U.S. Department of Commerce

National Bureau of Standards

NBS MEASUREMENT SERVICES

special Publication 250-32

A Calibration Service for 30 IVIHz

Attenuation and Phase Shift

Robert T. Adair and David H. Russell
INTRODUCING THE CENTER FOR ELECTRONICS AND ELECTRICAL ENGINEERING

The Center for Electronics and Electrical Engineering (CEEE) is the component of the

National Bureau of Standards charged with providing Bureau activities and services

supporting electrotechnology. In response to identified and anticipated needs, Center

programs provide national reference standards, measurement methods, supporting theory and

data, and traceability to national standards. Beneficiaries are U.S. industry, other

Government organizations, the academic community, and society at large. In fiscal year

1987, the Center calibrated nearly a thousand transfer standards for some 200 customers.

The Center is organized into four technical divisions, with the Electrosystems and

Semiconductor Electronics Divisions at Gaithersburg, Maryland and the Electromagnetic

Fields and Electromagnetic Technology Divisions at Boulder, Colorado. The Center

provides measurement research and services for:

o Conducted electrical signals and energy in the Electrosystems Division:

- dielectrics for advanced power systems

conducted electromagnetic interference

- waveform synthesis

- signal acquisition and processing

- automatic test equipment

calibration/testing strategies

0 Radiofrequency signals and interference in the Electromagnetic Fields Division:

radiofrequency to millimeter-wave electromagnetic fields and signals

general microwave and millimeter-wave instruments, components

microwave and millimeter-wave noise

microwave and millimeter-wave antenna systems

radiated electromagnetic interference; electromagnetic compatibility

monolithic microwave/millimeter-wave integrated circuits materials properties measurements at high frequencies

o Lightwaves, cryogenics, and magnetics in the Electromagnetic Technology

Division:

- optical fibers; integrated electro-optics

- superconducting materials

superconducting electronics

magnetic materials

o Semiconductor electronics, in the Semiconductor Electronics Division:

semiconductor materials, such as silicon and gallium arsenide

semiconductor materials modification

- semiconductor devices

- integrated-circuit test structures for rapid process assessment

For information, contact the Center at 1 -301 -975-2220 or write to: The Center for Electronics and Electrical Engineering, Metrology Building Room B-358, National Bureau of Standards, Gaithersburg, MD 20899.
NBS MEASUREMENT SERVICES:

A Calibration Service for 30 Mi-lz

Attenuation and Pliase Shift

Robert T. Adair and David H. Russell

Electromagnetic Fields Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, CO 80303

April 1988

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
Library of Congress Catalog Card Number: 88-600527

National Bureau of Standards Special Publication 250-32

Natl. Bur. Stand. (U.S.), Spec. Publ. 250-32, 184 pages (Apr. 1988)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1988

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
PREFACE

Calibrations and related measurement services of the National Bureau of Standards (NBS) provide the means for industry, government agencies, academia,

and others to relate the measurements they make to national standards and, by

extension, to the measurement systems of other countries throughout the world.

It is of crucial importance to improving U.S. productivity, efficiency, and quality

-- in short our competitive stance -- that measurements of appropriate accuracy can be made at all stages of product development, production, and marketing and

that it is possible to refer the results of these measurements to each other in a

meaningful way. NBS services provide essential support for satisfying these

needs, as well as measurement needs arising from societal concerns such as

health, safety, natural resources, and defense. The requirements of NBS clientele range from the highest ievels of accuracy realizable from advanced science and

technology to the practical levels of accuracy needed to support routine

production. A reference-level measurement may be the result of days of painstaking individual effort or may be provided by a semi-automatic measuring

system in minutes. The variation in customer needs and hence in NBS services

responsive to those needs is great.

The more than 300 different calibration services, measurement assurance

services, and special tests that are offered by NBS are described in NBS Special

Publication 250, NBS Calibration Sen/ices Users Guide. The Guide provides

essential technical details of NBS calibration and related measurement services,

such as levels of accuracy provided by NBS and the requirements to be met by

customers' transfer standards. It also provides information needed for placing

orders for these services and identifies technical and administrative contacts for each service.

Technical descriptions in the Users Guide are intended to be restricted to the

material needed by a potential customer to decide if a given service will meet

that customer's needs. Frequently, a customer may be interested in more

detailed and extensive information, such as the way in which the errors associated with a measurement are assessed. Beginning in 1987, NBS established a Special Publication 250 series which supplements the Guide. Each publication

in this series provides a detailed technical description of a specific NBS

calibration service, or closely related set of services, and includes:

o specifications for the service

o design philosophy and theory

o description of NBS measurement system used to provide service

o NBS operational procedures

o measurement uncertainty assessment, including error budget,

identification of systematic and random errors

o NBS internal quality control procedures

Special Publication 250-32, A Calibration Service for 30 MHz Attenuation and

Phase Shift, describes service offered primarily under NBS Test Numbers 61215C

(attenuation) and 61410C (phase shift) and the reference basis for related service

under NBS Test Numbers 6121 1C and 61230S. These services are provided by

the Microwave Metrology Group in the Electromagnetic Fields Division as part of a series of services offered by the Division in support of microwave and

millimeter-wave technology.

Ill

CONTENTS

Page

Abstract xvii

1.0 Introduction 1-1

1.1 Present Capabilities at NBS 1-2

1.2 System Overview 1-3

1.2.1 System Uncertainty. 1-3

1.2.2 Device Under Test Requirements = 1-4

1.3 Definitions 1-5

1.3.1 Insertion Loss 1-5

1.3.2 Attenuation 1-5

1.3.3 Standard Attenuation 1-6

1.3.4 Incremental Attenuation 1-6

1.3.5 Characteristic Insertion Loss 1-6

1.3.6 Insertion Phase Shift 1-7

1.3.7 Phase Shift Difference 1-7

1.3.8 Decibel 1-7

1.3.9 dBm 1-8

1 .3.10 Neper 1-8

1.3.11 Conversion from Nepers to Decibels 1-8

1.3.12 Propagation Constant ,e 1-9

2.0 Dual-Channel Rf Null System for Attenuation and Phase

Calibration 2-1

2.1 Description of 30 MHz Calibration System 2-4

V
CONTENTS (cont.)

Page

2.1.1 30 MHz Standard Piston Attenuator 2-4

2.1.1.1 Theory 2-4

2.1.1.2 Description 2-8

2.1.1.3 Uncertainties 2-10

2.1 .2 30 MHz TEii Launching Assembly 2-11

2.1.3 30 MHz Precision Phase Shifter 2-15

2.1.3.1 Description 2-15

2.1.3.2 Uncertainties 2-16

2.1 .4 30 MHz Coarse Phase Shifter 2-18

2.1.5 Level Set Attenuator 2-19

2.1.6 Rf Null Detecting System 2-20

2.1.7 Rf Source and Associated Circuitry 2-22

2.1.8 The Insertion Point 2-23

2.2 Uncertainty Analysis 2-23

2.2.1 30 MHz Attenuation Calibration Uncertainties 2-23

2.2.2 30 MHz Phase Shift Calibration Uncertainties 2-26

2.3 Procedure for Calibrating an NBS Model VII 30 MHz Piston

Attenuator 2-27

2.3.1 Calibration Procedure for NBS Model VII Attenuators 2-27

2.3.2 Attenuator Calibration Data Reduction 2-32

2.3.3 Tabulated Data and Calibration Results 2-33

2.3.4 Typical Report of Calibration for 30 MHz WBCO

- " Variable Attenuators 2-33

VI
CONTENTS (cont.)

Page

2.4 Procedure for Calibrating a 30 MHz Phase Shifter 2-^0

2.H.^ Calibration Procedure for 30 MHz Phase Shifter 2-40

2.4.2 Phase Shifter Calibration Data Reduction 2-45

2.4.3 Tabulated Data and Calibration Results for

30 MHz Phase Shifter 2-46

2.4.4 Typical Report of Calibration for 30 MHz Phase

Shifters 2-46

2.5 Conclusions - Dual-Channel Rf Null Technique 2-53

3.0 Measurement Uncertainty and Quality Assurance 3-1

3.1 NBS System Measurement Uncertainty 3-1

3.1.1 30 MHz Standard Piston Attenuator 3-1

3.1.2 30 MHz Standard Phase Shifter 3-2

3.1.3 Measurement Uncertainty for Attenuation 3-2

3.1.3.1 Uncertainties Associated with Typical

Attenuators 3-3

3.1.4 Measurement Uncertainty for Incremental Phase Shift 3-3

3.2 Typical NBS System Attenuation Calibration Results 3-4

3.2.1 Calibration of NBS Model SA-1 10-dB Step

Attenuator 3-4

3.2.1.1 Conclusions 3-5

3.2.2 Calibration of NBS-Designed WBCO Attenuators 3-5

3.2.2.1 Conclusions 3-7

3.2.3 Calibration of Commercial WBCO Attenuators 3-7

3.2.3.1 Conclusions 3-I6

VII
CONTENTS (cont.)

? Page

3.3 Typical NBS System Phase Shift Calibration Results 3-27

* 3.3.1 Conclusions 3-27

3.^ Intercomparison of Attenuation Calibration Results 3-36

3.4.1 Comparison with NBS "SQUID" System 3-36

- ~ 3.4.1.1 Conclusions 3-38

3.4.2 Comparison with NBS Six-Port System 3"38

3.4.2.1 Comparison Using the NBS Model SA-1 and

V _ the LF Six-Port ANA 3-38

3.4.2.1.1 Conclusions 3-38

3.4.2.2 Comparison Using a Step Attenuator and the

LF Six-Port ANA 3-38

3.4.2.2.1 Conclusions 3-41

3.4.3 Comparison with International Laboratories 3-41

3.4.3.1 Conclusions 3-48

3.5 Measurement Quality Assurance 3-48

3.5.1 Sunmary of Consistency of 30 MHz System

:' Measurements 3-48

3.5.2 Summary of Comparisons with NBS SQUID System 3-48

3.5.3 Summary of Comparisons with NBS Six-Port Systems 3-49

3.5.4 Summary of International Intercomparisons 3-50

4.0 Conclusions - 30 MHz Attenuation Measurements 4-1

5.0 Conclusions - 30 MHz Phase Shift Measurements 5-1

6.0 Summary of NBS 30 MHz Attenuation and Phase Shift Calibration

System Uncertainties 6-1

VIII
CONTENTS (cont.)

Page

7.0 References 7-1

8.0 Acknowledgments 8-1

9.0 Appendices 9-1

9.1 Appendix A: Excerpt from Reference 5 9-2

9.2 Appendix B: Complete Copy of Reference 10 9-^

9.3 Appendix C: Complete Copy of Reference 14 9-13

9.4 Appendix D: Excerpts from Reference 17 9-22

9.5 Appendix E: Drawings of System Ccmponents 9-29

IX

FIGURES

Figure No. Description Page

2.1 Basic Block Diagram of Dual-Channel Rf Null

Attenuation and Phase Calibration System 2-2

2.2 Complete Block Diagram of 30 MHz Dual Channel

Rf Null Attenuation and Phase Calibration System 2-3

2.3 View of upper portion of the 30 MHz Standard

Attenuator Assembly showing the Level Set Attenuator, the WBCO Standard and the Signal Launching

Assembly 2-5

2.4 View of upper portion of the 30 MHz Standard

Attenuator Assembly showing the Optical Readout for

the Linear Displacement Scale 2-6

2.5 30 MHz Standard Attenuator Assembly 2-7

2.6 30 MHz TEii Launching Assembly 2-13

2.7 30 MHz Launching Assembly with Matching and

Sampling Networks 2-14

2.8 30 MHz Precision Phase Shifter 2-17

2.9 30 MHz Level Set Attenuator with Drive Motors.. 2-21

2.10 Operator Calibrating an NBS Model VII Piston

Attenuator at 30 MHz 2-28

3.1 Calibration Results for NBS Model SA-1 10 dB Step

Attenuator, 1970 to 1982 3-6

3.2 Calibration Results for NBS Design Variable WBCO

Attenuators (10-dB increment), 1963 to 1985 3-8

3.3 Calibration Results for NBS Design Variable WBCO

Attenuators (20-dB increment), 1963 to 1985 3-9

3.4 Calibration Results for NBS Design Variable WBCO

Attenuators (30-dB increment), 1963 to 1985 3-10

3.5 Calibration Results for NBS Design Variable WBCO

Attenuators (40-dB increment), 1963 to 1985 3-11

3.6 Calibration Results for NBS Design Variable WBCO

Attenuators (50-dB increment), 1963 to 1985 3-12

XI
Figure No.

FIGURES (cont.)

Description Page

o

D' 71 L/cL± 1 Drat- 1 on Attenuators

tvcbUXUS i OI IMDO JJcblgll vdl ±dU±c \Nuy^U

(60-clB increment), 1963 to 1985 3-13

o QO L<i±i urauion

Attenuators

rteoUXUo i OL l\JDo iAroign Vdl idUXS vVDL'U (70-dB increment), 1963 to 1985 3-14

o

J' Q 1 urdu 1 on Attenuators

nesuxLS 1 or in do ijeoign udriduxe nuwj

(80-dB increment), 1963 to 1985 3-15

D' 1 U uai 1 Dra u i on Attenuators

riesuius I or uunmerciax variaDxe wduu

(10~dB increment), 1965 to 1985 3-17

oD' 1 1 uai 1 Drau i on Attenuators

nesuxGS I or L/QTimercia± variaoxe wtsuu (20-dB increment), 1965 to 1985 3-18

Q uai 1 Dra u i on Attenuators

nesuiLS I or (commercial variaoie wkl-u

(30-dB increment), 1965 to 1985 3-19

o 1

"2 L^dx 1 urdu 1 on Attenuators

riesuxus I or oorriuiGrcjicix \/<driciD-Le wduu

(40-dB increment), 1965 to 1985 3-20

oJ' L<i J. 1 Ul d on Attenuators (50-dB increment), 1965 to 1985 3-21

QJ' 1 R UdX 1 UI d L. i on Attenuators (60-dB increment), 1965 to 1985 3-22

O

1 D L<i±l UI dU iOri

Attenuators

R^OllT nGoUXUo "P (^K> /'-Nrnm /~\ v> Tol A/^OV^T ol^T^ TaTR^^O i UI UCJliUricI (Jld.X UdX id.L)Xc WDOU

(70-dB increment), 1965 to 1985 3-23

3. 1

7

Calibration

AbLenuauors

Results for Commercial Variable WBCO

(,ou-at5 mcremenu ; , lyoD to lyo^....

1 0 Calibration

Attenuators

nesuiLs I or i/Onmerciai variaDie wdl-u

(90-dB increment), 1965 to 1985 3-25

3. 19 Calibration

Attenuators

Results for Ccmmercial Variable WBCO

(100-dB increment), 1967 to 1985... 3-26

3. 20.1 Calibration Results for Commercial Phase Shifter A 3-28

3. 20.2 ,j, Calibration Results for Commercial Phase Shifter A 3-29

3. 20.3 Calibration Results for Commercial Phase Shifter A 3-30

3. 21 .1 Calibration Results for Commercial Phase Shifter B 3-31

XII
FIGURES (cont.)

Figure No. Description Page

3.21.2 Calibration Results for Commercial Phase Shifter B 3-32

3.21.3 Calibration Results for Commercial Phase Shifter B 3-33

3.21.4 Calibration Results for Commercial Phase Shifter B 3-34

3.21.5 Calibration Results for Commercial Phase Shifter B 3-35

3.22 Comparison of Calibration Results for NBS Design

WBCO Variable Attenuators (NBS 30 MHz System vs. NBS SQUID System) 3-37

3.23 Comparison of Calibration Results for NBS Design

WBCO 10-dB Step Attenuators (NBS 30 MHz System vs. NBS Six-Port ANA) 3-39

3.24 Comparison of Calibration Results for NBS Design

WBCO Variable Attenuators (NBS 30 MHz System vs. NBS Six-Port ANA) 3-40

3.25.1 Calibration Results from International Laboratories

for Commercial Fixed Coaxial Attenuator (3 dB) . . 3-42

3.25.2 Calibration Results from International Laboratories

for Commercial Fixed Coaxial Attenuator (6 dB) . . 3-43

3.25.3 Calibration Results from International Laboratories

for Commercial Fixed Coaxial Attenuator (10 dB).. 3-44

3.25.4 Calibration Results from International Laboratories

for Canmercial Fixed Coaxial Attenuator (20 dB) . . 3-45

3.25.5 Calibration Results from International Laboratories

for Commercial Fixed Coaxial Attenuator (40 dB) . . 3-46

XIII

TABLES

Table No. Title Page

1.1 Capabilities and Accuracies of 30 MHz Attenuation

Calibrations 1-2

1 .2 Capabilities and Accuracies of 30 MHz Phase

Calibrations 1-3

2.1 Uncertainties in NBS 30 MHz Standard Piston

Attenuator 2-11

2.2 Uncertainties in NBS 30 MHz Precision Phase

Shifter 2-18

2.3 30 MHz Attenuation Calibration Uncertainties 2-24

2.4 30 MHz Phase Shift Calibration Uncertainties 2-26

2.5 Tabulated Calibration Data on NBS Model VII

30 MHz WBCO Piston Attenuator 2-34

2.6 Tabulated Calibration Data on a Commercial

30 MHz Phase Shifter 2-4?

3.1 Mean Values of Fixed Attenuation Standards

Measured by Five International Laboratories

Including NBS 3-4?

6.1 Summary of 30 MHz Attenuation and Phase Shift

Calibration Uncertainties 6-1

XV

A CALIBRATION SERVICE

FOR

30 MHz ATTENUATION & PHASE SHIFT

A calibration service currently being offered by NBS for attenuation and

phase shift at 30 MHz is described. The service offers measurements on coaxial attenuators that are either fixed (standard attenuation) or variable

for incremental (step) attenuation. Waveguide-below-cutoff variable attenuators with coaxial connectors are also calibrated for incremental attenuation.

Ranges of capabilities and estimated limits of systematic and random uncer- tainty are presented.

Calibration of phase shifters which provide fixed (insertion) phase shift

and those with variable phase shift (phase shift difference) is described.

Ranges of phase shift and estimated limits of uncertainty are given in degrees.

However, a analler portion of this document is devoted to this calibration

service since it is requested only infrequently.

Definitions, capabilities of the system and techniques of calibration are given. The standards, measurement uncertainties, results from intercomparisons, quality assurance and statistical control of the system are discussed

and analyzed. Representative reports of calibration are also included.

Key words: attenuation ; calibration ; coaxial; incremental; phase shift ; standard; step; uncertainty ; waveguide-below-cutoff

.

XVII

1 .0 Introduction

The accurate measurement of the attenuation and phase shift of energy

in coaxial and waveguide transmission lines is a fundamental requirement in

the design, development and operation of most electronic systems. Attenuators

which decrease rf energy in a precisely known way and devices to change rf

phase accurately must be calibrated by comparison with reference standards

maintained by or traceable to the National Bureau of Standards (NBS). For

both technical and historical reasons, many rf, microwave and millimeter wave

measurements over the entire frequency spectrum are ultimately referenced to

30 MHz calibrations.

The NBS 30 MHz attenuation and phase shift calibration service has

been operating for many years. However, the current service is the result of

continuing improvements both in techniques and quality control. System capabilities and accuracies are presented and definitions of these parameters and

techniques of measurement are described. The NBS 30 MHz dual-channel rf null

system for attenuation and phase measurement is documented , including theory

of operation and discussion of uncertainties of the standard piston attenuator

and the precision phase shifter. Procedures for calibrating an NBS Model VII

piston attenuator and a commercial variable phase shifter are presented, as

typical examples, with tabulated data and calibration results. Sample reports

of calibration for each are included. NBS system measurement uncertainties,

quality assurance procedures and multi-year measurement trends are presented.

Intercomparisons of attenuation calibration data with other systems such as

the NBS SQUID and six- port systems, and with those of international laboratories, are discussed and summarized. Conclusions are given that indicate these

1-1
results are proof of the validity of the published accuracies of the

calibration service at NBS and that the system is in statistical control.

This report is a condensation of several of the many available published documents on rf attenuation and phase shift calibration. It deals almost

entirely with the calibration systems which are presently being operated by

the Microwave Metrology Group of the Electromagnetic Fields Division at the

Boulder Laboratories of the National Bureau of Standards. The laboratory approach is stressed herein and the reader desiring the formal theoretical approach is urged to consult the listed references as well as the other available material on this subject matter.

1 . 1 Present Capabilities at NBS

A complete listing of the measurements available from the Microwave

Metrology Group (including 30 MHz Attenuation and Phase Shift Calibrations) is

listed in a publication entitled, "NBS Calibration Services Users Guide 1986-

88" [1], This publication describes capabilities, accuracy and acceptable

standards plus relevant fee schedules in an appendix which is published every

six months [2]. Tables 1.1 and 1.2 present the general capabilities and accuracies of the 30 MHz attenuation calibration service in decibels (dB) and

phase calibration service in degrees (deg).

TABLE 1 .

1

Capabilities and Accuracies of 30 MHz Attenuation Calibrations

1 . Coaxial Fixed Attenuators (Standard Attenuation)

, Estimated ' Frequency ' Attenuation Range Limits of Uncertainty

MHz dB ± dB

30 0 to 100 0.02 to 0.0005 A^

1-2
2. Coaxial Variable (or Step) Attenuators (Incremental Attenuation)

Estimated

Frequency Attenuation Range Limits of Uncertainty

MHz dB ± dfi' 30 0 to 100 0.01 to 0.0005 A*

3. Waveguide Below-Cutoff Attenuators with Coaxial Connectors

(Incremental Attenuation)"

Attenuation Range Estimated

Frequency including initial Limits of Uncertainty

MHz insertion loss ± dB

dB

30 0 to 140 0.003 + 0.0003 A*

*A = the measured value of attenuation

TABLE 1 .

Capabilities and Accuracies of 30 MHz Phase Calibrations

Fixed Phase Shifters with Coaxial Connectors (Insertion Phase Shift)

and

Variable Phase Shifters with Coaxial Connectors (Phase Shift

Difference)

Estimated

Frequency Range of Phase Shift Limits of Uncertainty

MHz deg ± deg

30 0 to 360° 0.1 to 0.5

* A = measured value of attenuation

1 .2 System Overview

1.2.1 System Uncertainty

The limits of uncertainty stated in Tables 1.1 and 1.2 are the sums of

estimated systematic, random, and mismatch uncertainties. Their relative val1-3
ues are dependent upon the particular standard under calibration. Fixed and

variable coaxial attenuators, and fixed and variable phase shifters are

normally measured in a system having a characteristic impedance of 50 ohms.

Because measurement limits of uncertainty are degraded by any deviation from

this characteristic impedance, the types of allowable connectors are limited.

Connectors with a known plane of reference, such as the sexless precision

connectors or Type N and similar connectors which meet military standard

MIL-C-39012, are acceptable. Limits of uncertainty also depend upon the VSWR

of the individual instrument, quality of the connector, and the magnitude of

the attenuation and phase [3].

1.2.2 Device Under Test Requirements . All measurements on fixed coaxial

attenuators are made by the substitution method, which requires asexual connectors, or an attenuator with a male connector at one port and a female connector at the other. If an adapter is required to comply with the foregoing, it

must be supplied with the attenuator. The combination is calibrated as one

unit.

Since the only change in insertion loss is measured on coaxial variable attenuators, both ports may have identical connectors. The zero setting

of the variable attenuator, or some other setting if specified, is used as the

reference during calibration. Variable attenuators and incremental (step)

attenuators must have a repeatability of 0.01 dB or better.

1-4
1.3 Definitions

1.3.1 Insertion Loss . The 1959 IRE standard [4] gives two definitions of

insertion loss, one in which system mismatch is not specified, the other in

which the system is nonreflecting. The definitions contradict each other

since the insertion loss of an attenuator will be different for each case.

The measurement procedure for both definitions is to open the system, insert

the attenuator, and note the relative power absorbed by the load (or detecting

device) before and after insertion. The insertion loss in dB is computed from

these two values. If the attenuator is variable and remains in the system,

the initial and final powers absorbed by the load for two settings are used.

This determination is more properly called "Change in Insertion Loss."

Either definition is entirely adequate for a single, unique system,

but if the loss (or gain) measurement is to be transferred from one laboratory

to another, more must be specified about system conditions.

1.3.2 Attenuation . This is defined as the insertion loss in a nonreflecting

system (Fq = Tl = 0).^ These impedance matching conditions cannot be achieved

exactly because of imperfections in connectors or adapters and the inability

to ascertain when a system is precisely matched. Since attenuation cannot be

measured exactly, the more practical term "standard attenuation" has come into

more general use.

Tq and Tl are defined as the reflection coefficients of the generator and

load respectively.

1-5
1.3.3 Standard Attenuation . This is defined as the insertion loss of a linear two-port device in an essentially nonreflecting system which is initially

connected together at the insertion point by a standard connector^ pair or

waveguide joint. The nonreflecting condition is obtained in the standard coaxial or waveguide sections to which the standard connectors or waveguide joints

are attached. The standard attenuation is the ratio expressed in dB of the

power absorbed by the load before and after insertion of the two-port device

being calibrated.

1.3-^ Incremental Attenuation . Incremental attenuation is the change in

attenuation of a variable attenuator between a reference setting (usually

zero) and any other setting. The same restraints on system conditions apply

here as those for attenuation and standard attenuation. The term "differential attenuation" is sometimes applied to this case and usually refers to two

non-zero settings.

1.3.5 Characteristic Insertion Loss . This quantity, as defined in IEEE Standard 474^^1973, Specifications and Test Methods for Fixed and Variable Attenuators, Dc to 40 GHz [5], most closely describes the attenuation calibrations as

performed by NBS. An excerpt from this standard is included as Appendix A of

this document. The reader is encouraged to review the complete standard as

needed.

2a "standard connector" is one which is made precisely to standard specifications for the particular type of connector under consideration.

Standard connector pairs usually have low but measurable loss and re- flections [3,6,7].

1-6
1.3.6 Insertion Phase Shift is the phase change of a wave incident upon the

load before and after insertion of a two- port device between the generator and

load of a stable nonrefl acting system.

1.3.7 Phase Shift Difference is the phase change of a wave incident upon the

load, from an initial to a final condition, resulting from inserting a twoport device between the generator and load of a stable nonre fleeting system.

Note: The following conditions apply: (1) The frequency, the load

impedance, and the generator characteristics (internal impedance and available

power) have the same values before and after the device is inserted or

changed; (2) the joining devices (connectors or adapters) belonging to the

system conform to standard specifications (the same specifications must be

used by different laboratories, if measurements are to agree precisely); and

(3) nonreflecting conditions must be obtained in the uniform, standard

sections of transmission line on the system sides of the connectors at the

place of insertion.

1.3.8 Decibel . The decibel is one tenth of a bel3 and is defined fundamentally in terms of a power ratio:

P dB = number of decibels = 10 log -5^ , (1)

'2

where Pj is the incident power from an impedance matched source and P2 is the

net power into an impedance matched load after a device is inserted between

the source and load. If the powers Pi and P2 are associated with equal

^Warned in honor of Alexander Graham Bell

.

1-7
impedances, this power ratio can be expressed as the square of either the

voltage or current ratio.

Hence: Number of decibels = 20 log = 20 log (2)

1.3.9 dBm. This term indicates a power level with respect to one milliwatt,

P

Thus, power level in dBm = 10 log q-001 (3)

where P = power level in watts.

Similarly, power level in dBm = 10 log

q

where E is in volts

and R is in ohms.

1.3.10 Neper. A unit used to express the scalar ratio of two currents or two

voltages, where the number of nepers is the natural logarithm of the ratio.

Hence, nepers of attenuation = N = In = In ^1 . (5)

If the power ratio is the square of the above voltage or current ratio, then

(5) can be expressed as:

1 P

N = 3 In -p^ nepers (6)

1.3.11 Conversion from Nepers to Decibels .

One neper = 8.686 decibels.

1-8
1.3.12 Propagation Constant . The propagation constant, T, is defined as

where the ac series impedance of a transmission line is Z = R + jwL

in ohms per unit length

and the ac shunt admittance of a transmission line is Y = G + jcoC

in ohms per unit length.

From (7) it is seen that the propagation constant T will, in general,

have a real part and an imaginary part.

Hence, Y = a + j3 (8)

where, a = attenuation constant in nepers per unit length

and, 3 = phase constant in radians per unit length.

The voltage, E, propagates along the line a distance, I, as

T = /7z = /(R + ju3L)(G + jwC) (7)

E = A,e

jwt-TJl volts (9)

1-9
1 ; I':
2. 0 Dual Channel Rf Null System for Attenuation and Phase Calibration

Attenuation measurements are frequently performed below 1 GHz using

intermediate frequency (IF) or audio frequency (AF) substitution techniques.

These techniques have a number of sources of uncertainty since it is necessary

to convert from one frequency to another [8]. For this reason they are not

preferred and will not be presented in this document. The direct substitution

technique, whereby the standard attenuator and the attenuator under calibration operate at the same frequency, is a simpler approach with fewer sources

of uncertainty.

A basic block diagram of the unmodulated two-channel system employed

by NBS at 30 MHz is presented in figure 2.1 [9]. A two-channel nulled system

has fewer problems of level instability in the source and gain instability of

the monitor, and has high sensitivity. However, phase and magnitude adjustments must both be made and the system is more complex than a single channel

system. A range of attenuation measurement in excess of 100 dB can be attained with this system by placing the device under test (DUT) in the insertion point shown in figure 2.1. The resolution is very high for large signal

amplitudes. Better resolution can be maintained at small signal amplitudes by

using quadrature detection rather than a simple nulling approach. Thus to

obtain a successful system, a precision phase shifter of constant amplitude or

one with precisely known losses is required to achieve the null or quadrature

phasing of the two channels.

A complete block diagram of the present 30 MHz NBS attenuation and

phase calibration system is presented in figure 2.2.

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2.1 Description of 30 MHz Calibration System

2.1.1 30 MHz Standard Piston Attenuator

This standard is a circular waveguide-below-cutoff (WBCO) attenuator

which is a standard with a continuously variable attenuation, commonly called

a piston attenuator. The complete mechanical assembly is shown in figures 2.3

and 2.4. Figure 2.5 shows the drive and readout in more detail including an

earlier version of the signal launching assembly.

2. 1 .1 .1 Theory

The incremental attenuation of this type of standard can be accurately

predicted from only a knowledge of its dimensions. Thus a major advantage of

this standard is the determination of the attenuation (except for secondary

effects) by the fundamental units of length and time (frequency). When the

waveguide section is uniform and excited in only one mode by a sinusoidal signal below the cutoff frequency, the field will decay exponentially along the

guide. More specifically, electromagnetic fields existing in a uniform perfectly conducting waveguide can be expressed as a linear combination of terms

called modes. The electromagnetic field components for each mode are proportional to the term e~^^ j'^^, where T, the propagation constant, (see equation

10) is determined completely by the waveguide dimensions and frequency [10].

Thus, below the cutoff frequency, Y becomes an entirely real component and the

fields decay exponentially at a rate dependent on the mode of propagation.

The mode with the smallest decay rate is used to ensure mode purity at the

high attenuation levels.

2-4
Figure 2.3. View of upper portion of 30 MHz standard

attenuator assembly sliowing the level set attenuator,

the WBCO standard and the signal launching assembly.

2-5
Figure 2.4. View of upper portion of the 30 MHz standard

attenuator assembly showing the optical

readout for the linear displacement scale.

2-6
Level Set

Attenuator

Drive

Motor

for

Level

Set

Attenuator

Early Version

of TE11

Signal Launching

Assembly

TE11 WBCO

Standard

Attenuator

Optical

Readout

Drive Motor

for Standard

WBCO Piston

Attenuator

7 ^. Ji'

Figure 2.5. 30 MHz standard attenuator assembly.

2-7
The primary disadvantage of this WBCO standard attenuator occurs because it is a nondissipative device and therefore varying amounts of energy

are reflected rather than absorbed as the attenuation is varied. This results

in the need for a high minimum insertion loss (approximately 30 dB) to reach

the hi^ly linear attenuation range of operation. Also the terminal networks

must contain reactances which are frequency- dependent

.

2. 1 . 1 .2 Description

This WBCO attenuator has a launching coil and a moving probe or pickup coil to sample the decaying field and an indicating readout to correlate

the probe position with the attenuation level change. The coupling coils in

the attenuator must be sufficiently separated at all times to prevent mutual

coupling and loading effects from excessively affecting the excited mode.

This is the reason for the high initial insertion loss of WBCO attenuators. A

circular waveguide is chosen for ease of precise fabrication and because excitation symmetry is not critical. The desired excited field in this WBCO attenuator consists of the transverse electric (TE)ii mode which unfortunately is

not far in frequency from some higher modes. The transverse magnetic (TM)oi

mode has the greatest probability of causing difficulty since its attenuation

rate is closest to the rate of the TEn mode. Mode filters with metallic

strips are constructed to suppress the TM modes by over 60 dB v^ile reducing

the TEn mode by less than 0.5 dB.

A close approximation for the propagation constant, T, (in nepers per

meter) in the TEu mode is given by [10]:

2-8
1 ^ j / 1 -

1 -

2 - (^)l^

(10)

Where Sn = 1.8411838 = first root of the first derivative of the first-order

Bessel function of the first kind,

r = radius of the waveguide cylinder,

f = frequency of operation in hertz,

e = relative dielectric constant of the medium inside the waveguide,

V = 2.997925 x 10° m/s = velocity of light,

U

= permeability of guide wall (relative, usually taken to be

1.00000),

0 = 1.35 X lO'^ mhos/meter = conductivity of the brass waveguide wall.

Equation (10) illustrates that the most important quantities other than the

radius are the frequency and conductivity. Brown [11] shows that the quantity

in square brackets contributes a very small and usually negligible phase shift

at IF frequencies in waveguides constructed of good conducting materials. The

actual phase shift for the NBS attenuator is less than one degree (deg) in 100

dB of attenuation.

The displacement of the receiving coil relative to the launching coil

is measured with a steel ruled scale and optical projector. The scale is accurate to 2.54 ym (0.0001 inch) within any 15.24 cm (six inches) length. The

thermal coefficients of expansion of the stainless steel scale and the brass

waveguide are nearly the same. For a 2.222°C (4°F) temperature change, the

difference in the temperature coefficients would contribute a calculated error

of only 0.0001 dB per 10 dB attenuation change.

2-9
The brass waveguide has an outer diameter of 9.906 cm (3.9 inches) and

a length of 56.64 cm (22.3 inches). The internal diameter of the waveguide

(approximately 8.128 cm (3.2 inches)) is chosen to give an attenuation rate of

10 dB/2.54 cm (1 inch) of travel. For a perfectly conducting waveguide of

circular cross section of radius, r, in cm, and having TEn mode cutoff

frequency, f^, the attenuation rate, a, when operating at frequency, f , below

cutoff is:

' « = ^"V^ /" -(f-)' clB/cm (11)

where f^ = GHz [3]. (12)

The inside wall of the waveguide is coated with 0.127 ym to 0.254 ym (5 to 10

microinches) of rhodium. This presents a hard surface to the sliding silver

contacts of the piston and prevents corrosion of the brass guide without significantly affecting the conductivity of the waveguide surface.

Dimensional tolerances on the guide and the resolution and accuracy

with which the displacement between the exciting and receiving coils can be

measured are very important. The guide diameter must remain constant and be

perfectly circular. Any ellipticity in the guide will cause the propagation

constant to differ from the circular case, thereby possibly exciting degenerate modes of propagation. Angular variations along the major axis will produce undesirable variations in the exponential decay of the field within the

waveguide.

2.1.1.3 Uncertainties

Table 2.1 presents the uncertainties of the 30 MHz WBCO piston

attenuator as measured and calculated by Allred and Cook [10].

2-10
TABLE 2.1

Uncertainties in the NBS 30 MHz Standard Piston Attenuator

Systematic Uncertainties

Coaxial waveguide diameter

Linear displacement of receiving coil

Velocity of electromagnetic waves in

medium inside guide

Rf conductivity of guide

Rf permeability of guide

Total Systematic Uncertainty

Random Uncertainty

0.0003 dB/10 dB

0.001 dB/10 dB

Negligible for air

0.00026 dB/10 dB

Negligible for brass

0.00156 dB/10 dB

Negligible in controlled

environment

Total Uncertainty 0.00156 dB/10 dB

2.1.2 30 MHz TEii Launching Assembly

The input system on the piston attenuator is a major determining factor in the measurement range of the total system.

A system is needed which launches the single TE^ mode with an

intensity independent of the position of the receiving coil, and/or a system

which launches the desired mode so efficiently that the receiving coil never

has to be positioned near the input coil.

The following describes the approach used at NBS. A current sheet

with spatial TE i

i mode electric field distribution (two-dimensional polar coordinates) in the transverse plane of the waveguide is established as nearly

ideal as possible. This mode is launched in both directions from the current

sheet. If such a constant current sheet is obtainable and is independent of

2-11
the fields reflected from the pickup coil, the undesirable effect of interaction between coils will not create errors.

These conditions are approached by constructing the launching assembly

as illustrated in figures 2.6 and 2.7. The constant current sheet is

initially obtained by sampling the launching current and keeping it constant

by using negative feedback to the rf source. In the present system the

feedback loop is not actuated because the pickup and receiving coils are not

allowed to approach each other closely enough to interact and a more stable

solid state rf source has replaced the original source. This reduces the

overall dynamic range of the system by approximately 10 dB, however, for

normal calibrations. The resulting range of 140 dB is still adequate. In the

event of special needs for higher ranges, the feedback system can be

reactivated.

The attenuator waveguide was extended behind the launching coil in

order to terminate the field propagated from the back side of the launching

coil. Since the pickup coil absorbs some energy, it produces a reflected

field which passes through the launching coil with very little interaction and

is terminated by the same waveguide extension.

The launching assembly is constructed of small stainless steel tubing

through which water is passed to prevent excessive heating of the waveguide

which would otherwise change its dimensions. Mode filters are used to eliminate the axial electric fields (higher modes) caused by the reactive impedance

of the launching unit.

The resistive component of the launching coil is estimated to be between 0.01 and 0.1 ohm which is difficult to match to the 50-ohm rf source.

An impedance match is obtained by using a capacitive type impedance matching

2-12
Water Cooled TE^

Propagation Mode

Launching Coil

Figure 2.6. 30 MHz JE^^ launching assembly.

2-13
High Power

30 MHz Signal

Input Connector

Figure 2.7. 30 MHz launching assembly with matching and sampling networks.

2-14
network with a maximum rating of 200 watts. A 10-watt input to the matching

network produces an rf launching coil current of approximately 1.1 amperes.

The sub-assembly is shown mounted in figure 2.7.

2.1.3 30 MHz Precision Phase Shifter

2.1.3.1 Description

The constant amplitude precision phase shifter used at NBS consists of

a sliding airline trombone configuration as shown in figure 2.8. Non-constant

impedance construction is used since this system operates only at one single

frequency. The attenuation level variations are held to a minimum by terminating the precision fixed line sections in their characteristic impedance. This

can be accomplished only at a single frequency since the sliding section has a

lower characteristic impedance than the fixed sections of line. The fixed

line sections are terminated properly by placing a pi matching network on each

side of a 10-dB attenuator and installing this complete configuration in the

center of the moving section of line. This then provides the desired characteristic impedance at the sliding junction to properly terminate the precision

fixed sections of line. Additional attenuators and matching networks terminate other two ends of the precision phase shifter.

The outer conductors of the precision section of the phase shifter are

precision machined brass cylinders with 1.27. cm (0.5-inch) thick walls. The

inside walls are heavily plated with burnished silver, with a thin coating of

rhodium. The center conductors are brass rods with silver plate and rhodium

coating similar to that used on the outer conductors. The maximum deviation

of the critical diameters from the mean value is 8.89 um (0.00035 inch) which

2-15
could produce a calculated maximum characteristic impedance variation of

slightly less than 0.04 percent.

The four terminating impedance matching networks are adjusted until a

maximum change in phase range produces less than 0.01 ohm total impedance

change, measured on a sensitive rf impedance bridge.

Over the total range of the phase shifter (38 deg or 101.6 cm (40

inches) of travel), the change in level is less than 0.0005 dB. This range is

adequate when calibrating attenuators since piston attenuators normally have

negligible amounts of phase shift. The phase shift in dissipative attenuators

approximates their physical length, which is a small fraction of the phase

shifter travel.

As stated above, the trombone phase shifter has a range of travel in

excess of 101.6 cm (40 inches) which yields a phase shift of slightly over 38

degrees. The readouts of the devices under test are given in deg, and

therefore the results are computed and stated in deg, rather than in the SI

units of radians. A mechanical counter is connected to the phase shifter to

indicate precisely the travel of the shifter. One count on the counter

corresponds to a phase shift of 0.01142 deg.

2. 1 .3.2 Uncertainties

Table 2.2 presents the sources and magnitudes of the uncertainties in

the 30 MHz precision phase shifter [10].

2-16
Matching Network

Assembly

30 MHz

Signal

Output

Connector

Coaxial to Circular

Waveguide Transmission

Line Transition

Sections

Movable

Section of

WBCO Phase

Shifter

Stationary

Section of

WBCO Phase

Shifter

30 MHz Signal

nput Connector

Mounting Base

Figure 2.8. 30 MHz precision phase shifter.

2-17
TABLE 2.2

Uncertainties in the NBS 30 MHz Precision Phase Shifter (for a 36 degree

measurement)

Systematic Uncertainty

Mismatch uncertainty in the sliding sections 0.012 deg

Measurement of linear displacement and

Uniformity of diameter 0.048 deg

Losses in trombone for 30 degree increment 0.018 deg

Resolution of readout 0.06 deg

Random Uncertainty Negligible

Total Uncertainty 0.138 deg/36 deg

2.1.4 30 MHz Coarse Phase Shifter

This manually operated phase shifter consists of two commercial phase

shifters connected in series. These phase shifters have been modified by adding high resolution manual-drive mechanisms with which to adjust them. Refer

to the block diagram in figure 2.2 for its location in the circuit. These

phase shifters have a characteristic impedance of 50 ohms and an insertion

loss of approximately one dB each. Each of these phase shifters provides a

shift of 0 to 180 deg and is driven by gears. The gear ratios are chosen so

that one of the phase shifters acts as a coarse adjustment while the other

functions as a medium adjustment. This arrangement provides a fast and

convenient means of initially adjusting the phase leg to null the dual channel

system. The large 30 MHz trombone precision phase shifter provides the system

with the final complete rf null.

2-18
The coarse phase shift unit is necessary to calibrate a phase shifter

over a range greater than 30 deg since the precision phase shifter has a range

of only approximately 40 deg. The coarse phase shifter unit is then used to

change the phase shift reference (from 0 to 360 deg) so that the precision

phase shift standard can be used (bootstrapped) over a 360 deg range in steps

of 30 deg.

2.1.5 Level Set Attenuator

The rf power level adjusting attenuator is shown in figure 2.9 with

its associated fast and slow speed drive motors. It is a TM mode WBCO piston

attenuator. It consists of a variable capacitor formed by mating hemispherical electrodes inside a cylindrical waveguide. One of the electrodes is motordriven so that the spacing between them can be varied, thus changing the value

of attenuation within the waveguide. This particular design is chosen for

this attenuator because it produces no significant phase shift. (This mode

has no significant skin depth correction, and hence very small phase shifts

are associated with its level changes.) It has an attenuation constant of

20.9 dB/radius. The radius of the inside of the waveguide is approximately

1.27 cm (one-half inch) which gives an attenuation rate of sli^tly more than

15.74 dB/cm (40 dB/inch) of travel. Hence, this level set attenuator does not

introduce undesirable phase changes in the system and does not have to travel

very far to yield a significant change in attenuation. It is located in the

phase leg of the dual channel system as shown in figure 2.2. The amount of rf

signal propagation in this leg of the system is predetermined by the setting

of the TM mode level set attenuator. Optimum sensitivity of the entire system

may be maintained by pre- positioning this attenuator regardless of which

attenuator is under calibration (within the capabilities of the system).

2-19
Refer back to figures 2.3, 2.4 and 2.5 to observe the installed position of the level set attenuator with respect to the standard 30 MHz piston

attenuator.

2.1.6 Rf Null Detection System

The rf null detector is a double-conversion frequency-locked receiver.

The 30 MHz null detection system consists of an rf null detector Model NBS/SND

which is a synchronous detector designed, developed, and constructed at NBS

with a 30 MHz frequency plug-in unit (Model SND/PI-30A), [12]. This instrument is designed for extremely hi^ sensitivity consistent with simplicity of

operation. The detector is frequency-locked to the signal to be examined and

thus requires a synchronous reference voltage to achieve its high sensitivity.

A single gain control adjusts the sensitivity. The null signal is indicated

by two front panel center- indicating meters. A continuously-variable phase

control enables in-phase and quadrature components of the null signal to be

displayed individually on separate meters. The 30 MHz detector has a gain of

approximately 150 dB, a bandwidth of ±20 kHz, a 2-'dB noise figure, and a 360-

deg continuously-variable phase control. The input impedances of the two signal input ports and the reference signal input port are nominally 50 ohms.

The receiver has a dynamic sensitivity range of 90 dB without saturation which

allows the operator to locate the system null easily. The gain control on the

receiver also assists the operator to find the null rapidly and efficiently.

This null detector system is constructed of separately-shielded

modules which minimize the adverse effects of signal leakage and interference.

The maximum sensitivity of this 30 MHz detection system is approximately 1 nanovolt. The calibration range of the complete system is

2-20
Figure 2.9. 30 MHz level set (TM) attenuator with drive motors.

2-21
approximately 150 dB including the initial insertion loss of the attenuator

under calibration (20 to 30 dB in the case of a variable WBCO attenuator).

The resolution of the system (primarily due to the readout) is 0.001

dB when measuring a 100-dB change in attenuation on a piston attenuator (with

an initial insertion loss of 30 dB). Thus, the detection system has an attenuation resolution of better than 0.001 dB at 130 dB below the maximum (practical) 50 milliwatt (mW) output from the standard attenuator.

Similarly, the system has a phase shift resolution of better than 0.01

degree at similar rf signal levels.

2.1.7 RF Source and Associated Circuitry

The 30 MHz fixed frequency rf source which provides the signal for

this dual-channel attenuation and phase calibration system is represented in

figure 2.2. It consists of a 30 MHz ultra-stable, crystal-^controlled

,

continuous wave (CW) source and 50-watt linear amplifier which delivers

approximately 10 watts (W) of rf power to the attenuator launching system.

The frequency of this source is stable within 1 part in 10^.

The output power level of the rf source and power amplifier combination is sufficiently stable so that no external level circuitry is required.

This signal source arrangement is adequate to produce the nearly constant

current sheet in the TE ^ ^ launching assembly as mentioned in section 2.1.2 of

this document.

The key to adequate stability is the sampling of the reference channel

(phase shifter leg) at the launching coil of the standard attenuator. Minor

level variations are equally reflected in each channel and thus contribute

2-22
negligible error as long as adequate separation of the launching and receiving

coils is maintained.

2.1.8 The Insertion Point

The insertion point in a system is the point at which the system is

opened in order to insert the instrument being calibrated. The insertion

point is a very important portion of the attenuation and phase calibration

system. It must permit physical motion, be well shielded and must not

adversely effect the rest of the system in any way. These requirements are

met at the NBS Boulder Laboratories by using a combination of semirigid,

coaxial cable and double- shielded , flexible, coaxial cable. The semirigid

cables are brought to the front panel of the calibration console where they

are connected to precision l4-mm connectors. At this point, short lengths of

double- Shi elded, coaxial, flexible cables are connected. This doubleshielded cable has only one electrical shield since both layers of shielding

braid are lying against each other. A third separate shield is stretched over

the outside of these flexible, coaxial cables and clamped securely to the

connector at each end of each cable. This then produces flexible, coaxial

cables for the insertion point which are truly double- shielded cables that

reduce rf signal leakage to insignificant levels.

2. 2 Uncertainty Analysis

2.2.1 30 MHz Attenuation Calibration Uncertainties

Table 2.3 presents the sources and magnitudes of the uncertainties in

the 30 MHz attenuation calibration system [10, 12].

2-23
TABLE 2.3

30 MHz Attenuation Calibration Uncertainties

Systematic Uncertainties

Reference Standard Piston Attenuator (from Table 2.1) 0.0016 dB/10 dB

Resolution of Detecting System 0.0004 dB/10 dB

Maximum Rf Leakage (measured by field strength

meter) and reference channel variation due to

standard phase shifter. 0.001 dB/10 dB

Total Systematic Uncertainty 0.003 dB/10 dB

, - , ^ ,, + mismatch uncertainty

Random Uncertainty (3Sjj value) 0.001 dB/10 dB

Total Uncertainty ; 0.004 dB/10 dB

Typical Maximum Mismatch Uncertainty 0.001 dB/10 dB

Typical Total Uncertainty (including mismatch) 0.005 dB/10 dB

The total uncertainty quoted to a customer depends upon the resettability and repeatability of the standard being measured.

The uncertainty due to impedance mismatches when calibrating attenuators on this system has been calculated using the VSWR's of the system and the

attenuator being calibrated. The VSWR of this system is approximately 1.01.

Therefore calculations are based on the assumption of a maximum VSWR of 1.02.

Variable attenuators which are calibrated on this system have a similar VSWR;

thus a mismatch error of 0.001 dB is typical. The above generalized mismatch

uncertainty figure is verified with a substantial sampling of the VSWR's of

2-24
variable attenuators under calibration. Note that the added mismatch uncertainty only affects attenuation increments referenced to a zero setting on the

variable attenuator. An increment referenced to a higher starting point such

as 20 dB is not affected significantly by mismatch since a reflected signal

is 40 dB below the incident signal level.

During the calibration of fixed resistive attenuators at 30 MHz, the

actual VSWR is measured at both terminals of the properly terminated attenuator so any uncertainty in the attenuation measurement due to impedance mismatch can be calculated and taken into account.

The uncertainties due to rf leakage are difficult to measure precisely.

The entire calibration system is extremely well shielded in order to prevent

problems caused by rf leakage. The rf power source is housed in a solidcopper, shielded room; all interconnecting cables are made of semirigid coax;

NBS Type W flanged connectors are used at every interface except the insertion

point; all the coaxial connections are painted with conducting paint to

prevent rf radiation; and the null detection system is housed in a double

screened enclosure. This greatly reduces the possibility of significant rf

leakage. Thus the portion of the total uncertainty of the system due to rf

leakage as presented in table 2.3 is a conservative figure, particularly for

measured attenuation values below 60 decibels.

The uncertainty of calibration is usually not stated in a calibration

report as 0.005 dB/10 dB as listed in table 2.3. A more specific statement is

needed to better define the uncertainty of the measurement at attenuation values which are not at even 10-dB intervals. For a precision variable attenuator which is calibrated at 30 MHz, a general uncertainty statement may read as

follows: "The estimated uncertainty of the measured values at the indicated

2-25
points is 0.003 decibel plus 0.03 percent of the indicated change in insertion

loss in decibels." However, as a service to the calibration customers, the

actual uncertainty associated with each attenuation increment is calculated

and tabulated in the calibration report. The report lists separate values for

systematic and random uncertainties plus a total uncertainty for each point

measured. (See sample calibration report following table 2.5.) The previous

general uncertainty statement, however, is useful in describing NBS capability

in response to inquiries and in technical publications.

2.2.2 30 MHz Phase Shift Calibration Uncertainties

Table 2.4 presents the sources and magnitudes of the uncertainties in

the 30 MHz phase calibration system [10].

TABLE 2.4

30 MHz Phase Shift Calibration Uncertainties

Systematic Uncertainty

Reference standard trombone phase shifter

(from table 2.2) 0.138 deg

per 36 deg

Mismatch uncertainty 0 to 0.2 deg

Frequency stability (for 360° phase shift) 0.00036 deg

Phase shift in standard attenuator 0.01 deg

Resolution of coarse phase shifter 0.02 to 0.13 deg

2-26
Total Systematic Uncertainty 0.168 to 0.478 de|

per 36 deg

Random Uncertainty (typical 3% values) 0.01 deg

Total Uncertainty (nominal values) = 0.2 to 0.5 deg

per 36 deg

2. 3 Procedure for Calibrating an ^JBS Model VII 30 MHz Attenuator

Figure 2.10 shows an operator calibrating an NBS Model VII WBCO piston attenuator at 30 MHz. This calibration is performed in the following manner.

2.3.1 Calibration Procedure for NBS Model VII Attenuators

1. Connect a standards-quality, 50-ohm, 10-dB attenuator on the output end of the attenuator under calibration. This is necessary to

isolate the device under test (DUT) to insure proper a impedance

match when operating the Model VII at its low attenuation values.

(The 10-dB isolating attenuator can be removed when calibrating

the DUT at values above 20 dB)

.

2. Connect this combination into the insertion point with the input

of the Model VII connected to the output of the standard 30 MHz

attenuator impedance matching network as shown in figure 2.2.

3. Set the attenuation of the Model VII attenuator so that the

counter reads 00000 and dial reads 0. This must be done in a

manner which will remove the adverse effect of the backlash in the

drive mechanisms. The conventional procedure is always to

approach the desired setting of the attenuator from a lower value

2-27
2.10 Operator calibrating an NBS Model VII piston

attenuator at 30 MHz

2-28
of attenuation setting. This technique allows the very precise

setting of the desired attenuation value.

4. Adjust the receiver sensitivity to a low value by adjusting the

gain control.

5. Adjust the external phase and magnitude controls on the synchronous detector so that the meter needles are at mid- scale.

6. Follow the detailed instructions for operating the null detector

as stated in [11].

7. Adjust the coarse (manual) phase shifters until a null condition

exists (with the precision phase shifter approximately in the center of its range)

.

8. Adjust the standard piston attenuator until a deeper null is

reached. This can best be done by passing through the null point

several times in order to determine the position of the true null

point on the null indicator. The standard attenuator is operated

on fast speed until the approximate null is reached; then the

drive is switched to slow speed so the operator can stop the

movement of the standard exactly at the null point.

9. The precision phase shifter is adjusted until the phase is nulled.

This standard phase shifter also has both fast and slow speed

drive motors.

10. Renull both the standard attenuator and the standard phase shifter

to be certain the true system null has been found. (This may necessitate changing the null indicator sensitivity to keep the

needle on scale)

.

2-29
11. Check the system sensitivity by changing the Model VII attenuator

by 0.001 dB. The null indicator reading should change

significantly if the system sensitivity is sufficient. The

sensitivity can be changed by changing the power into the

(

• attenuator under calibration via the level set attenuator and by

readjusting the sensitivity controls of the null detector.

Set the attenuator under test back to the 0-dB position as explained in Step 3 above and again null the system.

12. Record the standard attenuator setting as read in the optical projector. This is tne 0-dB reference setting.

13. Remove the Model VII attenuator from the insertion point leaving

the 10 dB attenuator attached to the flexible cable.

14. Connect the insertion point together and renull the system as in

Steps 4 through 10 above.

15. Record this value from the scale on the standard attenuator's optical projector. This value is the initial insertion loss reference

setting.

16. Subtract the value obtained in Step 12 from the value obtained in

Step 15. This is the insertion loss of the NBS Model VII attenuator at the 0-dB setting (approximately 30 dB)

.

17. Repeat this procedure two or three more times and average the results. This average attenuation value is the insertion loss of

the attenuator being calibrated when it is set at 0 dB. If this

' insertion loss is not approximately 30 dB or if it has changed

appreciably from the previous calibration, the attenuator under

calibration should be suspected and checked for possible damage.

2-30
18. Repeat Steps 1 through 12 above to obtain a new O-dB reference

reading. This eliminates the possibility of erroneous readings

due to drift in the calibration system, and varying impedance effects.

19. Set the attenuator under test at exactly 1.000 dB, (the desired

calibration point).

20. Null the system as in Steps 4, 5, 6, 8, 9, and 10, and record the

attenuation value as seen in the optical readout on the standard

attenuator.

21. Repeat Step 19 and set the attenuator under test at 2.000 dB.

22. Repeat Step 20.

23. Continue this process until measurements are recorded for settings

up to 10.000 dB on the attenuator under test.

24. Return this attenuator to its 0.000 dB setting and obtain the O-dB

reference setting as in Steps 3 through 12. This value should be

within a few thousandths of a dB of the value obtained in the original Step 12.

25. The above procedure must be repeated to obtain readings at 15, 20,

25, 30, 35, 40, 45, 50, and 60 dB.

26. The 10-dB fixed resistive coaxial attenuator should be removed

from the output end of the NBS Model VII attenuator and the cable

connected directly to the Model VII output connector. This 10-dB

fixed attenuator may be removed since it is not needed for matching when the attenuator under calibration is operated at levels

such as 50 or 60 dB and above. The removal of this 10-dB fixed

2-31
attenuator increases the system sensitivity by 10 dB without changing the power input to the standard under test.

27. The attenuator under calibration should be set at 60.000 dB and

the system nulled as in Steps 4, 5, 6 8, 9, and 10.

28. Record this value of attenuation as read from the standard attenuator optical readout. This is then used as the reference reading

for the 70 and 80 dB calibration levels.

, 29. Calibrate the NBS Model VII attenuator at 70 and 80 dB in a manner

similar to the lower dB settings. If the system sensitivity is

, not sufficient the power into the attenuator under calibration can

be increased by changing the position of the level set attenuator

as necessary.

30. This entire calibration process is repeated at least two more

; < times so that the instrument is calibrated completely a minimum of

three separate times. These results are averaged and entered into

; a complete calibration report.

2.3.2 Attenuator Calibration Data Reduction

The attenuation calibration data are reduced in the following manner.

(Refer to table 2.5 for a typical data sheet).

1 . The attenuation value for each setting of the attenuator under

r. calibration as read from the standard attenuator is subtracted

fran its respective reference reading and recorded in table 2.5.

2-32
2. The average of the three columns of calibration results (change in

insertion loss) is calculated to the nearest 0.001 dB and

recorded

.

3. This column of averaged data (f) is then used along with the

three columns of data from Step 2 to compute the random

uncertainty (3 times the standard deviation (SD) of the mean

(Sx)) of the measurements. These computed values are recorded

in table 2.5 and entered in the calibration report.

4. The average insertion loss (with the attenuator under test set at

exactly 0 dB) is computed and rounded to the nearest 0.1 dB to be

entered in the calibration report. This 0-dB insertion loss is

measured by inserting and removing the Device Under Test (DUT)

,

with the same procedure as that used for calibration of fixed

attenuator. This approximate value is useful only for general

information and is not considered part of the precise calibration

results, and therefore does not include a reported uncertainty.

2.3.3 Tabulated Data and Calibration Results

Table 2.5 presents the tabulated calibration data on a typical NBS

Model VII 30 MHz WBCO piston attenuator.

2.3.4 Typical Report of Calibration for 30 MHz WBCO Variable Attenuators

Immediately following table 2.5 is a typical complete Report of Calibration issued on the 30 MHz attenuator whose calibration data appear in

table 2.5.

2-33
TABLE 2.5

TABULATED CALIBRATION DATA ON NBS

MODEL VII 30 MHz WBCO PISTON ATTENUATOR

tow I WU MKXT

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J r^^tmi^n/^/^f^i^nya^ test no.^^^,^^.

I

A9.99 9

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I ^^^o ^.^<g^

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2-34
Oat«

TABLE 2.5 (CONTINUED)

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2-35

70
Date

or MCASuncMorr

TABLE 2.5 (CONTINUED)

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Q <?(2^.

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2-36
U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NATIONAL ENGINEERING LABORATORY

Boulder, Colorado 80303

REPORT OF CALIBRATION

VARIABLE WAVEGUIDE BELOW-CUTOFF ATTENUATOR,

COAXIAL CONNECTORS

National Bureau of Standards

Model VII, Typical Example

Submitted by:

National Bureau of Standards

Division 723.01

Boulder, Colorado 80303

The measurements on this attenuator were performed under ambient conditions of

approximately 23° + 2° C and 40+5 percent relative humidity. The power

presented to the attenuator during the calibration was less than 300

milliwatts. The attenuator was terminated at each end in approximately 50 + jO ohms. The calibration frequency of 30 MHz was accurate to one part in

10^. The measured change in insertion loss when the counter is increased from

a 00000 reference setting and the dial is increased from a 0.000 reference

setting is indicated in the attached table.

The measured value of the "0 dB insertion loss" of the attenuator with the

counter set at 00000 and the dial set at 0.000 was determined to be

approximately 30.8 decibels.

Page 1 of 3

Test No. Sample No. 1 Date of Calibration: February 6, 1987

2-37
Variable Waveguide Below-Cutoff Attenuator,

Coaxial Connectors

National Bureau of Standards

Model VII, Typical Example

Measured

Counter Dial Change in Systematic Random Total

Setting Setting Insertion Loss Uncertai nty Uncertai nty Uncertai nty

dB dB dB dB

00010 0.000 1.001 0.003 0.002 0.005

00020 0.000 2.002 0.003 0.002 0.005

00030 0.000 2.998 0.003 0.003 0.006

00040 0.000 4.001 0.003 0.002 0.005

00050 0.000 5.000 0.003 0.003 0.006

00060 0.000 5.999 0.003 0.003 0.006

00070 0.000 7.002 0.003 0.003 0.006

00080 0.000 8.001 0.003 0.003 0.006

00090 0.000 9.000 0.003 0.003 0.006

00100 0.000 10.001 0.003 0.003 0.005

00150 0.000 14.998 0.005 0.002 0.007

00200 0.000 20.000 0.006 0.003 0.009

00250 0.000 25.000 0.008 0.003 0.011

00300 0.000 29.997 0.009 0.003 0.012

00350 0.000 34.999 0.011 0.004 0.015

00400 0.000 39.998 0.012 0.004 0.016

00450 0.000 44.997 0.014 0.004 0.018

00500 0.000 50.000 0.015 0.004 0.019

00600 0.000 59.997 0.018 0.004 0.022

00700 0.000 69.997 0.021 0.005 0.026

00800 0.000 79.993 0.024 0.005 0.029

This calibration data is valid only when the attenuator is set by approaching

the indicated value from a lower value of attenuation.

Page 2 of 3

Test No.

Date of Calibration:

Sample No. 1 February 6, 1987

2-38
Variable Waveguide Below-Cutoff Attenuator,

Coaxial Connectors

National Bureau of Standards

Model VII, Typical Example

Three measurements were made at each attenuator setting to find the mean value

of "Measured Change in Insertion Loss" and to estimate the standard deviation

(S.D.) of this mean. The total uncertainty is the sum of the systematic

uncertainty and the random uncertainty where the latter is defined as three

times the estimate of the S.D. of the mean.

For convenience, usually one or more intermediate reference settings are used

during calibration. To determine the estimate of the S.D. of the mean for a specific insertion loss setting which was measured with respect to an intermediate setting, the S.D. of the intermediate setting and the S.D. of the

specific setting were combined by taking the root-sum-of-the-squares of the

respective S.D. values.

For the Di rector.

National Engineering Laboratory Connie L. True, (303)497-3524

Robert T. Adair, Sr. Project Leader

Microwave Metrology Group

Electromagnetic Fields Division

Page 3 of 3

Test No. Sample No. 1 Date of Calibration: February 6, 1987

Reference: RTA

2-39
It should be noted that the spread in the three different columns of

data is no more than a few thousandths of a dB. This attests to the

stability, repeatability, and resettability of the entire dual channel

calibration system as well as the NBS piston attenuator being calibrated.

The dial on the NBS Model VII attenuator can be read to a smaller

value than 0.0005 dB which, along with its repeatability and stability, provides greater calibration accuracy than most 30 MHz attenuators which are calibrated at NBS.

2.4 Procedure for Calibrating a 30 MHz Phase Shifter

The units of this procedure are not given in SI units. The readout of

the device under test is given in degrees, and therefore the results are computed and stated in degrees.

A phase shifter may be calibrated over a 360-deg range at 30 MHz using

the same system shown in figure 2.10 with the phase shifter inserted in the

system instead of the attenuator under test. This calibration is performed in

the following manner.

2.4.1 Calibration procedure for 30 MHz Phase Shifter

1. Connect a standards- quality, 50-ohm, 20-dB fixed resistive

attenuator on the output of the phase shifter. This 20-dB

attenuator insures proper impedance matching of phase shifter and

system.

2. Adjust the 30 MHz receiver to low sensitivity by adjusting the

gain control.

2-40

.i
3. Connect this combination into the insertion point with the input

of the phase shifter connected to the output of the 30 MHz standdard attenuator matching network as shown in figure -2.2.

H. Set the phase shifter under calibration to 0 degree. This must be

done by approaching this setting from a setting below the one desired to eliminate the undesirable effects of any backlash which

might exist in the phase shifter drive mechanism.

5. Adjust the position of the 30 MHz standard phase shifter to a counter setting of approximately 3000 which will allow a phase shift

of sli^tly more than 30 deg since one count equals 0.01142 deg.

6. Adjust the external phase and magnitude controls on the synchronous detector so the meter needles are at mid- scale.

7. Follow the detailed instructions for operating the null detector

as stated in [12].

8. Adjust the coarse (manual) phase shifters until a null is reached.

9. Adjust the standard attenuator until a deeper null is reached.

This will necessitate increasing the sensitivity of the null indicator to keep the needle on a readable portion of the scale. This

standard can be moved toward the null position with the fast speed

drive motor until the null is passed. Then the slow speed drive

motor can be used to adjust the standard attenuator to the posi-.

tion of final null.

10. The precision phase shifter is next adjusted until a deeper null

is found. This phase shifter also has fast and slow speed drive

motors

.

2-41
11. Renull both the standard attenuator and the precision standard

phase shifter to be certain the true null of the system has been

found. This may require readjusting the system sensitivity for

more optimum use of the null indicator.

12. Check the system sensitivity by changing the setting of the phase

shifter under test to 0.01 degree. The null indicator reading

should change significantly if the system sensitivity is sufficient. The system sensitivity can be changed if necessary by

readjusting the power input to the phase shifter under test via

the level set attenuator and by readjustment of the sensitivity

controls of the differential amplifier and the null indicator.

13. Set the phase shifter under test to 0 deg as explained in step 4

above and again null the system.

14. Record the standard attenuator setting and the standard phase shifter counter setting. These values are the 0 deg reference values

shown in table 2.6 which follows section 2.4.2.

15. Remove the phase shifter from the insertion point leaving the 20

dB fixed attenuator attached to the flexible cable of the

insertion point.

16. Reconnect the insertion point and renull the system as in steps 5

through 11 above.

17. Record the value from the standard attenuator's optical projector.

This value is the initial insertion loss reference reading.

18. Subtract the value of attenuation obtained in step 14 from the

value obtained in step 17. This result is the insertion loss of

the phase shifter being calibrated at its 0 degree setting.

2-42
19. Repeat this procedure two or three more times and average the results to obtain the report value of the insertion loss of the

phase shifter when it is set at 0 degree. If this value of insertion loss is not approximately the same as the manufacturers nominal value or if it has changed appreciably from the last time it

was calibrated, the phase shifter under calibration should be suspected and checked for possible damage.

20. Repeat steps 1 through 14 above to obtain new 0-deg reference readings. This greatly reduces the possibility of erroneous readings

due to drift in the calibration system.

21 . Switch the null indicator out of the circuit and set the phase

shifter under test to exactly 30 deg. For illustrative purposes

the hypothetical calibration of this phase shifter will be performed at 30-deg intervals to reduce the amount of data to be

handled

.

.22. Run the standard phase shifter with the fast speed drive motor

until its counter reads approximately 200.

23. Switch the null indicator back into the circuit and renull the

system as in steps 5, 6, 7, 9, 10 and 11.

24. Record the values as read from the standard attenuator and the

standard phase shifter.

25. Adjust the setting of the standard phase shifter back to a counter

reading of approximately 3000. Notice that the phase shifter under test is still set at exactly 30 deg.

26. Repeat steps 5 through 11 above.

2-43
27. Record the standard attenuator and standard phase shifter readings.

These are the 30-deg reference readings.

28. Switch the null indicator out of the circuit and set the phase

shifter under test to exactly 60-deg.

29. Repeat steps 5, 6, 7, 9, 10 and 11.

30. Record the standard attenuator and the standard phase shifter readings.

31 . Repeat step 25 but notice the phase shifter under test remains set

at 60 deg

.

32 . Repeat s teps 5 thr ough 1 1

.

33. Record the standard attenuator and standard phase shifter readings.

These values are the 60-deg reference readings.

Since this precision phase shifter has a range of approximately

only 40 deg each successive 30-deg setting on the phase shifter

under test is used as a reference instead of a 0-deg reference.

' This allows the operator to step from 0 to 360 deg in increments

of 30 deg. This makes it possible to calibrate a phase shifter

all the way from 0 to 360 deg even though the standard phase

shifter has a capability of approximately 40 deg.

34. Continue this process until the phase shifter is calibrated from 0

to 360 deg.

35. This entire calibration process must be repeated a minimum of two

more times so that the instrument is calibrated completely at

least three separate times. These results are averaged and form a

complete calibration report.

2-44
2.4.2 Phase Shifter Calibration Data Reduction

The phase shift calibration data are reduced in the following manner.

(Refer to table 2.6 following this section for a typical data sheet).

1 . The standard phase shifter counter reading for each setting of the

phase shifter under test is subtracted from its respective

reference reading.

2. This is done for each of the three separate calibration runs, and

the three results for each setting of the phase shifter under test

are averaged.

3. These averages are then multiplied by 0.01142 deg per count to

convert the number of counts per interval to the number of deg per

interval.

4. These averages are successively added to obtain the total phase

shift for each setting of the phase shifter under test.

5. Notice that the phase shift for the 360-deg setting is slightly

less than 360 deg. This occurs since the operator must successively step the setting from 0 to 360 deg in intervals of 30 deg.

To correct for this a technique known as "closing the data" is

employed

.

6. Closing the data is accomplished by subtracting the actual 360-

deg measured value from 360.000 deg and dividing this number by

the number of intervals measured between 0 and 360 deg. This resultant angle, which is extremely small, is the correction which

must be added to the value of phase shift measured for the first

interval (the 30-deg reading in this case). Two times this correction must be added to the second interval (the 60 -deg reading) and

2-45
so on. The total correction which is added to the 360-deg data

should correct that measured value to 360.000 deg.

7. The attenuation value for each setting of the phase shifter under

calibration is subtracted from its respective reference reading.

8. These attenuation values are successively added algebraically to

obtain the amount of attenuation which is present in the phase

shifter at each setting of phase angle with respect to the original 0-deg insertion loss.

9. These three columns of data are averaged to obtain the values

which appear in the calibration report.

10. The column of averaged phase shift data is rounded to the nearest

0.01 deg and entered in the calibration report.

1 1 . The column of data of average attenuation change is rounded to the

nearest 0.001 dB and entered in the calibration report to the near-

.

, est 0.01 dB.

12. The average initial insertion loss data are computed and rounded

to the nearest 0.1 dB and entered in the calibration report.

2.4.3 Tabulated Data and Calibration Results for 30 MHz Phase Shifter

Table 2.6 presents the tabulated calibration data on a commercial 30

MHz phase shifter. These data are the averages of three separate calibration

runs on this particular device.

2.4.4 Typical Report of Calibration for 30 MHz Phase Shifters

Immediately following table 2.6 is a typical complete report of calibration issued on the 30 MHz phase shifter whose data appear in table 2.6.

2-46
o

3o

60

90

/go

^

TABLE 2 .

u TABULATED CALIBRATION DATA ON

A COMMERCIAL PHASE SHIFTER

^-^^^^^^^^^/^ \:h^Ji^.<9c^£L.r-,^^Z^^ )^<f>^L^^J'^

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30-
TABLE 2.6 (CONTINUED)

3oo

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33D

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KvtfO or MKASUMCMorr

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AJq. I (fp.J J,)

^ L ^ jV^ J — —X* IT

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2-48
TABLE 2.6 (CONTINUED)

^^^^

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Bamomctd*.

3n

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D.n7 ^ 7n ^ -e^

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2-49
TABLE 2.6 (CONTINUED)

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D.

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2-50
U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NATIONAL ENGINEERING LABORATORY

Boulder, Colorado 80303

REPORT OF CALIBRATION

VARIABLE COAXIAL PHASE SHIFTER

Merrimac Research and Development, Incorporated

Type R-30, Typical Example

Submitted by:

National Bureau of Standards

Division 723.01

Boulder, Colorado 80303

The measurements on this phase shifter were performed under ambient conditions

of approximately 23° ± 2° C and 40+5 percent relative humidity. The power

presented to the phase shifter was less than 1.0 milliwatt. The VSWR

presented to each terminal of the phase shifter was less than 1.05. The

calibration frequency of 30 MHz was accurate to one part in 10°.

The measured value of the initial insertion loss of the phase shifter with the

dial set at 0.0 was determined to be approximately 35.9 decibels.

The change in phase when the dial is increased from a 0.0 reference setting is

indicated in the following table. The change in insertion loss column

represents an incremental change in total insertion loss of the phase shifter

corresponding to the 30 degree dial setting increments. A negative value

indicates a decrease in insertion loss from the preceding calibration point.

Dial Measured Phase-Shift Change in Random

Setting Di f ference Insertion Loss Uncertai nty

degrees electrical degrees deci bel

s

degrees

30 30.05 0.02 0.07

60 60.11 0.04 0.04

90 90.65 0.01 0.16

120 120.89 -0.11 0.05

150 150.32 -0.03 0.19

180 180.16 0.06 0.09

210 210.29 0.02 0.04

240 240.34 0.04 0.07

270 270.83 0.01 0.06

300 300.90 -0.10 0.01

330 330.16 -0.03 0.13

360 359.97 0.06 0.04

Page 1 of 2

Test No. Sample No. 2

Date of Calibration: February 9, 1987

2-51
Variable Coaxial Phase Shifter

Merrimac Research and Development, Incorporated

Type R-30, Typical Example

The "Measured Phase-Shift Difference" in electrical degrees is the mean of

three separate readings taken during the measurement at the given dial

setting.

The random uncertainty of the measured values is equal to three times the

calculated standard deviation of the mean of the three separate determinations

at each dial setting.

The systematic uncertainties are + 0.1 degree and ± 0.01 decibel respectively

for each 30 degree increment. The total uncertainty for each phase shift

increment is given as the sum of the systematic uncertainty and the random

uncertainty. These incremental uncertainties are not accumulative since

closure within 0.01 degree was achieved at the 360 degree (0) setting.

Closure was similarly achieved for insertion loss variation.

For the Di rector.

National Engineering Laboratory Connie L. True, (303)497-3524

Robert T. Adair, Sr. Project Leader

Microwave Metrology Group

Electromagnetic Fields Division

Page 2 of 2

Test No. Sample No. 2

Date of Calibration: February 9, 1987

Reference: RTA

2-52
2.5 Conclusions - Dual-Channel Rf Null Technique

The basic direct substitution technique (as illustrated in figure 2.1)

has many advantages over a single-channel system as was mentioned previously.

Briefly this dual-channel unmodulated technique provides extremely high resolution, large cali brat ion- range attenuation, minimal effects of signal source

amplitude instabilities, and avoids the complexity and errors due to

modulation. A constant insertion loss phase shifter is necessary, however,

and allows the system to be used for precise phase shift calibrations.

A satisfactory dual-channel rf null attenuation and phase calibration

system similar to the NBS 30 MHz system can be constructed in nearly any wellequipped standards laboratory with existing or available equipment.

2-53

3.0 Measurement Uncertainty and Quality Assurance

3.1 NBS System Measurement Uncertainty

3.1.1 30 MHz Standard Piston Attenuator

The components of the uncertainty budget for the 30 MHz standard piston attenuator are listed in table 2.1. The key values are repeated here for

convenience

.

A. Uncertainty due to variation in the attenuator waveguide diameter:

0.0003 dB/10 dB.

B. Uncertainty in measuring piston displacement. This is governed by

the accuracy of the ruled steel scale and optical readout: 0.001

dB/10 dB.

C. Uncertainty in estimation of the rf conductivity of the waveguide

walls. This is the same order of magnitude as the machining tolerances on the waveguide itself: 0.00026 dB/10 dB.

This yields a total systematic uncertainty budget for the attenuation

standard of 0.00156 dB per 10 dB increment. Total maximum systematic uncertainty of the attenuator: 0.0016 dB/10 dB. It would be possible to reduce

this by one half by replacing the scale with a laser interferometer displacement measuring system. This technique has been implemented in the United Kingdom at NPL, and at CSIRO in Australia as well as by a commercial manufacturer

in the U.S. NBS plans to implement this improvement in the near future as

resources permit. Until recently the total systematic uncertainty of the NBS

attenuator calibration service has been adequate to meet defense and industry

requirements.

3-1
3.1.2 30 MHz Standard Phase Shifter

The components of the uncertainty budget for the 30 MHz standard trombone phase shifter are listed in table 2.2. The total uncertainty over its

36-deg measurement range does not exceed 0.1 38 deg.

A second key value related to this reference standard is its deviation

from constant amplitude of less than 0.0005 dB over a range of 30 deg. This

value is critical to assess uncertainties in measuring attenuation since it

affects the reference arm of the null system.

Systematic uncertainty of phase shifter: 0.1 38 deg/36 deg.

;

. Level variation over 30 deg: 0.0005 dB.

3.1.3 Measurement Uncertainty for Attenuation

The uncertainty budget for attenuation measurement is given in

table 2.3. The key components of uncertainty are repeated below for

convenience. '

: ;': :„ (

. _ A. Uncertainty of standard attenuator: 0.0016 dB/10 dB

B. System leakage and reference channel

•

. variation due to standard phase shifter: 0.001 dB/10 dB

C. Resolution of detection system: 0.000^ dB/10 dB

Total systematic uncertainty 0.003 dB/10 dB

D. Typical random uncertainty (3Sx value )^ 0.001 dB/10 dB

.. . , Total uncertainty 0.00^ dB/10 dB

The SSjj value is 3 times the computed standard error for the mean.

3-2
There are additional uncertainties in calibration if mismatch uncertainty is significant. Normally the uncertainty is between 0.001 and 0.002 dB

which leads to a typical calibration uncertainty of 0.005 dB for a 10 dB fixed

attenuator. This uncertainty is not applicable to WBCO attenuators where

the large value of their minimum insertion loss renders them insensitive to

terminating impedances.

3.1.3.1 Uncertainties Associated with Typical Attenuators

A. International comparisons and primary

standards lab quality devices: 0.003 dB/10 dB

B. Good quality calibration standards with

low rf leakage: 0.004 dB/10 dB

C. Average quality variable attenuators and

fixed devices with mismatch uncertainties: 0.005 dB/10 dB

3.1.4 Measurement Uncertainties for Incremental Phase Shift

The uncertainty budget for phase shift measurement is given in

table 2.4. The key components of uncertainty are repeated below for

convenience

.

A. Uncertainty of standard phase shifter

(36 deg range): 0.1 38 deg/36 deg

B. Miscellaneous (standard attenuator,

frequency stability, and coarse phase O.O3O deg/36 deg

shifter resolution):

Total systematic uncertainty over 36 0.168 deg

deg:

3-3
, , ,/ C. Typical random uncertainty (3S^ value) on

any increment: 0.01 deg

Minimum total reported uncertainty: 0.2 deg/36 deg

The uncertainty due to impedance mismatches can be neglected because

any variable phase shifter is isolated from the rest of the system by isolating attenuators whose VSWR is less than 1.01. The resultant phase shifter

uncertainty (incremental) is less than 0.01 deg due to impedance mismatches

and can be safely ignored.

3.2 Typical NBS System Attenuation Calibration Results

The following graphs are arranged in basic groups by type of attenuation standard.

3.2.1 Calibration of the NBS Model SA-1 , 10-dB Step Attenuator . (Figure 3.1).

The Model SA-1 step attenuator was designed and constructed by NBS for

several primary calibration laboratories and is based on the WBCO principle.

It is a device which produces a highly repeatable 10-dB step attenuation

measured by two gage blocks whose differential length is determined by an electronic null indicating system. The repeatability of setting is 0.001 dB and

the calculated uncertainty of the 10-dB increment is 0.004 dB.

Calibration of this device provides both an independent check of the NBS

primary standard absolute value and a measure of long-term stability of the

NBS measurement system.

Figure 3.1 is a plot of the calibration results of five independent SA-1

attenuators have been measured over a 12-year time span. All device values

lie within the assigned NBS uncertainty bounds except for one on test 951911

3-4
performed in 1972. Since the measured value of this unit returned to an expected value within limits in 1978 and values for the other units did not shift

unidirectionally in 1972, we can assume a minor mechanical defect was exhibited by test 951 91 1 . This could have been caused by foreign material lodged on

a gage pin which was subsequently dislodged or removed by recommended cleaning

procedures

.

3.2.1.1 Conclusions :

1. The assigned uncertainty limits are valid, and

2. The calibration system is in statistical control.

3.2.2 Calibration of NBS-Designed WBCO attenuators (Figures 3.2 through 3.9)

These NBS designed attenuators were calibrated over a working range of

80 decibels and results have been plotted for each 10-dB increment. As is the

case with the Model SA-1 , all of these devices are calculable standards based

on dimensional measurements. The individual models are only slightly

different from each other in mechanical details, and share a common waveguide

diameter and thus have approximately the same calculated uncertainty of 0.005

to 0.008 dB per 10-dB increment.

A careful examination of the ei^t individual plots indicates that in

over 22 years of calibration history for these devices using the same measurement system, there are only eleven values outside the assigned NBS uncertainty

limits. Ten of these measurement values were obtained between 1963 and 1966,

primarily for higher values of attenuation where rf leakage can cause significant uncertainty. In all of these cases the particular attenuators were refurbished by NBS to reduce leakage which solved the problem. The remaining out3-5
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has not been resubmitted since 1972. Apparently it has been retired from service .

3.2.2.1 Conclusions ;

1. The assigned uncertainty limits are valid and

additionally verified by comparison with

independently calculable attenuators.

2. The system has remained in statistical control over

a 22-year time span. These results were achieved,

even though during this time period the system was

rebuilt twice. The system was modified by adding a

new trombone phase shifter, replacing the null

detection system and upgrading the rf source three

times.

3.2.3 Calibration of Commercial WCO Attenuators

(Figures 3.10 through 3.19). This group of plots tracks the values of

14 separate attenuators over a 20-year time span (individual attenuators have

values for up to 19 years).

Since these attenuators were not designed by NBS, their calculated values

cannot be used to validate the absolute values of the NBS system. Their mechanical dimensions and waveguide material differ from NBS designs and thus

require different correction factors. The theory remains valid however, and

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the corrections used are apparently adequate based on examination of NBS calibration results.

Twenty years of calibration history show an outlier at 70 dB in 1965 for

test 806213. Since this was one of the first attenuators built by the manufacturer, and then was subsequently refurbished and has tracked almost perfectly

for 19 years, we can assume that this outlier is a valid point.

An outlying value for 806547 at 10 dB in 1970 is probably a valid point

since this attenuator shows a larger variation through the years than most of

the others. Internal mechanical instability would cause this.

The remaining outlying values at 90 dB for 8O6623 and 100 dB for 808406

are also assumed to be valid and undoubtedly due to rf leakage within the devices.

Since these excessive deviations from nominal values are readily

explained as due to the DUT and not due to the measurement system, NBS feels

confident that the reported values are correct.

The resettability of the NBS 30 MHz standard attenuator, being based on

an optical readout and scale, is superior in this respect to the attenuators

grouped under 3.2.2. As a result, this calibration history strongly validates

NBS claims to statistical control of our 30 MHz measurement system. The small

degree of scatter evidenced at 90- and 1 0O-^dB increments adds confidence that

the NBS system rf leakage is well controlled.

3.2.3.1 Conclusions :

1. Assigned uncertainty limits are valid.

2. The system is in excellent statistical control.

3-16
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3.3 Typical NBS System Phase Shift Calibration Results (Figures 3-20.1

through 3. 21 .5)

The following figures, 3.20.1 through 3.21.5, are based on an

extremely limited data base which makes it difficult to draw conclusions about

uncertainty estimates. The two devices, however, have been measured over a

significant time span (18 years in one case) and appear to validate adequate

system statistical control.

Figures 3.20.2, 3.20.3 and 3.21.2 through 3.21.5 show assigned error

limits at each phase shift value reported. The uncertainty limits are

indicated by vertical lines above and below the data points plotted in these

figures. For both devices at each value measured, the assigned uncertainty

bounds have been assigned conservatively and seem valid. Note that the 1975

repair of test unit 809499 shifted the measured values substantially but

reduced their deviation from nominal values for subsequent calibrations.

3.3.1 Conclusions ;

1. The phase shift measurement system is in statistical control.

2. The limited calibrations performed indicate the desirability of

phasing out the phase shift service calibration on this system.

Since NBS six-port measurement systems are capable of this measurement now and will provide this service when qualified, no further

evaluation of the 30 MHz phase shift measurement system is planned.

3-27
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3.4 Intercomparison of Attenuation Calibration Results

3.4.1 Comparison with ^ES "SQUID" System (Fi^re 3.22)

A series of comparisons involving the measurement of a calibrated WBCO

attenuator on a system based on a new concept, Superconducting Quantum Interference Device (SQUID), were carried out. This was done to lend confidence to

the theoretical uncertainty analysis of the NBS attenuation measuring system.

The SQUID is a loop of superconducting metal closed by a weak point

contact called a Josephson Junction, operating in a liquid helium bath. It

converts variations in magnetic flux to periodic variations in impedance which

are sensed at rf and microwave frequencies. This provides a convenient natural means of measuring electrical quantities such as voltage, current, power,

and attenuation [13il4,15,l6]. A system employing the SQUID for measuring

attenuation was constructed at NBS and used for measuring a transfer standard

WBCO attenuator.

The plot shown in figure 3.22 is taken from reference [14] and is typical of similar plots in the other references. It is apparent from observation

of these results and examination of the references that a totally independent

validation of NBS uncertainty bounds has been achieved. In addition, the comparison indicates that the uncertainty limits in this particular case are

quite conservative. However, this is insufficient to allow the uncertainties

to be arbitrarily reduced. The presence of rf leakage and its unpredictable

effects preclude such action at this time. A specific development of uncertainty analysis will be required to validate reduction of present calibration

uncertainties

.

3-36
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3.4.1.1 Conclusions ;

1. The present uncertainty budget is valid.

, 2. The absolute value of the attenuation rate is correct.

3.4.2 Comparison with NBS Six-Port System (Figures 3-23, 3-24)

3.4.2.1 Comparison Using the NBS Model SA-1 and the LF Six-Port ANA

To build confidence by further intercomparison, an NBS-designed Model

SA-1 10-dB step attenuator was calibrated using the NBS 30 MHz primary attenua

tion standard and the NBS low frequency dual six-port system. The comparison

was performed primarily to check the six-port, but a check on the NBS 30-MHz

primary attenuation standard was also achieved.

The plot (figure 3.23) shows 40 measurements with the 30 MHz primary stan

dard and 20 measurements with the six- port system. The averages differ by

only 0.002 dB which is well within the estimated uncertainty bounds of both

e transfer standard showed more occasion-to-occasion variability

than normal but the consistency was adequate for a confidence check on both

systems.

'

3.4.2.1.1 Conclusions :

1. The present uncertainty budget is valid.

2. The calculated attenuation rate is correct.

3.4.2.2 Comparison Using a Step Attenuator and the LF Six-Port ANA.

An additional comparison was performed using a step attenuator as a trans

fer standard at six fixed attenuation increments. This device exhibited excel

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lent repeatability as shown in figure 3.24. Examination of the plot shows a

significant deviation at 60 dB which is the current limit of the six-^port

range. This 60-dB point measured on the six-port, which is obviously in error, should be ignored in assessing the performance of the 30 MHz system.

3. 4.2.2.1 Conclusions :

1. The uncertainty budget is valid but conservative.

2. The calculated attenuation rate is correct.

3.4.3 Comparison with International Laboratories

The results of an international comparison of several fixed attenuation

standards are plotted in figures 3.25.1 through 3.25.5. This comparison spans

four years and was reported in [17].

The participating laboratories were:

1

.

NML: Australia

2. NBS: National Bureau of Standards

3. NRC: Canada

4. ETL: Japan

5. NPL: Great Britain

6. FOA: Sweden

7. OMH: Hungary

8. PTE: West Germany

A study of the data shown on the five plots for the five fixed standards indicates two laboratories reported results with substantial bias. The

values reported by NPL may be disregarded since they subsequently reported an

error in computation which invalidates their results. The values reported by

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Sweden include ancertainty budgets that are too large to be useful in examining the relationship of NBS to a mean value.

A decision has been made for purposes of this documentation to consider

only the values reported by Australia, Canada, Japan, West Germany and NBS.

Hungary was also eliminated because of the large uncertainty bounds associated

with their reported values. Table 3.1 below lists the means of the values

reported by the selected laboratories.

TABLE 3.1

Mean Values of Fixed Attenuation Standards Measured by

Five International Laboratories Including NBS

Nominal Value

of Standard

dB

3

6

10

20

^0

Mean of

Selected Labs

dB

3.0009

6.0409

10.0225

19.7178

39.4930

NBS Deviation

from Mean

dB

0.0001

0.0001

-0.0005

0.0002

0.005

Reported NBS

Uncertainty

dB

± 0.002

± 0.003

± 0.004

± 0.008

± 0.016

Examination of the results clearly lends confidence to both the absolute

values reported by NBS and the associated uncertainty bounds.

3-47
3.4.3.1 Conclusions :

1. The NBS uncertainty budget is valid.

2. The calculated absolute attenuation rate is correct within

the established uncertainty limits.

3.5 Measurement Quality Assurance

3.5.1 Summary of Consistency of 30 MHz System Measurements

Section 3.2 has a detailed multiple-year calibration history for three

different basic attenuator designs. The results show a remarkable degree of

measurement system control. The conclusions regarding the degree of control

of the measurement process are particularly significant considering the evolution, repair and rebuilding of the 30 MHz system that has taken place over the

past 22 years.

In addition to the affirmation of measurement control, the results also

confirm the validity of the uncertainty analysis and the assigned measurement

uncertainty. This is due to the measurements on attenuators with independently calculable values. Each device can be considered a separate check on the

30 MHz measurement system values.

3.5.2 Summary of Comparisons with NBS SQUID System

Section 3.4.1 describes the comparison plot shown in figure 3.22. This

plot, and similar ones published in references 13 through 16, clearly validate

the absolute attenuation rate calculated for the NBS 30 Mliz primary standard

of attenuation.

3-48
Although it appears that the typical calibration uncertainty limits

normally assigned by NBS are conservative, such a conclusion would be erroneous.

The effect of rf leakage depends on where it occurs in the system, how

it travels along exterior surfaces, where it recombines with the true signal

to be measured and with what phase. These effects are impossible to assess

with any confidence. An additional intangible factor is the effective source

impedance of the leakage signal. If rf energy is emerging from a narrow gap

in the system, this system will possess a very low source impedance. If the

source impedance is sufficiently low it is extremely difficult to ground any

of the surface- conducted energy or to prevent its reintreduction through small

gaps into desired signal paths.

At this time we feel the present uncertainty budget is appropriate for

all measured values, especially above 60 dB where leakage adds a significant

ancertainty contribution. In the future, the uncertainty limits below 60 dB

can be reduced by retrofitting a laser interferometer for displacement measurement as resources become available.

3.5.3 Summary of Comparisons with NBS Six-Port Systems

Section 3- ^-2 describes comparison plots shown in figures 3.23 and 3.24.

These plots of two different step attenuators were originally made to

illustrate the performance of the NBS 10-1000 MHz dual six-port ANA system.

Figure 3.23 compares measurements made on an NBS designed 10-dB step

attenuator based on the WBCO principle. The scatter of the observed data reflects a resettability problem with the Model SA-)1 rather than random varia3-49
tions in the NBS primary standard. In a similar sense, the scatter of the

six- port data probably reflects the same problem.

The significant conclusion to be drawn from figure 3.23 is the close

agreement of the mean values. The two systems are totally different in principle; one is based on the decay of an evanescent mode and the other on a dual

reflectometer . Both systems produced nearly identical results. The results

clearly show that the NBS system is providing values within assigned

uncertainty limits.

Figure 3.24 com.pares measurements made on a resistive step attenuator

at six values of attenuation. The individual steps have been normalized to

their nominal values (i.e., the 10-dB step actually measures 9.989 dB) . The

significance of the plot is the correspondence of values measured with two

independent systems. As was concluded from figure 3.23, the NBS primary

standard is providing measurements well within established uncertainty limits.

3.5.4 Summary of International Intercomparisons

Section 3.^.3 describes an extensive comparison of fixed attenuators by

primary laboratories from seven countries in addition to the United States.

Measured values for five fixed attenuators are plotted in figures 3.25.1

through 3.25.5. A table showing NBS deviation from an adjusted mean is also

included to reflect the comfortable margin provided by the assigned NBS uncertainty bounds. It should be noted that these limits are titter than normally

assigned by NBS. This is due to a larger number of individual measurements

above the normal quantity, thus reducing the standard deviation of the mean.

3-50
An analysis of these results offers the most conclusive evidence of all

that the NBS system is providing measurements within our assigned uncertainty

limits.

3-51

4.0 Conclusions - 30 MHz Attenuation Measurements

It has been proven that the MBS Attenuation Measurement System as

documented in this text is operating under statistical control and is

providing calibrations well within stated uncertainty limits.

It is also reasonable to conclude that assigned uncertainty limits

could be reduced by hardware modification of the displacement measurement system. The development and marketing of improved 30 MHz WBCO attenuators in the

United States and in Great Britain require that NBS undertake a modification

program as soon as practical to maintain our assigned primary standards mission.

4-1

5.0 Conclusions - 30 MHz Phase Shift Measurements

The NBS Phase Shift Measurement capability has been sparingly used over

the past 18 years. Even with a limited data base the uncertainty analysis

appears to be conservative. The ability to use the concept of closure at 0

and 360 degrees further validates the assigned uncertainty limits (refer to

Section 2.4.2).

As an example, the 1969 calibration of an R-30 resolver lacked closure

by 0.76 deg based on measuring 12 separate 30-deg increments. This represents

a deviation of 0.06 deg for each 30-deg increment. A comparison of this with

the estimated uncertainty of 0.2 deg yields a fairly safe margin.

The lack of closure for test 807850 over 18 years averaged 0.3 deg for

a deviation of 0.025 deg for each 30-deg increment. Inspection of figures

3.21.1 throu^ 3.21.5 validates control of the measurement process over the 18

years. Figures 3.20.1 through 3.20.3 yield a similar conclusion for test

809499.

In sammary, the phase shift measurement capability has reasonable assigned uncertainty limits and appears to be in good statistical control.

The limited data base for assessing measurement control, the limited

use of this service and the lack of independent accuracy validation lead to

the conclusion that phase shift measurements should be a special test service

rather than a calibration service.

5-1

6.0 Summary of NBS 30 MHz Attenuation and Phase Shift Calibration

System Uncertainties

TABLE 6.1

Summary of 30 MHz Attenuation and Phase Shift

Calibration Uncertainties

Quantity /Device Uncertainty

ATTENUATION:

International Canparisons and Primary

Standards Laboratory Quality Devices 0.003 dB/10 dB

Good Quality Calibration Standards with

Low Rf Leakage 0.004 dB/10 dB

Typical Commercial Fixed and Variable Attenuators 0.005 to 0.01

dB/10 dB

PHASE SHIFT:

Good Quality Phase Shifters with Low Rf

Leakage and Nearly Constant Insertion Loss 0.2 deg

per 36 deg

Average Quality Phase Shifters 0.5 deg

per 36 deg

6-1

7.0 References

[I ] Uriano, G.A. ; Garner, E.L. ; Kirby, R.K. ; Reed, W.P., eds. NBS calibration

services users guide. 1986-1988 Edition. Natl. Bur. Stand. (U.S.) Spec.

Publ. 250; 1986 July. 204 p.

[2] NBS calibration services users guide 1986-1988 edition fee schedule.

Natl. Bur. Stand. (U.S.) Spec. Publ. 250 Appendix; 1986 July. 94 p.

[3] Beatty, R.W. Microwave attenuation measurements and standards. Natl. Bur.

Stand. (U.S.) Monogr. 97; 1967 April. 45 p.

[4] IRE standards on antennas and waveguides: Definitions of terms (1959).

Proc. IRE. 47,(4): 568-582; Standards 59 IRE 2.S1 . 1959.

[5] IEEE standard specifications and test methods for fixed and variable

attenuators, dc to 40 GHz. IEEE Stand. 474-1973. 24 p.

[6] Beatty, R.W. Effects of connectors and adapters on accurate attenuation

measurements at microwave frequencies. IEEE Trans. Instr. 13: 272-284;

1964.

[7] Beatty, R.W. Insertion loss concepts. Proc. IEEE. 52(6): 663-67I ; 1964.

[8] Russell, D. H. High frequency calibrations systems. Notes from

High- Frequency and Microwave Attenuation Seminar. March 1968.

[9] Russell, D.H. ; Larson W. Rf attenuation. Proc. IEEE. 55(6): 942-959;

1967.

[10] Allred, C.M.; Cook, C.C. A precision rf attenuation calibration system.

IRE Trans. Instr. 2li (2): 268-274; I960 September.

[II] Brown, J. Corrections to the attenuation constants of piston attenuators.

Proc. lEE (London), 96 (III): 491-495; 1949 November.

7-1
[12] Stoltenberg, R.E. Rf null detector NBS/SND. Natl. Bur. Stand. (U.S.)

NBSIR 73-302; 1973 June. 83 p.

[13] Kamper, R.A. ; Simmonds, M.B. ; Adair, R.T. ; Hoer, C.A. Advances in the

measurement of rf power and attenuation using SQUIDs. Natl. Bur. Stand.

(U.S.) Tech. Note 661 ; 197^ September. 27 p.

[14] Adair, R.T. ; Simmonds, M.B.; Kamper, R.A. ; Hoer, C.A. Rf attenuation

measurements using quantum interference in superconductors. IEEE

Transactions on Instrumentation and Measurement. ir^23 (4): 375-381; 1974

December.

[15] Adair, R.T. ; Frederick, N.V. ; Sullivan, D.B. Rf attenuation measurement

system using a SQUID. Natl. Bur. Stand. (U.S.) NBSIR 77-863; 1977

September . 1 46 p

.

[16] Sullivan, D.B. ; Adair, R.T. ; Frederick, N.V. Rf instrumentation based on

superconducting quantum interference. Proc. IEEE. 66(4): 454-463; 1978

April.

[17] Rapport de la 15® Session, Ccxnitd Consultatif d'Electricit^ ; Bureau

International des Poids et Mesures, Annexe El 5, E81-E94, 1978.

7-2
8.0 Acknowledgments

The authors would like to express their sincere appreciation to the following people for their assistance in producing this document; L.F. Saulsbery

for supervising the calibration services; Connie L. True for calibrating the

sample devices under test and preparing the measurement results; Robert M.

Judish for his help in properly reporting these measurement results; Edna M.

Jones and J. Kathleen Hillen for preparing the sample calibration reports;

Eleanor Livingston for technical editorial assistance; Shirley Deeg for handling the publication details; and Terry Yenser, Marlene Deutsch and Karen

Forberg for preparing the manuscript.

We would also like to express our gratitude to the many technical staff

members who assisted in the design, development, construction, and maintenance

of this measurement system.

Furthermore, we would like to thank the technical readers M. Crawford, R.

Lawton, and D. Vecchia for their valuable assistance in completing this document .

8-1
A
9.0 Appendices

9.1 Appendix A

Excerpt from Reference 5.

9.2 Appendix B

Complete copy of Reference 10.

9.3 Appendix C

Complete Copy of Reference 14.

9.4 Appendix D

Excerpts from Reference 17.

9.5 Appendix E

Drawings of System Components.

9-1
9.1 Appendix A

Excerpt from Reference 5.
IEEE Standard

Specifications and Test Methods for

Fixed and Variable Attenuators, DC to 40 GHz

Including Trial-Use Sections on

Insertion-Loss Repeatability and

Characteristic Insertion Loss of a Noninsertable Two-Port

1. Purpose and Scope

This performance standard covers absorptive and reflective attenuators, both fixed as

well as continuously variable or variable in

Hxed steps, both manual and programmable

types. It does not cover electronic or solidstate-type attenuators.

This standard permits the user to select for a specification those minimum performance

parameters which characterize an attenuator.

A list of preferred test methods is included

permitting verification of the attenuation

characteristics.

Practical minimum performance limits are furnished for various applications. These are

for guidance only and will improve with time.

2. DeHnition of

Characteristic Insertion Loss

2.1 Interpretation of Characteristic Insertion

Loss. An attenuator is ideally a linear net- work which may be in the form of a trans- mission line or waveguide component designed to reduce the input power by a predetermined ratio. The ratio of input to output

power is commonly expressed in logarithmic

terms such as decibels. The power output

ratio as commonly used in the "characteristic

insertion loss" relation is shown in Fig 1. The

ratio specified is equal to the characteristic

insertion loss since source and load are reflec- tionless. The term "attenuation" is used rather loosely and means "characteristic insertion

loss" as defined in Fig 1. Attenuators include

absorptive and reflective devices, having at

least two ports.

Pl.NPUT-cX P0UT?UT->

Figl

Definition of Characteristic Insertion Loss

PlNPUT Incident power from Zq source PoUTPUT = Net power into Zq load

Pjfjpuj. Characteristic insertion loss = 10 logjo ~" (dB)

Po UTPUT

There are fixed attenuators, continuously

variable, and step attenuators. Only Zo

matched, two-port attenuators, designed for use in a Zo system, are treated in this standard.' They are reversible except when specially noted as, for example, for a high-power

attenuator. All attenuators in this standard

are passive, linear, resistive or reactive, nominally symmetrical in impedance.' Voltagevariable attenuators, including vacuum tube

or solid-state types, are not covered in this

standard.

To specify a variable attenuator, one must

know its end use. If the device is used to extend the range of a power meter, one re- quires to know its terminal-to-terminal or

total loss. This is described by the characteristic insertion loss. However, in most applications the variation above the mimimum loss

is of major interest. One specifies then the

' Section 8. published for trial use. includes attenuators having different input and output impedance.

9-3
9.2 Appendix B

Complete Copy of Reference

9-4
A PRECISION RF ATTENUATION CALIBRATION SYSTEM

BY

C. M. ALLRED and C. C. COOK

Reprinted from IRE TRANSACTIONS

ON INSTRUMENTATION

Volume 1-9, Number 2, September, 1960 PRINTED IN THE U.S.A.

9-5
A Precision RF Attenuation Calibration System

C. M. ALLREDf, member, ire, and C. C. COOKf, member, ire

Introduction

THE XEED for higher accuracy in attenuation

measurements has kept pace with the advances in electronics. In an effort to meet the demands in this field, a precise and accurate system for the meas- urement of attenuation has been developed.

The system discussed operates at 30 Mc, but similar

systems under construction are designed to operate at other frequencies. Choosing a single frequency of operation allows designs that increase the stability, extend

the measuring range, lessen the problems of leakage,

and enhance the over-all accuracy.

Thic System

Description of the System

Achieving a system with sensitivities of 0.001 db, ac- curacies of a few thousandths of a db, and a range ex- ceeding 120 db requires careful design and special techniques. With such large ranges of attenuation to be

measured, the monitor should be capable of voltage

gains of 10"* or more. Because of the stability problem of such a monitor and the desired sensitivity of 0.001 db,

it was decided to operate in a two-channel system and

use a null response. As is well known, the use of two-

* Received by the PGI, June 24, 1960. Presented at the 1960 Conference on .Standards and Electronic Measurements as paper 6-2.

t National Bureau of .Standards, Boulder, Colo.

channel techniques greatly lessens the problems of level instability of the source and gain instability of the

monitor. High sensitivity is also inherent in such sys- tems. One may consider the increased complexity of the

system and the necessity of making adjustment in both

phase and magnitude as payment for the advantages.

The block diagram of the system is shown in Fig. 1.

SOURCE -

AUTOMATIC LEVEL CONTROL

MATCHING NETWORK

LEVEL CONTROL

CONTINUOUS PHASE

SHIFTER

STEP

PHASE

SHIFTER

CURRENT

SAMPLING h- UNIT

PISTON ATTENUATOR

COMBINING NETWORK

MATCHING NETWORK

UNKNOWN

ATTENUATOR

* MONITOR

MATCHING NETWORK

Fig. 1

BIock; diagram for attenuation measuring system.

The RF source is a 30-Mc crystal-controlled trans- mitter capable of 200 watts output with low residual

modulation. The low resistive component of the piston

attenuator launching coil is coupled to the 50-ohm

source by a special impedance-matching network. The

9-6
I960 AUred and Cook: A l^rccision R.b Allermalion Caiihralion Syslem 269

current in the laiinrliin.u coil energizes the cliaiiiiel coiitaiiiint^ tlie phase sliiiter and also supplies the injxit to an automatic level control network connected to the source. Tliis network is used to keei") the current in the

hiunchini; I'oil constant. The continuous i)recision |)h.ise

shifter having low incidental level changes coiniects to

a step adjustable phase shilter. The attenuator to be

tested is inserted between niatchini; networks in the

channel containin.u the jiiston attenuator. The two

channels are brought together in <i special conil)ining

unit which presents correct impedances to the respective channels, minimizes interaction between the channels and has <i low insertion loss. The system is completed b>" a higli-gain monitor.

Measurements are made by adjusting both the standard attenuator and phase shifter until a null response is obtained. This is done with and without the attenuator

under calibration in the system. The change in the

standard attenuator and phase shifter readings gives

the value of attenuation and phase shift of the unknown.

In its present form, the phase shifter lias no accurate displacement measuring device and no attempt will be

made to evaluate the phase measuring characteristics of the system.

Front and rear views of tlie complete system

mounted in a console are shown in Figs. 2 and 3, re- spectively.

Standard Attenuator

Properties : Piston attenuators are used quite extensively for precision attenuation measurements.'"^ The

major advantage of such attenuators is that the atten- uation is determined (except for secondary effects) by

the fundamental units, length and time (frequency).

Another advantage is that close impedance matching is usually not a stringent requirement.

The attenuator has its disadvantages. It is essentially a nondissipative instrument and reflects varying

amounts of energy rather than absorbing it as the at- tenuation is varied. As a result, the minimum insertion

loss is quite high for linear operation and the terminal

impedances are reactive. Usually, frequency sensitive

networks are used for impedance matching. An additional problem occurs because of the permeability and

finite conductivity of the material used for the waveguide. These cause a second-order elTect on the attenuation constant. This requires a determination of the

permeability and conductivity of the material used in the guide wall. Since the attenuation constant oc is a slowly varying function of frequency, a single scale cannot be used over wide frequency ranges without cor-

' D. E. Harnett and N. P. Chase, "The design and testing of multirange receivers," Prog. IRE, vol. 2,1, pp. 578-59,1; June, 1935.

^ R. E. Grantham and J. J. Freeman, "A standard of attenuation

for microwave measurements," Trans. A TEE, vol. 67, pp. 535-5,17; June, 1948.

^ C. G. Montgomery, "Technique of Microwave Measurements,"

M.I.T. Rad. Lab. Series, McGraw-Hill Book Co., Inc., New York.

N. Y.,voI. 11, ch. II, pp. 679-719:1947.

Fig. 2 —Front \ iew of attenuation measuring system.

Fig. 3—Rear view of attenuation measuring system.

rection. Only output signal ratios are measured; the re- lationship between input and output, if desired, must

be determined by other means.

Theory: Fields existing within a uniform perfectlyconducting waveguide can be expressed as a linear

combination of terms called modes. The field components for each mode are proportional to the quantity,

f,-yz+]iot^ where the propagation constant 7 is purely

imaginary and is determined entirely by the guide di- mensions and frecjuency.

Below a certain frequency, called the cutofT fre- quency, 7 becomes purely real and the fields decay ex- ponentially at a rate dependent upon the mode. To in- 9-7
270 IRE TRANSACTIONS 0\ INSTRUMENTATION Seplomher

sure mode puritx" at lii.^li attenuation lexels, the mode

with the smallest deca>- r,ite is commonl>' used.

In the actu.il case, the jiermeability and hnite eonductivitx' ot the i^uide walls and the ]')ro])ert ies of the

medium within the i^uide add .i small im.it;inar\- and

real part to the abo\'e propaii.uion const. int. A good approximate equation for the propau.it ion

constant oi the 7 £11 mode is gi\"en b\";^ '''

= 111 /l _ (^^' _

1

1 + ,/ 1 -

1

puC/ J

V/u/cr

where

:

a = pln'sical radius of guide = 1.841 1S3S, a constant which is the first root of the first derivative ot the first-order Cessel Function of the first kind

/= trequency

C = velocity of light iii an unbounded medium having the electrical properties equal to that within

the guide

ju = permeability of guide wall

MKS system of units are used throughout. With the

operating frequency so far below the cutoft' frequenc\",

neglecting the effect of even moist air within the guide

as compared to vacuum gives rise to an error less than

1 part in 10^ (C for vacuum = 299793.0 + 0.3 km/sec.')

Circular Waveguide : In the system described, circular

waveguide was used with the excited field consisting of the TEn mode. The displacement of the receiving coil relative to the launching coil is measured b>' a ruled

scale and optical projector. The scale is accur<ite to 0.0001 inch in any 6 inches.

The guide is composed of brass and has <in outside di- ameter of 3.9 inches and a length of 22.3 inches. The in- ternal diameter of the guide was chosen so as to give an

attenuation rate of 10 db per inch. This diameter was

measured at 2-inch intervals along the guide. The a\-erage diameter was 3.19725 inches with a maxinuim ^•ari- ation of 0.00003 inch. The accuracx' of the measure- ments are within +50 millionths of <in inch. These

measurements were made at 6<S°h^ while the s\steiu is operated about 4°F above this temper.it ure. The ther- mal coefiicieiits of expansion of the stainless steel sc.ile

* J. Brown, "Corrections to the attenuation constants of jiislon attenuators," Pmc. IEE, vol. 96, pt. ^, pp. 491-495; .\o\cnil)er, 1949.

* C. M. .Alired, "Chart for the 'I'Kn mode piston .it tenualor,

J. Res. NBS, \ ol. 48, pp. 109-1 10; February, 1952.

J. W. M. DuMond, "i'rcsent status of precise inform. 1 1 ion on the universal phssical c(jnstants. H.is the time arri\ed for their ado|)tion

to replace our present arl)itrar\ < ()n\ ent ion.d sl.indards?" IKK

TuANS. OS Lnstkumicntaiion, \()1. 1-7, pp. 1,?6 175; December,

1958.

and the br.iss guide are a])i)roxim.itel\' the s.ime. If thev were e(|U<il, temi)erature v.iri.itions would have negligible elfect. Assuming a con^erv.it i ve 5 parts per million (20 percent) difTereiice in their coefficients, a calculable error of 0.0001 db per 10 db could arise for the

4°[" temjier.it ure v.iri.ition. An uncert.iint\' of 0.0001

inch in the di.imeter ol the guide .it 6<^°l-~ adds an er- ror of 0.0003 db per 10 db. The dc conducti\ itv of the

guide w.is foimd to be 1.35y^mhos jx'r meter. From Chambers and Pippard' and Busse\',^ it is conservative to say

tli.it the RF conductivit}' does not decrease more th.m

10 per cent from the bulk dc v. due. Assuming the RF

coiiductivit>' li.is decreased from the dc value b\- 5 per

cent, this \alue of conductivitx" will be fairly certain to + 5 per cent. Such an uncert.iint>' gives rise to an error

of 0.00026 db per 10 db.

The inside wall ol the guide has a thin coating (5 to

10 microinches) ot rhodium. This provides a hard sur- face for the silver sliding contacts of the piston to bear

upon and prevents corrosion ot the brass surface. The

effective conductivity of the guide surface is insignifi- cantK' altered from tli.it ot the brass itself.

Input Syston

The input s\'steni of a piston attenuator is important,

as it plays a major role in the over-all measurement

range. The high initial insertion loss inherent in piston

attenuators arises from lack ot mode purity and the in- teraction of the output on the input when the coil separation is small. What is needed is an input system that

launches the single TEn mode with an intensity independent of the position of the output coil, or a system

that launches the desired mode with such a strong in- tensity that the output coil need not come close to the

input coil. Both approaches are simultaneousK' used.

Barlow and Cullen' reduce the interaction effect b>' making the magnitude of the generator and load resis- tive impedances equal to the characteristic impedance

of the attenuator. Weinschel, Sorger, and Hedrich'" re- duce the effect b>' considering the entire attenuator as a mutual inductive coupled tuned bandhlter and adjust

the generator impedance for minimum deviation from

linearity.

.A different .ipproach is used here. II one could .ichie%e

.1 current sheet with .i spatial distribution in the tr.ins- verse phme of the guide li.uing the same form .is the

f.imiliar electric field ixittern of the TEn niode, the desired ewiiiescent mode would be l.umclied in both di- rections trom the current sheet. Furthermore, it the current sheet were const.uit (infinite imped.mce gener-

' R. G. Chambers and .\. R. Pipp.ird, " Fhc EtToct of Method of

I'rep.iration on the 1 ligh-FrequencN' Surf.ice Resistance of Met.ils,"

Inst, of Metals, London, i-aiu., Mono.nraph No. l.\ pp. 281-29,>; 195.v

* II. Iv. Busscx', ".Staiutards and measurements of micro\va\'e skin <lepth-conducti\it\\ surf.ice imped,incc. and Q, " this issue, p. 171.

'•' II. M. I?.irlo\v .ind .\. I,. Ciillen, "Micro\v.i\e Me.isurements,

Const.ible and Co., Ltd., London, Knc;., pp. ,^84-,?88; 1950.

IL O. Weinschel, G. V. Sorger, .lud .\. L. Hedrich, "Relative

\-oltmctcr for V'HF/IIHF sign.il gener.itor .itteniiation oliliration,

IRI' I'kans. on InstuumI' n I .\ tion, yo\. 1-8, pp. 22-,^; March, 1959. 9-8
I960 Allred and Cook: A Precision RF Attenuation Calihiation System 271

ators) and independent of the fields reflected from (he

pickup coil, the interaction effect would cease (o exist. The above conditions are approached by constructing

the l.iunching coil after the above pattern (see Fi.u;. 4). The constant current sheet feature is approached by

sampling the launching current and keeping this current constant by means of negative feedback to the RF

source. The attenuator guide has been extended beyond tlie launching coil for a twofold purpose. The pickup coil must produce a reflected field since it absorbs energy.

This reflected field passes through the launching coil with little interaction and is terminated by the guide

extension. The field excited by the launching coil in the

guide extension is also terminated.

The problem of matching the low resistive component

(estimated to be between 0.01 and 0.1 ohm) of the

launching coil is quite severe. This is accomplished by means of a special network utilizing small ceramic ca- pacitors in a ladder arrangement. These capacitors have

a high RF voltage and current rating; this permits

operation of the matching network at inputs to 200

watts. A 100-watt input produces a current of the order

of 35 amperes in the launching coil. The launching unit is constructed of small stainless

steel tubing and water is passed through the unit to pre- vent excessive heating of the guide which would change

its dimensions.

Mode filters are also used, since the reactive impedance of the launching unit gives rise to some axial

electric field. Performance of the input system is discussed later along with the over-all system performance. A detailed

report of such input systems is being prepared for publication.

Phase Shifter

A precision continuous phase shifter was needed

which had level changes less than 0.001 db as the phase was varied. This placed the following restrictions on the

phase shifter: the section of the phase shifter whose electrical length is varied must have a very uniform characteristic impedance, it must be terminated in this value of impedance, and the line must be sufficiently

large to reduce the wall losses due to the finite conductivity of the metal.

The phase shifter is of the trombone type (see Fig. 5). This type consists of two stationary transmission lines connected together by a U-shaped transmission line which moves relative to the stationary section in a telescoping manner. Single-frequency operation per- mitted use of the simplified nonconstant impedance

construction. The stationary sections of the phase

shifter consist of precision coaxial lines which are terminated at both ends in their characteristic impedances.

The moveable section is dimensionally stable but nonprecise. The undesirable level changes caused by imperfectly terminating the precision line are lessened if

Fig. 4—Launching coil assembly similar to the one described.

Fig. 5—Phase shifter.

both ends are closely matched to the characteristic impedance of the line. A 10-db pad bracketed by impedance matching networks has been built into the center

of the moving section. This provides isolation between

the two halves of the trombone and the correct terminating impedances for the corresponding ends ot the

precision section. Additional pads and matching units are provided for terminating the other two ends.

The outer conductors of the precision section of the

phase shifter are electroformcd copper cylinders. A

heavy silver plate with thin rhodium coating is on the

inside walls. The inside diameters are 3.33 inches, outside diameters, 3.9 inches, and lengths, 22.3 inches. The

center conductors are brass rods with silver plate and

rhodium coating similar to that used on the outer con-
272 IRE TRANSACTIONS ON INSTRUMENTATION September

ductors. Tlic diameters are 1.44 inches. Maxiimini departure ot the critical (haineters from the mean value

is 0.00035 inch. I'he maximum chant;e in characteristic

impedance at any point due to these diameter variations is less than 0.04 per cent. These are c.dculated

vari<itions and represent pairini; the worst possible

combinations ot diameter measurements. The aver.ii.;'- ing etTect ol the smooth v.iriations in the diameters

would produce a much smaller variation in characteristic impedance.

The complete phase shifter was made operational by

adjusting the four terminatini!; matchini; networks until input and output impedance chans^es were very small

as the moving section was varied. These changes were

less than 0.01 ohm for both real and reactive components as measured on an RF bridge having high differ- ential sensitivit}'.

The constancy of output level of the phase shifter was

measured using crystal diode detectors in a ver\' sensi- tive differential circuit. The maxinmm level variation was less than 0.0005 db. This occurred for a 33° phase

shift. The phase shifter level change will be signific<inth'

less tlian this in the case of most piston attenuators and

dissipative attenuators operating where the attenuation

is essentially independent of frequency since the phase

shift is usually small in these attenuators. In an\' case, corrections can be made.

The Combining Junction

The two channels are brought together by means of a special network. This network minimizes interaction be- tween the two channels which would otherwise require

excessive padding to maintain impedance match. The

network" is based on the bridged-7" circuit. Such a net- work, if ideal, completely isolates the two channels from

each other, presents each channel with the correct matching impedances, and would have an insertion loss of only 3 db. The actual network has the following

measured characteristics:

Isolation between inputs:

Input Impedance:

Input 1 Input 2

Insertion Loss: Input 1 to output

Input 2 to output

110 db

50.4-fiO ohms

50.9+jO ohms

4 db

4 db. The combining junction with cover removed is shown

in Fig. 6.

. System Performance

The system is essentially a primary standard and

therefore does not recjuire calibration. In comparisons

with other standards, agreement has been within the

corresponding error limits. Tests to check the self-con- sistency of the system have been made by measuring a

" C. M. Ailred and C. C. Coolc, "A multiple isolated-input net- work with common output," to be published in /. Res. NBS.

Fig. 6—Combining junction.

fixed value of attenuation at various initial positions of the attenuator, at different input power levels, and vari- ous initial positions of the phase shifter. The system is new and a tew additions and modifications are yet to be

made. The main addition will be a special low-noise

stable monitor using phase detection designed to fit the system's special requirements. The present monitor

is a slightly modified ordinary commercial communication receiver.

Sensitivity

The system has a sensitivity greater than 0.001 db at

a level of 80 db below 1 volt output of the standard at- tenuator. In principle the sensitivity would increase by

a factor of 10 for every 20-db increase in level. Instability of components and the fact that the signal is not

strictly a pure single frequency sine wave prevent the

sensitivity in a null system from completely achieving

the ideal.

Stability

All components were constructed and mounted so as

to give the system stability. For example, solid semiflexible coaxial line is used throughout. The stability is indicated by the following calibration data of a commercial attenuator, Table I. The time sequence is from

left to right and each row is a repeat of the attenuator

settings. A lapse of about one hour occurred while data were being taken. This means that the time lapse between succcesive values in a given column represents

roughly 12 minutes. All values are in db. Instabilities

do occur sometimes, as indicated in the last two readings and a few components have had to be changed.

Normally, quite a few readings can be taken before a

drift of 0.001 db is noticed. As the difference between

two readings gives the value of attenuation desired,

the drift usually does not impair the accuracy significantly.

9-10
1960 Allred and Cook: A Precision RF Attenualion Calihralion System 273

TABI.R I Data Showing STAnii.n y of Sysh:m

88 212 87 213 86 212 85 212 84 210 83 205

88 212 87 212 86 212 85 212 84 220 83 205

88 212 87 213 86 212 85 212 84 220 83 206

88 212 87 213 86 212 85 212 84 225 83 208

Linearity

The linearity of the attenuator at close coil separations is good but the point of departure from linearity

(due to the interaction effect) could not be ascertained.

The problem occurs because of heating effects in the

pickup coil as the output level increases. This slow

thermal drift occurs before any interaction effect is noticed.

The equivalent change in linearity produced by this high level thermal drift is about 0.006 db at the 3-volt

level and is essentially absent at the 1-volt level. A stable 10-db step of a dissipative attenuator was

measured at various positions of the standard attenuator. The results are given in Fig. 7. The first point on

the left, for example, gives the value of 9.971 for the

nominal 10-db step of the dissipative attenuator when

the standard attenuator is operated within the 23- to 33-db region. The 1-volt output level is at about the

33-db position. The first point deviates from the others

because of the above-mentioned thermal drift in the

pickup coil when operated at the 3-volt output level (23-db position). The last four points show deviations

due to poor signal-to-noise ratio. When these data were

taken, the temperature control system for the water

flowing in the launching unit was not installed and the

input end of the attenuator was a few degrees colder

than the output end. A rough calculation of this effect

is indicated by the dashed line and show^s that, when in proper operation, the system will be more linear. There

has been insufficient time to take new data.

Measuring Range

The data in Fig. 7 do not represent the range of the

system, as additional padding had to be added to the

attenuator channel at higher output levels (less attenuation) to permit nulling with the phase shifter leg. The

last nine positions, however, represent roughly the level

of the signal at the monitor. The last point, for example,

is taken at 140 clb below the 1-volt level. Thus the data

on the graph represent a measurement range of 150 db.

Each point was obtained by averaging 6 measurements. The standard deviations of the last five points

were, respectively: 1.2, 1.6, 8.1, 6.2, and 30.3 thousandths of a db. The data include any nonreproducibility in the 10-db step of the dissipative attenuator.

A ccuracy The errors discussed do not include those due to mismatched impedances presented to the attenuator under

calibration. There are situations where, because of high

1- 9 980

LlJ 9.978

ac

=)inS 9 976

Q. 9 974

LU

»—

</> 9972

ODO

° 9970

— — — —

--

1

1

23 33 43 53 63 73 83 93 103 ATTENUATOR POSITION

113 123 133 143

Fig. 7—Attenuator linearity test.

initi.il insertion loss, the measurement is essentially in- dependent of impedance mismatch. Such cases occur in most piston attenuators and also in those dissipative attenuators having sufficient padding as an integral

part of the attenuator. The total system error, which is a function of the

range of measurement, A, can be separated into its parts.

Let

where

Et =^ Em + Eg + E-^ + En

£( = total system error. £m = error in measuring system. This can be

subdivided into those errors due to the

scale and those due to lack of resolution in the projection equipment.

Scale error = 0.001 db for 0<.4<60 db, 0.002 db for 60<.i <120, 0.003 for 120<.4 <180 db.

Resolution error is somewhat less than 0.001 db for any value of A

.

= errors due to uncertainties in values of guide

diameter, guide conductivity, and temperature

effects. As indicated previously, this is well

within 0.001 .4/10 db.

£<(, = errors due to level changes in the phase shifter. These are known sufficiently well to leave the

uncertainties small compared to other errors. £„= errors due to the uncertainties caused by the

random fluctuations of noise. If at large values

of .1(.4^100 db) six measurements are aver- aged, the results of tests shown in Fig. 7 would

indicate reasonablv safe values of £„ to be:

En= ± 0.002 db for 90 <

= + 0.004 db for 100 <

= ± 0.01 db for 110 <

= + 0.02 = + 0.05

.4 ^ 100 db

.4 ^ 110 db

.4 S 120 db

db for 120 < .4 ^ 130 db

db for 130 < .4 < 140 db.

These could be reduced by averaging over a greater

number of measurements. The above values of £„ are

9-11
274 IRE TRANSACTIONS (

based on tlio assumption lliat the input sit^nal level to the unknown attenuator (attenuation values, A) is 1 volt. If this is raised to 3 volts:

E,/ = ± 0.03 db for 130 < .4 ^ 140 db

/':,/ = + 0.06 db for 140 < A ^ 150 db

where £,,' includes the effect of noise and the thermal

drift in the pickup coil. The cond)inc\tion ot these errors into a total error

gives:

Et = ± (^0.002 + 0.001 —^ db for 0 ^ .4 ^ 60 db

\ 10/

Et = + (0.003 + 0.001 db for 60 < .4 < 90 db

V 10/

£, = + 0.015 db for 90 < .4 ^ 100 db

N INSTRUMENTATION September

El = + 0.018 db for 100 < /I ^ 110 db = + 0.025 db for 110 < yl g 120 db

El = ± 0.037 db for UO < A ^ 130 db

El = + 0.068 db for 130 < yl ^ 140 db.

A^Min, if the 3 volt level is iisechinstead of the 1 volt:

Et = ± 0.048 db for \iO < A ^ 140 db

Ei= + 0.079 db for 140 < yl ^ 150 db.

ACKNOWLKDGMENT

Others have helped in various phases of this work and

the authors gratefully acknowledge the contributions

of the following: D. H. Russell, E. C. Wolzien, R. L. Peck, R. Barkhaus, R. Brunner, M. A. Mulligan, A. L. Schuster, P. A. Nichols, R. C. Darr, W. H. Long, and

P. L. London.

9-12
9.3 Appendix C

Complete Copy of Reference 1^.

9-13
RF Attenuation Measurements Using Quantum Interference

in Superconductors

ROBERT T. ADAIR, MICHAEL BANCROFT SIMMONDS, ROBERT ANDREW KAMPER,

CLETUS A. HOER

Reprinted by permissuin from IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT

Vol. IM-23, No. 4, December 1974, pp. 375-381 Copyright 1975 by the Institute of Electrical and Electronics Engineers, Inc. PRINTED IN THE U.S.A.

9-14
IKEK TRANSACTIONS ON INSTRUM KN TA I'ION AND MKASURKM lONT, VOI.. IM-23, NO. 4, 1)1 ;c | ;M 11 lOlt 1974 375 RF Attenuation Measurements Using Quantum Interference

in Superconductors

ROBERT T. ADAIR, MICHAEL BANCROFT SIMMONDS, ROBERT ANDREW KAMPER,

SENIOK MEMBER, IEEE, AND CLETUS A. HOER, MEMBER, IEEE

Abstract—A unique portable system has been developed for measuring RF attenuation over a dynamic range of 62 dB at 30 MHz.

A superconducting quantum interference device (SQUID) is the

basis of the system. A SQUID is a loop of superconducting metal

closed by a weak point contact called a Josephson junction, operating

in liquid helium. It converts variations in magnetic flux to periodic

variations in impedance which are sensed at microwave frequencies. This provides a convenient natural means of measuring electrical quantities such as voltage, current, power, and attenuation.

I. INTRODUCTION

A TRANSDUCER that converts variations in magnetic flux into nearly perfect periodic variations in microwave impedance which are sensed as the change in the microwave reflection coefficient is known as a super- conducting quantum interference device (SQUID).

The period of a SQUID corresponds to one magnetic flux quantum (2.067854 X IQ-'^ Wb). This provides a convenient natural means of measuring attenuation.

These devices are very accurate over a wide dynamic

range. Electrical quantities are measured by counting

periods (flux quanta) in the response of a SQUID in the same manner that length can be measured by counting

wavelengths of light emitted by a laser. Under ideal conditions, if the SQUID input current /

is an RF current, then the SQUID ouput response is the

zero-order Bessel function of the magnitude of the RF

input current. Thus the output of the microwave readout circuit is proportional to Jo{2wI/h) where / is the RF input current amplitude and U is the current necessary to drive one quantum of magnetic flux into the SQUID. U need

not be known to make attenuation measurements. The

values of the argument 2-wI/Iq at the flux quanta nulls or zeros can be found in a table of Bessel functions. A

single measurement system can be used to measure attenuation from dc to 1 GHz \w\ih. accuracies comparable to

existing conventional techniques. Several successful prototype measurement systems have been constructed at the

National Bureau of Standards based on the SQUID [1].

The major advantages of this new technique for measuring RF attenuation include the following.

Manuscript received July 3, 1974; revised AuKust 19, 1974. This

paper is a contribution of the Nati(mal Bureau of Standards and is not subject to copyright.

The authors are with the Institute for Basic Standards, National Bureau of Standards, Boulder, Colo.

1) The relative ease of construction of the system, e.g., the accuracy of the measurements does not depend on

high precision machining of mechanical parts such as in waveguide below cutoff attenuators.

2) The system does not require a standard of attenuation. It requires only a table of Bessel functions to deter- mine the exact change in attenuation between any two

given flux quanta nulls. 3) This technique provides a broad frequency range of operation without tuning (0-1 GHz in one system).

4) The readout technique makes it relatively easy to automate measurements with this system.

II. SQUID DETAILS

A. Principle of Operation

The basic SQUID system configuration is shown in Fig. 1, where I, represents the Josephson current and /

represents the input current. In addition to the usual leakage and displacement

currents that flow through any metallic contact, a Josephson junction passes a component of current (the "Josephson current") which is controlled by conditions in the

superconductors on either side of the junction. If the

superconductors are connected together to form a loop

closed by the junction, then the Josephson current depends upon the magnetic flux <j) linking the loop

Is = /csin (27r</)/</)o). (1)

Ic depends only on the strength of the particular contact. The quantity </)o is a fundamental constant of nature

known as the flux quantum

00 = h/2e = 2.0678538 X lO-'^T-m^ (2)

where h is Planck's constant and e is the charge on the

electron. This arrangement of a small superconducting loop

closed by a Josephson junction is the basic form of the

SQUID. Since this device is the heart of the whole system, we will analyze its properties a little further, following

Silver and Zimmerman [2].

The total magnetic flux 4> linking the loop is the sum

of two terms

</. = + Lis (3)

where is the flux from some external source driving

9-15
376 IKKK IHANSACTIONS ON INSTKUM KNTATIUN ANU M IJASUREM KNT, DKCKMBKR 1974

the device and L is the inductance of the loop. Strictly

speaking, the current in (3) is the total current (including leakage, etc.) flowing through the junction. However, squid's are usually designed so that the Josephson

current (1) is the dominant term; thus we may obtain an approximate understanding of the action of the device

by neglecting the other contributions to the current. We

may therefore combine (1) and (3)

:

SUPERCONDUCTING LOOP AND JUNCTION

4> = 4>x + Lie sin {'2tr(i> /4>o)

or, alternatively,

L = h sin [27r(</), + LL)/4>,'].

(4)

(•"))

Inspection of (")) shows that the current 1^ has a periodic dependence on the external magnetic flux </)j. If we

add any whole multiple of </)o to </)x, the sine function is unchanged and therefore the current Is is unchanged also. Remembering that the E]\IF V around the loop is just

d4> (It, we can see that the device presents a nonlinear

impedance to alternating current which is also a periodic

function of the applied magnetic flux c^^. The standard technique for using a SQUID as a sensor

of magnetic flux is to monitor this variation in impedance

by coupling the device inductively to a readout circuit operating at some convenient radio frequency, as shown

in Fig. 1 C2]-[4]. (These references give the details of readout circuits operating at 30 MHz and the output signals that can be obtained). In any circuit with stable geometry the magnetic flux </)j is proportional to the current /. The flux quantum is therefore a natural repeating

unit with which to measure current. The periodic response

of the impedance of the SQUID to variations of magnetic

flux driven by the current / in this circuit is monitored by

a microwave system which detects variations in the micro- wave reflection coefficient of the SQUID.

The basic response of a SQUID system to the current

to be measured is displayed in Fig. 2. This is an oscillo- scope display obtained with a slowly varying current /. Monitored in this way, the periodic response of the SQUID

to magnetic flux has degenerated into a simple and re- markably pure .sine function.

When the input current / is an RF current, the system

records an average f)ver a .segment of Fig. 2. The width of the segment is determined by the amplitude of the RF

current, and its location can be moved by simultaneou.sly

applying a dc bias current. As the amplitude of the

RF current varies, this averaged response reflects the

basic periodicity of the SQUID. This is shown in Fig.

3, which is an oscilloscope display obtained by applying a slow amplitude modulation to an RF current at

6.") MHz applied to the SQUID. In the approximation, the

basic re.spon.se to current shown in Fig. 2 is a sine function

sin (27r///ii), and the averaged response to RF current shown in l-'ig. 3 can be .shown to be the zero-order Bessel

junction ./o(27r///o) [1]. In both expressions /„ is the

current required to drive one (juantum of magnetic flux into the SQUID. It may be determined with a single

MICROWAVE READOUT

CIRCUIT

FiK- 1. Basic SQUID system, defining components and currents.

Fig. 2. Basic microwave reflection coefficient response to slow- variations in input current /.

Fig. 3. Averaged microwave reflection coefficient response to a slowly modulated RF input current /.

measurement using dc. Notice that the frequency does not enter explicitly into these expressions.

B. Physical Configuration

Figs. 4 and ") show a drawing and a photograph, re- spectively, of the L-band SQUID used in this work. It is a reentrant cavity that resonates at 1.2 GHz with a loaded

Q of about 2"). The coffin-like shape was chosen to facili- tate packing multiple SQUID's into a confined space in a small cryostat. The microwave readout system contains

L-band components connected via oO-fi coaxial line. It is critically coupled to the cavity of the SQUID. The

signal at 30 ]\IHz to be measured is coupled in via a 3- turn coil terniinated by a oO-fi load connected directly to the S(^UII). It re(|uires 10 //.\ to induce a magnetic flux of one (juantuni. We chose this value of Iq for a convenient

power level for measuring attenuation; it can be adjusted over a range of about 20 dB by changing the number of

9-16
ADAIR el a}.: RF AITKNUATION MKASURKMIONTS 377

Induclonoe Region of Covity

CopocitoDce Region

of Cavity

Signol Coil

, ft)int Contoct

SECTION A-A

2S/^m Dieleclnc Filled Gop Fixed Niobium Screw

tot Oottom

Point

- Ad)ust.-nent Port

Fig. 4. Resonant L-band SQUID. This is a reentrant cavity with

the point contact and the microwave coupling placed at points chosen to match impedances.

Fig. 5. Resonant L-band SQUID, showing RF input coupling coil and connection for microwave drive.

turns on the coil. This SQUID generates readout signals

close to the theoretical optimum power (2 pW).

The two halves of this SQUID are made of solid Babbitt

alloy (4.0-percent Sn, lO.o-percent Sb, and 85-percent Pb)

for ease of fabrication. It is superconducting at approximately 8 K. The finished SQUID must resonate within

the passband of the readout circuit at 1.2 GHz. This can

be accomplished by trimming the metal parts or the dielectric spacer. This SQUID was machined by a computercontrolled milling machine.

The SQUID is assembled by bolting the two halves

together. The joint is then sealed (electrically) with

Rose's metal (50-percent Bi, 25-percent Pb, 25-percent

Sn) applied with a soldering iron with no flux. Three SMA connectors are soldered to the body of the

SQUID with Rose's metal which is superconducting at

approximately 8.5 K. Two of these are wired to the signal

coil, while the third, which carries the L-band drive, is connected across the dielectric (polyimide plastic) gap

to the opposite side of the cavity. This is most conveniently done by attaching a copper pin to the center con- ductor of the SMA connectors. and pressing a matching

socket into the lid of the SQUID. A suitable socket may

easily be obtained by taking the center conductor out of a

female SMA connector. The point contact is between a sharp-tipped 0.8-mm

UNM screw and a plated niobium foil, 1 mm by 2 mm

by 0.02 mm, both plated with a Pt-W alloy, as illustrated in Fig. 6. The niobium foil is spot welded to a 2-56 NC

niobium screw. This passes through the lid of the SQUID

and should be held in place by a lock nut. The small

0.8-mm niobium screw passes through the main body of the SQUID. The far end is flattened to the shape of a

screwdriver, which engages with a removable adjusting

rod in a guide tube passing out through the top plate of

the cryostat. A small leaf spring takes up the backlash of

the screw when the drive is disconnected.

These junctions can survive electrostatic discharges

100 times greater than that which would burn out an

uncoated (unplated) point contact of the same configuration. They behave electrically like an uncoated point

contact with a shunt resistance of about 0.1 9.. This does

not noticeably degrade the readout signal obtainable from

squid's at frequencies ranging from 30 AIHz to 9 GHz.

It brings the bonus of a tendency to increase the purity of the sine-functional form of the basic response shown in

Fig. 1, thereby improving the convenience and accuracy

of RF measurements with these devices [1].

III. MEASUREMENT SYSTEM

The system as shown in Fig. 7 can be used to measure

variations in attenuation with no conventional calibration

standard. A stable signal generator is connected to the

SQUID through the variable attenuator under test. The SQUID is inductively coupled to the center con- ductor of a 50-fl coaxial line, which passes through the

SQUID. Variations in the current flowing in this line cause variations in the magnetic flux linking the superconducting loop formed by the Josephson junction and the

end of the cavity. Because of quantum mechanical interference, the microwave reflection coefficient of the device

is sensitive to these variations in magnetic flux. For

attenuation measurements, one end of the coaxial line is terminated with a 50-ft load, and the other is connected

to the RF system on which measurements are to be made.

Fig. 7 shows the basic layout of the components used

to realize this system. The microwave system is driven

by an Z/-band signal generator delivering a few nanowatts

of power to the 20-dB directional coupler. The power level at the SQUID is therefore of order lO^'i W. The reflected microwave signal is amplified by a solid-state amplifier,

with a gain of about 50 dB, and rectified by a crystal

diode detector. This millivolt level signal is applied to the lock-in detector, where it is amplified to an operating

9-17
378 IKKK TRANSACTIONS ON INSTRUM KNTATION AND M lOASURKMKNT, UKCKMBKR 1974

Nb Screw

Sputter Coated Surfaces

Configuration of Coated

Contact Junction

Fig. 6. Stabilized point contact. This is a spring-loaded contact between niobium parts plated with a Pt-W alloy. Fig. 8. System for automatic counting of nulls and interpolation between nulls.

St MHI SICUL SOUICE

SICIU U»El

COITIOl CIICUIT

IIICCEI

CIICUIT

lOO-ll KIECTO

•ITN

•ULL KDIMIM

L IMO UPUriEt

IIIK ClltSIH DEIECIOR

iriEiuiioi

UIOCI

TEST o SOUlO o*

If IIPIJI ^

aoniLiiioi 1 DC HIS

fllH LOf nSS FILTEI

L-KIO OSCIIUTOK

J

!(l It y COUHEI

mClOIHE DIKE IIPIII

Fig. 7. Basic system for measuring RF attenuation showing

modular packaging.

level of a few volts. An oscilloscope is used to monitor the

dc bias and modulation levels in the SQUID. The modulation is a 1-kHz sine wave. Modulation and dc bias are applied to the SQUID via a low-pass filter connected to the RF line. This must pass the bias and modulation,

but present at least 60 dB of attenuation to signals at 30 MHz. The high degree of attenuation is required to prevent crosstalk between the microwave and measuring

channels: some of the low-frequency components are mounted in common boxes, which presents possible paths

around the attenuator under test. Bias and modulation

levels are of the order of 10-^ A at the SQUID.

The 30-MHz source is a crystal-controlled solid-state

oscillator. An amplifier of comparable stability raises this level to the maximum permitted by the attenuator under test. All connections are made with semirigid coaxial line (with solid conductors) or double-shielded

flexible coaxial line (with braided conductors). With

this precaution and some care with connectors, leakage

does not appear to be a significant problem.

The null indicator on the lock-in detector is used to

locate the nulls of the response function Jo{2wI/Io) as the attenuator under test is adjusted. The system is set on a sequence of these nulls, and the reading of the attenuator dial is noted at each null. The dial readings are then

compared with attenuation ratios calculated with a table

of Bessel functions.

To eliminate the tedious task of counting the nulls visually by watching the null indicator, a semiautomatic

system was devised for counting the nulls, as well as inter- polating between them. This system is shown in Fig. 8. Nulls are counted by a counter, driven by the lock-in

detector in the L-band readout system, as the incident

power is slowly reduced from the working level to a very

low level. The incident power is then restored to its working level and a servo loop is closed to lock it to the

nearest null. The servo voltage is measured by a digital

voltmeter, which can be calibrated against the corre- sponding small change in power level ^\ith sufficient ac- curacy for interpolation between nulls. The circuit for controlling the power level was developed after trying

several commercial voltage-variable attenuators and

modulators, which were rejected because of their high

insertion loss and inconvenient control voltage characteristics. This circuit is also shown in Fig. 8. It consists of a well-balanced 180° hybrid junction with a field-effect transistor acting as a variable termination on one of the

side ports.

When the gate of the transistor is held at ground potential, the two side arms of the hybrid junction are extremely unbalanced, so their reflections combine constructively and the device transmits power with less than

3-dB attenuation. When a large negative bias is applied

to the gate of the transistor, its conductance is shut off' and it presents an impedance consisting mainly of the

capacitance between channel and gate. This is balanced

by a small capacitor terminating the opposite port, so that the two signals cancel and the transmitted RF power

is attenuated by 60 dB. At intermediate bias levels there

is a convenient linear relationship between bias voltage

and transmitted RF voltage over a large part of the range

9-18
ADAIR et al.: rf Ai-rKNt'Ai'ioN mioashrkmionts 379

Fig. 9. Complete 3()-MHz attenuation measurement system in- cluding the attenuator under test.

of attenuation, enabling nulls in the response of the SQUID

to be counted at a steady rate when the bias voltage on

the gate of the transistor is varied as a simple linear function of time. Because of the high RF level (0.25 W), the

transistor does draw significant gate current, which in- troduces harmonic distortion at intermediate bias levels. However, this does not appear to interfere with counting,

and precise settings are always made with the gate at ground potential (i.e., the condition of maximum RF sig- nal transmission) . The servo loop to interpolate between

nulls does not yet function satisfactorily, and refinement

of the frequency response will be required to minimize the

noise in the system before we will be able to evaluate the

accuracy of interpolation.

The cryostat [5] is made of glass, with two copper

radiation shields in the vacuum space between the inner

and outer walls. These shields are attached to the inner

wall near the neck, so that the escaping helium gas cools them. The interstices between them and the walls are

filled with several layers of aluminized polyester film, for additional radiation baffles. Xo liquid nitrogen cooling

jacket is required. Starting with a warm system, a day's

running including the initial cool down requires about 2 1 of liquid helium. Fig. 9 shows the complete compact

system.

IV. ATTENUATION MEASUREMENTS

This system is capable of matching the accuracy of existing methods of measuring attenuation at 30 MHz

such as the National Bureau of Standards (NBS) Calibration Service using a piston attenuator. However,

achieving this accuracy requires careful attention to setting

the optimum operating conditions.

The basic source of systematic error is a deviation in the response of the SQUID and its readout circuit to RF

current from the simple form Jn(2ivI/Io) . This is caused

by harmonic distortion of the simple sinusoidal response

of the system to direct current. The complete distortion

analysis is found in Section VI. A routine has been developed for initial adjustment of

th(; system to minimize systematic errors. A minicomputer

has been prf)grammed to analyze experimental data and

list and plot the results of calibration runs.

The procedure for system setup is as follows.

1) Adjust the contact pressure at tin; Josephson junction until maximum signal occurs at a microwave power

level not exceeding —80 dBm at the SQUID.

2) Adjust the dc bias level and make fine adjustments

to the microwave power level until the reflected micro- wave signal appears exactly symmetrical on an oscillo- scope display such as Fig. 2. Tests with a spectrum analyzer have shown that this has the effect of eliminating

even-order (i.e., second, fourth, etc.) harmonic distortion.

3) With a digital ac voltmeter, observe the modulation

depth which just nulls out the desired signal and set the

modulation depth at exactly one-third of that level. This nulls out the effect of third harmonic distortion.

After using this procedure, the systematic errors in measurements with the system are usually less than

± 0.01 dB at the first null, less than ± O.OOo dB at the

second null, less than =b 0.003 dB at the third null, and

negligibly small (compared with random setting errors) thereafter. Errors exceeding these amounts can usually

be traced either to external interference or to violation

of one of the rules in the setup procedure. Random errors have been consistently less than ± 0.002 dB rms. Measurements were extended to cover the first 900

nulls in the response of the SQUID system which provides

a dynamic range of nearly 62 dB. The accuracy obtainable with the last 800 nulls appears to be as good as \\-ith the first 100. The tedium of counting was eliminated by

using an electronic system to count from one measured

setting to the next. For the greatest accuracy, the first and second nulls in the response of the SQUID system can be ignored, at the

sacrifice of 11 dB in dynamic range. The remaining 898

nulls would then cover a dynamic range of 50 dB with

confidence that systematic errors are less than ± 0.002 dB.

The procedure for calibrating an attenuator is to note

the readings on its dial corresponding to a sequence of

nulls of the response of the SQUID. A simple computer

program compares these readings with attenuation ratios

calculated from a table of Bessel functions and prints out the deviations.

V. MEASUREMENT RESULTS

An NBS model VII piston attenuator was used for testing this SQUID system. This attenuator was first calibrated by the NBS Calibration Service and then used

in a series of tests with the new SQUID system. With

everything adjusted properly, the results illustrated in

Fig. 10 were obtained. This is a plot of the deviation from

actual attenuation versus dial setting for the piston

attenuator, representing the results of the average of three separate calibration runs on each system. The dots

represent measurements made with the SQUID, while

the crosses at 5-dB intervals represent the information

supplied by the NBS Calibration Service. The estimated

limits of error of the NBS Calibration Service [6] are represented by divergent lines that are drawn symetrically with respect to the abscissa for convenience. These

9-19
380 IKKK TRANSACTIONS ON INS'l'RU M |;NTATI0N AN'I) mkasurkmknt, ukckmbkr 1974

0 10 20 30 40 50 60 ATTENUATOR SETTING. dB

Fig. 10. Comparison of the calibration of a variable attenuator

using the SQUID system (dots) with the NHS Calibration Service

(crosses). The solid lines represent the estimated limits of error

of the NBS Calibration Service.

lines illustrate the relationship between the measurement

results and the error limits. The average rms deviation of the first three measure- ments at each point taken by the NBS Calibration

Service was =b 0.0011 dB. The rms deviation of the meas- urements taken with the SQUID from a smooth curve

draAMT. through the calibration points was =t 0.0017 dB,

the major contribution coming from the last two points

at high attenuation. These correspond to the first and sec- ond nulls of the response of the SQUID, which are the

most prone to errors due to harmonic distortion. On the

other hand, the power level in the NBS calibrating system

is raised at 50 dB to a higher level for measuring high

attenuation. This is known to increase the systematic

error in the range above 50 dB. Apart from these considerations based on previous knowledge of the idio- syncrasies of the two systems, the difference in scatter between the +wo sets of measurements is not statistically

significant in such a small number of samples.

The most obvious feature of Fig. 10 is the large dis- crepancy between the estimated limits of the systematic

error of the NBS calibration and the degree of agree- ment between the two entirely independent methods of measuring attenuation. Clearly, the estimated errors are very conservative, but so long as one accepts them it is difl^cult to say which system is testing which. We hope

that after further careful comparison of measurements

made by the two systems it will be possible to revise the

estimate of errors and issue reports of calibration giving

better justice to the quality of the measurements that are actually made.

VI. ANALYSIS OF SYSTEMATIC ERRORS

The measurements described are based on the assumption that the instantaneous response of the microwave

.system to current through the SQUID has the pure

sinusoidal form expressed in (G),

P = Pn + Pi cos (27r///o) (6)

where P is the microwave power reflected from the SQUID.

Let us nf)W entertain the notion that this is not a perfectly accurate assumption [7].

First, we replace (6) by

P = Po + E cos {2irnl/h) (7)

n

to allow for harmonic distortion of the response. Next, we recognize that the current / has several components,

I = Ib + Im sin (2x/jw0 -|- h cos (2ir/0. (8)

The first term is the dc bias, the second term is the

modulation {/m = 1 kHz), and the third term is the RF

input to be measured (/ = 30 MHz for the measure- ments reported in the previous section). Combining

(7) and (8) , and taking a time average over the excursions

of the RF component Ii, we find that the amplitude Vm

of the voltage presented to the lock-in detector at fre- quency /.w is Vm = 2GZPnSm {2TmlB/h)Ji{2irnIm/h)J,{2imh/h)

n

(9)

where G is the response of the microwave crystal rectifier (in volts per watt)

.

Inspection of (9) reveals that the effect of harmonic

distortion of the basic response of the system [(7) ] on the

time-averaged response to RF current is to mix in some

zeroth-order Bessel functions of multiple argument. The

coefficients of these extra terms are functions of both the

dc bias level and the depth of modulation, so we can manipulate them by a proper choice of these parameters.

In practice we observe that the leading term P2 appears

to dominate the distortion, and this can be eliminated

exactly by setting Ib = 0.25/o and h, =-- 0.305/o. The

presence of this distortion can be detected immediateljbecause it affects the odd and even null points differently. In particular, a small second harmonic distortion moves

the odd and even null points by approximately equal

amounts in opposite directions. This will become obvious on a plot similar to Fig. 10, since the odd and even null points will separate into distinct branches.

We always observe some distortion of this kind, and

adjust the bias level and modulation depth to null it out. The results displayed in Fig. 10 give us confidence that

when the odd and even nulls are consistent with each

other this source of error is essentially eliminated.

The other prime source of systematic error lies in the

relationship between the RF current to be measured and

the magnetic flux to which the SQUID actually responds.

This depends upon a geometrical factor, which may be

perturbed by variations in the distribution of the electro- magnetic field with changes in frequency and (to a much

smaller extent) intensity. One major advantage of super- conducting metals is that the penetration depth for electro- magnetic fields is small (--^10"' m) and insensitive to frequency through the radio and microwave range. The

penetration depth is also slightly sensitive to the intensity

of the field, but this effect is negligible at the level of precision of most measurements at radio frequencies. At

frequencies sufficiently high so that the linear dimensions

9-20
l^:^:K rRANSAc riONS on ins i'rumiinta tion and mkasuhiomiont, V()i> iM-23, NO. 4, i)i;(,'i:Miti;H 1!)74 381

of the SQUID beconu' a significant fraction of the wavelength, it is necessary to consider the effect of standing waves on the distribution of the fields. This may become

significant for measurements with swept frequency ex- tending into the low microwave range. Corrections to a

calibration performed \\'ith direct current are calculable

and would be of the order of 1 percent at 1 GHz. These

corrections do not affect measurements of attenuation

conducted at a fixed frequency.

VII. CONCLUSIONS

We have shown that, over a dynamic range of G2 dB,

a SQUID can be used to calibrate an attenuator in agree- ment with the NBS Calibration Service to within ±0.002

dB rms. The measurements were made at 30 MHz because

the piston attenuator used as a transfer standard is a narrow-band device. The SQUID could be used equally

well at any frequency from zero to over 1 GHz [8].

We believe that when this system is fully developed it will be a strong contender for the position of primary

standard of attenuation. This work is continuing, with the

aim of making further refinements and extensions of these

systems.

ACKNOWLEDGMENT

The authors wish to thank their colleagues, N. V.

Frederick, J. E. Zimmerman, and D. B. Sullivan for their

contributions to this work.

REFERENCES

[1] R. A. Kamper, M. B. Simmonds, C. A. Hoer, and R. T. Adair, "Measurement of rf i)ower and attenuation using superconductiiiK quantum interference devices," Nat. Hur. Stand., Tech. Note 643, pp. 12-(j3, Aug. 1973.

[2] A. H. Silver and J. E. Zimmerman, "Quantum states and transiti<ins in weakly connected superconducting rings," Phys. Rev.,

vol. 157, no. 2, p. 317, 1<)67.

[3| J. E. Zimmerman, P. Thiene, and J. T. Hardmg, "Design and

oi)eration of stable rf-biased superconducting point-contact

quantum devices and a note on the properties of perfectly clean metal contacts," J. Appl. Phys., vol. 41, no. 4, p. 1572, 1970.

[4] D. H. Sullivan, "Superconducting quantum interference devices: An operational guide for rf-hiased systems," Nat. Bur. Stand., Tech. Note 029, pp. 3-10, Nov. 1972.

[5) J. E. Zimmerman and J. D. Siegworth, "Portable helium dewars

for use with superconducting magnetometers," Cryogenics, vol.

13, p. 158, 1973.

[6] "Calibration and test services of the National Bureau of Standards," Nat. Bur. Stand., Spec. Publ. 250, Dec. 1970.

[7] R. A. Kamper, M. B. Simmonds, R. T. Adair, and C. A. Hoer "Quantum mechanical measurement of RF attenuation," Proc. 1972 Applied Superconduclivily Conf., pp. 696-700.

[8] , "A new technique for RF measurements using super- conductors," Proc. IEEE (Lett.), vol. 61, pp. 121-122, Jan. 1973.

9-21
9.4 Appendix D

Excerpts from Reference

9-22
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NBS-n4A (REV. 2-8C) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS SP-250/32

2. Performing Organ. Report No 3. Publication Date

April 1988

4. TITLE AND SUBTITLE ^^gg Measurement Services:

A Calibration Service for 30MHz Attenuation and Phase Shift

5. AUTHOR(S)

Robert T. Adair and David H. Russell

6. PERFORMING ORGANIZATION (If joint or other than NBS, see ;n struct/on sj NATIONAL BUREAU OF STANDARDS

U.S. DEPARTMENT OF COMMERCE

GAITHERSBURG, MD 20899

7. Contract/Grant No.

8. Type of Report & Period Co-zered Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Same as item #6 above.

10. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 88-600527

Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual sumnnary of most significant information. If document includes a significant

bi bliography or literature survey, mention it here) A calibration service currently being offered by NBS for attenuation and phase shift

at 30 MHz is described. The service offers measurements on coaxial attenuators that are either fixed (standard attenuation) or variable for incremental (step) attenuation. Waveguide-below-cutof f variable attenuators with coaxial connectors are also

calibrated for incremental attenuation. Ranges of capabilities and estimated limits

of systematic and random uncertainty are presented.

Calibration of phase shifters which provide fixed (insertion) phase shift and those

with variable phase shift (phase shift difference) is described. Ranges of phase

shift and estimated limits of uncertainty are given in degrees. However, a smaller

portion of this document is devoted to this calibration service since it is requested

only infrequently.

Definitions, capabilities of the system and techniques of calibration are given. The

standards, measurement uncertainties, results from intercomparisons quality assurance

and statistical control of the system are discussed and analyzed. Representative

reports of calibration are also included.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolonsj

attenuation; calibration; coaxial; incremental; phase shift; standard; step;

uncertainty ; waveguide-below-cutof f

.

13. AVAILABILITY

Unl i mi ted

I I For Official Distribution, Do Not Release to NTIS

^j]] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

[^31 Order From. National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

184

15. Price

USCOMM-DC 6043-P80
.1 i
THE SP 250 SERIES ON NBS MEASUREMENT SERVICES*

SP 250-1

SP 250-2

SP 250-3

SP 250-4

SP 250-5

SP 250-6

SP 250-7

SP 250-8

SP 250-9

Spectral Radiance Calibrations SN003-003-02792-8 $3.50

Far Ultraviolet Detector Standards SN003-003-02810-0 $4.25

Radiometric Standards in tlie Vacuum

Ultraviolet SN003-003-02806-1 $6.50

Fricke Dosimetry in High-Energy Electron Beams

SN003-003-02816-9 $2.75

Alpha-Partide Calibrations SN003-003-02823-1 $2.00

Regular Spectral Transmittance SN003-003-02805-3 $3.25

Radiance Temperature Calibrations SN003-003-02827-4 $2.25

Spectral Reflectance SN003-003-02812-6 $7.00

Calibration of Beta-Partlde-Emitting

Ophthalmic Applicators

SN003-003-02817-7 $2.00

SP 250-10 Radioactivity Calibrations with the "4^"

Gamma Ionization Chamber, and Other

Radioactivity Calibration Capabilities

SN003-003-02824-0 $2.25

SP 250-1 1 Dosimetry for High-Dose Applications

SP 250-12 Neutron Personnel Dosimetry

SN003-003-02811-8 $2.50

SP 250-13 Activation Foil Irradiation with Californium Rssion Sources

SP 250-14 Activation Foil Irradiation by Reactor Cavity

Rssion Sources SP 250-15 Photometric Calibrations SN003-003-02835-5 $4.25

SP 250-16 Calibration of X-Ray and Gamma-Ray

Measuring Instruments

SP 250-17 The NBS Photodetector Spectral Response

Calibration Transfer Program

SP 250-18 Neutron Source Strength Calibrations

SP 250-19 Calibration of Gamma-Ray-Emttting

Brachytherapy Sources

SP 250-20 Spectral Irradiance Calibrations SN003-003-02829-1 $5.50

SP 250-21 Calibration of Beta-Partide

Radiation instrumentation

SP 250-22 Platinum Resistance Thermometer

Calibrations SN003-003-02831-2 $17.00

SP 250-23 LIquid-in-Glass Thermometer

Calibration Sen/ice

SP 250-24 Standard Cell Calibrations SN003-003-02825-8 $2.75

SP 250-25 Calibration Sen/ice for Inductive Voltage Dividers

SP 250-26 Phase Angle Calibrations

SP 250-27 AC-DC Difference Calibrations

SP 250-28 Solid-state DC Voltage Standard Calibrations SN003-003-02842-8 $2.00

SP 250-29 Traceable Frequency Calibrations SN003-003-02844-4 $2.25

SP 250-30 GOES Satellite Time Code Dissemination:

Description and Operation

SN003-003-02845-2 $2.75

SP 250-31 Mass Calibrations at the National Bureau

of Standards SP 250-32 A Calibration Service for 30 MHz

Attenuation and Phase Shift SP 250-33 A Calibration Sen/ice for Voltage Transfomiers and High-Voltage Capacitors

•Those entries containing a stock number (003-003 ) and price can be purchased from the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402. GPO will accept checks, money orders, VISA, and Mastercharge. For more information, or to place an order, call (202) 783-3238. Be sure to use the stock number In all orders. Titles without stock numbers are In preparation.
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Stimulaling America s Progress

1913-1986