table 6.3.5 Data for determining the long-term instability (drift)

of the (UUT)

Power Sensor

GAL

Factor Power Change in Power Level

Frequency Time for 50 r^Hz Level Power Change

(riHz) (Min) (Kuut) (yW) (nW) i%)

50

10

20

30

HO

50

60

-

6.3.6 Display Functions

The metering subsystem transfers the power or energy output of the bolometer bridge with suitable amplification to, typically, a controlled digital display. The features of automatic zero, zero carryover, autoranging and display

provide proper control of zero indication, and versatility in selection of scale

factors and units of measurement.

The following power meter display features must all be evaluated: (1

)

automatic zero; (2) zero carryover; (3) autoranging, which eliminates

resetting the readout to zero for each scale of sensitivity level, and (4)

functions of the display such as resolution and annunciators for different

types of units of measurement.

6-26
6.3.6.1 Automatic Zero

A typical specification for performance of the automatic zero capabilityrequires that a value of zero within ±15^ of full scale be automatically displayed

on each sensitivity range setting after the initial value is selected on the most

sensitive range.

llhen the display of the UUT is manually set to zero on the 10 yW range,

any change in the least significant digit (LSD) from reading to reading

(A LSD) must not exceed 100 nV/ typically. These units must be recorded

accurately for each sensitivity scale, as formatted in table 6.3.6.1.

Readings should be taken at least three times at any sensitivity and the

results examined to determine whether the UUT meets the desired specifications.

These readings could be taken until three reproducible values are obtained or

the average of three readings could be calculated, to see if the specifications are being met.

Table 6.3.6.1 Data for testing the automatic zero of the

Unit Under Test (UUT)

Range

Reading A LSD

1st 2nd 3rd Average Max. Deviation Limits

(full scale)

1. Most sensitive

2. Next most sensitive

3. Next most sensitive

4. Next most sensitive

5. Least sensitive

6.3.6.2 Zero Carryover

Zero carryover is defined in Section 2.1.22 and its performance test is

described in [4] as follows:

"4.11.3. Zero Carryover. For multirange instruments only, normally

zeroed on the most sensitive range, state maximum acceptable deviation from

6-27
zero indications for any range switch setting, expressed in percent of full

scale."

The procedure following initial internal calibration of the UUT requires

setting the zero of the meter on the most sensitive scale. Several readings of

this display should be taken and any variation of the LSD in the digital display

should be noted in table 6.3.6.2. To calculate percent of full scale, divide

the value of the any deviation of the average reading from nominal value by the

full scale reading, keeping the units consistent, and multiply this ratio by

100.

The procedure is repeated for each range but the initial setting of the zero of the meter should not be repeated. The function of this test is to

eval'uate the carryover of the zero to each additional range selected.

Table 6.3.6.2 Data for determining the zero carryover

of the Unit Under Test (UUT)

Range

Reading A LSD

1st 2nd 3rd Average Max. Deviation

{% full scale)

Limits

1 . Most sensitive

2. Next most sensitive

3. Next most sensitive

4. Next most sensitive

5. Least sensitive

6.3.6.3 Autoranging

The autoranging capability of a power meter refers to the automatic

switching of readout through several ranges for any given measurement. This

feature can be evaluated with a single frequency such as 100 HHz from the

signal source. The test configuration is shown in figure 6.3.6.3. The test is

performed by a manual increase in the power output level from the signal

source over a suitable range such as that from -30 dBm to +10 dBm while the

readings displayed on the UUT are observed, to see that the instrument

6-28
SIGNRL

SOURCE

UNIT UNDER TEST

POWER

METER

nDRPTER

(IF REQUIRED)

POWER

SENSOR

Figure 6.3.6.3 Typical test setup for testing of the autoranging,

display, and annunciator capabilities of the Unit Under Test (UUT)

6-29
automatically selects the appropriate range and indicates the appropriate

power level. The reading in decibels is recorded for each power level setting

in a table such as that shown in table 6.3.6.3. The equivalent reading in

watts is also recorded for each range. The evaluation is completed byrepeating the procedure over the range from +10 dBm down to -30 dBm.

The automatic selection of each range in sequence may be interrupted at

any range as needed. If the power output of the signal is then increased, an OVERRANGE annunciator should be activated. This activation should be recorded

in the Overrange column together with the power level at which this occurs.

This power level should be compared with the specifications provided for the

UUT for this capability.

Table 6.3.6.3 Data for determining the autoranging capability

of the Unit Under Test (UUT)

Signal Source UUT Indicated Ranges

Frequency

(MHz)

RFOP

(dBm)

1 2 3 4 5 OverMode Mode Mode Mode Mode range

100 -30

-20

-10

+ 10

-10

-20

-30

dB watt dB watt dB watt dB watt dB watt

i

6.3.6.M Display

Display characteristics include digital or analog format, or both, and

annunciators typically indicate either decibels or watts as selected.

The test configuration of figure 6.3.6.3 is suitable for this test. A

single frequency, usually 0.1 GHz, is applied to the UUT, with either decibels

or watts selected on the UUT. A minimal rf output level is selected for the source signal. This is increased incrementally while the number of digits

6-30
displayed on the UUT is observed for each range of pov/er level. All

observations are recorded including all digits displayed at each level. A

useful format for recording these data is given in table 6.3.6.4.

The test procedure is repeated with the UUT set in the alternate mode.

In the watt mode the UUT display is typically required to indicate values out

to hundreds of nanowatts in the performance test for long-term instability

(drift). Therefore, when the UUT scale is set on 10 yW, the display must show

three digits to the least significant decimal place in this mode to indicate

hundreds of nanowatts.

Table 6.3.6.4 Data for testing the display of the

Unit Under Test (UUT)

Signal Source UUT

Frequency

(GHz)

RFOP

(dBm)

No. of Power Level Display Digits

Decibel Mode Watt Mode Analog

Range Yes/No

1

2

3

4

5

6.3.6.5 Annunciators

The display usually includes annunciators for both v;atts and decibels.

In the watt mode these typically illuminate the ranges in mW, or 10"^ W; or

)jW, or 10"^ W. The decibel mode normally indicates dBm, or dB, or dBr

(relative dB).

The test configuration of figure 6.3.6.3 is used to evaluate the annun- ciator capability. A single frequency, usually 0.1 GHz, is applied to the UUT

from a signal source. Rf output levels, from -30 dBm to +10 dBm on the signal

6-31
generator, are applied to the UIJT, which is set on the decibel scale. Each

display is observed and recorded in a format such as that of table 6.3.6.5.

While in the decibel mode, one may observe the dBr function. The dBr

annunciator is illuminated, and +10 dBm is entered in the UUT as a reference

level. Then the rf output from the signal generator is decreased in steps,

while the display in dBr is observed and recorded.

Next, watts are selected and the test is repeated. The watt mode

annunciator units (mW or 10"^ W, for example) are observed, and readings are

also entered in table 6.3.6.5.

Table 6.3.6.5 Data for testing the annunciators of the

Unit Under Test (UUT)

Required Annunciators

UUT Annunciators J

Decibel Mode Watt Mode

dBm dB dBr mW uw

mW or 10"^ W

yW or 10"^ W

dBm

dB

dB relative

6.3.7 Internal Power Reference Source

Power meters are generally provided with an internal power reference

source. This is necessary as a known source of power to verify and adjust the

sensitivity of the power sensor. This power reference source is used in

open-loop power measurements made with thermocouple or diode sensors, but not

with thermistor bolometer mounts, which are closed loop measurements.

However, all instruments allow for any type of power sensor. This source is an oscillator of single frequency and power level. It is permanently

installed by the manufacturer and is not adjustable. It is required in order

to verify the calibration factor of non- therm is tor bolometer mounts. The

6-32
stability of the internal power reference must be verified at the necessaryoperating temperature range of the instrijnent and for a typical time period of one year.

The impedance of this internal source is a function of frequency and

standing wave ratio (SWR) and hence is determined only for a specific SWR.

Detailed procedures follow for testing the performance of this source.

6.3.7.1 Internal Oscillator Frequency

The frequency of the internal reference oscillator may be evaluated

with the test configuration shown in figure 6.3.7.1. This frequency, usually

50 MHz, is measured on a frequency counter. The results are recorded in a table such as table 6.3.7.1 and compared with those allowed by the specifications for this test.

Table 6.3.7.1 Data for determining oscillator frequency of the

internal power reference source of the Unit Under

Test (UUT)

UUT

Ref Oscillator

Specified Frequency

(MHz)

Frequency Counter

Reading

(MHz)

50.0

6.3.7.2 Internal Reference Power

The internal power reference source is typically required to provide

1 mW at the frequency of the internal reference oscillator.

The reference oscillator port of the UUT is connected to the reference

standard as shown in figure 6.3.7.2. The reference oscillator is not turned

on at this time. The dc voltage, Vj, in millivolts is read on the DVM of the

reference standard and recorded in table 6.3.7.2. The reference oscillator of

6-33
FREQUENCY

COUNTER

UNIT UNDER TEST

REF 05C

OUTPUT

POWER

METER

Figure 6.3.7.1 Typical test setup for measurement of the frequency of

the internal power reference source of the Unit Under Test (UUT).

6-34

I
r- — •— — — — — —- -~

1 REFERENCE STRNDPRD

w

^maa^ ^^^m ^,^„^

REFERENCE

PONER

SENSOR

REFERENCE

POWER

METER

L - .

1 ^HH« ^am^ m t

V

1 DIGITAL

VOLTMETER

REF OSC

OUTPUT

1 IKITT

LJINJ. 1 UNDER

TEST — _- _ _-m _- — _- -I

Figure 6.3.7.2 Typical test setup for measurement of the output power

level of the internal power reference source of the Unit Under Test

(UUT).

6-35
the UUT is then turned on and a similar voltage reading, V2, is obtained in

millivolts and recorded in table 6.3.7.2. A resolution of 10 yV should be

attainable for each reading.

The rf power output of the reference oscillator is then calculated as follows:

Pdc = ^^^^^200^^ ' ^°' ^^^^ ^^^ ^" ®^- ^•''^' ^^'^^

p

Prf = ^

[mW] (as in eq. 5.2), (6.7)

where P^^q is the dc substituted power, Kj is the power sensor CAL factor

of the reference standard, (from table 5.2.1), and P^f is the measured output

power of the reference oscillator of the UUT.

Three independent sets of readings are recorded in a format such as that presented in table 6.3.7.2.

An average of these three readings, P^f , is also calculated and

recorded. The difference between P^f and the manufacturer's value of 1 •^^avg

mW is calculated as follows:

Power difference in percent = ± ^^^

~

: x 100. (6.8)

This value is then recorded in table 6.3.7.2 and compared with the allowable difference as stated in this specification of the UUT.

6-36
Table 6.3.7.2 Data for determining the output power

of the internal power reference source of the

Unit Under Test (UUT)

Frequency

(MHz)

Ref Power

Sensor

CAL Factor

(KJ

DVM Calculated Values

(mV)

Va

(mV)

pdc

(mW)

Prf

(mW)

Prfavg

(mW)

Pdiff

50.0

6.3.7.3 Internal Power Stability

A typical specification for stability of the internal power reference

source requires that the frequency and output level remain within ±1 .2 percent

of the values supplied by the manufacturer, for a period of one year over the

temperature range specified. The difference between the specified values and

the measured values can be calculated. Equation (6.8) may be used to

determine the difference in percent of the long-term stability of the power

output level. A similar calculation for long-term stability of the frequency

of the internal standard is as follows:

Percent Drift = + Frequency measured (MHz) - 50 MHz

50 MHz 100. (6.9)

6-37
A useful format for this information is provided in table 6.3.7.3.

Table 6.3.7.3 Data for determining the output power stability of the

internal power reference source of the Unit Under

Test (UUT)

UUT

Specified Power Reference Measured Power Reference

Difference

in %

Frequency

(MHz)

Output

Level

(dBm)

Frequency

(MHz)

Output

Level

(dBm)

Freq. Output

Level

50.0

6.3.7.4 Internal Source Impedance

The impedance of the internal power reference source is a function of

frequency, so a specified value is valid at one specific frequency. The

purely resistive value of impedance is achievable only in the dc case. At all

other frequencies inductive and capacitive reactance components create values

of impedance which are complex numbers and vary with frequency and location on

a transmission line. Since the internal power reference source is used to

calibrate the power meter sensors, it is designed to have specific electrical

characteristics so that it does not introduce additional errors during the

calibration of the power meter. The power reference source in a typical power

meter provides a fixed output of 1.00 mW at 50.000 MHz. Furthermore the power

reference source is constructed so that the characteristic impedance at the

output port is designed as a purely resistive 50-Q impedance. A useful method

[19] for evaluation of uncertainty limits for the internal source impedance

follows

.

are:

Assumptions for a transmission line at radio and ultra-hi^ frequencies

(1 ) the line has low losses; hence, resistance R is small;

6-38
(2) distributed circuit parameters are discrete constants based on a unit length of line.

With these assumptions, the following approximations may be made:

R « wL, (6.10a)

G << wC, (6.10b)

v;here R, L, C, and G are the resistance, inductance, capacitance and

conductance per unit length of line, respectively. Based on these

inequalities, the following approximations are valid:

Z = R + jwL = jcjL, (6.11a)

Y = G + jwC = j'oC. (6.11b)

Then the characteristic impedance of the line, Zq, may be defined and

approximated as

Zq = [(R + jwL)/(G + jwC)]^2 = (L/C)^^ (6.12)

Similarly, the propagation constant, Y, may be expressed as

T = a + j3, (6.13)

where a = the attenuation constant in nepers per unit length and 3 = the phase

constant in radians per unit length.

The general transmission line equations may be v;ritten for a line of length,

i, and termination Z^ as

V = V„cos ex + 11, Z sin fix (6.1^a)

= V^cos 3x + j(V^/Z^)Z^sin P>x,

and I = I cos 3x + J(V /Z )sin 3x. (6.l4b)

6-39
Since voltmeters and ammeters read magnitude without regard to phase, the

magnitudes of the voltage and current on a transmission line at a point, x, become

I VJ = V^[(cos^ 6x + (Z^/Z^)2sin2 Bx)]'^^ , (6.15a)

I ig = I^[(cos^ Bx + (Z^/Z^)2sin^ Bx)/^ . (6.15b)

VJhen sin Bx = 1, Vj. is a maximum.

Then Vx„ax = \(V^t>' (6-1<^^>

Similarly, when sin Bx = 0, Vy- and I^ are minimum.

Then V^ . = V„, (6.17a) ^mm i

and ly • = In (6.17b) %in 2,.

A useful parameter for impedance evaluation is the voltage standing

wave ratio, VSWR. This is defined as the ratio of maximum to minimum voltage

on a transmission line at a specific frequency [3] and is given by

VSWR = V^ax/Vmin (6.1 8a)

and ISWR = Imax^^min- (6.1 8b)

Then using eq (6.1 6a, 6.17a), eq (6.1 8a) becomes

VSWR = Z /Z„ (for Z > Zj (6.19a)

o I, o i

and using eq (6.l6b, 6.17b), eq (6.l8b) becomes

VSWR = zyz (for Z < Z J . (6.19b)

2, o o il

The value of the VSWR of the internal power reference source at the specified

frequency is given by the manufacturer. The upper and lower limits of

6-40
uncertainty in Z^ may be calculated with the use of eq (6.19a, 6.19b). The

following example illustrates this procedure.

Given: Z = R = 50 fi

and VSWR = 1 .05 at 50 MHz.

To find: (a) Z where Z > Z max

and (b) Z^ where Z > Z min °

Then: (a) Z = (VSWR) (Z ) = (1.05)(50 ^) = 52.50 fi max

(b) Z„ = (VSWR/Z )= 47.62 fl mm

The nominal value of the impedance of the internal power reference source

(as stated by the manufacturer) should be recorded. A useful format is shown in

table 6.3.7.4.

Calculate the limiting values of the internal power reference source

impedance as shown above and record these values in table 6.3.7.4. These

values can then be compared with the specification of this test. A possible

alternate method is the use of an rf impedance bridge to measure the power

reference source impedance. The bridge must be characterized at the frequency

of interest.

6-41
Table 6.3.7.4 Data for determining the impedance limits of the internal

power reference source of the Unit Under Test (UUT)

Frequency

(MHz)

Impedance

(n)

VSWR Calculated Limits

Lower Upper

50.0 1.05

6.3.8 Power Sensors

6.3.8.1 Sensor Voltage Standing Wave Ratio (VSWR)

The following maximum values of voltage standing wave ratio (VSV/R) are typical specifications over the listed frequency ranges and for the power range

specified in Performance Test 6.3.1.

Frequency VSWR

10 MHz-1i| GHz 1.4

14-18 GHz 1.5

18-26.5 GHz 1.6

6.3.8.1.1 Part 1 : (10-100 MHz)

After the initial calibration procedures are completed, the equipment

is connected as shown in figure 6.3.8.1.1 for the frequency range of

10-100 MHz.

A dual channel power meter is used in this test. This contains two

separate measurement channels, A and B. Since these channels are independent

of each other, each may be calibrated according to the methods for calibration

of a UUT described in Section 6.3.1.1 for 10 to 100 MHz, in Section 6.3.1.2

for 0.100 to 18.0 GHz, and in Section 6.3.1.3 for 18.0 to 26.5 GHz.

6-42
CORXIRL

SIGNRL ^

SOURCE °^ ^

SWITCH SENSOR R ^ Ch R Input

DURL

POWER

METER

Ch B Input

^ 1 ^ ^

'

y

wW

r SENSOR B

VSWR BRIDGE

RTIN ^

OUT

LNIT IM3ER TEST

UNI1

1

^ UNDER TEST

1 POWER

SENSOR — POWER

1 ^ METER

1

Figure 6.3.8.1.1 Typical test setup for measurement of power sensor

VSWR of the Unit Under Test (UUT) for the frequency range from

10 to 100 MHz.

6-43
From eq (6.1 8a) VSWR = VjT^ax/^min •

In addition, V^^^ =

'^i

"^ ^r (6.20a)

and V^iin = Vi - V^ , (6.20b)

where Vj^ and V^ are the incident and reflected voltages on the transmission

line [3].

Therefore, VSWR =

| (V^ + Vp)/(Vi - V^) |. (6.21)

However, VSWR cannot be measured but must be calculated from values of

the reflection coefficient, r. r is defined in Section 2.1.16, which is

paraphrased here, as the ratio of the reflected wave, in volts, to that of

the incident wave in volts [3], as follows:

since r = V^/V^, (6.22)

then, from eq (6.21 ), VSWR = (1 + | r |)/(1 - | r |)

.

(6.23)

The use of a VSWR bridge, as figure 6. 3. 8. 1.1 indicates, requires the

characterization of this bridge for VSWR as a function of frequency over the

frequency range of interest. Since VSWR cannot be measured directly but must

be calculated from values of r, these must be known for each frequency of

interest. They are determined from the power measurements on both Channels A

and B of the dual channel power meter. The square roots of these power terms

provide the values in volts from which to calculate r. Loads with known VSWR must be used to determine the characteristic

curve of the bridge. The transfer function of the VSWR bridge typically is

linear with frequency over the desired VSWR range. However, a direct reading

6-44
in VSlffi is not available from the VSWR bridge, and the readings are not

constant as the frequency is varied. Therefore, a bridge calibration factor

is necessary for each test frequency.

The characterization of the bridge shows that a calibration factor

e^bridge^ must be applied to the readings on power sensor B to determine the

true reflection coefficient of the load being measured. To obtain the necessary characteristic curve of the VSWR bridge, standard reference mismatch loads

with known values of VSWR and | r | are connected in sequence to the test port

of the VSWR bridge. They provide fixed reference points on this curve. A

power level of incident power, Pj^, of +13 dBm (20 mW) on Channel A is set with

the signal source rf output power level at the three suggested frequencies of

10 MHz, 50 MHz and 100 MHz (for this frequency range). Then the ratio of the

known reference value of | r | to the square root of the power of reflected

power, Pjo, at power sensor B (with Pj^ held constant at 20 mW) is taken as a multiplication factor, Mj^^j^^gg. This is shown in the following set of

equations.

In general, ~

| f | ={^f\ (6.2^1)

However, for the bridge,

Pv^V/

I M = Kbridge IfrY' . (6.25)

where K is a bridge factor selected for the frequency of interest from the

bridge characteristic curve described above.

Since P^ is held constant, (6.26)

I rI = ^bridge (^r)'^' • (6.27)

Since values of r and P^ are known, Mbpi(jgg can be determined for each

frequency of interest as follows:

6-45
M I r

I bridge ,. r,s "bridge = ' V = y' • (6.28)

(Pr)' (Pi)'

Channel A is selected with the external coaxial switch shown in figure

6.3.8.1.1. The frequency of the signal source is set to 10 MHz at an rf power

of +13 V dBm (20 mW), as measured on power sensor A of the dual channel power

meter. This value, P^, is recorded in a table such as table 6.3.8.1.1.

Then the external coaxial switch position is changed to the RF JH port

of the VSViR bridge and the RF OUT port is connected to power sensor B of the

dual power meter. The UUT is also connected to the VSWR bridge at the test

port. The value of power measured by power sensor B, Pg, is also recorded in

table 6.3.8.1 .1 . The value of the UUT reflection coefficient, rTjuT, may be calculated as follows:

I PuUtI = (^bridge) (Pb)^/S (6.29)

and then is recorded in table 6. 3. 8. 1.1.

The VSWR of the power sensor of the UUT may be calculated as follows:

VSWRuuT = f4-

TUUT

TUUT

(6.30)

This is also recorded in table 6.3.8.I.I;

The reading P^ of power sensor A may vary by ±1 dB due to variations in

the signal source output level. Line losses may also contribute to variations

in power sensor measurements.

Compensation to M|-))oj_(jp.g values for variations in Pp^ are made as follows;

^^'bridge = f^ridge [(20 mW)/PA]^/^ (6. 31)

The value of M'l^pijjgg should be used when the signal source output level is

other than +13 dBm (20 mVO.

6-46
This procecjure is repeated for frequencies of the si.^al source set

at 50 MHz and 100 t'^Iz using the appropriate values of M(-)p2.df7e ^^^ these

frequencies.

Table 6.3.8.1 .1 Data for determining the power sensor VSVJR of the Unit Under

Test (UUT) for the frequency range from 10 to 100 MHz

Signal

Source

Sm Bridge

Multiplier

Dual

Power

Meter

Calculated

Values

Frequency

(MHz)

RFOP

(dBm) ^''^ bridge)

Compensated

^bridge

(M' bridge)

Pa

(mW)

Ps

(mW) TUUT vsvmyuT

6.3.8.1.2 Part 2: (0.1-18.0 GHz)

In this procedure the VSWR of the UUT power sensor is obtained by the use of a dual directional coupler. The UUT power sensor is connected as a load to the TEST port of the dual directional coupler (see figure 6.3.8.1.2.).

The coupler should be calibrated by the manufacturer for the frequencies of

interest to determine the actual (X)upling factors. This will prevent the

introduction of significant uncertainties into this measurement from the coupler,

These coupling factors apply to specific dual directional couplers. No two

couplers have identical values. Typical values in table 6.3.8.1.2 are included

for information only and are not to be used in actual measurements. Couplers

should be identified by serial number to allow consistent use in the test set-up

and to prevent confusion in the application of specific coupling factors.

Figures 14.1. a and I4.1.b in Appendix 1^.1 are plots of coupling factors for a typical coaxial coupler for two ranges of frequencies. Figure 6.3.8.1.2 shows

that the power sensor of Channel A on the dual power meter senses the incident

power, Pi_, in the dual directional coupler with respect to the TEST port

6-47
SIGNRL

SOURCE

SENSOR

R

RMPLIFIER

UNIT

UNDER

TEST

INCIDENT

UUT

SENSOR

TEST

DURL

DIRECTIONRL COUPLER

INPUT

SENSOR

B

REFLECT

Ch R Input

DUAL

POWER

METER

Ch B Input 1

Figure 6.3.8.1.2 Typical test setup for measurement of power sensor VSWR of the Unit Under Test (UUT) for the frequency range from

0.1 to 18.0 GHz.

6-48
(^itest^ and that the power sensor of Channel B on the dual power meter senses

the reflected power, Pjo, in the dual directional coupler with respect to the

TEST port, (^r^est^* '^^^ values of the forward coupling factor, Cp, and the

reflected coupling factor, Cr, for each dual directional coupler at each

frequency of interest should be tabulated in table 6.3.8.1.2 in decibels for

future reference. Each of these typical coupling factors is also given as a ratio in table 6.3.8.1.2. An example of the conversion of units is as follows;

Given: Cp = 22.50 dB (for 100 MHz).

r = P2/P1

?! = 1 unit

Since, 22.50 = 10 log r, by definition,

then, log r = 22.50/10

and,

^ r = lO^-"" = 177.83. (6.32)

Then,

P2 = (r)(Pj = 177.83 P, . (6.33)

The VSliR of this load is determined in a procedure of several steps. First

the power is measured at the incident and reflected ports of the dual

directional coupler on Channels A and B of a dual power meter. The

calibration factors of these sensors of the dual power meter for the

frequencies of interest are then included to give values of actual power at

the incident and reflected ports of the directional coupler. Then these

values are translated to the TEST port of the coupler by applying the

coupling factors of the incident and reflected ports with respect to the TEST

port. These twice-modified values are the actual values of the incident and

reflected power applied to the IJUT power sensor at the TEST port. Finally,

they are used to calculate the reflection coefficient, r, and VSWR of the UUT

power sensor.

6-49
The equipment is connected as shown in figure 0.3. B.I. 2 after the

completion of all the calibration procedures just described. The following

steps compose the measurement procedure:

1. Set the rf output level of the signal source to +10 dBm and record this

frequency and output level in table 6.3.8.1.2.

2. Record in table 6.3.8.1.2 the calibration factors of the dual power meter

sensors. These are K;^ of the power sensor of Channel A and Kg of the

power sensor of Channel B for each appropriate frequency.

3. Measure the power, P^, of Channel A and the power, Pq, of Channel B on the

dual power meter and record these values in table 6.3.8.1.2.

4. Calculate the corrected value, ^A^^, of P/^ to include K;^ and calculate the

corrected value, ^B^, of Pg to include Kg for the appropriate frequency,

as follows:

PAc = (Pa)(Ka), (6.34a)

PBc = (Pb)(Kb), (6.34b)

and record these values in table 6.3-8.1.2.

5. Calculate the value of Pj^ as follows:

^itest = (%) (Cp), (6.35a)

and record this value in table 6.3.8.1.2.

6. Calculate the value of ' r^gg^^ as follows:

Potest = (''Be) (Cr), (6.35b)

and record this value in table 6.3.8.1.2.

6-50
4-3

ES-i CDc

(U

4-5

Ci-I o

00 o > • CO o

CO o

0)

CO »— ^ d 5 S o o

ex S-1

4-> bO

bO ^ E

(U 4J oc

CD

:3cr

CD Q) O (D <^ x:

4J i-l

CT3

O

Q ^

CM•

COcn

CD

CO

g00> CO

ij CD i o :^ ~R

CO >—1 P C CO CD > iC'

c/:

t4 CD jj

(D 4J CO

IS CO CD D .-H 4-> a. 3 t-l o Cu p CO P o CO

(D

4-J

•l-( cu

•i-H D-OmCI, o<

t-i IX

CD

CD 5:

Cu

i-, CD5O <c

Cu Cu

1—1 3 CO Q u:<X

>^ ^ CTv CM CTn ^3-

_

cv ,

,

VO cn CT^ LO CM o> ^ cc ^ . . • , . • . o M3 o OO O vO ^- CO LTi t>- rH CO C7> C7> o LO CM ^T LTi ^:T CX r—1 ,

,

O

COo O •iH o LO C7> cn .=3- cn CM ,

O cx t>- LPi yo o c:)> ,

I>- a^ I>- nH >> m , • . . . . , CO t-H xu C\j C7> cr\ o ,

,,,,

c v.^ CM ,

^— CM CM CM CM CM CNJ o

•r-l 4JO cn

O CM :=r OO CO ^r

O •=T CD oo o\ C7> in ^

CM C7^ ^=r C7^

i-, [l. . • • •M o S-. t>^ LTi ^=r C3> CM cn t— C3> T Q

i-H t- CO CO CO cn o ' o '~

1—1CO COo

:3 '.—1 o .=r o> CM 1

^q- CT^ C7^ o>

Q ex ^-~, LTi on CM LPi CM ,:=r cn ^T

>, cc • • • • • • • • • H -o CM C7^ C3^ C7^ ,

o o o O

CM ' * ' CM CM CM CM CM

,—V

CD Ou E O o CQ

O t-, t, a 3 K + O

>.O

1—1

C y—^

CO (D

N ,— LO

O ;r- O CAJO

O o OO

CD P . • . bO (3^ O o O T " CM* "^ CM ^ o ^=r Co' •^ (D ^^ c c ^

tT 00 !Lj CD Q)

Pl, -lO bO 6-51
7. Repeat the procedure with the appropriate dual directional coupler and

signal source for frequencies of 0.5, 1.0, 2.0, 6.0, 10.0, 14.0, and

18.0 GHz.

8. Calculate the values of reflection coefficient, and VSWR of the UUT

power sensor, for all measurements just performed, where, from eq (6.24),

ruUT = [(Pr)/(Pi)]^^%

and, from eq ( 5.30)

,

VSWR = i-^ lumi

TUUT

9. Record these values in table 6.3-8.1.2.

6.3.8.1.3 Part 3: (7.0-26.5 GHz)

The frequency range from 7.0 to 26.5 GHz is specific for the use of

waveguide directional couplers with the appropriate adapters. This frequency

range includes the frequencies of 7.0 to 18.0 GHz which are included in

Section 6.3.8.1.2. However, all the measurements of Section 6.3.8.1.2 are made with coaxial dual directional couplers, while all of Section 6.3.8.1.3

measurements require waveguide directional couplers and appropriate adapters.

The following procedures must be completed before performance tests are

made;

(1

)

System calibration procedure for this frequency range.

(Section 5.2.3).

(2) Initial internal calibration procedure of the HUT.

(Section 6.2.1 ).

(3) Initial conditions of the signal source (Section 6.2.2).

(4) Frequency range and power range performance tests.

(Section 6.3.1 .3).

6-52
The performance test for the VSWIJ of the power sensor in this frequency

range is performed with a waveguide reflectometer using the appropriate waveguide directional couplers for the frequency ranges of interest.

The equipment is connected according to figure 6.3-8.1.3. A frequency

of 7.0 GHz is set on the signal source with an rf power of +10 dBm. The power

sensors on channels A and B on the dual power meter measure incident power,

Pj_, and reflected power, Pp.

Since the magnitude of the reflection coefficient, | F |, is used to calculate values of VSlffi, the value of | r | of the UUT, | fuuT |» ^"^st. 'oe determined.

By definition | F | is proportional to the ratio of reflected voltage to incident voltage in a transmission line, where. the load is purely resistive [3].

Thus, by definition, in terms of power,

I F| = C[^]'/^ . (6.36)

The proportionality factor, C, may be determined from the measurements

of Pi and Pjo of a load whose impedance is, ideally, a known value and is purely

resistive. A short circuit (sc) termination is useful here because we can assume | F | = 1. The values of '^isc and ^Vqq are recorded in table 6. 3. 8. 1.3-

Pr \^2

Then 1 = C ( ^^ 1 , (6.37)

^sc

Pi \ y^ or c^^ =

( ^ ^ . (6.38)

The termination is then replaced by the UUT and iTT,T^ and

^r,,,,^ are measured on channels A and B respectively and recorded in

table 6.3.8.1.3.

6-53
SIGNAL

SOURCE

DUAL

POWER

METER

Ch A Inputs Ch B

r

A

1

1

A

AMPLIFIER

POWER 1 SENSOR

R

1

POWER

SENSOR

B

AD

1 Y

=IPTERS —

INCIDENT

PORT

-< — ADAPTERS

J REFLECTED 1 PHDT nUK 1 ^

T

TERMINATION

OR

UUT

1 .

1 Lw.

1 1 1 1 1 1

1

I i_ 1 1 TMQl IT i.iQv/tT(~i iTr>r- -rr-f—

r

PORT REFLECTOMETER PORT

Figure 6.3.8.1.3 Typical test setup for measurement of power sensor

VSWR of the Unit Under Test (UUT) for the frequency range from

7.0 to 26.5 GHz.

6-54
Table 6.3.8.1.3 Data for determining the power sensor VSWi of the Unit

Under Test (UUT) for the frequency range from 7.0 to

26.5 GHz

Source Generator

Waveguide

Band

(WR)

Dual Power

Meter UUT

Calculated

Values

Frequency

(GHz)

Level

(dBm)

Pi P^

sc sc

(mW) (mW)

Pi

UUT

(mW)

Pr

UUT

(mW)

TuUl] VSU'R

7.0 +10 112

10.0 112 -

8.2 90

12.4 90

10.0 90

12.4 90&75

12.4 62

18.0 62

12.4 62

15.0 62&75

18.0 42

26.5 42

6-55
Solving for | Tuui \, we have

Tttt UUT

= Csc

P \ V _njuT » ^

'iUUT

(6.39)

UUT

p p • \y "UUT/ lUUT \

^

•-sc / -"-sc (6.40)

This value is recorded in table 6. 3. 8. 1.3.

The value of VSWR is then calculated from eq (6.30) as follows

1 + I r

VSl^/R = UUT

'

I ^iniT I

and recorded in table 6.3.8.1.3.

6.3.8.2 Sensor Operating Resistance

The operating resistance of coaxial power sensors is not easilymeasured but can be calculated. The rf impedance of these coaxial power sensors (typically 50 Q) must be considered rather than the dc resistance

(usually 200 Q, as discussed in Section 4.1). Vector components of the

operation impedance are involved at all frequencies.

Since the bolometer mount impedance varies with given values of VSWR, it

may be calculated from a knowledge of the values of VSWR which are obtained for

different frequencies. The relationship of VSWR to impedance is shown in figure

6.3.8.2 for a given value of VSWR. As the values of VSWR increase:

(a) The uoper limit of the impedance will increase proportionally to

VSWR.

(b) The lov;er limit of the impedance will decrease in inverse proportion

to VSWR at a relatively slower rate.

These uncertainty limits which were derived in Section 6.3.7.4 may be

determined in the following way:

6-56
IMPEDANCE OR ADMITTANCE COORDINATES

Figure 6.3.8.2 Relationship of VSWR to impedance at microwave frequencies

for a value of VSWR of 1.05.

6-57
(a) To find an upper limit of impedance multiply impedance times

VSWR: (50 i^)-(VSWR).

(b) To a lower limit of impedance divide impedance by VSWR:

(50 i^)/(VSWR).

The value of impedance inscribed on the sensor by the manufacturer is

recorded in a format such as table 6.3.8.2.

The limits of operating impedance can be determined from the VSWR measure- ments performed in Sections 6.3.8.1.1, 6.3.8.1.2 and 6. 3. 8. 1.3. The

appropriate values of frequency ranges and VSWR (SWR) are found in Section

6.3.8.1 and recorded in table 6.3.8.2.

Upper and lower limit values of operating impedance are entered in table

6.3.8.2.

Table 6.3.8.2 Data for determining the sensor operating resistance

of the Unit Under Test (UUT)

Power

Sensor

Model No. Serial No.

Frequency

Range

(MHz) VSWR

Inscribed

Operating

Resistance

(n)

Calculated

Impedance Limits

Lower Upper

(fi)

6.3.9 Extended Power Measurement Capability

The system calibration procedures with the proper initial conditions on

the signal source and the UUT are performed first. Then the equipment is

connected as shown in figure 6.3.9. A typical frequency of 10 MHz is selected

6-58
' 1 INTT 1 INnrP TF:sT 1 SIGNRL

SOURCE

1

1

1

1

1

1

POWER

MLILR

^ r

1 i L

RMPLIFIER 1 w

POHER

SENSOR ' ^

1

Figure 6.3.9 Typical test setup for measurement of extended power

capability of the Unit Under Test (UUT).

6-59
Table 6.3.9 Extended power measurement data from the

Unit Under Test (UUT)

Amplifier

Output

(nominal)

(W)

UTT

Signal Source

Frequency

(GHz)

PuUT

Indicated

(mW)

0.05

0.1

0.5

7.0

8.2

10.0

12.4

15.0

18.0

6-60
on the signal source and the rf power is increased until the amplifier output

matches the specified level for the power sensor. The UUT power reading should be recorded in table 6.3.9 which provides

a suggested format for recording the UUT power measurements at all frequencies

of interest between 10 MHz and 18.0 GHz. Since thermistors and barretters

have limited capacity for handling power measurements, it may be necessary to

reduce the input power level with the insertion of a calibrated attenuator or

a power divider. Several types of these are available [3].

6.3.10 Meter Overload Protection

Typical overload protection capability is stated in the manufacturer's

specifications, but it is important to determine the true protection capability of a power meter within specified limits of overloads applied to the input

connector of the UUT. A customary limit for an overload of average power is

100 mW. A typical limit for a sudden increase in the energy creating an overload is 10 yJ/pulse or 5 W peak.

The performance test to determine the protection capabilities for these

overloads requires equipment such as (1) a pulse generator of variable range;

(2) amplifiers to cover the frequency range from 10 MHz to I8.O GHz; (3) a timing device capable of measuring 5 or more minutes, and (4) an oscilloscope

with a range from dc to 300 MHz.

After the initial calibration of the UUT, the equipment is connected

according to figure 6. 3. 10. Initially the amplifier is connected directly to

the oscilloscope to set the pulse generator to produce a pulse with a duration

of 2 )js, a peak amplitude of 15.8 V and a repetition rate of 10 kHz.

The value of the pulse peak amplitude of 15.8 V satisfies the

requirement of 5 W peak, which is calculated as follows:

Given: P = 5 W peak

R = 50 a

Or

R

then, V = (PR) 1/2

= [(5)(50))V^ = 15.8 [V]. (6.il2)

6-61
TIMING

DEVICE

r 1

AMPLIFIER

1

1

OSCILLOSCOPE

UNIT

UNDER

TEST

Figure 6.3.10 Typical test setup for measurement of overload protection

capability of the Unit Under Test (UUT).

6-62
The pulse duration of 2 ys with the peak amplitude of 5 V/ satisfies the

requirement of an input to the UUT of 10 yJ of energy, calculated as follows:

Energy = (5 W) (2 ps) = 10 [W-ys, or yJ] . (6.43)

The repetition rate of 10000 pulse/s satisfies the requirement of 100

mW (0.1 W) of average power, calculated as follows:

Average Power = jgg^^g^^^— =0.1 [W average]. (6.44)

The pulse generator is then turned off. The amplifier is removed from

the oscilloscope and connected to the UUT. The timing device and pulse generator are then turned on simultaneously, and the pulse input is applied to the

UUT through the amplifier. At the end of 3 min, the timing device and pulse

generator are turned off simultaneously.

Any visible adverse effects on the UUT are recorded in table 6.3.10.

The system calibration for the frequency range from 10 to 100 MHz is

completed, followed by all performance tests for this frequency range. All

results are recorded in table 6.3-10.

The overload protection test is repeated and the system calibration

procedure for the frequency range from 0.1 to 18.0 GHz is completed. Performance tests in this frequency range are then carried out at 0.5 and 2.0 GHz.

All results are recorded in table 6.3.10.

6-63
Table 6.3-10 Overload protection data from the Unit Under Test (UUT)

Unit Under Test

Frequency Indications Other Effects Performance Tests

(GHz) (Pass/Fail)

0.10

0.50

2.0

6-64
7.0 Calculation of Results

It is generally more efficient to obtain calculated results from measurements while the measurements are in progress. This increases the awareness

of any anomalies and the opportunity to verify the validity of results.

Sample data sheets are provided with each measurement procedure in this

document, with columns arranged in the sequence of the test procedure steps,

and labeled with the names and units of the required intermediate measurements

or calculations. The progression in an orderly fashion across the data sheet

to the final column of results is designed to facilitate the testing,

documentation, analysis and review of the power meter's evaluation.

7-1

8.0 Estimation of Measurement Uncertainty

Measurement uncertainty is composed of several uncertainties arising

from various sources throughout the system. Total measurement uncertainty of

the instrument under test must be determined by evaluation of the

contributions of uncertainties arising from individual sources within the system. These individual uncertainties affect the total measurement uncertainty

in varying degrees. Their contributions are analyzed and the total uncer- tainty determined.

8.1 Uncertainties Due to Impedance Mismatches

When a source transmits power to a load, at least two impedance values

are present in this system. These are: (1) Zg, the impedance of the source

(or a generator) and, (2) Z^,, the impedance of the load. Each of these

impedances is a complex number, having both magnitude and phase angle. The

available power from the source is designated Pp- and the power received by the

load is P^. In the ideal case, maximum power is transferred to the load

when Zg_ is equal to Zg*, the complex conjugate of Zg. In reality, however,

there is never a perfect match between the impedances of the source and the

load. Reflections of electromagnetic fields occur at the load and some of the

forward wave is reflected back to the source. The energy of these waves are voltages and currents which are complex values with both magnitude and phase

angle. At microwave frequencies a more convenient parameter than voltage is

used: the complex reflection coefficient, r, with magnitude of p, and phase

angle, (p. T is defined in Section 2.1.16. When r is expressed in terms of

voltage it is the ratio of the reflected voltage to the incident or forward

voltage, and hence is dimensionless. When T is expressed in terms of power, p is squared since P = V^/Z from Ohm's law. The phase angle d), is typically not

known, so only p is measurable, r then is expressed as | r |. r is also

defined in terms of Zg and Zg and designated fp- and T^ respectively. The

characteristic impedance, Zq, typically 50 + jO $7 for a coaxial line, appears

in these definitions. The reflection coefficient Tg, at the generator or source, is defined as

8-1
1-1

J [

I + 1

g o r=/^. (8.1)

and similarly the reflection coefficient at the load, T^, is defined as

y ^ _^ o 'i~ Z^ + Z^- (8.2)

The ratio of Pg to P^ is termed the conjugate mismatch loss, which is

designated here as Zg*ML. In general,

P

I 1 - r r 1^ Zg^ML = 10 log pS = 10 log .- . I „

| 2^ fi : I p -TFV [dB]. (8.3)

This ratio cannot be less than 1 since Pg is either equal to or greater

than ?i [20].

VJhen Pg and Pg, do not equal to

P = P 6 , ^ fft 4)

If li equals Zg*, then Pg, equals Pp-^, P^ equals Pg and Pj^ is

maximum. In the general component form, Zj^ = Rj^ + jX^ and Zg = Rg - jXg, so that in this case Ri + jXy^ = Rg - jXg. The real terms Rg and Rj^ are equal in magnitude, while the reactive terms are equal but opposite in sign, so that this combination of Zg and 1^ is purely resistive.

If there are no reflections from the source, Tg = 0, and

P. = Pg (1 -

I r„ n (8.5)

8-2
In reality, there are reflections at the source also. These occur v;hen

power reflected from the load returns to the source and is re-reflected by the source back toward to the load. Then Tg does not equal 0, and Z^^ML is

modified by an "interaction factor," designated | 1 - Tg^T^ \^ [4].

When a transmission line is terminated in Zq, then Z^ = Zq and Pg^ = Pq. There are no reflections at the load, so T^ = 0. When the source is

reflective, Tp- does not equal zero, so that

o

P^ = Pg (1 -

I Fg p) . (8.6)

Thus, for the general case, eq (8.3) holds.

If only the magnitudes of the complex variables Tp and r^ are measurable, the uncertainty, \]^, due to impedance mismatches can only be

defined within limits. U^ in dB can be expressed as

U^ = 10 log (1 ±1 T^T^ |)2 [dB]. (8.7)

Ufj] reaches a maximum, U^^ ^^^y-, when the product | fgl^ | is positive

and real. Thus:

Um max = ^0 log (1 +

I rgfj^ |) ^ [dB]. (8.8)

The magnitude of U^^ ^^^-^ will always be a positive number but can never exceed

20 log 2 or 6 dB.

A minimum value of U^, 11^ ^^^ occurs when the product | TgT^ \ conbines with 1 exactly out of phase (negative, real). Thus:

Um min = TO log (1- | T^Ti |) ^ [dB]. (8.9)

Um min is always negative, and its magnitude is greater than the

magnitude of U^ ^^y-, but usually by a very small amount [2].

If the mismatch uncertainty limits are given in percent deviation of U^j, from a magnitude of 1, rather than in decibels, this may be expressed as

8-3
Urn {%) = 100 [(1 ± I rgFji |)2 -1]. (8.10)

If the term in parentheses is expanded, eq (8.10) becomes,

Urn (fO = 100 [(1 ± 2 I TgF^ I +

I ^g ri Tji P - 1] . (8.11)

The product | Tgr^ | is usually less than 0.1 and | Tp |^| Yi Y

is negligible,

so eq (8.11) may be written as:

Um {%) = 100 (±2 I rgr£ |)

= ± 200 I V^Yi |. (8.12)

Equation (8.12) provides a useful approximation to the maximum and minimum

limits of the mismatch uncertainty, \i^.

8.2 Uncertainties Due to Power Sensor

The efficiency, n, of a device is the ratio of the useful output power

to the input power. In the case of a thermistor mount, n may be expressed as

rf pov/er absorbed by bolometer

net power delivered to bolometer mount

The output power is the equivalent dc or low frequency power, Psub that is

substituted by the bolometer unit. The power Pj^, delivered to the load,

is designated Pg for power delivered to sensor. Similarly Vi is designated

Fg, the reflection coefficient of the sensor. Thermistor sensors however,

experience some losses internally due to differences in heating effects and

spatial distributions of the rf and dc power within the sensor material [3].

These substitution losses are frequency-dependent. Therefore, a more realistic expression of sensor efficiency is the effective efficiency, rie- This is defined in Section 2.1.12 for bolometer units as "the ratio of the

substitution power, Pgub' to the total rf power dissipated within the

sensor." [^] The effective efficiency, rie» ^^Y be expressed as

8-4
p ^ sub , o . ^ N ng=

p

. (8.13)

Psub is usijally measured and Pg is calculated from Pgub/'^e* Since Pgub

is frequency- dependent , rie is also.

The sensor is a load, and mismatch losses between the source and the

sensor occur in the same fashion as those for the general loads discussed in

Section 3.1. The mismatch loss factor at the sensor is designated as

(1 -i^sr).

A method for measuring the effective efficiency of uncalibrated thermistor mounts or other povjer sensors is described by Russell [21]. This measurement method uses a six- port network analyzer. One or more thermistor mounts

of known efficiency are connected to the measurement port of the six- port

network analyzer and used to generate a system constant, K^, for each

frequency of interest. The calculation of K^ includes the known effective

efficiency of the standard mount, its reflection coefficient, and the system

reflection coefficient. K^ relates the available power, P^q, at the standard

mount to the dc power, Pj_, measured at the incident sidearm oort of the

six- port network. The value of K^ remains constant over an extended period of

time if the network is not changed in any way. Several connections are made

to each known power standard mount in turn and the averages and standard

deviations are computed for each frequency. These data are stored. Then the

uncalibrated mounts are connected to the measurement port and the values of

P^Q are obtained for these mounts. The effective efficiency of each mount

under test is then calculated using the new measurements and the values of K^

for the appropriate frequencies.

The combined values of mismatch loss and effective efficiency are

contained in a term more frequently used than Tie- This is the calibration

factor, Kg, which appears as Ki, K2 or K3 (depending on the frequency range of

interest) in Sections 5 and 6. The definition of Kg from Section 2.1.11 is:

P Ks= p^ = n^ (1 -

I Tg p) . (8.14)

8-5
The measurement of Kg is usually determined by a reference standard

laboratory and is supplied by the manufacturer of the sensor [2]. Since ne is

specific for each sensor at each frequency of interest, the values of Kg which

are provided by the manufacturer for each specific sensor should be used with

the appropriate frequencies.

8.3 Uncertainties Due to Power Meter Instrumentation

The power meter instrumentation contributes uncertainties which arise

from various sources within the meter. Instrument uncertainty can be caused

by nonlinearities in circuits, imprecise attenuators used for various range

displays, and uncertainties in amplifier gain. These are combined in an uncertainty term provided by the manufacturer within designated limits.

Power sensor uncertainty and instrument uncertainty are not easily

separated. A procedure for determining this combined uncertainty is given as follows

Select the appropriate calibration factor, K^, of the reference

power sensor where n = 1, 2 or 3 depending on the frequency range of

interest.

Enter K^ into the power meter (UUT) . (The UUT power measurements

^PUUT ) ^oi" tl^® frequencies of interest are tabulated in meas Sections 6.3.1.1, 6.3.1.2, and 6.3.1.3. These values of

PUUT will be similar to the value of Pdc^.) meas

Solve for the calculated value of the power reading of the UIJT (PuUT^aic) as follows:

p = l^£n. (8 15)

calc n

The UUT measurement uncertainty is then calculated as the difference,

in percent, between the power actually measured by the UUT and the calculated

value of the power applied to the UUT.

8-6
p p UUT , - UUT

Measurement uncertainty in percent = 5--- x 100. (8.1 6)

calc

8.4 Uncertainties Due to Internal Reference Oscillator

The reference oscillator, which is used with thermocouple or diode

sensors, but not with thermistor mounts, may contribute an uncertainty in

power output which must be specified by the manufacturer. The reference

oscillator also has a reflection coefficient due to any mismatch at the

operating frequency. Since the reference frequency is low in relation to the

typical faeasurement frequencies, this reflection coefficient contributes a mismatch uncertainty factor of approximately ±1.2 % [2]. Thermistor detection

is free of these two sources of error because thermistors are closed-loop

devices and do not require a reference power level, as discussed in Section

6.3.7.

8.5 Thermocouple Effects at Lead-Sensor Interface

The connections of the two thermistor leads to the thermistor oxide

material may form thermocouples when the bias current is an alternating current. Since the temperature of the thermistor material is maintained at approximately 100°C above room temperatiire, or about 125°C, and if both contacts

have slij^tly different temperatures, this thermocouple effect produces a dc

current. This current may add to or subtract from the dc current in the meter.

The uncertainty in power measurements due to this effect usually does not

exceed 0.3 yW. It may be eliminated for low-level power measurements with a

dc supply with reversible polarity for the dc substitution power. The

reversal of the dc polarity provides the sum and difference of the

substitution and thermoelectric powers [2].

A power meter for measuring power at rf , mw and mmw frequencies has

been developed which eliminates lead errors associated with the bridge leads

[22]. The Wheatstone bridge in this meter is not self- balancing. A current

is passed throu^ the bolometer mount while voltage is sensed across it, so

the resistance of the bolometer is defined at the dc terminals of the mount.

This reference plane eliminates the effect of bridge lead resistance that

1-7
could otherwise introduce uncertainties, particularly in the case of long

leads.

8.6 Digital Readout Uncertainty

This uncertainty is the ±'/2 count uncertainty in the least significant

digit of a digital display. It may be canceled if the difference between two

power readings is required, or it could be additive, in the worst case, making

an uncertainty of ± 1 count maximum [2]. The units of the least significant

digit are usually nanowatts as discussed in Section 6.3.5 when those of the

measured power are microwatts. The percent of uncertainty would then equal

approximately ± 0.^%.

8.7 Offset Voltage Uncertainty

Uncertainty in power measurements can be introduced by the offset

voltage, which forces the meter to read zero when no rf, yw or mmw power is

sensed. The zero setting is made on the most sensitive range as specified by

the manufacturer. The uncertainty contribution from this source may be ± 0.55^

when the measured power, P,^, is 50 |jW and full scale equals 100 yW [2].

8.8 Zero Carryover Uncertainty

An additional uncertainty can occur when the zero carryover mechanism,

which is designed to eliminate manual resetting of the zero point when

changing display scales, operates with different offsets on different scales.

The uncertainty from this source is typically ± 0,255 [2].

8.9 Short-Term Instability

A source of uncertainty is noise, or short-term instability. This is

usually specified as a change in meter indication over an interval such as one

minute, for constant input power, constant temperature and constant line

voltage [4]. The uncertainty contribution from this source is approximately

± 0.05r, [2].
8.10 Long-Term InstabilityLong-term instability, (also known as long-term stability or drift

[4]), is specified for a period of one hour, with constant input power,

constant temperature and line voltage [4]. The drift is usually caused by

changes in the zero-settings of the display scales. On high ranges, this

effect is insignificant. For low scales with their increased sensitivity this

can introduce uncertainty. The warm-up interval specified by the manufacturer

should be observed. In addition, if the zero is reset immediately prior to a reading, these effects can be eliminated.

V\fhen the rf power is low, a constant-current source may be used in

order to avoid large uncertainties in the substituted power. This can be a resistor whose value is approximately 100 times that of the bridge resistance.

Any changes in load impedance will then be approximately one percent or less.

Accuracies of 5 percent or better have been obtained in this manner with a 50-n single thermistor bridge at powers from 1 to 100 raW [23].

8.11 Total Measurement Uncertainty

Total uncertainty is calculated from all the sources discussed above.

The power delivered to a load, Pj, is less than the ideal ( fg = 0) source

power, Pp., by the mismatch uncertainty factor, U^,

where

Tj = &.--:: f^ 17)

from eq (8.3).

The net power at the sensor is converted from rf power to the equivalent dc or substituted power, Psy^, but in the process Psub ^^ modified by ne of the sensor and the magnitude of the mismatch loss between the sensor and

the source. The uncertainty in the sensor mismatch is expressed as

"s - irrr-Tf-TT • '''''

8-9
which is an uncertainty only if rie ^^^ \ ^s \ ^i^e unknown

With the substitution of eq (3.14), eq (8.18) becomes

U3 = ^ . (8.19)

's

Finally, this twice -modified power from the generator reaches the power

meter instrumentation where further modifications occur to the power measurement, due to imperfections in range-changing attenuators, amplifiers, and any

reference oscillator mismatch. These effects are multiplicative and multiply

Pgyl3 as cascaded amplifiers multiply gain. They are represented by the

multiplicative factor, m, [2] which appears in eqs (8.20, 8.21) below.

The sum of the uncertainties introduced by zero offset, zero carryover,

noise and drift is additive algebraically to the power meter reading.

8.11.1 Worst Case Uncertainty

Worst case uncertainty, U^^, considers maximum values, algebraically

added, of the deviation of a power measurement, P^, from an established

reference or ideal value, Pq-, of power at the generator. This ideal value

would be the maximum value, Pp- mp^xf that P^^ could achieve if measured at the

generator. Consequently, using the power meter reading, Pry^, this becomes

P - (mismatch uncertainty) f Pm - offsetm^y) /o p^N

g max ~ [K . ] (m . ] and

s min mm

'wc

p

_ [mismatch uncertainty! [Pm ~ offsetm;:^Y] r8 21)

g^ min ~ [k J [m J

^ s max ^ max'^

for Pm may also be shown as;

8-10
(1) an absolute differential in pov/er:

Uwc = (Pg max ' \ Pg min P

" Pm? (8.22a)

(2) or as a fractional deviation:

U„c = P^i!!ax_lPgJ!ml ; (8.22b)

^m

(3) or as a percent of P^:

Uwc = ^e ma y ^1 Pg f"in I x 100; (8.22c)

^m

(4) or a deviation in dB from P^:

U^c = 10 log [Pg max +

| Pg min p/Pj. (8.22d)

If all of the uncertainties are expressed in decibels or in percent,

they are all algebraically additive [2].

8.11.2 Root -Sum-Square (RSS) Uncertainty

Root -sum- square (RSS) uncertainty is a more realistic method of uncer- tainty assessment than worst case uncertainty. It is based on the assumption

that most of the uncertainties of power measurements, even though systematic

rather than random, are independent of each other. And therefore can be

combined as independent variables.

This method specifies the changes of each component of uncertainty in

fractional form, as the ratio of the change of the component to the component

itself. Each ratio is then squared, the sum taken and the square root of the

whole obtained.

8.11.3 Calculation of Total Measurement Uncertainty

The total measurement uncertainty of the pov/er meter (UUT) is comtxDsed

of the sum of the uncertainties contributed by:

8-11
(1

)

the power sensor uncertainty and the instrument uncertainty (which

cannot be easily separated), as discussed in Sections 8.2 and 8.3;

(2) the calibration factor uncertainty that is measured and recorded in

Performance Tests 6.3.2.1, 6.3.2.2, and 6.3.2.3;

(3) the reference oscillator uncertainty (in power measurements with

nonthermistor mounts) due to a difference in power level from 1 mW

which is measured and recorded in Performance Test 6.3.7.2, and

(4) the reference oscillator uncertainty (in power measurements with

nonthermistor mounts) due to mismatch (discussed in Section 8.4);

(5) the thermocouple effects at the lead-sensor interface when

applicable (Section 8.5);

(6) the digital readout uncertainty when applicable (Section 8.6).

The offset factor includes:

(7) the uncertainty in zero offset voltage (Section 8.7);

(8) zero carryover uncertainty (Section 8.8);

(9) short-term instability (noise) (Section 8.9);

(10) long-term instability (drift) (Section 8.10).

The appropriate calibration factor uncertainties must be read from

their respective tables and entered in table 8.11.1. The total measurement

uncertainty is then calculated at each frequency and recorded in table ^.11.1.

The resultant total measurement uncertainty is valid only for the specific

instrument under test with its associated power sensor or sensors at the

frequencies used during calibration.

8.12 Uncertainty Analysis of Power Measurements for known VSWR values

The limits of uncertainty in values of power measurements at a load may

be determined for specific frequency ranges if the VSWR at the source (or

generator) is known for those ranges. The reflection coefficient of the

source, Tg, is determined without a load because the presence of the device

whose power is to be measiored constitutes a load.

8-12
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8-13
step 1 : To determine Tgi

Given,

Source VSWR (Worst Case)

1.06

1.10

Frequency Range

0.01 - 8.0 GHz

8.0 - 18.0 GHz

Since, from eq (6.23),

1 +

I rI (VSWR)g = YTTTY^-i (8.23)

. V, I p I ( VSWR)g- - 1 then. I r 1=

g ^ vsWR)i . 1

I (VSWR)g + (8.24)

For the frequency range of 0.01 - 8.0 GHz,

r I . 1^4 = 04 = 0.029.

g

I 1 .Oo + 1 2.06 (8.25)

For the frequency range of 3.0 - 18. GHz,

I ^gl = 1.10 . 1 = 271^= °•^^^• (8.26)

Step 2

:

To determine T^:

Example: Assume a value for the VSWR at the load, (VSWR);^, of 1.10.

Since, from eq (6.23),

1 + I r,

1 -

I r, I

8-14
then,

(VSWR) - 1

T TO - 1 10

I I

I (VSWR)^ + 1 1.10 + 1 2.10

step 3 • To determine the power measurement uncertainty in percent:

From eq (8.12), U^ {%)- ± 200 Ir rJ .

Typical values of uncertainty in power measurement are calculated for

the two solutions of Fg given above. Nine values of VSWR of the load are assumed for each value of Tp-. These uncertainties are tabulated in table

o 8.12.1.

8-15
Table 8.12.1 Calculated values of typical power measurement

uncertainty in percent for known VSliJR values.

Frequency

(GHz)

Source Load Uncertainty

vsm ^ 1 VSWR h

±200 ir^r^l

0.01-18.0 1.06 0.029

1.00

1.10 0.048 0.28

1.20 0.091 0.53

1.30 0.130 0.75

1 .40 0.167 0.97

1.50 0.200 1.16

1.60 0.231 1.34

1.70 0.259 1.50

1.80 0.286 1.66

1.90 0.310 1.80

8.0 - 18.0 1.10 0.048

1.00

1.10 0.048 0.46

1 .20 0.091 0.87

1.30 0.130 1.25

1 .40 0.167 1.60

1.50 0.200 1.92

1.60 0.231 2.22

1 ,70 0.259 2.49

1.80 0.286 2.75

1.90 0.310 2.98

8-16
9 . Summary

The Importance of power measurements is described. Differences in methods of measurement at low and high frequencies are presented. The theory of

conversion of high-frequency energy to heat in a sensing material is presented.

Various common types of sensors are described. Tests to determine the performance of power meters are presented, together with suggested formats for

recording results. Sources of uncertainty in measurements are analyzed, and

the relative contribution to total instrument uncertainty from each source is

presented. Measurements which are made with a heat-sensitive sensor are shown

as typical results with this method of detection.

9-1

10.0 Conclusions

The use of energy conversion principles for the detection of

high-frequency power and its conversion to a do or low-frequency power permits

the use of the instrumentation currently available for power measurement in

the low-frequency region. These techniques have been developed and refined

over the past years. They provide power measurements which are reproducible

within calculable limits of uncertainty and which are acceptable for most

purposes. More sophisticated techniques of measurement are available but are

usually reserved for higher precision.

The tests presented in this report are sufficient to evaluate the

performance of power meters currently in use over the specified frequency

range. Confidence in the test results is based on an linderstanding of the

principles of detection, conversion and quantification of power embodied in

the thermistor sensor method.

As technology such as communications requires higher frequencies than

those of today, new methods of power measurement will require similar but more

precise energy conversion methods in order to use the existing power

measurement instrumentation described here.

10-1

11.0 Acknowledgments

The authors wish to express their appreciation to John D. Smilley,

Galen H. Koepke, and John T. Stanley for their constructive evaluation of this

document and recommendations for enhancement of the procedures involved in

power meter performance assessment; to John P. Wakefield and Manly P. Weidman

for their valuable technical guidance; and to Neil T. Larsen, whose extensive

work in this field has provided authoritative suggestions and source material.

Special acknowledgment is accorded to James R. Major for valuable

contributions in mathematical derivations and circuit design and graphics.

The development and optimization of the test setups and verification of

the measurement procedures by Richard L. Ehret greatly enhanced their

reliability for reproducibility of results.

Shirley Deeg of the NIST Information Office provided invaluable

professional publication management. Terry Yenser and Sharon Huntoon

contributed many hours of patient preparation of this document. Darwin Miner

and Dean Eicher of MASC Graphic Support Services provided professional graphic

support in all facets of the art work.

11-1

12.0 References

[1 ] Hewlett-Packard. [Microwave pov/er measurement. Application Note 6M.

1969. November.

[2] Hewlett-Packard. Fundamentals of rf and microwave pov/er measurements.

Application Note 64-1. 1977 August.

[3] Lance, A.L. Introduction to microwave theory and measurements . New York: McGraw-Hill Book Company; 1964. 308 p.

[4] IEEE Standard, Application guide for bolometric power meters, IEEE Std

470-1972; Subcommittee on Power Measurements of the IEEE

Instrumentation and Measurements Group Technical Canmittee on Hi^-

Frequency Instruments and Measurements. The Institute of Electrical

and Electronics Engineers, Inc. 1972.

[5] Jay, F., ed. in chief. IEEE standard dictionary of electrical and

electronic terms , ANSI/IEEE Std. 100-1984. 1174 p.

[6] Larsen, N.T. Review of microwave power standard principles, history,

and needs. Natl. Bur. Stand. (U.S.). Internal Memorandum; 1985 May.

[7] Engen, G.F. A refined X-band microwave microcalorimeter . Natl. Bur.

Stand. (U.S.). Journal of Research; 63C (1): 817/77-824/82; 1959

July-September.

[8] Macpherson, A.C.; Kerns, D.M. A microwave microcalorimeter. Rev. Sci.

Instr. 26 (1): 27-33; 1955 January.

[9] I-Iudson, P. A.; Allred, CM. A dry static calorimeter for rf power

measurement. IRE Transactions on Instrumentation; 1-7 (3-4):

809/292-813/296; 1958 December.

[10] Harvey, M.E. WR15 millimeter wave microcalorimeter. Natl. Bur. Stand.

(U.S.). Technical Note 618; 1972 May. 41 p.

[11] Zapf, T.L. ; Harvey, M.E. ; Larsen, N.T. ; Stoltenberg, R.E. Ultrasonic calorimeter for beam power measurements. Natl. Bur. Stand.

(U.S.). Technical Note 686; 1976 September. 31 p.

[12] Weidman, M.P. ; Hudson, P. A. WR10 millimeter wave microcalorimeter.

Natl. Bur. Stand. (U.S.). Technical Note 1044; 1981 June. 11 p.

[13] "General characteristics of thermistors," Application Data , Section

3703, General Electric Company, Magnetic Materials Business Section,

Edmore, Michigan; 1-4; 1962 October.

[14] Hemenway, C.L. ; Henry, R.W. ; Caulton, M. Physical electronics. New

York, NY: John Wiley and Sons; 1967. 450 p.

[15] Sachse, H.B. Semiconducting temperature sensors and their applications . New York, NY: John Wiley and Sons; 1975. 380 p.

12-1
[16] Selby, M.C.; Behrent , L.F. A bolometer bridge for standardizing

radio- frequency voltmeters, Natl. Bur. Stand. (U.S.) J. Research

(44): 15-30; 1950 January.

[17] Engen, G.F. A dc-rf substitution error in dual element bolometer mounts,

Natl. Bur. Stand. (U.S.) Report 793^; 1963 August. 24 p.

[18] Weinschel Engineering. Rf and microwave equipment and components.

1984-85.

[19] Jordan, E.G.; Balmain, K. G. Electromagnetic waves and radiating

systems. New Jersey: Prentice-Hall, Inc. 1968. 753 p.

[20] Kerns, D.M. ; Beatty, R.W. Basic Theory of waveguide junctions and

introductory microwave network analysis. London, England. Pergamon

Press; 1967. 150 p.

[21] Russell, D.H. Microwave power measurements using the dual six-port,

(private communication); 1986 January.

[22] Larsen, N.T. NIST Type IV rf power meter operation and maintenance,

Natl. Bur. Stand. (U.S.) NBSIR 77-866; 1977 October.

[23] Improved thermistor bridge for rf power measurements. NBS Technical

News Bulletin, 40 (9): 13^-5; 1956 September.

12-2
13.0 Suggested Additional Reading

Beatty, R. W. Intrinsic attenuation. IEEE Transactions on Microwave

Theory and Techniques. MTT-11 (3): 179-182; 1963 May.

Beatty, R. W. Insertion loss concepts. Proceedings IEEE, 52 (6):

663-671; 1964 June. (Footnote in HP Appl. Note 64, p. 2-12).

"Temperature Compensation," Application Data , Section 3702, General

Electric Ccmpany, Magnetic Materials Business Section, Edmore,

Michigan; 1-4; 1964 May.

Oldfield, L.C. Uncertainties in electrical measurements. Invited

paper presented at Second British Electromagnetic Measurements

Conference. 1985 October.

Komarek, E.L. Performance characteristics of an automated broad-band

bolometer unit calibration system. IEEE Transactions on microwave

theory and techniques. Mf^T-25 (12): 1122-1127; 1977 December.

Larsen, N.T. ; Clague , F.R., "The NBS type II power measurement system,"

Adv. Instrum. vol. 25, Pt. 3, paper no. 712-70, in Proc. 25th Annu.

ISA Conf. (Philadelphia, PA), Oct. 26-29, 1970.

Weast, R.C. ed. in chief. CRC handbook of chemistry and physics,

67th edition. Chemical Rubber Company; 1986-87. 2408 p.

Laverghetta, T.S. Handbook of microwave testing. Canton, MA: Artech House,

Inc. ; 1981. 520 p.

Thompson, B.J. Rf power meter update. Test & Measurement World.

7 (6): 94-95; 1987 June.

Rumfelt, A.Y.; Elwell, L.B. Radio frequency power measurements.

Proceedings IEEE, 55(6): 837-850; 1967 June.

Hewlett-Packard. HP Test & Measurement News. 1988 May/ June.

13-1

1^.0 Appendices

Appendix 14.1

Calibration Results for

Typical Coaxial Dual

Directional Couplers

a. Frequency Range: 0.05 to 2.0 GHz.

b. Frequency Range: 2.0 to 18.0 GHz.

14-1
23

^

22

QQ

2 21

o

CO UUi

S 20

Q.

OO 19 -

18

_;

1 1 ! 1 1 1 1 1 1 Forward Power _

. 1 +"—-+ Reflected Power 2

-'

y\

—

- ^A A P^

+

— V

^^r \w ^ ^ ^

—

1 1 1 1 1 1 .,1 1 1 " 0.050 0.245 0.635 1.025 1.415

Frequency (GHz)

1.805 2.000

Figure 14.1.a. Plots of forward and reflected coupling factors of a typical

coaxial dual directional coupler in dB with respect to the OUTPUT

Port for the frequency range of 0.05 to 2.0 GHz.

O

LL

O)C

Q.D

OO

23

19

18

Forward Power

+ + Reflected Power -

^^t+Htt^:,

w**%<^-

2.000 5.200 8.400 11.600 14.800

Frequency (GHz)

18.000

Figure 14.1.b. Plots of forward and reflected coupling factors of atypical

coaxial dual directional coupler in dB with respect to the OUTPUT

Port for the frequency range of 2.0 to 18.0 GHz.

14-2
Appendix 1^1.2

Calibration Factors for a Typical

Reference Power Standard

14.2.1 Ki (0.01-0.10 GHz).

14.2.2 K2 (0.10-18.0 GHz).

14.2.3 K3 (18.0-26.5 GHz).

Table 14.2.1 Values of calibration factor Ki for a typical reference

power standard for the frequency range from 0.01 to 0.10

GHz [13]

Frequency CAL Factor

(GHz) Ki

0.010 0.9388

0.03 0.9900

0.050 0.9905

0.100 0.9877

Table 14.2.2 Values of calibration factor K2 for a typical reference

power standard for the frequency range from 0.10 to 18.0

GHz [13]

Frequency CAL Factor Frequency CAL Factor Frequency CAL Factor

(GHz) K. (GHz) K, (GHz) K,

0.100 0.9842 4.0 0.9598 10.0 0.9041

0.500 0.9831 5.0 0.9538 11 .0 0.8977

1.000 0.9781 6.0 0.9442 12.0 0.8901

1.150 0.9753 7.0 0.9235 12.4 0.8947

2.0 0.9659 8.0 0.9116 14.0 0.8926

3.0 0.9643 9.0 0.9039 15.0

16.0

17.0

18.0

0.8817

0.8860

0.8776

0.8616

14-3
Table 14.2.3 Calibration data for a typical reference power standard

measured by the National Institute of Standards and

Technology for the frequency range from 18.0 to 26.5 GHz*

Effective GAL

Frequency Reflect].on Coefficient Efficiency Factor

(GHz) (D (np) (K3)

Sample Sample Sample Sample Sample Sample

1 2 1 2 C\J

18.0 0.198 0.121 0.982 0.975 0.943 0.961

20.0 0.019 0.115 0.976 0.971 0.976 0.958

22.0 0.090 0.158 0.976 0.971 0.968 0.947

24.0 0.107 0.127 0.978 0.971 0.967 0.955

25.0 0.078 0.073 0.977 0.967 0.971 0.962

26.5 0.086 0.121 0.977 0.966 0.970 0.952

Sample values from bolometer mounts calibrated at NIST.

14-4
Appendix 14.3

Tuner Settings for a Typical Waveguide

Rf Power Transfer Standard

Table 14.3 Tuner settings for a typical waveguide rf power transfer

standard for the frequency range from 18.0 to 26.5 GHz**

Frequency Tuner Setting (micrometer reading)

(GHz)

18.0

19.0

20.0

21 .0

22.0

23.0

24.0

25.0

26.0

26.5

**NIST laboratory calibration

Tx T. Ts T^

0.243 0.050 0.146 0.069

0.335 0.051 0.336 0.045

0.415 0.041 0.360 0.039

0.389 0.046 0.379 0.040

0.426 0.395 0.395 0.042

0.151 0.052 0.399 0.039

0.181 0.061 0.157 0.0^7

0.193 0.042 0.162 0.048

0.202 0.039 0.188 0.055

0.200 0.049 0.194 0.052

14-5
NBS.IUA iR^.

' U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NIST/TN-1310

2. Performing Organ. Report No. 3. Publication Date

December 1988

4. TITLE AND SUBTITLE

Performance Evaluation of Radiof requency , Microwave, and Millimeter Wave Power Meters

5. AUTHOR(S)

Eleanor M. Livingston, Robert T. Adair.

6. PERFORMING ORGANIZATION (If joint or other thar) NBS. see in struct/on sj National Institute of Standards and Technology

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

10. SUPPLEMENTARY NOTES

1^2] Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here) Measurement techniques are described for the evaluation of the electrical performance

of commercially available radiof requency (rf )

, microwave (mw) and millimeter wave (mmw)

power meters which use bolometric power sensors and typically operate from 10 MHz to

26.5 GHz for an average power range of 10 yW to 10 mW with appropriate attenuation

for higher power ranges.

Power measurements at dc and low frequencies are relatively straightforward since

voltage, current, and impedance are discrete entities from which values of power may

be calculated through the use of Ohm's law. For radio, microwave and millimeter wave

frequencies, however, these become complex, interactive, distributed parameters. Impedance mismatch, leakage, and nonlinear responses must also be considered. The

principle of the bolometric method of measurement of rf , mw and mmw power is

presented.

Techniques are described for analysis of: ranges of frequency and power, operating

temperature, stability, response time, calibration factor, extended power measurement,

overload protection, and characteristics of the internal power reference source. Some automated methods are discussed. Block diagrams of test setups are presented.

Sources of uncertainty in the bolometric method are analyzed.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

bolometer; dc substitution; microwave power; millimeter wave power; power measurement

radiof requency power; temperature compensation; thermistor; uncertainty.

13. AVAILABILITY

[j5 Unlimited

I I For Official Distribution. Do Not Release to NTIS

nX] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

[^^ Order From National Technical Information Service (NTIS), Springfield, VA. 22161

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PRINTED PAGES

158

15. Price

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