NBSIR 77-863

RF ATTENUATION MEASUREMENT SYSTEM USING A SQUID

Electromagnetics Division

and Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

September 1977

Robert T. Adair

Nolan V. Frederick

Donald B. Sullivan

Prepared for

Army/Navy /Air Force

Calibration Coordination Group

NBSIR 77-863

RF ATTENUATION MEASUREMENT SYSTEM USING A SQUID

Robert T. Adair

Nolan V. Frederick

Donald B. Sullivan

Electromagnetics Division

and Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

September 1977

Prepared for : Army /Navy /Air Force

Calibration Coordination Group

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director
IMPORTANT NOTICE

Certain commercial equipment is identified in this report. This identification

does not imply endorsement by the National Bureau of Standards nor does it imply

that the equipment identified is necessarily the best available for the purpose.
CONTENTS

Page

1. GENERAL INFOR>IATION 1-1

1.1 Introduction 1-1

1.2 Specifications 1-2

1.3 Description 1-3

1.3.1 Description of SQUID Control Unit 1-6

1.3.2 Description of SQUID Readout Unit 1-7

1.3.3 Description of the SQUID Signal Processing Circuits 1-26

1.3.3.1 The 1-GHz Biasing Circuit 1-26

1.3.3.2 The 1-kHz Zero Detecting Circuits 1-33

1.3.3.3 The 2-kKz Phase Sensitive Detector Circuits 1-33

1.3.3.4 The Counter-Pulse Generating Circuits 1-33

1.3.4 Description of the SQUID 1-34

1.3.5 Description of the Cryogenic Vessel 1-42

2. THEORY OF OPERATION 2-1

2.1 General Information 2-1

2.2 Principle of SQUID Operation 2-1

2.3 Detailed Analysis of SQUID Operation Theory 2-4

2.4 Theory of the SQUID Measurement Process 2-8

2.5 Attenuation Measurements Using the SQUID System 2-9

2.6 Bessel Function Zero (Null) Counting Techniques 2-12

3. OPERATING PROCEDLUE 3-1

3.1 General 3-1

3.2 System Components 3-1

3.3 Connectors, Controls, and Indicators 3-1

3.4 Preparation for Use 3-10

3.5 Preliminary Setup and Adjustments 3-12

3.6 Operating Procedure 3-13

3.6.1 Introduction 3-13

3.6.2 Calibration of a Variable Attenuator 3-13

3.6.3 Calibration of a Fixed Attenuator 3-15

3.6.4 Reduction of Calibration Data 3-15

3.7 Data Reduction 3-15

3.7.1 Data Reduction Using a Table of Bessel Functions 3-15

3.7.2 Data Reduction Using Calculated Bessel Function Values 3-25

3.7.3 Data Reduction Using a Programjnable Calculator 3-26

iii
CONTENTS (Continued)

4. ERROR ANALYSIS OF THE SYSTEM 4-1

4.1 General Information 4-1

4.2 Systematic Errors 4-1

4.2.1 Harmonic Distortion — 4-1

4.2.2 Phase Sensitive Detector Errors 4-3

4.2.3 Null Meter Offset • 4-4

4.2.4 RF Leakage 4-6

i' 4.2.5 External rf Noise 4-6

' 4.2.6 SQUID Control and Readout Units 4-8

4.3 Random Errors—• 4-8

4.3.1 The Device Under Test (DUT) 4-8

4.3.2 SQUID Control and Readout Units 4-9

4.3.2.1 RF Source and Amplifier 4-9

4.3.2.2 Coaxial Switch (Set-Run relay in rf signal path) 4-9

4.3.3 Phase-Sensitive Null Detector 4-9

4.3.4 RF Leakage— 4-9

4.3.5 Noise 4-9

4.4 Total System Uncertainty — 4-10

5. CONCLUSIONS 5-1

6. ACKNOWLEDGMENTS 6-1

7. REFERENCES 7-1

8. COMPONENT INFORMATION • 8-1

9. APPENDIX A. FREQUENCY SPECTRUM FROM THE SQUID 9-1

10. APPENDIX B. CIRCUIT DIAGRAMS AND COMPONENT DETAILS 10-1

11. APPENDIX C. SYSTEM OPERATION AT OTHER FREQUENCIES . 11-1

Iv
LIST OF FIGURES

Page

Figure 1.1 The SQUID attenuation measurement system 1-4

Figure 1.2 Block diagram of attenuation measurement system 1-5

Figure 1.3 SQUID control unit 1-8

Figure 1.4 DC and 1-kHz circuits (for bias and detection) contained in the SQUID

control unit 1-9

Figure 1.5 Block diagram of the dc and 1-kHz bias circuits and 1-kHz and 2-kHz

phase sensitive detectors 1-10

Figure 1.6(a) Schematic diagram of dc and 1-kHz bias circuits and 1-kHz phase

sensitive detector 1-11

Figure 1.6(b) Schematic diagram of dc and 1-kHz setup controls 1-12

Figure 1.7 Microwave bias components contained in the SQUID control unit 1-13

Figure 1.8 Block diagram of microwave bias (1 GHz) circuits 1-14

Figure 1.9(a) Schematic block diagram showing power supply connections for SQUID

bias (1 GHz) components 1-15

Figure 1.9(b) Schematic diagram of ultra stable dc supply for microwave components— 1-16

Figure 1.10 SQUID readout unit 1-17

Figure 1.11 Front view of rf signal source and null indicator portion of the

SQUID readout unit 1-18

Figure 1.12 Top view of rf signal source and null indicator unit containing (left

to right) the power supplies, the 2-kHz phase sensitive detector, the

count generating circuits, the 1-kHz phase sensitive detector, and the

rf signal source 1-19

Figure 1.13 Top view of rf signal source and null indicator main frame showing

power supplies 1-20

Figure 1.14 Rear view of rf signal source and null indicating unit showing rear panel connectors 1-21

Figure 1.15 30-MHz plug-in module showing output level adjust components 1-22

Figure 1.16 Front view of rf source module 1-23

Figure 1.17 Top view of rf source module 1-24

Figure 1.18 RF output level control characteristic curve 1-25

Figure 1.19 Front view of the 2-kHz phase sensitive detector plug-in 1-27

Figure 1.20 Side view of 2-kHz PSD plug-in 1-28

Figure 1.21 Schematic diagram of 2-kHz bandpass amplifier and phase sensitive

detector 1-29

Figure 1.22 Front view of null indicator plug-in 1-30

V
LIST OF FIGURES (Continued)

Page

Figure 1.23 Side view of null indicator plug-in • 1-31

Figure 1.24 Schematic diagram of null indicator and null counting trigger circuits 1-32

Figure 1.25 Illustration showing the operation of the pulse generating circuit

which activates the digital counter to indicate the Bessel function

zero number 1-35

Figure 1.26 Side view of SQUID 1-36

Figure 1.27 End view of SQUID 1-37

Figure 1.28 View of SQUID probe assembly 1-38

Figure 1.29(a) Diagram of SQUID cartridge with permanent point contact 1-39

Figure 1.29(b) Diagram of SQUID body containing cartridge 1-40

Figure 1.30 Voltage versus current characteristics of a SQUID point contact

cartridge with a 10 microampere critical current 1-41

Figure 1.31 Schematic diagram of SQUID circuit 1-43

Figure 1.32 Plot of measurement results using high critical current cartridge

and insufficient reference level on double-balanced mixer 1-44

Figure 1.33 Plot of measurement results with insufficient reference level on double-balanced mixer 1-45

Figure 1.34 Calibration curve fit to data taken on variable attenuator and plotted

with computer 1-46

Figure 1.35 Interpolation between calibration points using computer curve fit

shown in figure 1.34 1-47

Figure 1.36 Liquid helium storage vessel 1-48

Figure 2.1 Basic SQUID system configuration • 2-1

Figure 2.2 SQUID response to current 2-3

Figure 2.3 SQUID averaged response to rf current 2-3

Figure 2.4 Response to microwave biased SQUID 2-6

Figure 2.5 Relative sideband amplitudes of the SQUID response — 2-7

Figure 2.6(a) Basic block diagram of the SQUID attenuation measurement system 2-10

Figure 2.6(b) Block diagram of the complete system 2-11

Figure 2.7 Basic block diagram of system for counting of nulLs and interpolating

between nulls 2-15

Figure 3.1 The SQUID attenuation measurement system with index numbers 3-2

Figure 3.2 Front view of SQUID readout unit with index numbers 3-3

vi
LIST OF FIGURES (Continued)

Page

Figure 3.3 Top view of SQUID readout unit with index numbers 3-4

Figure 3.4 Rear view of SQUID readout unit with index numbers 3-5

Figure 3.5 Front view of SQUID control unit with index numbers 3-7

Figure 3.6 Descriptive view of microwave bias (1 GHz) components contained in

SQUID control unit 3-8

Figure 3.7 Descriptive view of 1-kHz and dc bias circuits contained in SQUID

control unit 3-9

Figure 3.8 Sample calibration data sheet 3-16

Figure 3.9 Typical calibration data sheet 3-17

Figure 3.10 Basic block diagram of fixed attenuator calibration setup 3-18

Figure 3.11(a) Sample calculation of fixed attenuator calibration results using a previously calibrated variable attenuator as a readout device 3-19

Figure 3.11(b) Sample calculation of fixed attenuator calibration using a previously

calibrated variable attenuator 3-20

Figure 3.11(c) Example of fixed attenuator calibration without using a previously

calibrated precision variable attenuator 3-22

Figure 3.11(d) Theoretical values of attenuation as determined by the first 100 zeros

of the zeroeth order Bessel function 3-23

Figure 3.12 Sample calculation of maximum mismatch error present in fixed

attenuator calibration 3-24

Figure 3.13 Typical program for data reduction 3-27

Figure 3.14 Calibration results using 15 zeros 3-28

Figure 3.15(a) Calibration results using 200 zeros 3-29

Figure 3.15(b) Calibration curve for attenuation measurements using 200 zeros 3-30

Figure 3.16(a) Calibration results using 400 zeros 3-31

Figure 3.16(b) Calibration curve for attenuation measurements using 400 zeros 3-32

Figure 3.17 Calibration curve plotted by computer 3-33

Figure 3.18 Interpolation between calibration points using computer curve fit

shown in figure 3.17 ^ — 3-34

Figure 3.19 Plotter program 3-35

Figure 4.1 Error due to PSD amplifier offset 4-5

Figure 4.2 The calculated effects of various sources of systematic error compared with the experimental results of a typical "bad" run 4-7

Figure 4.3 Report of calibration on variable attenuator 4-13

Figures 10(a) Drawings and pictures of the system and accessories 10-2

- 10(q)

vii
LIST OF TABLES

Page

Table 2.1 Signal and error terms from the SQUID 2-7

Table 2.2 Theoretical values of attenuation change between Bessel functional

zeros compared to the attenuation values from a typical device under

test ——. . 2-13

Table 3.1 Description of system components- 3-1

Table 3.2 Connectors, controls, and indicators on the SQUID readout unit 3-6

Table 3.3 Connectors and controls on the SQUID control unit 3-10

Table 4.1 Odd harmonic errors for triangular inteference pattern • 4-3

Table 4.2 Comparison of calibration results for a NARDA Model 779 10-dB fixed

attenuator- 4-11

Table 4.3 Comparison of calibration results for variable attenuator 4-12

Table 8.1 Components contained in SQUID readout unit mainframe 8-2

Table 8.2 Cryogenic components 8-2

Table 8.3 Major components in SQUID readout unit 8-3

Table 8.4 Components in rf source plug-in 8-4

Table 8.5 Major components in SQUID control unit 8-5

Table 8.6 List of suggested external coaxial cables & adapters 8-6

viii
RF ATTENUATION MEASUREMENT SYSTEM USING A SQUID*

Robert T. Adair, Nolan V. Frederick, and Donald B. Sullivan

This report describes a unique portable system for measuring attenuation

at 30 MHz over a range of 50 dB to an accuracy of 0.005 dB per 20 dB. This

system does not require any reference standard. A SQUID (Superconducting

Quantum Interference Device) with its associated instrumentation is used to determine attenuation in terms of Bessel Function Zeros. A SQUID is a loop of

superconducting metal closed by a weak point contact called a Josephson junction, operating in liquid helium.

The system specifications, description, and theory of operation are presented. A complete system operating procedure including data reduction

techniques is given along with a discussion of sources of errors. Considerable additional information and diagrams are presented as an aid

to the user in understanding and operating the system.

Key words: Josephson junction; quantum interference; rf attenuation;

superconductivity.

1. GENERAL INFORMATION

1.1 Introduction

This document contains a description, specifications, operating procedures, theory of

operation, and parts list for the RF Attenuation Measurement System based on the SQUID.

This system, designed and constructed by the National Bureau of Standards (NBS) , Boulder,

Colorado, is a compact portable system designed as a very precise standard for calibrating

various types of laboratory attenuators. This system does not require any reference standard.

It is relatively inexpensive and easy to set up and operate. This attenuator calibration

system has several unique features:

a. 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.

b. The system does not require a standard of attenuation. It requires only a table

of Bessel functions to determine the exact change in attenuation between any two

given flux quanta nulls.

c. This technique provides a broad frequency range of operation without tuning.

d. The readout technique makes it relatively easy to automate measurements.

A superconducting quantum interference device (SQUID) can be thought of as 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. Most

of the applications of SQUIDs, e.g., magnetometers, gradiometers , etc., have capitalized on their high sensitivity and their unique periodic response to magnetic flux. However, the rf

attenuation application is the first which attempts to capitalize on the particular characteristics of the waveform of the rf biased SQUID. In this respect, the success of the continuing

efforts on the attenuation application is a measure of the utility of the SQUID waveform.

The period of a SQUID corresponds to one magnetic flux quantum

(<))^ = 2e/h = 2.067854 x 10 Wb) . This provides a convenient natural means of measuring

attenuation.

*Superconducting Quantum Interference Device

1-1
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 I is an rf current, then the SQUID

output 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(2ttI/Iq) where I is the rf input current amplitude and Ig is the current necessary to drive one quantum of

magnetic flux into the SQUID. Iq need not be known to make attenuation measurements. The

values of the argument 2ttI/Iq at the flux quanta nulls or zeros can be found in a table of

Bessel functions. A properly constructed single measurement system can be used to measure attenuation from dc to 1 GHz with accuracies comparable to existing conventional techniques.

Several successful prototype measurement systems have been constructed at the National

Bureau of Standards based on the SQUID [1,2].* The system described here operates only at

30 MHz primarily to calibrate 30-MHz variable waveguide below-cutoff attenuators.

This SQUID system for rf attenuation measurement has been improved over earlier systems

by a number of significant changes. A redesign of the L-band SQUID has resulted in a significantly simpler geometry which provides an adjustable coupling for precise matching to the

electronics. The redesigned SQUID contains a permanently adjusted point contact in a replaceable cartridge.

Attenuation measurements with this system rely heavily on proper signal processing

in the room temperature components, and a careful study of these conditions indicates a series

of areas where errors can be generated. These signal handling problems and appropriate solutions are discussed in detail. This system is engineered for routine measurements in a real

standards laboratory environment.

1. 2 Specifications

Electrical

Frequency of Operation 30 MHz

(can be altered with appropriate

rf source plug-in modules)

Input and Output Impedances 50 .+ jO ohms

(VSWR 1.05 at insertion point)

Attenuation Measurement Range 50 dB

Resettability ± 0.001 dB

Repeatability ± 0.001 dB

Calibration Accuracy ± (0.005 dB/20 dB)

RF Input Power to Device Under Test 250 mW maximum

AC Power Requirement 115 VAC, 60 Hz

1.0 Ampere (nominal) I

*Figures in brackets indicate the literature references at the end of this paper.

1-2
Connectors at Insertion Point

SQUID Control Chassis

Dimension:

Width 5.9 cm Depth 17.2 cm

(including knobs)

Height 21.2 cm Mass 2.4 kg

Mechanical

Precision Type N

SQUID Readout Chassis

52.0 cm

50.0 cm

40.3 cm

21.9 kg

Cryogenic

Dewar

Gross Capacity

Evaporation

Height

(with casters)

Outside Diameter

Mass Empty

(with casters)

Mass Full

(with casters)

Neck Inner Diameter

33.3 liters

2.0%/day max. 111.4 cm

53.3 cm 33.1 kg

37.3 kg

38.1 ram

SQUID

Material Babbitt

(with Niobium Point contact)

Height 3.7 cm

(including connectors)

Diameter

Mass

3.4 cm

305 gm

1.3 Description

The system shown in figures 1.1 and 1.2 is a precise attenuation measurement system

having an accurate dynamic range of 50 to 60 dB nominally. This means an actual measurement range of 50 to 60 dB when calibrating an NBS Model VII attenuation standard which

has an initial insertion loss of 30 dB. Basically the system consists of an rf biased

SQUID; an electronics package (the SQUID Readout Unit) figure 1.3, consisting of an rf

signal source (30 MHz in the original system), amplifier, rf level control circuit, digital

counter with trigger circuit, oscilloscope, and associated controls and power supplies; and

the null indicator for the NBS designed phase-sensitive detector which serves as the (Bessel

Function) null detector. A second electronics package (the SQUID Control Unit), figure 1.4,

mounts on top of the Dewar. This unit contains the L-Band pump frequency components on one

side and the signal processing electronics on the other side. This measurement system is

complete when the device under test (DUT) is connected in the measurement channel at the

insertion point.

The system, exclusive of the DUT and the associated interconnecting cables and hardware,

will be elaborated on here.


Figure 1.2 Illustrates the interconnections of the system components. The major

changes from earlier systems [3] have been (a) to replace the simple diode detector with a double-balanced mixer to linearize the 1-GHz detection process and (b) to add a second

harmonic phase sensitive (coherent) detector in parallel with the main signal channel. The

1-GUz components and the main signal processing electronics are housed in an alximlnum box

which is attached directly to the top of the 30-liter liquid helium dewar containing the

SQUID. The SQUID connects to this box via a short length of semi-rigid coaxial cable.

Every effort was made to minimize the reflections in the 1-GHz system since these reflections distort the frequency response of the system. Ground loops have been minimized to

prevent unwanted interactions between circuit components, and these components have been

very carefully shielded from external interference. Highly stable components have been

used throughout the dc bias and signal processing (1-kHz) circuits so that there are no difficulties in adjusting and maintaining the proper SQUID operating conditions. The

rationale behind the addition of the second harmonic detector is explained in the theory

section of this document.

1.3.1 Description of SQUID Control Unit

A major advance in this system over previous prototype systems has been the complete

repackaging and improvement of the electronic readout system. The availability of smaller

and substantially better components in the 1-GHz range has allowed us to move a major portion of the readout system into a small package on top of the cryogenic vessel. The close

proximity of SQUID and readout has completely eliminated some long-standing difficulties

with interference and bias stability. The readout system is now remarkably stable and

should present no further problems. The motivation for a new packaging approach for this

attenuation measurement system was the need for resolution at the thousandth of a dB level,

as well as the ever-present problems with interference, rf leakage, and ground-loop currents.

The outstanding performance of the readout system has provided the opportunity to

systematically define the range of operating parameters over which good attenuation calibrations can be made. The results of these tests are included in this report and clearly

indicate a performance which meets our earlier expectations. The effect of nonoptimum

settings is not great, and once set, the optimum (microwave pump) frequency should not need

resetting unless the SQUID is CHANGED.

The Control Unit contains the dc, 1-kHz, and 1-GHz bias circuits and is mounted on the

Dewar head as shown in figure 1.1. The 1-GHz bias components (i.e., the oscillator, attenuator, directional coupler, amplifier, and double-balanced mixer) are mounted as near as possible to the SQUID to reduce the frequency-dependent variations in signal level which are associated with line resonances generated by slightly imperfect impedance matching. These

elements are mounted in a thermally-stable, rf tight, machined-aluminum box. Every effort

has been made to design and construct the bias circuits for maximum stability. There is no discernible pickup or interaction between the different circuits. Typically, t^ie fractional

variations of 1-kHz and dc bias signals are of the order of a few parts in 10^ with 10%

variations in line voltage and 1°C variations in temperature.

1-6
The bias and setup controls shown in figure 1.3 are mounted on the aluminum enclosure

to eliminate pickup and thermal effects. The dc and 1-kHz circuits are illustrated in

figures 1.4, 1.5, and 1.6. The 1-GHz components are on the reverse side as shown in

figures 1.7, 1.8, and 1.9. The manually-tuned phase shifter in the lower left quadrant

of figure 1.7 serves to deliver the reference signal to the double-balanced mixer. The

phase of the reference signal is matched to the primary signal phase to assure a proper

phase relationship at the mixer over a wide tuning range. The use of a double-balanced

mixer ensures linear detection of only the signal component which varies as the zeroth

order Bessel function. All the 1-GHz elements are state-of-the-art commercial components.

The mechanical attenuator used in previous units has been replaced with a voltage variable

attenuator which is housed in the oscillator enclosure.

1.3.2 Description of SQUID Readout Unit

The Readout Unit (shown in figure 1.10) consists of the RF Source and Null Indicating

Unit, a digital counter for counting the Bessel function zeros, and an oscilloscope to monitor the SQUID interference pattern during the setup procedure.

The RF Source and Null Indicating Unit mounts in the Readout Unit cabinet and contains

the system power supplies, the 2-kHz phase sensitive detector, the 30-MHz crystal controlled

source, the circuit for 30-MHz level control, the readout null meter, and the count generating

circuits. This unit is illustrated in figures 1.11, 1.12, 1.13, and 1.14. The components

are mounted in modular units, and one need only replace the rf source (30-MHz) module in

order to change to another calibration frequency.

The level control circuit shown in figure 1.15 is a precisely-controlled, manuallyoperated rf output level-set attenuator. The variable capacitor (TMC2) acts as a variable termination on one port of the hybrid junction contained in the RF Signal Source

plug-in module which supplies the Device Under Test with the calibrating frequency signal.

The combination of the variable termination (TMC2) and the 180° hybrid junction

serves as a variable attenuator on the output of the 30-MHz source. The rf signal source module (shown in figures 1.15, 1.16, and 1.17) consists of a 30-MHz crystal-controlled oscillator, a 30-MHz amplifier, and a signal level controller

which operates like a variable attenuator as shown in figure 1.19. This 30-MHz signal

appears at the "RF OUTPUT" jack (J4) on the rear panel of the SQUID Readout Unit. The

Setup/Run switch on the front panel of the plug-in controls a coaxial relay which switches

the rf signal into a 50-ohm load when the switch is placed in the "SETUP" position. This

allows the SQUID control parameters to be set up for optimum operation of the system

without the 30-MHz measurement signal interfering.

The rf signal level controller consists of a 180° hybrid Junction with 65 dB of Isolation between the E and H arms. The rf output from the 30-MHz amplifier is fed Into the H

arm, and the rf output from the E arm is connected via J4 to the input port on the Device

Under Test. Collnear arm No. 1 is terminated in a variable piston capacitor with a range

from 0.7 to 30 picofarad. Collnear arm No. 2 Is also terminated with a variable piston

capacitor which serves as a variable termination. See figures 1.15, 1.16, 1.17, and 1.18.
1

Figure 1.3. SQUID control unit
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In the SQUID control unit.

1-9
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SCHEMATIC DIAGRAM

RF SOURCE PLUG-IN

21V

30 MHz

AMPLIFIER

l30iL II

Figure 1.15. 30-Ifflz plug-in module showing output level adjust components.
1-23 I
; PRECISION

FREQUENCY SOURCE

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1-25
The hybrid junction connected in this configuration operates as a very good variable rf

attenuator having an insertion loss of 3 dB and a range of 65 dB which is a significant

improvement over available commercial voltage variable attenuators. Figure 1.15 illustrate*

the basic connections for this device. When the capacitor on hybrid arm No. 1 is maxlmtm,

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

the capacitor on arm No. 1 is minimum, it is balanced by the piston capacitor terminating

the opposite port, so that the two signals cancel and the transmitted rf power is attenuated

by as much as 65 dB. At intermediate capacitance settings there is a convenient relationship between the capacitor dial setting and rf output voltage over the range of attenuation

as shown in figure 1.18. This allows nulls in the response of the SQUID to be counted at a steady rate when the capacitor dial on the source plug-in is varied. Because of the high

rf level, the power out of this source should be set to the desired level with a power

meter connected to jack J4 prior to connecting a DUT into the system. Usually precise

settings (calibration) of the Device Under Test are always made with the capacitor near its

maximum (i.e., the condition of maximum transmission of rf power which allows the maximum

dynamic range)

.

Figure 1.18 presents the characteristic curve of this variable attenuator.

1.3.3 Description of the SQUID Signal Processing Circuits

The SQUID signal processing circuits consist of the following:

1. The 1-GHz biasing circuit, figures 1.2, 1.7, and 1.8.

2. The 1-kHz or zero detecting circuits (contained in the SQUID Control Unit),

figures 1.2, 1.4, 1.5, and 1.6.

3. The 2-kHz phase sensitive detector circuits (contained in the SQUID Readout

Unit), figures 1.19, 1.20, and 1.21.

4. The counter-pulse generator and null indicator circuits (contained in the SQUIDReadout Unit), figures 1.22, 1.23, and 1.24.

The function of each of these circuits is described below.

1.3.3.1 The 1-GHz Biasing Circuit

The 1-GHz biasing circuit (figs. 1.2, 1.7, 1.8, and 3.6) consists of an Avantek type

VTO 8090 voltage tunable (.96 - 1.6 GHz) oscillator, an Avantek UTF015 voltage variable

attenuator, a 60-dB fixed attenuator and an Omnl-Spectra type 20063-20 directional coupler.

These components furnish the proper amount of 1-GHz power to the SQUID to permit it to

generate the required rf -biased SQUID response (see figs. 2.2 and 2.4). The rf-biased SQUID

response is shown as a sine-wave. This is not the "characteristic" response of an rf-biased

SQUID; however, it is the response required for this particular application. The "characteristic" response of the rf-biased SQUID is a sharply peaked triangular wave, whereas the

SQUIDS used for rf-attenuation work are modified so as to yield a sinusoidal rather than a triangular response. The signal emerging from the SQUID passes up through the directional

coupler into the 1-GHz amplifiers (Avantek types UTO 1011, UTO 1521, and UTO 1511). The

1-26
Figure 1.19. Front view of the 2-kHz phase sensitive detector plug-in.

1-27
Figure 1.20. Side view of 2-kHz PSD plug-in,

1-28
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1-29


INPUT FROM I KHZ PSD

METER

AMPLIFIER

ABSOLUTE VALUE

CIRCUIT

BLOCK DIAGRAM

NULL COUNT

OUTPUT

(TO COUNTER)

INPUT FROM I KHZ PSD

PT(H)

±1 IN5228A

IN5228A

OUTPUT

01 4= TO

> J L 1 r >

, HOT CARRIER N

COUNTER J j\

P7(E)

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3.6K lOOK

DIODES -

, HP 5082- 2811 IOO-0-IOO/xA

NULL INDICATOR

+ I5V -I5V o

P7(K) P?(J) TO METER SELECTOR SWITCH

ON 2KHZ PSD PLUG-IN SCHEMATIC DIAGRAM

P7(A) P7(C) P7(D) P7(L)

Figure 1.24. Schematic diagram of null indicator and null counting

trigger circuits.

1-32

numn
last of these amplifiers (UTO 1511) drives the "R" port of a Merrimac-type DMM 2-500 doublebalanced mixer. The "L" port of this mixer is driven by the 1-GHz phase shifter (Merrimac

Model psm 2/22401) which receives its signal through a 3-dB fixed pad from the VTO 8090

oscillator

1.3.3.2 The 1-kHz Zero Detecting Circuits

The output from the double-balanced mixer goes to the 1-kHz preamplifier Aj (see

figs. 1.4, 1.6, 1.8, and 3.7).

The output of this preamp (A^) is sent two ways; it goes to the 1-kHz amplifier

(A3, A4, and A5) and to the video amplifier A2.

The signal from A2 goes to the VIDEO output BNC connector on the control unit (which

goes to the oscilloscope's vertical input) and to the main cable and thence to the 2-kHz

amplifier and synchronous detector (PSD)* in the 2-kHz PSD plug-in in the Readout Unit

(see figs. 1.19, 1.20, and 1.21). The signal from the preamp which is sent to the 1-kHz

amplifier is amplified and sent to the 1-kHz PSD. The reference for this PSD is generated

by the 1-kHz oscillator A7. This oscillator also provides the 1-kHz bias signal. The

1-kHz PSD output goes to A5, is amplified, and is sent to the meter amplifier Ag (fig. 1.24)

in the null indicator plug-in in the Readout Unit chassis via the interconnecting cable.

1.3.3.3 The 2-kHz Phase Sensitive Detector Circuits

The output from the video amplifier A2 goes to the 2-kHz bandpass amplifiers (see

fig. 1.21) and into the y2 input of the BB 4205K multiplier. The 1-kHz reference signal

goes through the 1-kHz phase shifter after which its amplitude is squared by the BB 4205K

multiplier. The output of this multiplier ( ^j^ -^ ) becomes the X2 input to the second BB 4205K

multiplier. Recall that the y-. signal into this multiplier comes from the 2-kHz bandpass

amplifiers. The product of these two signals ( ^^q ^) is proportional to the 2-kHz component

of the detected SQUID rf signal and is proportional to the asymmetry of the rf bias (1-GHz)

operating point of the SQUID. This resulting signal is presented to the null indicator (via

the 1-kHz - 2-kHz selector switch) when the system is in the setup mode.

1.3.3.4 The Counter-Pulse Generating Circuits

The output from the 1-kHz PSD also goes to a variable dead-zone dual comparator Ag,

which drives an absolute value circuit Aiq and A^^ (see figs. 1.22, 1.23, and 1.24). These

circuits generate a trigger which goes to the counter via a BNC connector (J2) at the rear

of the Control Unit chassis. The width of the dead zone is adjusted to prevent false counting

due to noise. The action of these circuits is illustrated in figure 1.25.

*PSD: Phase Sensitive Detector.

1-33
1.3.4 Description of the SQUID

Figures 1.26 and 1.27 show the SQUID, and figure 1.28 shows the complete probe assembly

containing the SQUID for attenuation measurements. The adjacent tube Is plated with a Pb-Sn alloy upon which a thin sheet of mu-metal is wrapped. This serves to further shield

the SQUID from low frequency fields. The bracket at the top is a mechanical support for

the Control Unit electronics.

We have long been aware of two different approaches to the achievement of a sinusoidal

Interference pattern from a SQUID. We have concentrated on the operation of the SQUID in a highly damped mode, a method which calls for the addition of shunt conductance. While this

helps, we now find that a low value of critical current provides the most significant

improvement in measurement results. The mathematical description of the system operation

is more difficult in this regime; however, it is a mode of operation which generates much

lower levels of harmonics. A high critical current reflects hysteretic losses into the tank

circuit while a low critical current results in a predominantly reactive effect.

The major source of difficulty encountered with earlier systems was the adjustable

point contact. Calibrations generated by these systems were occasionally quite good, but

dramatic changes often accompanied the readjustment of the contact; a situation which is

Intolerable for routine calibrations [4]. Recently, Petley et al. [5] have used a network

analyzer to study the junction response and have generated an empirical method for contact

adjustment.

Our solution to the problem is to completely eliminate routine junction adjustment

with the use of permanently adjusted contacts of prescribed characteristics. These contacts

are made within a small cartridge which is inserted into a specially-designed, toroidal

SQUID. This approach permits the replacement of the cartridge should the contact fail.

This arrangement also permits us to make a four- terminal I-V measurement and to thus set

the contact for a desired characteristic.

Figure 1.29 shows the SQUID and a cross section of the cartridge with its permanently

adjusted contact. The glass approximately matches the total expansion of Nb between 4 K and

300 K.The two halves of the niobium cartridge are fused to a thin layer of a borosilicate

glass which electrically isolates them. The glass we have chosen has a total thermal

expansion (between 4 K and 300 K) which closely matches that of niobium thus reducing axial

motion of the contact members during temperature cycling.

The point and anvil which form the junction are finished with a fine (#500 grit) emery

paper, and are then surface oxidized by a hydrogen-oxygen torch in a manner similar to that

described by Strait [6]. Aging effects are reduced by placing a microscopic drop of epoxy

on the point of the junction. This is allowed to set after a suitable contact adjustment

is completed. We have subjected three separate junctions to more than 100 cycles between

300 K and 78 K in a 14-hour period with no discernible changes observed in the I-V characteristics at 4 K. Figure 1.30 Illustrates the I-V characteristics of a SQUID point contact

cartridge having a critical current of 10 microampere. A gradual aging over the last 15

months has resulted in 10 to 20% Increases in the shunt resistance. While lesser changes

1-34
Figure 1.25. Illustration showing the operation of the pulse generating

circuit which activates the digital counter to indicate

the Bessel function zero nunber

1-35
1-36
Figure 1.27. End view of SQUID.

1-37
1-38! I
1-39
SQUID SIGNAL

READOUT INPUT

Figure 1.29(b). Diagram of SQUID body containing cartridge.

1-40
I,10;UA/DIV

p.

o

in

>

Figure 1.30 Voltage versus current characteristics of a SQUID point

contact cartridge with a 10 nicroanpere critical current.

1-41
in critical current have occurred, there is no well established trend toward higher or lower values. We find that contacts with a shunt resistance of one ohm and critical current of ^ 5 generate a rather pure sinusoidal interference pattern (in a SQUID with

L = 5 X 10 "'^ H) and quite consistent measurements of attenuation result, if all other

-9

operating conditions are properly set. At a SQUID inductance of ^ 10 H, the L/R time

-9

constant is 10 seconds, and thus the transition time for flux entry into the ring is of

the same order as the period of the pump oscillation. From electronic analog simulation

[7], we note that this results in a rounding of the normal triangular interference

pattern [8] into a nearly sinusoidal response. The harmonic purity of the desired

sinusoidal interference pattern is further enhanced by operation in the nonhysteretic

mode (i.e. , Li / <p < 1) [8]

.

c o ^ The SQUID into which this cartridge is inserted is shown in the bottom half of figure

1.29. The inductor for the 1-GHz resonant circuit is a one-turn copper strip in the toroidal

cavity. The dc bypass of the coupling capacitor is simply a 1-cm length of 0.025-mm diameter

resistance wire. Coupling between the SQUID and resonant circuit is readily adjusted by

physically moving the inductor, and an ideal match of the resonant circuit to the line is

achieved with the variable coupling capacitor. A schematic diagram of the SQUID circuit

appears in figure 1.31.

Figure 1.32 illustrates a calibration run performed with improper circuit parameters.

Two separate problems are indicated here. The strong deviation at the upper end is generated

by the use of a rather large critical current, about 10 yA for cartridge //3. The plus-minus

error alternation of odd and even zeros results from operation on a nonlinear portion of

the double-balanced miKer (insufficient mixer bias which is easily corrected). Figure 1.33

is a repeat run with a low critical current 2 \iA) cartridge and emphasizes the splitting

of zeros. As described in previous reports, a number of programs have been developed for the

HP 9830 desk calculator and plotter which is used with the system. Figures 1.32 and 1.33

show the utility of these peripherals. Figure 1.34 is a computer plot of a recent run with

a curve giving a third polynomial fit to the data. This fit to the data allows interpolation

as illustrated in figure 1.35. Thus, one could easily generate a table showing attenuator

deviations at regular attenuation intervals.

1.3.5 Description of the Cryogenic Vessel

The liquid helium storage vessel which provides the cryogenic bath for the SQUID is

shown in figure 1.36.

This Dewar has a gross capacity of 33.4 liters of liquid helium. It does not require

an outer shield containing liquid nitrogen for cooling as in earlier dewars. This vessel

uses superinsulation and recovers sensible heat by an ultra shielding system in a high vacuum to obtain the excellent thermal performance it enjoys. The inner portion of this

Dewar along with the neck and mounting flange on top are constructed of stainless steel.

The inner diameter of the neck is nominally 2.2 cm. The operating pressure inside the

vessel is 3.45 kilopascals (0.5 PSI) as determined by the 0.64-cm diameter relief valve.

1-42
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1-43
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56

57

58

59

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61

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yjD25 DB

Fl.G;ure 1.32.

0,, 000 +0„025 DB

Plot of measurement results using high critical current cartridge and insufficient reference level on doublebalanced mixer.

1-44
THE HLiriBER OF DflTfl POINTS TFIKEH IS 30 THE MEHN VALUE OF (T-ti:) IS -3.02593E-03

THE STHHr-hRD DEVI ATI ON IS 5.73731E-t33

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DEVIHTIOH FROM THE HEflN IH DECIBELS

VERSUS HTTENUfllOR SETTING IN DECIBELS

-0.025 DB 0,000 +0.825 DB

41 . * 41 42 * 42

43 . * 43 44 * 44 45 . * 45 46 .* 46 47 . * 47 48 * . 48 49 . * 49 50 * . . 50

51 . # 51 52 * 52

53 . * 53 54 * . 54

55 . * 55 56 *. 56 57 . * 57 53 * . 58

59 . * 59 60 . * .. 60

61 .* 61 62 * . 62

63 . * . 63

64 * . 64 65 . * 65 66 * . 66

67 . * 67 68 * . 68 69 * 69 70 . 70

71 . 71 72 . 72

73 * . 73

+ + + + + 0 + + + + + -0.025 jE +0.025 DB

Figure 1.33. Plot of measuremEnt results with insufficient reference

level on double-balanced mixer.

1-45
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| tntftrpolatlon bttwatn cAllbratioa points using cotqiuter curve fit shown in figure 1.3^.

1-A7

There is also a 1.27-cin diameter relief valve rated at 68.95 kilopascals (10 PSI) on the

inner neck and a 1.27-cm diameter relief valve rated at 55.2 kilopascals (8 PSI) on the

outer neck. The evaporation rate is specified at 2.5% per day maximum. The incorporation

of this storage vessel into the SQUID system has extended the continuous operating time for

the system to nearly one month.

This vessel is designed to withstand the rigors of commercial surface transportation.

Before transporting, however, the relief shut-off valve must be open and all other vent

valves must be closed so that the boil-off gas is circulated between the neck tubes and

vented out the relief valve. Aircraft transportation of this container is allowable provided an absolute pressure relief valve set at 104.8 kilopascals (15.2 PSIA) is installed.

This valve is available as an option from the manufacturer.

1-49

2. THEORY OF OPERATION

2.1 General Information

This section contains the basic theory of operation for the RF Attenuation Measurement

System, using the Superconducting Quantum Interference Device as the standard and heart of

the system.

2.2 Principle of SQUID Operation

configuration is shown i Josephson current and I represents the input current

The basic SQUID system configuration is shown in figure 2.1 where I^ represents the

SUPERCONDUCTING LOOP

AND JUNCTION

MICROWAVE

READOUT

CIRCUIT

Figure 2.1.

SQUID

Basic SQUID system configuration,

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 I^ depends upon the magnetic flux 4" linking the loop:

Ig = I^ sin(2^(()/())o). (2.1)

I^ depends on the degree of coupling for the particular contact. The quantity <^q Is a fundamental constant of nature known as the flux quantum.

4)0 = h/2e = 2.0678538 x IQ"^^ \Jh (2.2)

where h is Planck's constant and e is the charge on the electron.

2-1
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 [9].

The total magnetic flux (}> linking the loop is the sum of two terms

= <1) + LI (2.3)

X s

where (|)^ is the flux from some external source driving the device and L is the iiiductance

.

of the loop. Strictly speaking, the current I^ in eq (2.3) is the total current (including

leakage, etc.) flowing through the junction. However, SQUID 's are usually designed so that

the Josephson current eq (2.1) 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 eq (2.1) and eq (2.3):

(() = (f)^ + LI^ sin(2TT(})/(J)o) (2.4)

or, alternatively,

. ^ Ig = sin[2TT((^^ + LIg)/(t>0]. (2.5)

Inspection of eq. (2.5) shows that the current I^ has a periodic dependence on the

external magnetic flux <^^. If we add any whole multiple of <^q to <j)^, the sine function is

unchanged, and, therefore, the current I^ is unchanged also. Remembering that the EMF V

around the loop is just d(|)/dt, we can see that the device presents a nonlinear impedance to

alternating current which is also a periodic function of the applied magnetic flux (j)^. 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 figure 2.1 [8,9,10]. (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 I. 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 I in this circuit is monitored by a microwave system which

detects variations in the microwave reflection coefficient of the SQUID.

The basic response of a SQUID system to the current to be measured is displayed in

figure 2.2. This is an oscilloscope display obtained with a slowly varying I. Monitored

in this way, the periodic response of the SQUID to magnetic flux has degenerated into a simple and remarkably pure sine function. This response is obtained for a specific pump

frequency (1 GHz) level. Increasing the 1 GHz level further results in flattening of the

upper portion of the interference pattern and eventually a null condition. Still further

1 GHz level increases cause the interference pattern to reappear with a 180 degree phase

shift. This progression continues at higher 1 GHz levels, therefore, the SQUID response

is periodic with 1 GHz pump level also.

When the input current I is an rf current, the system records an average over a segment of figure 2.2. The width of the segment is determined by the amplitude of the rf

current, and its location can be moved by simultaneously applying a dc bias current. As

2-2
2-3 I i- 96839 ~|
the amplitude of the rf current varies, this averaged response reflects the basic periodicity

of the SQUID. This is shown in figure 2.3, which is an oscilloscope display obtained by

•applying a slow amplitude modulation to an rf current applied to the SQUID. In the approximation, the basic response to current shown in figure 2.2 is proportional to cos (ZttI/Iq) , and the averaged response to rf current shown in figure 2.3 can be shown to be the zero- order Bessel function Jo(2itI/Io) [1]. In both expressions Iq is the current required to

drive one quantum of magnetic flux into the SQUID. It may be determined with a single

measurement using dc. Notice that the frequency does not enter explicitly into these

expressions.

2.3 Detailed Analysis of SQUID Operation Theory

Under certain predetermined conditions (to be elaborated upon later), the detected

response of a SQUID to flux <f> is approximately sinusoidal and may be written

V((t) = V cos(2tt(},/4.o) (2.6)

recalling that (i>Q is the flux quantum ((^q = h/2e = 2.0678538 x lO'"*"^ Wb). The action of

the system as an attenuator calibrator is illustrated by writing cf) as <^ sin w t where the m m

subscript m denotes "measuring." Taking a time average, eq (2.6) may then be written

V(<f) = VJq(2ii^J<^o). (2.7)

Since the zeros of the zeroth order Bessel function are well known, the ratios of the

amplitudes <}) at these zeros can be precisely determined. Attenuation is derived from a m

ratio of these amplitudes, and we thus have a means of calibrating attenuators.

One of the attractive features of the SQUID system is that the frequency of the

<})^ signal is not restricted to a single value as it is for waveguide-below-cutof f attenuators. Instead, a 1-GHz biased SQUID system is usable from audio frequencies up through

at least 100 MHz. The usable dynamic range decreases, however, as the frequency of the

measured signal approaches the pump frequency (1 GHz).

Figure 2.4 illustrates the response characteristics of an rf biased SQUID as defined

in eqs (2.6) and (2.7).

Since the performance of this system depends directly on the harmonic purity of the

SQUID response, it is valuable to assess the effect of small variations from the ideal

response. The purpose of this exercise is to illustrate that a good number of effects of

nonideal response can be eliminated or greatly reduced by selecting proper bias conditions.

Besides the pump signal at o)^ (1 GHz), the SQUID is subjected to the measuring signal at

frequency oj (30 MHz for this work), a 1-kHz (oj,) bias for phase sensitive location of m d

nulls, and a dc bias.

In general, the detected response of the rf biased SQUID (including harmonic distortion) may be written

oo

V((})) =

I V cos(27rn<))/(i)o), (2-8)

n=l

"
where * $ sin o) t + sin i.t + 4, . The first term is the 30-MHz measuring signal, the m m a a D second term is the 1-k.Hz modulation, and the final term is the dc bias. It is useful to study the complete response rather than to limit interest to the detection signal at

1 kHz. With the use of standard Bessel function expansions of terms of the form

cos (A sin X), we can write

where -^j^CX) is the nth order Bessel function of X and the quantities M, D, and B are

(2ir(J)^/(()o) , 2tt(J)^/({)q) , and (2tt(|)^/(()q) , respectively. Only the first of four similar terms is

displayed. The depth of modulation at lo^ becomes quite large in normal operation, thus

generating a large number of sidebands around w^. On the other hand, for the low-frequency

modulation w^, optimum operation requires a unique value for D which results in very few

sidebands at multiples of lo , from each of the nw sidebands of co . Figure 2.5 depicts the

d m L. ° nature of the frequency spectrum. The spectrum is for ideal SQUID response (no harmonic

distortion), and half of the sidebands are eliminated if B = 0 or B = ti/2. Phase information of eq (2.9) is not shown. Sideband A (fig- 2.5) is detected by the system to locate

the zeros of Jg.

Consider first the signals which appear at the low-frequency sidebands of the carrier.

Table 2.1 lists the first three terms of the harmonic expansion for the low-frequency sidebands about L^^. The desired information is Jo(M) as found in the very first term. Note

that setting B = tt/2 (i.e., adjusting the bias so that tj)^ = (^q/U) nulls even harmonic

distortions of the SQUID response at this first sideband. In practice we locate two

adjacent nulls on the lo^ detector and then use a specially designed resistive divider to

bring the current midway between these. The nulling of the second harmonic term can be

made more complete by the following process which minimizes V2. Note that, at 2a)^, the

odd terms are zero and the second term is maximized for B = tt/2. If the 1-GHz detector is

linear, the even harmonic content of the interference pattern is almost solely dependent on

the amplitude of the pump signal (at w^) , and thus a detector of 2oj^ provides an unambiguous

method of adjusting the pump frequency amplitude. The effects of second harmonic distortion

are then doubly nulled. The third harmonic term is nulled by adjusting D so that Ji(3D) = 0. To do this the 1-kHz amplitude is increased to null the signal, and the amplitude is

then divided by 3. This value puts Ji(D) near its first peak, thus maximizing sensitivity

to the desired signal. It is also important to note that J 3 (3D) is now near a maximum. This

makes the 3a)^ sideband of interest. Referring to table 2.1, we note that the second term

at 3uj^ is zero because B = Tr/2( dc bias properly set) and the first term contributes no error since it varies as Jo(M) and thus has nulls in coincidence with the desired term.

However, the third term at 3w^ is of concern because the argument is 3M and the term is nonzero when JqCM) = 0. Ideally a phase-sensitive detector detects at a single frequency,

but is is quite common for these detectors to have a significant sensitivity to odd harmonics

Jo(nD) + 2 I J (nD)cos(2ja) t) [+ ... j=l ^ (2.9)
2-6
RELATIVE SIDEBAND AMPLITUDES OF THE SQUID RESPONSE

Fi,",urcj 2.5. Relative sideband amplitudes of tlie Sf)UID response.

Table 2.1

SIGNAL AND ERROR TERMS FROM THE SQUID

ANGULAR

FREQUENCY

"^c - V,Jo(IVI)J,(D)sinB + V,Jo(2M)J,(2D)sin2B + V3J^(3M)J,(3D)sin3B + -

"^c - 2<^d V,Jo(M)Jj(D)cosB + V,Jo(2MMj(2D)cos2B + VjJgOMU^ODfcosSB -

-

t 3<^j V,J„(M)J3(D)sinB + V^jQ(2M)J3(2D)sin2B + V3 JoOMMjODIsinSB + - - -
of the signal frequency. One solution to this problem Is simply to filter out harmonics of

between the double-balanced mixer and phase-sensitive detector and to use a sinusoidal

reference waveform in the PSD's multiplying circuit.

Another type of potential problem Is the Intermodulatlon distortion which Is common

to double-balanced mixers. All signals which reach the mixer are subject to harmonic

generation and further mixing with the subsequent possibility of generating error signals

At the detection frequency of + w^. The lowest order of these terms Involves the

combination 2'(ajcmd +a) +10,) - (cocmd +2a) +a),) = oj +0),. The amplitude of the two sidebands which'

c d

contribute to this process can be found in eq. (2.9). The efficiency with which these are com- bined to generate an error is determined by the power levels of the signals at the mixer;

in essence, significant intermodulatlon distortion is present when the undesirable signals

can, of themselves, turn on the mixer diodes. At the signal levels of our system (< 1 mW)

,

this signal Is more than 30 dB below the desired signal. Furthermore, this error term

depends on the percent of harmonic distortion (i.e., V2/V1) and is thus further reduced

by the setup procedure. We estimate that this error is < 0.0001 dB in our system. Higher

order combinations are also possible, but a quick inspection reveals that the problem

rapidly becomes negligible because higher order Bessel functions of D are involved.

2.4 Theory of the SQUID Measurement Process

The measurement process is depicted in figure 2.4. The response of the 1-GHz biased

SQUID to flux Is shown as V(({i) (upper left). (}> is the input flux which, for this system,

is illustrated immediately below V((t>) as ()> (t) + <(),(t). The critical characteristic of m a

V(((i) is its sinusoidal shape; i.e., V((})) should be accurately described as V(<(i) » V sln(2ir^/^o) •* Any departure from this condition is a source of error in the measurement process. This

effect will be discussed in section 4, Error Analysis of the System. We will assume here

that the response is a sine function. The input flux is the algebraic sum of three fluxes,

a dc flux, a 1-kHz or zero detecting flux, and a 30-MHz flux. While the flux at the 30-MH2

signal frequency is injected by the signal coil, the dc and low frequency biases are introduced at the microwave readout coil. The dc flux is not explicitly depicted In

figure 2.4; however, it is this flux which positions the 1-kHz and 30-MHz abscissas along

the 41 axis of the V(,(p) function; i.e., the dc flux has the effect of moving 6 (t) + j(t)

m a

to the left or right in figure 2.4.

Clearly, the dc flux determines whether or not V((()) = V sin 4) or V((^) V slnC^S)

where 6 Is a measure of the error in the dc flux setting. In figure 2.4 the ratio of frequencies of i^j^(t) and 4>j(t) is, of course, not to scale. For V(<j)) and <() as shown, the

SQUID response is shown (upper right) as V(.<p(t)); i.e., the upper right picture Is a reasonably accurate plot of V((^) - f f*jjj(t) + ^^(t)) = V sin [2iT(4^(t) + 4j(t))/(^o) where

* (t) - M slnCZiro) t) and 4>j(t) - D sin(2Tr(jjjt) . The time average of V(*(t)), after It m ffl d d

has been aultlplled by 8ln(w^t), is shown in the lower right plot for 0 <_H <^ 10. For

the particular case at hand (M - 4) a dot on the plot identifies the value of

<V(4>(t))sln Ujt>. The analytic expression for this signal is the zeroth order Bessel

function Jo(M) [11]. Clearly, for those amplitudes of the 30-MHz measuring signal (M's)

*(j)0 - h/2e - 2.0678538 x lo"-'"^ Wb.

2-8
where <V(())(t))sin t^jt> is zero, M must have the tabulated values of the zeros of JgCx).

For example, the first zero of JqCx) occurs at x = 2.A048 ... [11]; the second occurs at

X = 5.52007 ... The ratios of the amplitudes (M's) at these two zeros must be

(5.52 ...)/(2.40 ...) and this ratio represents 20 log^Q[(5.52 ,..)/(2.40 ...)] dB or 7.217 ... dB. The distance between zeros is rather large for the first few zeros; however,

consider the distance or dB difference between the 39th and 40th zeros: The 39th zero of

Jo(x) occurs at X = 121.73 the 40th at x = 124.89 and the dB difference for these

two zeros is only .2213 dB. This difference continues to decrease (slowly) with increasing

zero number which, of course, corresponds to higher and higher values of M, the 30-MHz

measuring signal. Clearly, if one can vary the value of the 30-MHz signal smoothly from

til t h

the i to the r zero, the ratio of signals M to M. is given by the ratio of the

t h t h

r 1 arguments of Jo(x) at its r and i zeros, and if one can (by varying M smoothly) be

certain of r and i, it is possible to measure a fairly wide range of attenuation. The

present system will determine (i.e., count) over 1000 zeros. This corresponds to a range

of over 60 dB. The system is equipped with a manual attenuator in the 30-MHz source. This attenuator is controlled by the front panel dial.

2 . 5 Attenuation Meaurements Using the SQUID System

The system as shown in figures 2.6(a) and 2.6(b) can be used to measure variations in

attenuation without a 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 conductor of a 50-^ coaxial line, which

passes through the SQUID. Variations in the current flowing in this line cause variations

in the magnetic flux linking the super-conducting 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-^ load, and the

other is connected to the rf system on which measurements are to be made.

Figure 2.6 shows the basic layout of the components used to realize this system. The

microwave system is driven by an L-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 10 W. The reflected microwave signal is amplified by a solid-state amplifier,

with a gain of about 50 dB, and detected by a double-balanced mixer. This millivolt level

signal is applied to the lock-in detector, where it is amplified to an operating 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 microwave line. This fiiust pass the bias and

modulation, but present a significant attenuation at 1 GHz. The high degree of attenuation

is required to prevent crosstalk between the microwave and measuring channels.

2-9
9(K

LU><

tn z o

CD CC

LL. CO

CC

uca

(UM

COo

(0

t3o*

CO

(U 43ou

00n

•HMuoH

a

O (U •H *J

CO CO

cd pq CD

so

CM

(UUa

•H

(X4

2-10
2-11
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 phase sensitive detector is used to locate the nulls of the

response function Jo(27rI/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.

The details of this procedure can be understood by carefully examining the contents of

table 2.2, where the zeros of the zeroth order Bessel function (column two) have been

obtained from a book of tables [11].

The attenuator under test is adjusted until it is set precisely on the first Bessel

function zero. This value of attenuation is recorded in column six of table 2.2. The

attenuator is then adjusted to the precise valu^ which corresponds to the second zero of

the Bessel function. This process can be continued to include any desired zero in the

range of the system. The values of attenuation change from a given zero to another zero (appearing in column seven of table 2.2) can be compared with the theoretical change

between those same two zeros (appearing in column five of table 2.2).

The difference between the theoretical value of attenuation change and the indicated

value of attenuation change as obtained from the readings on the attenuator under test

gives the error in the attenuator under test. This value appears in column eight of table

2.2. This difference in attenuation in dB can be normalized to the mean value of the

difference and plotted as a calibration curve on the Device Under Test (DUT) , as illustrated

in figure 3.14.

The mechanics of these calibration details are discussed fully in section 3 "Operating

Procedure."

2.6 Bessel Function Zero (Null) Counting Techniques

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 interpolating between them. (Refer to section 1.3.2.) This system is shown in figure 2.7.

Nulls are counted by a digital counter, driven by the lock-in detector in the L-band readout system, as the Incident rf power is slowly reduced from the working level to a very low

level manually via the level control dial on the front panel of the RF Source Plug-in

Module. The incident rf power is then restored to its working level slowly to the nearest

null. The rf output power can be measured by a microwattmeter and a 3-dB coupler on the

output port J4. The corresponding small change in rf power level from the level at which

the measurement is being made (between nulls) to the nearest adjacent null can be measured.

This value can then be compared to the change in rf power between the nulls on each side of

2-12
2-13
the point in question with sufficient accuracy for interpolation between nulls. The circuit for controlling the rf output power level was developed after trying several com- mercial voltage-variable attenuators and modulators, which were rejected because of their

high insertion loss and inconvenient control voltage characteristics. This manually

variable-attenuator circuit is shown in figures 1.15 and 2.7. It consists of a wellbalanced 180° hybrid junction with a variable piston capacitor acting as a variable

termination on one of the side ports as described in section 1.3.2.

This technique to interpolate between nulls has not been used routinely since the

system is more easily operated in a manual mode. The accuracy of interpolation between

zeros using this technique has not been evaluted thoroughly although the resolution of the

RF Level Control dial is nominally 0.01 dB which should be adequate for calibrating fixed

attenuators

.

The simpler technique of calibrating a fixed attenuator by placing it in series with a variable attenuator has been successful. The variable attenuator is first calibrated using

the SQUID System; then the fixed attenuator is inserted as described in section 3.6.3.

This technique eliminates the need to interpolate between Bessel Function Zeros in most

cases.The interpolation technique is included in the system to provide maximum flexibility

and to allow the use of further semi-automatic data processing and control of the system if

desired.

2-14
C

CO 1 H-—

CNI LU <-> LU1 1—

a.

>— 3Co

C! •Hoo

M-l6

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CO iHH

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cu

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CO ;x U 4J bO QJ

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2-15

3. OPERATING PROCEDURE

3.1 General

This section contains information on preparation for use, identification, and description of controls and indicators, and a step-by-step operating procedure.

3 . 2 System Components

The individual system components are described in table 3.1 and are identified by

index numbers in figure 3.1 which is a view of the total system.

Item

No.

1.

Item

Dewar

2. SQUID Control Unit

3. Digital Counter

4. SQUID Readout Unit

5. Oscilloscope

6. Device Under Test

Table 3.1. Description of system components.

Description

This 30-liter Dewar contains the liquid helium bath in which

the SQUID must be submerged for proper operation of the

system.

This unit contains the dc-bias circuits, the 1-kHz bias and

modulation circuits, and the 1-GHz biasing circuits for the

SQUID.

This counter provides a readout for the semiautomatic

counting of the nulls at the Bessel function zeros.

This unit contains the dc power supplies, the null indicator

circuitry for the phase-sensitive detector and the rf signal

source which provides the calibration signal for the device

under test.

This device provides a visual representation of the SQUID

interference pattern for use during system setup and

operation.

This is a typical variable attenuator being calibrated by

the SQUID Attenuation Measurement System.

3 . 3 Connectors, Controls, and Indicators

The SQUID Readout Unit connectors, controls, and indicators are described in table 3.2

and are identified in figures 3.2, 3.3, and 3.4 by index numbers. The SQUID Control Unit

connectors and controls are described in table 3.3 and are identified in figures 3.5, 3.6,

and 3.7 by index numbers.

3-1

3-3
1/2 CO

in

3-4

I

a

•H

4-t 3

O

cu

t2

CO

(U •H>

oH

CO

5-1

•H

Item

No.

Table 3.2. Connectors, controls, and indicators on the SQUID readout Unit.

Item Description

1. AC Power Input

(on rear panel)

2. Fuse

3. On/Off Switch

4. Pilot Light

5. 2-kHz Zero Adjust

6. Detector Selector

Switch

7. Zero Circuit

Energizing Switch

8. Dead Zone Adjustment

9. Null Indicator

10. RF Source Plug-in Unit

11. Setup/Run Switch

12. RF Output Level Set

Control

13. RF Output Minimum

Adjust

lA. Jack ^0

15. Jack -^1

16. Jack '2

17. Jack

18. Jack

Provides connection for 115-volt, 60-Hz power cable.

Protects circuits and power supplies in the unit.

Connects and disconnects ac power to the internal circuits.

Provides visual indication when ac power is applied to

the unit.

Provides adjustment of the 2-kHz phase-sensitive detector

zero reference.

Provides the selection of the 1-kHz phase-sensitive detector

or the 2-kHz phase-sensitive detector to be indicated on

the null meter.

Provides momentary engagement of the 2-kHz phase-sensitive

detector zeroing circuit for initial system setup.

Provides for adjustment of the dead zone near zero on the

null indicator for proper null counting with the digital

counter.

Provides visual indication of the system null during setup

and operation.

30-MHz signal source plug-in unit, which supplies the calibrating frequency to the device under test.

Provides a means of switching the rf signal into a 50-ohm

load during the system setup procedure.

Provides vernier adjustment of the rf signal source output

level applied to the device under test.

Provides a means of reducing the rf output to zero when the

RF Output Level Adjust is turned to minimum (fully ccw)

.

Auxiliary output from null indicator.

DC power and ac signal connector to the control unit

atop the dewar.

Output from count circuit to drive digital counter.

Auxiliary output connector (not used)

.

RF output connector which supplies the calibrating signal

to the Device Under Test.

3-6

ULTRA-STABLE CONTROL VOLTAGE SUPPLY

FOR 1-GHz OSCILLATOR AND VOLTAGE ^

VARIABLE ATTENUATOR

Figure 3.6. Descriptive view of microwave bias (1 GHz) components

contained in SQUID control unit.

3-8
Figure 3.7. Descriptive view of 1-kHz and dc bias circuits contained

in SQUID control unit.

3-9
Table 3.3. Connectors and controls on the SQUID control unit.

Item

No. Item Description

Video Output

Connector

DC Bias No. 1 Control

DC Bias No. 2 Control

4. DC Setup/Run Switch

1-kHz Bias Control

1-kHz Setup/Run

Switch

A BNC Connector provides the means for applying the SQUID

interference pattern to the oscilloscope.

This control provides the means for setting the dc bias

on the SQUID during system setup.

This control provides the means for setting the dc bias on

the SQUID during system setup.

This switch provides the proper circuit connections for the

dc setup and operation of the system.

This control provides the means for setting amplitude of the

1-kHz bias on the SQUID during system setup.

This switch provides the proper circuit connections for the

1-kHz setup and operation of the system.

10.

11.

1-kHz Sync Output

DC Power/ac Signal

Connector

1-GHz Bias Connector

1-GHz Frequency

Control

1-GHz Bias Control

A BNC connector provides the signal to synchronize the oscilloscope with the 1-kHz SQUID interference pattern.

This connector provides the means for applying dc power to the

Control Unit from the Readout Unit and the proper connections

for the 1-kHz signals between these two units.

An SMA connector provides the interface between the SQUID

control unit and the 1-GHz port on the SQUID.

This control allows the adjustment of the microwave pump

frequency for proper operation of the SQUID.

This control allows the proper setting of the 1-GHz amplitude

for proper operation of the SQUID.

3.4 Preparation for Use

1. Bleed the pressure off the helium Dewar by opening the vent valve slowly.

2. When the pressure reaches zero, remove the mounting plate screws from the mounting

plate which contains the filling valves, relief valves, pressure gauge, etc.

3. Remove the mounting plate mechanism from the Dewar and cover the hole immediately with

a clean rag or similar item to contain the helium and prevent moisture from the air

from entering the Dewar. Moisture in the Dewar will freeze and cause problems.

Verify that the helium Dewar contains sufficient liquid helium for the system to

operate using the dip tube provided. Ten liters is adequate for several days

running time.

3-10
5. Remove the rag from the Dewar neck and insert the SQUID probe a few inches and quickly

wrap the rag around the SQUID probe.

6. Slowly lower the SQUID until helium gas starts escaping around the rag.

7. Continue to lower the SQUID probe very slowly to prevent excessive boil-off of the

liquid helium.

8. Fasten the SQUID probe mounting plate to the Dewar' s neck flange with the mounting

screws provided.

9. Attach the SQUID control chassis to the mounting bracket on the mounting plate

(fig. 3.1). Care should be exercised during this process to avoid damaging the SMA

connectors on the semirigid coaxial cable which connects the SQUID Control Unit to the

SQUID probe mounting flange.

10. Connect the dc/signal cable to jack Jl (fig. 3.4) on the rear panel of the SQUID

Readout Unit and to jack Jl (connector 8 in figs. 3.5, 3.6, and 3.7) on the SQUID

Control Unit located on top of the Dewar.

11. Connect a 25-cm long coaxial cable (with BNC connectors) from jack J2 on the rear panel

of the SQUID Readout Unit to the signal input jack on the rear panel of the digital

counter in the SQUID Readout Unit cabinet.

12. Connect a two-meter length of RG9B/u coaxial cable having precision Type N male con- nectors on each end, between the rf signal output jack J4 on the rear of the SQUID

Control Unit and the input port on the Device Under Test.

13. Connect an RG9B/u cable three meters in length with precision Type N connectors from

the output of the Device Under Test to the SQUID input port at the mounting bracket

on the Dewar.

14. Connect an appropriate length rf cable (RG55/u) having BNC connectors on each end from

the SYNC output jack on the SQUID Control Unit to the HORIZ input jack on the rear panel of the oscilloscope in the SQUID Readout Unit cabinet.

15. Connect the special rf cable (RG55/u with a BNC connector on one end and the oscilloscope rear panel vertical input connector on the other) from the "Video" output jack

on the SQUID Control Unit to the "VERT A" input jack on the rear panel of the oscilloscope contained in the SQUID Readout Unit cabinet.

16. Connect the ac power cord housed in the rear of the SQUID Readout Unit to a 115 V,

60 Hz power source.

17. Turn on the digital counter, the SQUID Readout Unit, and the oscilloscope.

18. Connect the Device Under Test to the proper ac source if appropriate.

3-11
3 . 5 Preliminary Setup and Adjustments

1. Turn on power switches on the SQUID Readout Unit, the oscilloscope, and the digital

counter.

2. Allow approximately one-half hour for the system to stabilize.

3. Adjust oscilloscope for five mV/div sensitivity.

4. Set the oscilloscope sweep speed to .2 ms/div.

5. Set oscilloscope sweep sync to external.

6. Throw all setup , run switches to setup.

7. Turn all bias controls (two d£ bias controls and the 1-kHz bias control) to full CCW.

8. Turn 1-kHz bias control three turns CW.

9. Put control panel setup , run switch on rf source plug- in to setup .

10. Adjust the £l_ dc^ bias control for a zero indication on the phase-sensitive detector

output meter (null indicator)

.

11. Adjust jl2_ dc_ bias for the next zero and throw the dc bias toggle switch from setup

to run .

12. Turn the 1-kHz bias control CW until the null meter reads zero, throw the 1-kHz

setup , run toggle from setup to run .

13. Switch the null indicator switch to the 2-kHz position.

14. Depress the meter zero button and zero the null indicator using the 2-kHz zero adjust control.

15. Adjust the rf bias control (1-GHz amplitude) for zero on the null indicator.

16. Switch the null indicator switch back to the 1-kHz position.

17. Throw the 1-kHz toggle to setup and adjust the 1-kHz bias for zero on the null

meter and return toggle to run.

18. Throw d£ bias toggle to setup , turn both d£ bias controls full CCW. Now adjust

#1 dc bias (CW) for zero on the null meter, adjust //2 dc bias (CW) for the next

zero on the null meter.

19. Throw the dc_ bias toggle to run .

20. Throw the 1-kHz bias toggle to setup and adjust the 1-kHz bias for zero on the null

meter. Throw the 1-kHz toggle to run.

-^-1 9
21. Switch the null indicator to the 2-kHz position.

22. Adjust the rf bias (1-GHz amplitude) for zero (second harmonic) on the null indicator.

23. Switch the null indicator back to the 1-kHz position.

24. Throw the 1-kHz toggle to setup , adjust the 1-kHz bias for zero on the null meter, and

throw the toggle to run.

25. Throw setup , run toggle on the control panel of the rf source plug-in to run .

26. The system is now set up and ready to operate.

3 . 6 Operating Procedure

3.6.1 Introduction

The attenuator to be calibrated will be referred to as the Device Under Test (BUT) . A

good quality 10-dB fixed attenuator (VSWR <_ 1.01) should be placed on the input of any

attenuator calibrated with this system. This will make certain the DUT is terminated in

nominally 50 + jO ohms to eliminate any system caused mismatch error.

3.6.2 Calibration of a Variable Attenuator

1. Set the DUT to a value near its maximum attenuation setting.

2. Go through the preliminary setup procedure as outlined in section 3.5 of this document

to make certain the system is properly set up, adjusted, and ready for operation.

3. Prepare a data sheet similar to the one shown in figure 3.8 to cover the range of

attenuation values desired.

NOTE: The first 10 Bessel Function Zeros cover a range of nominally 20 decibels.

The first 100 Bessel Function Zeros cover a range of nominally 40 decibels.

The first 200 Bessel Function Zeros cover a range of nominally 48 decibels.

The sensitivity of the SQUID used in this system is nominally -80 dBm which

means that the first Bessel Function Zero occurs at approximately 100 dB

below the 250 mW being applied to the DUT. Thus, if the initial insertion

loss of the DUT is nominally 30 decibels, the first Bessel Function Zero

would occur at an attenuator setting of approximately 70 decibels.

RECALL: The Bessel Function Zero number increases as the signal level applied to the

SQUID increases which means the attenuator setting in dB goes down as the zero number goes up! See figure 3.9.

3-13
4. Adjust the DUT in the direction of decreasing attenuation until the Null Indicator

reads zero. This indicates the first Bessel Function Zero has been reached. Set the

DUT very carefully to a value which sets the Null Indicator precisely on Zero.

CAUTION: If the DUT is moved to a setting past the value which provides a zero indication on the null meter, the attenuator under test should be returned to a higher reading, and the zero reading approached again from the high side.

That is, when calibrating a variable attenuator, the indicated null on the

meter should always be approached by turning the DUT in the same direction

for every reading. This will eliminate the effect of any backlash in the

i, attenuator under test and thus improve the repeatability of the measurements.

5. Repeat the reading at the first zero several times to check the system repeatability.

The readings should repeat to within 0.001 to 0.002 dB.

6. Record the attenuator readings and proceed onto the second Bessel Function Zero which

is approximately 7.2 dB from the first zero.

7. Record this attenuator setting and proceed to the next zero and so on.

8. The operator may count the zeros manually or the digital counter may be used.

CAUTION: The automatic Bessel Function Zero counting circuitry cannot recognize the

difference in an up count and a down count. This means if a zero null

indication is overshot the counter will register one additional count each

time the Bessel Function Zero is crossed. Thus, getting back to a given

attenuator setting' to approach the zero from the correct direction will cause errors in the automatic counter readout.

9. Continue taking readings on the DUT at the desired Bessel Function Zeros until the

series is complete.

10. Return to zero number 1 and repeat the original reading. This will indicate the

stability of the system and the repeatability of the system and the DUT.

NOTE: A minimum of three sets of readings should be taken for the calculation of

the mean value of attenuation at each setting for the particular Device Under

Test. This will provide measurements with the minimum desired statistical

control. More measurements should be taken on different days to provide

attenuation mean values with a higher confidence level.

11. A different range of values may be calibrated on a Device Under Test by placing fixed

attenuators in series with the input and output of the DUT.

3-14
3.6.3 Calibration of a Fixed Attenuator

A fixed attenuator may be calibrated by placing it between two good quality 10-dB

fixed attenuators (VSWR < 1.01) in series with a variable attenuator which has been previously

calibrated on this system. The block diagram in figure 3.10 illustrates this procedure.

The insertion loss of the fixed attenuator may be obtained by making a short calibration

run on the variable attenuator (with the fixed attenuator in the system) and comparing

these results with the original results on the variable attenuator. This process is

illustrated in figures 3.10, 3.11(a), and 3.11(b). Figures 3.11(c) and 3.11(d) illustrate

the calibration of a fixed attenuator without the use of a precalibrated precision variable

attenuator.

If the VSWR of the fixed attenuator under test is significant (VSWR > 1.05), then the error due to mismatch must be calculated and included in the sources of error for the calibration results. See figure 3.12 for an example of this.

3.6.4 Reduction of Calibration Data

Calibration results may be calculated from the raw data manually using a book of tables

containing Bessel Functions or with the aid of a programmable calculator or a computer.

The choice of computers and data reduction techniques is virtually unlimited in today's

world of advanced technology. The following discussion presents a few suggested methods for

calculating the calibration results from the measurements made using the SQUID System.

These techniques are certainly not the only ones available but have been convenient for our purposes

.

Recall that the SQUID response is of the form [V(c)] = \'J'.{2n^ /6n) where c is the m m

flux applied to the SQUID from the output .of the Device Under Test, and 2" and are constants. The zeros of the zeroth order Bessel Function can be taken from a Book of Tables

[11] . Taking the ratio of the tabulated value of any two Bessel Function Zeros as amplitudes allows the calculation of the attenuation change between those two zeros. This

theoretical value is then com.pared with the indicated change in attenuation as obtained from

the readings on the Device Under Test which produced the two respective Bessel Function

Zeros

.

Let us consider the first and tw^entieth zeros from the Book of Tables [11],

3.7 Data Reduction

3.7.1 Data Reduction Using a Table of Bessel Functions

J 0,20

= 62.04846 & J 0,1

= 2.40482.

So the attenaution change between the first and twentieth zeros is

20 log

'62.04846^ 2.40482.

= 28.233 dB.

Now looking at the measured values of attenuation from, the data taken on the DUT which

appear in figures 3.9 and 3.15, we see that the value at the twentieth zero is 44.386 dB and
LOG SHEET

KIND OP MEASUREMENT

INSTRUMENT TESTED _

Mfg.

U. S. DEPARTMENT OF COMfKERCE

NATIONAL BUREAU OF STANDARDS

RF ATTENUATION

DATE

Sheet no. observer

Model S/N

ZERO

NO.

1 Run Nn

Tlmo 1 line _ H

1

1

2

4

D

7

QO

Q

1 n1 u

1 0

1

5

20

25

40

50

fin

fin —m—

^

Figure 3.8. Sample calibration data sheet.

Special C( indltlonsjy 3-16

NBS-2S5A USCOMM*NBt-Oe

(•-72)
LOG SHEET

KIND OF MEASUREMENT

INSTRUMENT TESTED _

Mfg.

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

RF ATTENUATION

DATE Snt^i

Sheet no

observer

Variable A ttenuator

S Model S/N

ZERO

NO.

Run No.

—

Time ^^^^^^^^^^

1

1 72. ^t<^

2

_

3

-

4 •SB. 862 r~ 5

6 55. 0^9

" 7 S3.7o9

- .

8

9 5/454

- —

10 50.514

12 48.B93

15 4C».9a2

A4.2d^

4i.4Z3

Ao.625

/in

50

fin 34.764

80 j;i.aS7

inn 3o.3\(

1 Fieure 3.9. TvDical calibration data sheet.

Special Co nditions L 3-17

J

N BS-255A

(6-72)

USCOMM-NBS«DC
SQUID READOUT UNIT

AND

RF SOURCE

PRECISION

lOdB •

FIXED ATTENUATOR

FIXED ATTENUATOR PRECISION

10 dS

FjXED ATTENUATOR

(OPTIONAL)

PRECISION

VARIABLE

ATTENUATOR

(DEVICE UNDER TEST)

¥ w

Figure 3.10. Basic block diagram of fixed attenuator calibration

setup.

3-18
< c

•z 'j:. <

PQ

inoc

•a

(U u

tou

•H < H c < z — < >

EK

c/2

C

O

PiaNooM

CA

E3

ffJ OH<HH

<JOXM

<:ooMHM

iJ<: 2

=3o< o C Z H X \ S 5 s:;

N3 3

COoo

vC

oc

C> z vD

n z CO cn o

roc Z

CN CM

<3-

CN

CN CN I

lti cc

CN CN ! 0^

CN L-i <3-

-3" inico

CN CN CTi <r c^

si 3 Z Em O Et^ MQ

CN c;

<3- < < <>

E-l o

PiH

t3a

a CO > 1—

• CN a a < a aa a [ < a a

II

a z H lO o 1 AT <1-3 <du X z H C_J a 1—

1—

Q CT\ z Q z Z a z o t—(

IIa

i—

a z < a <3- < C 00 a C z < '—

• CN aH > c

c-^

U 1 H (—

< o 1—

i a < -^ a^ a

CO < M a a C30 cq , < < u a H H <£ X <r H oo a « z c a < ,— o Di a 

o Q d a a

II 1 x AT o c-c 1 II a > HU • a a a C c- CN z z Z c H H z

v: < o a o < a: a z o o o + E—

N o H < -a < < 1 z < Z < Z a a CN CO < H o H a < < < z a a z a T a a

r-i =:

a 5 3 II < Q < a 1—1 a < a a oo a a H o z > a z > a X a > a u 1—( o a a a a u a a Q a a a < H > z a u z Z o • aa o OO a a '-I 1 00 a a H < s —1 z b < 3 a o o U Z a z

'Jl 00 Za CO Z H < d < H < r-i > z H

CO3o

•H>

0)

toG

•H

CO33

CO(Uo

•HUu

COo . 0) h u O -H

4J >

CO 0) 3C

(U •!-> u 3 u o

CO T3

CO

<U

h

X

•H CO

U-( CO

M-l CO co

•HU

CO rH3O

iH

COO

0) ^ rH CO B M

CO CO cn > 3 3 -19
CALIBRATION OF A FIXED ATTENUATOR

USING SEVERAL ZEROS AT ONCE

FIXED ATTENUATOR POSITION DIFFERENCE

ZERO NO. OUT IN dB

1 53.5A2 43.679 9. 863

1 53.542 43.680 9.862

36 480 Q7 • 866 OOv

3 42.444 32.577 9.867

4 39.764 29.900 9.864

5 37.701 27.836 9.865

6 36.050 26.187 9.863

7 34.652 24.792 9.860

8 33.458 23.599 9.859

9 32.399 22.536 9.863

10 31.466 21.606 9.860

1 53.545 43.675 9.870

MEAN VALUE OF DIFFERENCE - X - 9.8635 dB

- 9.864 dB

STANDARD DEVIATION - S^^ - 0.00318 dB

STANDARD ERROR = Srr » 0.00092 dB

This mean value is Incorrect only by the amount of nonllnearlty

In the variable attenuator being used as the readout. This value

includes only one connect and disconnect operation. The average of

more runs should be taken to include a better random sample of the

connector repeatability.

Also mismatch error at the insertion point has not been

accounted for here.

The average value of the NBS calibration of this 10 dB fixed

attenuator over the past three years is 9.858 dB.

Figure 3.11(b). Sample calculation of fixed attenuator calibration

using a previously calibrated variable attenuator.

3-20
CALIBRATION OF A FIXED ATTENUATOR WITHOUT USING

A PRECALIBRATED PRECISION VARIABLE ATTENUATOR

EXAMPLE OF A 20 dB FIXED ATTENUATOR CALIBRATION

1. Select the portion of the SQUID scale to use [from figure 3.11(d)] based on fixed

attenuator nominal value and resolution desired.

For this example, zeros 3 and 28 will be selected giving an attenuation range of

31.1867 dB - 11.1224 dB = 20.0643 dB. (Note the spacing between zeros 27 and 28

is 0.3188 dB.)

2. Insert the Device Under Test, the insertion point fixed pads, and a variable

attenuator which permits coverage of the desired range (as in figure 3.10).

3. Set the variable attenuator to a value greater than that required to obtain the

first Bessel Function Zero. Reduce the attenuation of this attenuator until zero number 3 is reached. Record the zero number and the variable attenuator reading.

These numbers are a, and a . a

4. Remove the Device Under Test from the system and reconnect the system at the

insertion point.

5. Slowly adjust the variable attenuator for less attenuation until the closest Bessel

Function Zero is reached. You're at zero b, and a^^. Note, the exact number of zero b is yet to be determined. Record a^.

6. Carefully adjust the variable attenuator for more attenuation until the closest Bessel

Function Zero above b is reached. Read the attenuation value from the variable

attenuator and record it as ^°te the exact zero number b+1 is yet to be

determined. (Take care to compensate for backlash in the variable attenuator.)

7. Set the variable attenuator approximately midway between and c^^j^ ^.nd reset the

Bessel Function Zero counter to zero.

8. Increase the attenuation of the variable attenuator until zero number 1 is passed.

The zero counter now indicates the number of zero b. Record this number and b+1.

9. The attenuation of the Device Under Test = attenuation difference between zeros a and b from figure 3.11(d) + the interpolated attenuation value between zeros b and

b+1 from figure 3.11(d) and the variable attenuator readings.

10. Calculate a^,,„.

3-21
ZERO

NUMBER

ATTENUATION VALUE IN dB

FROM VARIABLE ATTENUATOR FROM FIGURE 3.11(d)

a - 3

b - 27

b+1 - 28

a = 24.644

a

= 24.790

a,^, = 24.472

b+i

Ta = 11.1224

a Ta^ = 30.8679

Ta^+l = 31.1867

Attenuation of Device Under Test = aDUT

a, -a

b a

a^^^ = 19.7455 + (0.3188)

''0.146^ 0.318

= 19.892 dB

Considerable care must be exercised during the counting operation since the error of one zero count will introduce a gross error in the final attenuation value.

Note, mismatch error has not been accounted for yet.

Figure 3.11(c). Example of fixed attenuator calibration without using a previously

calibrated precision variable attenuator.

3-22
ZERO

NUMBER

ATTENUATION

BETWEEN ZEROS

ZERO

NUMBER

ATTENUATION

BETWEEN ZEROS

1 nnnn uuuu jx JO7A . A701 t JUX

o

i. 7/ 9179 ^9jz JD7A "^QQA . J? ?D

•yJ XX XZZH 1 9 9 A ^7 jD7A 7A'^8 • / D JO

X1 7J OU 5 0 J't JD7A . Q98Q 7ZO7

cJ XJ ODUX ccJJ J77/ . naoo uoyu

D X1 7/ jxou JO 77 9 A A 9 J / . ZtDZ

7 XO 1:7 77 A0n7

oo 9n XU1 nQ9^ z JO^a 77 ';'i9A J / . J JZ'+ Qy ^X91 xoz 1 Q? ^0 77 701 J / . / UX

1 n 99 xuzo 1 n9A ou 9 7 a A a

J / . o'+oX XX 9 9 Q ^nA A1ox •3 7 QQ 9 T J / . yy z

xz Z9 7J

7 9 9 Q / ZZ 7 A9oz O Q 1 o A 1 JO . X j'tX X1 J Zt9/, A 79 9 '+ JZZ A7Oj 9 8 9 7 9 A JO . Z / JD

1 A XM- Z9 ^J UOOU AOfA 78 A 1 0 Q JO . 'txuy XJ Z39 AQ 7 7 A"; Dj 78 A A

J-0 . JtOX

XU1 z9fiu 9A7A AADO JO. 78 A7Q D 7 / 7 J X

1 7/ z9 fio 8090 o u z u A70 / JO78 . 81OX'J'+ OA xo Z9 7/ J U J 0 AaDo JO Q 9Q R . 3 jy

X71 q z97/ 781 7 / OX / AO J70-7 • OAAa U D U 0 zo98 Z9 J79QZ 7 70 jy90 xyzz 109 9 ^9Ro U U ± 7 71 jy9Q • jx91 J 7 9Q 79/ z J7Q-7 . A77a H J / 0 9Q Af^^ H U X ^9 77/ J jy70 Jssao jou

9A 9Q 8O J7A8H o 7A J70^7 . A7AA u / D D 7n 1 Q 70 71; /J jy9 0 7Q 9 A . / y JD

9fi 70 S 770 7A/ D jy90 . QOQO yuy

97 70 8A7Q OD / 7 77 AO . 09uzz9 Qy 9a 71 XOD 1 8fi7/ 7a/o AOtU . X17^7 J J

90 71 A Q A 9 t ytz 70 AO 9 A A

tU • Z4D

JX71 < 7Q1 9 / 7XZ anOU AO 7^ =^0 H u • J J J y JZ79 . 0787 U / 0 J aiOX AOH U • AAA9 H DH Z 79 79 -57^67 _J U J R9oz AO ^71

HU . J / XX

JZ79 69U ^ JSfiu R70J AO'tU • A7fi7 D / D / 7A jZ79 O OO 7 OHaA An 781

/ oxu

7S 77 1 L^R 0J AOtU • 88A1 001X

7fi 7 7 7860 aA00 AO Q a A 0 '+U . yoDU

77 7 7 69DZD6 J 087/ A 1 08 6 7 "tl. . UOD / 7a 77 a 7 BB00 A 1 1 a A 9 'tX . XoD J 70 "3/. oaUODOAQ BO hX. A 1 9 C A 7 Z04 / 7 A jUOX 7081 on ttX A 1 9 8 9 0 . JoZU

7 A JZ•^9 7Q 01yx A 1 A 7 a 9 'tX • 4 / 0 J 7 A 7 7 A 09yz AHX1 '^ 7 7 A . J

/

JH

A7 7A QA01 ^tux 07yJ '+X . D D / D AA 7 ^ xtuy 1 A 00 OA tXAI . 7607 / DU

/

/. ^ J J . T Q 7 9 J J /z oi; yj A'ti1 8^90 . ojzy

46 35. 5292 96 41.9441

47 35. 7170 97 42.0343

48 35. 9008 98 42.1237

49 36. 0808 99 42.2121

50 36. 2572 100 42.2996

Figure 3.11(d). Theoretical values of attenuation as determined by the first 100

zeros of the zeroeth order Bessel function.

3-23
MEASURED IMPEDANCE of 10 dB Attenuator Under Test

Female End Z « 48.5 @ 0" Terminated in 50.0 @ 0" ohms

Male End Z = 49.3 ^ 0° Terminated in 50.0 @ 0" ohms

Model VII WBCO Attenuator Input Z = 50.0 @ 0* ohms

SQUID System Output Impedance with 20 dB Attenuator on Output of 30 MHz

Source « Z « 50.5 -2° ohms.

VSWR CALCULATION For SQUID System Output

Z-Z

Reflection Coefficient = p " -^i^ =

3Q'3;j;3Q = 0.00497

o

VSWR

1+ p 1 + 0.00497

1- p 1 - 0.00497 1.010

and VSWR at Input to Variable Attenuator = 1.000

Similarly, 10 dB DUT Female End VSWR =1.031

and the 10 dB DUT Male End VSWR =1.014

CALCULATION OF MISMATCH ERROR at the Insertion Point

- VSWR of Device Under Test (DUT) = 1.031

« VSWR of Impedance the DUT Looks Into = 1.010

Mismatch = F = 0.000409

2

[1.031x1.

1.031x1.01

01 -4

Maximum Mismatch Error in dB " 10 Log^Q (1+F)

- 10 Log (1 + 0.000409) - 0.0018 dB

So the Worst Case Maximum Mismatch Error For This 10 dB Attenuator Being

Calibrated in the SQUID System Under These Conditions is ± 0.002 dB.

Figure 3.12. Sample calculation of maximum mismatch error present in

fixed attenuator calibration.

3-24
the value at the first zero is 72.619 dB. The difference between these values is 72 . 619-4A . 386

which is 28.233 dB. This indicates that the theoretical value and the measured value of

attenuation between the first and twentieth zeros are identical. This then states that

there is no error in the Device Under Test (to the overall accuracy of the SQUID system)

between the settings of 72.619 dB and 44.386 dB. Similarly, let's examine the results

between the third and twelfth zeros. The Book of Tables states = 36.91709 and -Jq 3 = 8.65372. Thus the theoretical

change is 20 log

36.91709

8.65372

= 12.600 dB. The measured values between the same two zeros

(from figures 3.9 and 3.15) are 3 " 61.498 dB and = 48.893 dB, so the difference

is 61.498-48.893 = 12.605 dB. Then the difference T-M (theory-measured) is

12.600-12.605 = -0.005 dB which indicates an error in the DUT of 0.005 dB between the

settings of 61.498 dB and 48.893 dB. A calibration curve can be constructed for the DUT

using the measurement data in this manner. The curve in figure 3.15 is a typical calibration curve plotted by a programmable calculator.

3.7.2 Data Reduction Using Calculated Bessel Function Values

Arguments of Bessel Function Zeros may be calculated when a Book of Tables is not

available or sufficiently inclusive.

The close approximation of any zeroth order Bessel Function can be calculated using the

following relationship:

^o,s =

-

where S = the zero number of interest,

= 0.78540566,

= 0.04055529, and

= 0.00808324.

Thus the first zero of the zeroth order Bessel Function is

^ = TT - + + = 2.40482552

also

and

^0,100 = 1°°^ - ^0 ^ I50 ^ Tl^ = 313.374266.

Values calculated in this manner can be used in the data reduction techniques explained

in section 3.7.1.

The following example is a further illustration of this technique: - T n ^^r,r,r 1 0-0^0555 , 0.0080832

^0,30 = - 0-785406 + 3^ + (30)^

= 93.4610 and J = 2.4048.

U, J.

3-25
So the dB change between the two Is

Theoretical Value - T = 20 log 31.7910 dB. ^^'^g^gj

Mow from figure 3.15 the measured values at the first and thirtieth zeros are \ . T

"^0 1 " ^^-^^^ -^0 30 " ^0-825 dB.

The difference in measured values is

M - 72.619 dB - 40.825 dB = 31.794 dB.

Then the difference between the theoretical and measured values is

T - M - 31.791 - 31.794 = -0.003 dB.

This, then» is the amount of error in the DUT between the readings of 40.825 dB and

72.619 dB (to the accuracy of the SQUID System).

3.7.3 Data Reduction Using a Programmable Calculator

The relationship presented in section 3.7.2 can easily be solved with a relatively

inexpensive programmable desk, calculator. A typical program for the HP 9830 Is presented

in figure 3.13.

The results can be displayed in tabular form and in graphic form as illustrated in

figures 3.14, 3.15, and 3.16.

A further sophistication of this process is the use of the plotter which is driven by

the calculator. A laboratory type calibration curve on the Device Under Test can be drawn

automatically on the plotter. A typical calibration curve is shown in figure 3.17.

Calibration values at convenient attenuator settings between the measurement points can be

read from this curve. A more convenient method of obtaining calibration values at intermediate points along

the curve is to query the calculator. The curve in figure 3.17 is a poljmomial fit to the

original measurement results. The operator has the option of asking the calculator for the

calibration results for any given attenuator setting within the limits of the plotted

curve. Typical results of this process are displayed in figure 3.18 along with additional

information such as the coefficients of the polynomial fit and statistical information on

the data contained in the calibration curve. The plotter program which generated the information appearing in figures 3.17 and 3.18

is presented in figure 3.19.

3-26
10 DIM N[50]5P1[50]!T[50].S[50]

20 DISP ••TYPE IN NUMBER OF DRTfl POINTS''

30 INPUT H0

50 FOR K=l TO H0

60 REFiri HCKIjMCK]

70 I=N[K]

80 Jl=£:. 4o4o3

'?0 J== 1*3. 141 5'?-265358-0 . 73540566+6 . 640552 •?. I +6 . 00S0S324 I t S 100 TCK>20*LGT( J.'Jl

)

116 NEXT K 126 n=T[ 6 ]-i-MC 6 ]• 130 FOR K=l TO N0

140 TCK]=H-TCK]

150 S=S+T[K]-M[K]

160 G=G+':T[K J-MCK j;'T2

170 FORMRT F^.e- F13. 4. Fl 1 . F13. PI -

,

130 NEMT K 196 H=s--No 200 Sl=SQRtG -'NO-fltS)

240 PRINT

250 PRINT " THE MEAN VRLUE OF (T-M;' IS "H 260 PRINT

270 PRINT • THE STfiNIiHRU DEVI AT I ON IS •'SI 230 PRINT

290 PRINT

300 PRINT I THEORY MEHSURED T-M CT-M)-HEhN"

310 PRINT ^ - " 320 PRINT

330 FUR K=l "!U N0

340 WRITE as? i70)N[K];TCK];M[K];T[K]-Pl[ K]; (T[K]-M[K])-S- H0

350 NEXT K 360 PRINT

370 PRINT

380 PRINT

390 PRINT - DEVI ATI OH FROM THE MEHN IN DECIBELS"

400 PRINT " VERSUS HTTENUhTOR SETTING IN DECIBELS"

410 PRINT

420 PRINT

430 PRINT

440 PRINT -0.025 DB "TRB34" 6. 060"ThE59"+0. 025 DB" 450 PRINT + + + + + 0 + + + + +" 460 PRINT

470 I = INT':T[He])

480 FOR L=l iU No

490 K=H0+1-U

500 IF I+6.5:>T[K] then 546

5 1 0 PR I NT THE5 ? I , TRE36 ". , TRB64

526 1=1+1

530 IjOTO 500

540 IF flBS(:u[K]-M[K]>-R;'>0.6005 THEN 570

550 PRINT TRB5.' I.TRB36 ^*^ 5TRB64j I 560 GOTO 630

576 IF (:T[K]-M[K]j-fl<6 THEN 626

580 IF (TEK J-N[K])-R<0.025 THEN 660

590 MCK]=TCK]-0.025-fl

600 PRINT THBS? I<ThB36". "ThB<:36+1000*c <T[ K ]-M[ K ]-H> ) > "*"ThB64j I 610 GOTO 630

620 PRINT TRBSj I ! TAB ( 36+ 1000*(: < TC K ]-M[ K ] >-fl;:' > "*" TRB36 " . "TRB64j I 630 1=1+1

640 NEXT L 650 DATA 1? 72= 338; 2 J 65. 142? 3? 61 . 213- 4? 53 . 524' 5. 56. 474; 6; 54. 32!. 7? 53. 419

660 DATA 3 ? 52 . 226 ? 9 ? 5 1 . 1 68 ? 1 6- 56 .231-12? 48 . 665 ? 1 5 ? 46 . 629 ? 26 ? 44 . 093 ? 25 ? 42 . 1 32

670 DATA 30? 37. 806? 40? 35. 238? 56? 33. 337? 66? 31 . 749? 30? 29. 233? 166? 27. 292

686 DATA 156? 15.972? 266 ? 1 3 . 473 ? 366 ? 9 . 946 ? 466 ? 7 . 447 ? 566 ? 5 . 568 ? 660 ? 3 . 922

690 DATA 700? 2. 582? 300? 1 . 421 ? 960? 6. 399

700 PRINT

710 PRINT " + + + + + 0 + + + + +" 720 PRINT "

. -0.625 DB "TAB34" 6. 000"TAB59"+0. 025 DB"

PRINT

PRIH^

PRINT THE NUMBER OF DATA POINTS TAKEN IS"N0

730 PRINT

740 PRINT

750 PRINT

760 PRINT

770 STOP

Figure 3.13. Typical program for data reduction.

3-27
THE NUMBER OF DhTh POINTS TRKEH IS 12

THE NEFiN ' 'FlLUE OF ':t- H) 18 7. 2 398 IE 84

THE STHr-iriRRn DE V I ATI 0 \ \ I :E; 2 „ 1 683 IE 83

I THEOF:r NE HSU RED T N (T M) HE

1. S I 0 u !' iC.

"i \"'4 „ 1:::, 1 \6

t".t l'".! l"U l"j k) « tJ 8 8 8 8 „ Fi Q B 7

2

..j =...|

.... o 0 „ 398 l;:J II k} 8 2 S Q „ Fi 8 2.

O I -f € ( 1:::, .1. „ 4o,::: £i „ fei 9 5 G Fi „ Q 8 '"I- S' A

'4 o 8 U 2.

i-i

...1 i~i „ 883 k) 1, y y ti kj :, kl 8 '.::' 5

.J ""i 7499 56 ,. 758 k\ „ k\ ti y 1 V\ „ 8 0 iZl t:' J -...I iJ 9 2 iJ

i:::- c

...1 ...I „ 892 k) „ 8 8 8 8 8 « tl 0 i'''

r' 7882 53 „ 698 8 « 8 8 2 2 8 n tl ki i. -"I 5 8 8 3

ir - J

„ ::582 8 „ IJ 8 1 i;:! 8 „ Fi I;3 ;|. Q 51 4471 51 „ 445 8 .1 8 8 2 1 tl B ki 8 1 '4

1 0 50- 5874 58 „ 587 8 1, 8 1 j 8 4 k'\ „ 8 0 Fi '~:> 12 48, 387 1 48 « 889 - 8 „ 8 8 1 9 -0 „ 0026

15 48, 9124 46 „ 3 1 i 8 „ 0 8 1 4' U „ iSi 0 Fi 6

D :[ T ]: i:j n f-- i? o h t \\ e: h e k\ \-\ i w n e: c i b e l £; V e f: 2 u 2 h t' t e: h u r i" ill F: 2 e t' t I N i: ;[ h n e: ij i b e i. 2

2\ 11 ki 2 ki + i?i - - I- + 01,025 DB

^ I46

47

48

49

50

51

52

53

54

55

56

5?

if

60

61

62

63

64

65

66

67

68

69

70

71

72

73

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

6 9

70

71

•1 - - "I -0.025 HB

•+ ki- 0 „ 0 0 0 +8 „ 0; DB

Figure 3.14. Calibration results using 15 zeros.

3-28
THE HUriBER OF DhTh POINTS TRKEH IS 24

THF MCflW '.'Hi 1 IF i a I 1 Q u.

1 n c

'-; T H hJ Ti Pi P Ti Ti F .'T AT TON T '-; '"; c o f1 iTh c „ f-i

I THEORY - MEflSilREn T-M (T-N)-ME

1 72.6176 72. 619 -0. 0020 -0 . 0037

65. 3993 65 . 397 0. 0028 0.00 1 0

3 61 . 4946 6 1 . 493 -0 . 0034 -0. 0052

4 53. 3072 53 . 302 0 . 0052 0. 0035

5 56. 7569 56 . 760 -0. 003 1 -0. 0048

6 55. 0990 55 . 099 0. 0000 -0. 0013

•j7 J 1' • 1 y r d 53. 709 -0. 001

8

-0 . 0036

1-1 O 52. 5073 52. 504 0. 0038 0. 0020

9 51 . 4541 '51 . 454 0 . 000 1 -0 . 00 1

10 50. 5144 50. 514 0. 0004 -0. 0013

12 43. 3941 43. 393 0. 001 1 -0 . 0006

15 46. 9194 46. 92 3 -0 . 0036 ~0. 0054

20 44. 3341 44. 3 8 6 -0. 00 1

9

~0 . 0037

25 42. 4240 42. 423 0. 001

0

-0 . 0008

30 40.3253 40. 325 0 . 0003 "0 . 0009

40 :-:3 . 3 03 9 38. 310 -0. 001

-0. 0029

50 36 . 3593 36. 359 0. 000 8 ~0. 0010

60 34. 7 63

9

34. 764 0. 0049 0. 0031

80 32.2611 . iL. • L- -J 1 0. 004 1 0 . 0023

100 30.3174 30.311 0. 0064 0. 0047

120 23. 7302 28.721 0. 0092 0. 0074

150 26. 7334 26. 781 0. 0074 0.0056

175 25. 4474 25.440 0. 0074 0. 0056

200 24. 2360 24.282 0. 0040 0. 0022

Figure 3.15(a). Calibration results using 200 zeros.

3-29
54

liEVIRTIOH FRO 11 THE HERN IH DECIB

V E R S U S h T T E U H T' 0 R S E T T I h i C;; I \-\ D E C:

I"i +

3 y 40

41

42

43

44

45

4 b

47

43

49

50

51

59

60

61

6 2

6

'3 64

65

6 6

67

6 3

69

70

71

Q „ Q 2 5 I) B

Figure 3.15(b)

Pi .,000 +0 „ 025

Calibration curve for attenuation measurements using

200 zeros. 3-30
THE NUMBER OF DRTfl POINTS TRKEN IS 24

THE MEHN VnLUE OF (T-M) IS 2 . 7 7 4 6 2 E - 0 3

THE STHNDHRD HE VI AT I ON IS 5. 71733E-03

I- THEORY MERSURED T-M < T-M) -ME

1 72. 9670 72 . 980 -0,0130 -0.0157

2 65. 7493 65 . 752 -0. 002 2 -0. 0050

3 61.8446 61.847 -0. 0024 -0. 0052

4 59. 1572 59. 155 0. 0022 -0 . 0005

5 57. 1069 57. 112 -0 . 005 1 -0. 0078

6 55. 4490 55. 449 0 . 0000 -0 . 0028

-f

1 54. 0572 54.057 0. 0002 -0. 0026

8 52.8578- 52, 856 0 . 00 1 8 -0 . 0009

9 51.3041 51 . 806 -0 . 00 1

9

-0. 0047

10 50. 8644 50. 865 -0 . 0006 -0 . 0033

12 49. 2441 49.241 0. 003 1 0. 0004

15 47. 2694 47.267 0. 0024 -0 . 0004

20 44. 7341 44. 730 0. 004 1 0. 0013

25 42. 7740 42. 772 0. 0020 -0. 0008

30 41. 1753 41. 173 0. 0028 0. 000

40 38 . 6589 'Z* C' C' -J 0. 0039 0. 001 1 50 36 . 7098 36. 705 0. 004 8 0 . 0020

60 35. 1.189 35. 115 0 . 0 0 3 9 0. 001

80 32.6111 32. 602 0. 0091 0. 0063

100 30. 6674 30.660 0. 0074 0. 0047

150 27. 1384 27. 132 0.0064 0. 0036

200 24 . 6360 24.625 0.0110 0. 0082

300 21 . i 105 21.099 0.0115 0. 0088

400 18. 6099 18.595 0.0149 0. 0122

Figure 3.16(a). Calibration results using 400 zeros.

3-31
lEVIRTION FROM THE MERH IN DECIBFL

E F: S LI S h 1 J E H 1.1 H T' 0 R S E T T I \-\ G I H D EI C: i: B

31

34

46

41

45

4 b

4?

50

51

54

59

61

i325 DB y „ U

+ --0 -

I f

18

19

£1,

64

65

66

67

68

69

70

71

i-

- -

-I -

-I -

-I + •" -<;:}- i 1 1 1- 0„025 DB 0„000 +i; Figure 3.16(b). Calibration curve for attenuation measurements

400 zeros.

3-32

-

I"

i „ iZi 2 5 using
LDI11 I— rnm Ln

Li- 1 1 Ll. CJ 11 1

1

z ex. 1rv i f • 1—1 1 J Ld 11 t£] I— 1 1 f 1

f 1 LJ —" Ln UJ LL. _J >- Ll. Ltl >- LJ 1 r*i LTI 1 1 Lu LU 1 _J 1

1 1 — 1 nLTI L_i LL. 1 n rv q: — :: CL U ! CL

J— 1- cc m CE IX

ZD ZD ZD

U Z LD Z UJ

LJ Z u UJ LJ 1— 1 1— h- h- m

h- in h- 1— cr

u >- re ! cr t2i m

-BB'BS

-BB'B5 III m

_j

'BB Bh ^

(2i

-BB'BE

LD

crz m

21 _J

q: CD

L_

— Z Ul

Ulm

on

l-BB'BZ ^

ZD

Ul

I—

I-cr

l-BB'BI I X

t—

Lrl

rvi

cr

— > Ul u ^

1^ —1

cr <- > I 3-33
FT. HO

CORP:: CiJE'

E 0 > =

B ( 2 -

R SQUFiPE

0

1. i

!

'1

Vcuhlu::'

'i-'vChlc:>

Y (CflLC)

'i ( CRL.C

)

V<ChL.C)

Y( CflLC;

Y( CflLC

;

= 42

YC CflLC; X = ?44

YC CflLC;

Y( CflLC

:

X-?48

Y( CflLC

;

X = ?50

Y( CflLC

;

! ~ ' :'' 3 Y( CflLC

:

Flsure 3.13. Interpolation between calibration points using computer

curve fit shown in figure 3.17.

3-34
1 000 n I M CC 66 ] ? BC 1 1 ] START

[010 FOR 1=1 TO 11

.020 CC I ]=BC I ]=0

.030 NEXT I .040 FOR 1=12 TO 66

,050 CC n=0

,060 HEX I I ,070 BC 1 ]=1

050 i\=\\=S 1 =S2 = S3=S4 = S5=0

090 DISP riRX. DEGREE=" ; 9

100 ri2=9

110 IF D2>9 THEN 1090

120 DISP "XHINj XMflX J INCRN. = ; 0» 88? 10

130 X1=0

140 X2=S0

150 ^3=10

160 DISP "YMINjVMflXs INCRM.=";-0.025?+0= 025j0.01

170 Yl =-0.025

180 V2=+0.025

190 V3=0.01

200 I = 0<2-yi)---27

210 J=':Y2-Yn/17

220 Y5=Y1-2*J

230 Y6=Y2+J

240 SCALE -8 ? 90 ? -0 . 845 5 0 . 855

242 XRKIS -8 . 025 ? 1 0 ? 0 ? 38

244 YflX I S 0 ? 0 . 005 - 8 . 825 ? 8 . 82

250 PLOT X25Y1

260 PLOT KIjYI

279 PLOT yi5Y2j-l

280 1.1= Yl

290 V=Y2

300 T=Y3

310 Z=FNL0

320 U=X1

330 V=X2

340 T=X3

350 Z=FNL1

360 X3=I

370 Y3=J

3S0 Z=FNK0

390 LRBEL 3j 1 ? 8? 2--3;' 400 DISP "ENTER 1 TO PRINT DhTR"?

410 INPUT P9

420 IF P9#l THEN 1468

430 PRINT

440 PRINT "PT. NO. 'TflE14"X"TflB2S"Y"

450 PRINT

460 DISP "PRESS 'ENTER DRTfl' KEY"

470 END

480 FORNRT 2F7.2

490 DBF FNL<Z)

500 X=RBSU

510 Y=RBSV

520 P=INTLGT<X+'::Y-X>*'::Y>X>)

530 P0=(P<-1 OR P>2)

540 LRBEL 1 . 5? 2? Z*RTNlE + 99? 2--3>

550 FOR K=U TO V STEP T 560 PLOT Kl^ N0T Z+K*ZjK* NOT Z + Y1*Z? 1 570 CPLOT -7.3^-0.3

580 LRBEL ( 1480)K.--(: NOT P8 + P8* 1 0tP )

" -

"

590 NEXT K

600 IF P0=0 THEN 1630

610 LRBEL (f)" X10T"p;

630 RETURN O Figure 3.19. Plotter program

3-35
CO

<

H

<5Q

PiM

H

u^ -Id;

3Z*

r-_

1

I

U~i CO

Lil OJ

C=-j '£>

G'

1—1 LU

= G'

G' —

t

t~i _J

1 t—

I

OJ vi- LU ir

cr-. CO f- IC

:r

j

.0 Z^ 'Z

'11 GI Q_ 1— !— 1—1 CO 1—

f

u_ LU ai iX Li_ 1—1 Z2I

! 1 1—1 !—i 1—

<

LU n L±J G' G' G' '3!' 'S'

-I—

I

Lil '•£1 r-- CO iT' '3 C G' Gi 1—1 n—

1

O

U

C/3 U

H

w

M

H

-ti i—

4

LU

ixi o

-U

I •r-I 'X

L

5l CO

L

o_ Zl! lT. LL. CC' 1—1 CO h-4

Ll. 1—

1

:z: Ll. 1—i zsz

i—

1

1=1 i—1

1—

1

LU 1=1 LU

'Si T1

o j CO y .1 '•£" '3

Lu LU

I—

!

t— i— CO CC'

b-.i b-.i CO OJ 01 LU LU

CC' 'X iX

T—i T i CC' !— 1

! 1

1

-Ii CC'

OJ OJ

i— ii it

1—

1

!x Ix o LU LU

CC= =10' CO Cl.

i I IJ.I

•J :+:

li:

Ll.

Li_ LU

1 I (_j

lii

ll;

'Z'Z'

~\\ Ii CO •zr-. 0~.< 'I'Zi

•Zi' 'IT'

'ZiZ' 1—

1

'ZiZ' 'ZiZ'

i— h- h- h3-36
SELECT DEGREE

1000 IF H <= D2-W THEN 1250

1010 niSP DEU.REu.=";

10-'0 INPUT in

10^.0 IF Bl <= B2-W THEN 1960

1040 niSP "MnK DEU="?D2-W

1050 END

1060 IF W=0 THEN 124U

1070 T=0 . i 10S0 FOR 1 = 1 TiJ Dl + 1 10'30 EC I 1=0

1100 FOR J=l TO ril-I+2

1110 R = a+J-i>*'-I'2+2-t?.5+'.I+J'^'

1 120 BC I ]=BC I 1+Ci: T+J ]*CC R ] 1130 NE^^T J

1140 T = I*(D2+(>;-I J 1150 NEXT I 1160 R1=0

1170 FOR 1=2 TO Di + 1 11K0 R1=R1+CL I*CD2+c.3-I J^-

1190 NEXT I - . 1^00 T0=ci: •;D2+i>*';Di::+i::>^-

J

l^io T0=T0-CCri2+l TT v 1220 BISP ^^jJONE"

1230 END

1240 IF N>D2 THEN I2,y _ 1250 I' ISP "NOT ENOUGH h'UlNTb

1260 END

1270 P=W=1

1280 D2=D2+1

12'='0 FOR J=l i'-' D'^ JIl^/^H^^fx^SSsTi^-USE LONER «fiXIHUH DECREE

1296 PRINT

1297 PR in;

1293 END

1300 CLP ]=SQRCCP]

l -HO FOR 1 = 1 10 B2-J + 1 1320 CCP+I ]=CCP+I T-CCP]

1330 NEXT I 1340 R=P+I

1350 S=R _ , 1360 FOR L=l HJ UZ-J

1370 P=P^i

^ -•c•a FHP M=1 m D'ii + 2-J-L ^ ^ }|?0 CC R+ll-i 3=6C R+M- 1 ]-CC P ]*CC P+M-i 3 1400 NEXl M

1410 R=R+!1-1

1420 NEXl L 1430 P=S

1440 NEXT J

1450 T=':B2+l>*fDi:+2.J^2

14f-:0 FOR 1 = 1

!Li B2-1

1470 T=T-1-I

14ft0 C[T]=1/CCT]

1490 FOR -1=1 TO D2-I

1500 P=D2+1-I^-' . 1510 p = P*CD2+l-':P-l>-^:^^-i

1520 R=P-J

1530 S=0

1540 U=I+J+1

1550 V=P

1560 FOR K=l TO J

1570 V=V+U-K

1580 S=S-CC R+K V ] 1590 NEXT K

1600 C;CP]=^-CCR]

1610 NEXT J

1620 NEXT I 1630 CC 1 ]=1--CC 1 ] .1640 GOTO 10.- 0 3-37
COEFFICIENTS

1000 IF li^Q THEN 1110

1010 PRINT

1020 PRINT CuEFFICIE-NTS"

1030 PRINT

1040 FORNFlT F3,0?F12„4

1050 FOR I~l TO Dl+l

1060 mi T E ( 1 5 ^ 1 0 4 0

:) "

E

( :i: -

1 "

>

b i: i i 1070 \\e>-:t I 10iEi0 PRINT

1090 PRINT 'R SQURRE --^ "Rl/'TO

1100 PRINT

1110 END

PLOT

1 000

1010

1020

1030

1040

1050

1 060

1070

1 030

FOR ;: y=fn:: IF Y-^ PLOT

I'j iJ T 0

PEN

NEXT

Z = FN!- END

TO 2 STEP (X2-

Vb THEN Id'.

"> 1 Fl 0

1. 1

1-,

LETTER

1000

1010

1 020

1 030

1040

1050

DISP "i INPUT I LRBEl

LETTER

Z=FNK0

END

TER : :i: i:

ESTIMATE

1000 DISP

1010 INPUT K 1020 DISP Y(CHLC> = "FNZX

1030 END

LABEL GRAPH

9 9 0 S C RLE 0) 6 Q

,

2 .

7

5 ? 2

.

7 5

1000 LRBEL ( * 5 2 ? 1 , 7 H y , 1 0/ 1 5

)

1010 PLOT 15:. •-2. 25? 1 1020 L R B E L ( ) R T T E H U R T 0 R S E T' T i: \\ G I l-i D E H: I E E 1. 1030 PLOT 5 1. 0= 75? 1 1040 LRBEL (*>"t DEVIATION FROM NuMINflL"

1050 LABEL (*) "VALUE IN DECIBELS"

1060 PLOT 35? 3? 1 1070 L R B E L ( * ) R T T E N U R T 0 R C ft L I B R Fl T I 0 hi

1030 LRBEL (*) "USING SQUID SYSTEM"

1090 L R B E L * " R T T E N U R T

0

R M 0 DEL N 0.

" 1100 LABEL (*) "RTTENURTOR SERIRL NO."

1110 LRBEL ( *

>

" DATE OF CAL I BRAT I ON :

1120 L A B E I... ( * ) "DEGREE OF P 0 L Y H 0 M I R L F I T s " 1130 LABEL "SYSTEM OPERATOR:."

1135 LETTER

1140 END ^ ,o
4. ERROR ANALYSIS OF THE SYSTEM

4. 1 General Information

Determining the exact contribution to the total error in a measurement system of all

possible sources of error is a very difficult task. This section will be limited to a discussion of the major significant contributors to the total system error. The errors in

any system may be separated into two general categories; systematic errors and random

errors.

4. 2 Systematic Errors

Systematic errors can be defined as the errors which cause the average of a well

defined set of measurements to differ from the true value by a constant amount during

repeated measurements. The systematic error is common to each measurement in the set.

4.2.1 Harmonic Distortion

Section 2.3 provides a description of the Fourier frequency components which result

from distortion of the interference pattern. (Details of the derivation of eq. (2.9) are given in section 10, appendix A.) Section 2.3 describes bias set-up procedures which

eliminate many of the errors resulting from harmonic distortion. In this section we consider such errors in detail. Eq. (2.9) and table 2.1 are useful references for this

discussion.

The first low frequency sideband of the carrier contains the desired information as well as some effects of distortion.

00 V ^ = y 2V •J-(nM)J, (nD)sin nB . (4.1)

c d n=l

The first term of the series contains the desired response, Jq(M), and it is desirable to

reduce other terms in the expansion to a minumum. If B is selected so that sin 2B = 0,

that is B = — (or I, = I /4), then the second term, and for that matter all even terms,

I bo are zero. The third term of the series can be made equal to zero by a judicious choice

for D. D = 2ttI^/I^ is adjusted so that J^(3D) = 0, a situation which fortunately puts the

first term, Jj^(D), near its first maximum. Unfortunately, the odd terms at n = 5 and above

are not nulled by this technique.

This procedure, the adjustment of dc and low frequency biases, is the method used to

null out the effects of harmonic distortion of the interference pattern, but one should

recognize that at least the even harmonic content of the pattern can be nearly completely

eliminated by a simple procedure. The even harmonic content is almost solely dependent

on the amplitude of the pump signal (oj^) if the detector used to demodulate the signal

is linear. The sidebands at 20), from the carrier

4-1
V ^„ = y 2V -J (nM)J„(nD)cos nB (A. 2) c d n=l

can be used to affect the adjustment of this amplitude. If one starts with B = -n/l as before, then the odd terms in this series are nulled. The even terms appear at large

amplitude and one can adjust the oj^ amplitude to null this term. Having done this,, the even harmonic terms are doubly nulled (small and sin nB - 0)

.

Even though we can minimize certain terms in eq. (4.1), it is useful to estimate the

magnitude of errors which could arise, thus indicating just how much care must be exercised

in the bias setup procedure. In the limit of small distortion (which we assume is the

usual case), that is, small values for the quantities ^^^^-^^ can make a rather simple

approximation for the magnitude of the errors produced by the distortion. Noting the

identity dJQ(M)/dM = -Jj^(M) and using a linear approximation for the Bessel functions it

is easy to show that

'o<"jo,k>

where

V J, (nD)sin(nB)

n 1 . 'n V^J^(D)sin(B) ^^-^^

and i , is the kth zero of J„ . Thus, the deviations AM depend on the harmonic number

o,k 0 n of the distortion and on the number k of the particular Bessel function zero. For even values of n, it will in general be possible to doubly minimize a . That

n

is, the setup procedure allows one to minimize both ^^/^-^ ^i^*^ sin (nB) /sin (B) . However,

consider the situation where is not zero. For a fixed even value of n, the quantity

J_(nj )/J (j ) alternates in sign as k is increased in integer units from 1. The

absolute magnitude of this quantity quickly approaches a constant for larger values of

k. One normally works with a logarithmic scale so that the errors take the form

20 log[l + (AM^ ^/j^ ^) ] . For n = 2 and = 0.01, the error is 0.017 dB at the first zero and oscillates in sign at higher order zeros. Expressed in decibels, the error decreases

at higher zeros since j^ ^ increases with k. At the seventh zero the error is 0.002 dB

.

V^/V^ is typically less than 0.1 and the magnitude of sin (2B) /sin B - 2B can readily be kept

below 0.01. S^*"^ smaller as n takes on higher even values while sin(nB)/sin B = nB

gets larger (for a fixed error in B) . The net result is that < .001 can be readily

achieved and this results in negligible erro^ at even zeros. Note that a resolution and

stability of B = 2TrI,/I bo = 0.01 or 1,^/1 bo ^ 0.001 is required.

Errors due to odd harmonic distortions do not alternate in sign and are of considerably

more concern. The underdamped SQUID interference pattern is triangular and this develops

into a sinusoidal pattern as damping is increased. It is quite likely that some ^ remnants

of the triangular behavior persist even when the visual appearance is nearly sinusoidal.

A-2
in fact, we speculate that the higher order odd harmonics are attenuated more than the Icfwer

order ones. The Fourier coefficients for a triangular pattern take the geometric series

values of V^/V^ = 1/9, V^/V^ = 1/25, V-,/V^ = 1/49, etc. The setup procedure dramatically

reduces the effect of the third harmonic distortion since D is selected so that J^(3D) = 0 and thus = 0. Odd terms of order 5 and higher remain, however, and it is instructive

to estimate their effect. Since we don't have accurate estimates for V /V,, we take the

n 1 triangular values given above as a worst possible case. Table 4.1 lists the decibel errors

for the 5th through 11th odd harmonics for this worst case. As before B - ''/2 and

J^(3D) = 0 so that 3rd harmonic errors are nulled. Note that errors for n = 7 are worse

than for n = 5. To show how well D must be set we note that at the first zero, if D is

displaced from its proper setting by 1.5% (a = .044) the error is AM = .0028 or 0.010 dB

i »

J

(for worst case, i.e., V^/V^ = 1/9). Development of a sinusoidal interference pattern

dramatically reduces the quantities V /V^ , thus making these errors insignificant.

Table 4.1. Odd harnonic errors for triangular interference pattern.

ZERO • ERROR

NUMBER Fifth Seventh Ninth Eleventh

Harmonic Harmonic Harmonic Harmonic

k V^/V^=l/25 V^/V^=l/49 V^/V,=l/81 V^^/V^=l/121

1 - 0.005 dB 0.004 dB 0.003 dB - 0.002 dB

2 - 0.001 dB 0.006 dB 0.001 dB - 0.001 dB

3 * 0.004 dB * *

4 * 0.003 dB * *

5 * 0.002 dB * * +

* Magnitude of error is less than 0.001 dB + Error drops below 0.001 dB at the 12th zero

4.2.2 Phase Sensitive Detector Errors

Any signal which adds to the 1-kHz null detecting signal and which does not go to zero simultaneously with it will cause a displacement of that null. Possibilities for such errors are examined in the following discussion.

4-3
The low frequency signal is amplified and applied to a phase sensitive detector (PSD)

.

The signal and a reference voltage V^(t) at 1-kHz are applied to a mixer, the output of

which is passed through a low-pass filter and then amplified. The output can be expressed

as

\ . ' T/2

V = 1/T / V (t)V (t)dt (4.5) psd r s

where T is one period of the 1-kHz oscillation and V^(t) is the signal derived from the

1-GHz double balanced mixer and intermediate amplifier (this signal has all the components

given in eq. (2.9)). Ideally, if V^(t) were purely sinusoidal, the output V^g^ would

contain only the 1-kHz components of eq. (2.9) which are given explicitly in eq. (4.1).

This follows from the orthogonality of the sine and cosine functions. However, in practice

V (t) does contain significant harmonics particularly odd value ones and these can be a concern. The third line of table 2.1 displays the response at 3co^. The first term of

this causes no concern since its zeros are in coincidence with the desired response and

the second term is doubly nulled by the setup process. But the third term which represents

third harmonic distortion is near a maximum (J^(3D) ~ 0.42 for J^(3D) = 0) and is thus a potential source of error. This problem is resolved by a simple means. The bandwidth of

the low frequency amplifier which precedes the PSD is narrowed so that only the 1-kHz

component of the signal is applied to the PSD. This eliminates response to sidebands at

2(jj^, 3aj,, etc. The signal applied to the 2-kHz PSD is similarly filtered at 2co, to

d d d

eliminate the same problem at that frequency.

4.2.3 Null Meter Offset

It is essential that the null indicating meter read zero when a null is obtained with

the Device Under Test (variable attenuator). If this condition is not satisfied, that is,

if there is a dc offset signal from the phase-sensitive detector amplifier (see fig. 3.7)

when there is no 1-kHz signal being sent into the 1-kHz amplifier, the data will be erroneous

(see fig. 4.1). The net effect of this type of error shows up as a "splitting" of the data.

That is, the indicated zeros are alternately to the right then to the left of the correct

zeros. This is illustrated in figure 4.1. The amplifier is a very low drift-type amplifier, and the PSD diodes are matched so as to minimize this offset. It is occasionally re- assuring to check the zero offset of the PSD and amplifier A^ . This is accomplished by

turning the gain control in the 1-kHz amplifier (see fig. 3.7) counterclockwise approximately 25 turns or until the rather indistinct clicks occur at the end of its adjustment

range. This operation removes any 1-kHz signal from the PSD driver A^. If the null meter

does not read precisely zero adjust the "BALANCE" pot near A^ to zero the meter. After

this is done, the gain control must be turned clockwise approximately 25 turns to bring

the system to maximum sensitivity.

A similar situation occurs with the 2-kHz PSD circuit. In this case, instea'd of

affecting the zero lo cations directly, the effect is through the 1—GHz bias level. That

4-4
4-5
is, a false zero from the 2-kHz PSD results in an asymetric response of the SQUID because

of improper 1-GHz bias level. See section 2.3 where the effect of 1-GHz bias error is

discussed more fully.

The 2-kHz PSD amplifier offset is adjusted from the front panel of the SQUID Readout

Unit. It is accomplished as follows:

1. throw the PSD switch to the 2-kHz position,

2. press the ZERO push-button switch,

3. adjust the NULL ADJ pot for a meter null,

4. release the ZERO push-button switch, and

5. return the PSD switch to the 1-kHz position.

Since rf signals traveling by different paths from a common source combine coherently,

this source of error also causes a constant offset with respect to current. The errors measured in dB, therefore, vary with order number in exactly the same way as the error caused by third harmonic distortion, as shown in figure 4.2. Once again, this error has

arbitrary sign depending on the phase of the leakage signal.

Let us assume that an external rf signal of amplitude is interfering with the

signal of amplitude which is being measured. The approximate form of the resulting

signal X is then

where to is the angular beat frequency. The functional form of the response of the SQUID

system is then

4.2.4 RF Leakage

4.2.5 External rf Noise

X = X^ + X, cos ojt

V oj

l/o)

/

Jp,(X + X^ cos ojt) • dt.

Using the integral form of J_, and inverting the order of integration, we find

1 V ^ - j J^CX, sin ())) • cos(X sin ^) • d(j).

Making the approximation

1 - 1/4 X2

we f ind

V ^ JqCXq) 8^ [Jo^V - '^2(V]

4-6
too< m <

ri.

aM

4-1 CO CO

CO

Q

(4_l to Q 4J ,—

CO

0) CO o cuM 0

CO CO

CO3Q i

•H

)^

CO OJ&

1)

0)

CO 4JU

(U

M-l

U-l(U %

T3

(U (U

J.)

M

cfl CO H • 3 c O o 3

.H CJM

COO

MO T3 u CO u

OJ

aP *N0I1VIA30

u

•H

4-7
At the zeros of J^,

and

Since

J,(jQ) = 2 . J, (jj/j'0

we find

V

4j

0

J,(jo) .

Hence, to the first order, the displacement 6X of the zeros of the response by this perturbation is

6X = -V/f- . x2/4jQ .

2 2 Hence, the displacement in dB is 20 log^^Cl + X^/Aj^). Note that this error is always

positive. Paradoxically, in the presence of rf interference more power (less attenuation)

is needed to set on the nulls. The error affects the first null strongly, and the others

very little. Typical errors from this source are also shown on figure 4.2.

4.2.6 SQUID Control and Readout Units

The Control Unit and Readout Unit contributions to the systematic error of the total

system are negligible if they are functioning correctly and operated properly (see sections

3.4, 3.5, and 3.6). NOTE: Harmonic content in the rf signal source can cause serious

errors in the measurement results due to harmonic distortion in the SQUID response.

4.3 Random Errors

Random errors for a given well defined set of measurements can be defined as the errors causing a scattering of the measurement results during repeated measurements. The

effect of random errors may be reduced by taking the mean of many repeat measurements.

4.3.1 The Device Under Test (PUT)

Any such device is subject to random errors due to nonrepeatability of the mechanical

drive and positioning mechanism, as well as the mechanical or optical readout and possible

rf leakage at high attenuation values. After these devices are used for long periods of

time, normal wear can cause poorly fitting components which contribute to random errors.

4-8
Calibration (which provides an evaluation of linearity and mechanical tolerances, as well as the repeatability) of these devices is the primary function of the SQUID system.

Calibration of DUT's on a regular basis will greatly increase the ability of a laboratory to

maintain an accurate record of the device's performance and find any sudden occurrence of

excessive errors in the device.

4.3.2 SQUID Control and Readout Units

These units have a negligible contribution to the system total error (provided they are operating properly as previously discussed). However, any significant power supply

fluctuations or ground-loop currents have the potential of causing these units to generate

random error. Any noticeable errors generated in these units would indicate a malfunction

in one or more components.

4.3.2.1 RF Source and Amplifier

Normal random fluctuations in these devices have no significant effect on the total

system error since these units are well regulated and well isolated from the SQUID.

4.3.2.2 Coaxial Switch (Set-Run relay in rf signal path )

This device will have no significant effect on the random error of the system provided

it is functioning properly. Its repeatability and VSWR characteristics were investigated

thoroughly.

4.3.3 Phase-Sensitive Null Detector

This device should contribute a negligible amount of random error to the system when

it is given sufficient warm-up time and operated properly as stated in sections 3.4, 3.5,

and 3.6 of this document. However, this instrument could produce random error if it were

subjected to abnormally high levels of rf signals, rf leakage, rf noise, and line voltage

irregularities

4.3.4 RF Leakage

RF leakage is always a real threat in any measurement system. When sufficient care is

taken in using correct cables and in making each connector secure (tighten carefully with a wrench), this system is not appreciably affected by rf leakage. This was verified during

the final system check.

4.3.5 Noise

Electtical noise consists of unwanted disturbances which tend to obscure the desired

component of a signal. Noise is characterized by a random distribution of amplitude and

frequency [12]. Within the operating range of the system, the net effect of the noise

components in this system averages to a negligible value, provided the system is operated

4-9
properly. Noise effects in the system (at high sensitivities) will only be noticeable on

the phase-sensitive detector null indicator. This random. fluctuation of the null indicator

has been reduced to the optimum level by presetting the gain of the appropriate amplifier.

The useful limit of the system is reached when the noise obscures the signal which produces

a distinct null count indication.

4.4 Total System Uncertainty

The accuracy of the composite system can only be determined by adding the uncertainties caused by all possible sources. This is not an easy task since the actual value

of each of these separate uncertainties is difficult to express as a fixed number.

All sources of error in this system appear to be negligible compared to the uncertainty contributed by the Device Under Test provided the system Setup and Operation procedure is strictly adhered to. Thus the total systematic error of the system is well within

the design goal of ± 0.005 dB/20 dB. The principal sources of the random errors are the

repeatability of the Device Under Test and the effect of the noise on the phase-sensitive

null detector.

When fixed attenuators are calibrated with this system, any uncertainties due to such sources as mismatch and phase shift must be accounted for.

Tables 4.2 and 4.3 compare calibration results obtained on the NBS primary standard to

those obtained on the system discussed in this report. In table 4.2, the DUT was a NARDA

Model 779 10-dB fixed attenuator, S/N 01066. In table 4.3, the DUT was an NBS Model VII

attenuator, S/N 3.

4-10
Table A. 2. Comparison of calibration results for a NARDA Model 779

10-dB fixed attenuator.

DUT Values

Using SQUID

System

dB

9.861

Actual readings obtained on the SQUID System at NBS are given below.

DUT Variable Attenuator (NBS Model VII, S/N, 3)

Position Settings (at zero Number 2)

dB

out 56.577 56.574 56.576 56.575

in 46.712 46.709 46.709 46.708

9.865 9.865 9.867 9.867

Uncorrected Mean Value = 9.866 dB.

Correction from figure 3.15 is -0.005 dB.

Thus the Corrected Mean Value = 9.861 dB.

The discrepancy between these two methods of calibration is

0.003 dB, which is within the uncertainty of the SQUID System.

The uncertainty on the value measured by the NBS primary

standard is much larger than this.

NOTE: Connector repeatability is included in these measurements, but mismatch error has not been calculated

separately.

DUT Values

Using NBS

Primary Difference

Standard in Results

dB dB

9.858 0.003

4-11
Table 4.3. Comparison of calibration results for variable

attenuator.

(NBS Model VII, S/N 3)

DUT Values

DUT Values Using NBS

DUT Using SQUID Primary Differences in

Settings System Standard Results

dB dB dB dB

20-30 10.000 9.996 0.004

30-40 10.001 10.002 0.001

40-50 10.002 9.999 0.003

NOTE: These SQUID System values were obtained from figure 3.18.

The NBS System values were obtained from figure 4.3.

These results (tables 4.2 and 4.3) verify the accuracy of this system

as being well within the accuracy goal of the system over the attenuation range of 20 to 50 dB (50-80 dB of actual attenuation in the

measurement channel which includes the 30 dB minimum insertion loss in

the variable attenuator being calibrated)

.

Similar results were obtained during many different laboratory

intercomparisons

.

This same procedure can be applied to any desired range of values on

the DUT by inserting fixed (or variable) attenuators in series with

the DUT to preset the attenuation value at the first Bessel Function

zero.

4-12
U,?. DE? A-IT'^'^F^'T OF C;Q-^''^F^CE

''ATinMAL ^U^EAU OF '^TA^'DARHS

r.'.^TITUTE FO'-: BASIC ^TA'l^A^^D^

"OULOIR, COLORADO ^05C1

:^FPO^^T nF CALI3RATI0'i

VA.^IAILF ./AVEGUIDE ^ELOW-C'JTOFF ATTE^'U ATOR,

COAXIAL CO^'^IECTO^.S

MATIOf'AL "^'J.IEAU OF STANDA.^'^?^

r.ODEL VII, SE.-^IAL "lO. 3

SU^flTTEn BY:

^'ATIO^'AL 'U^FAU OF STA'.'DARDS

EL E CT :^ 0^'^ A

g:i lT I c s n I \/i ? 1 0^l CIRCUIT- STA^IDARDS '^ECTION

THE ?lEAS'JnEr E''T^ O'-' THIS ATTENUATOR WER'^ ?ERFOR'"ED U^TER A'^BIE^T

CO^'DITIO'iS OF APPRO^T' ATELY '^S DEGREES CE^'TIGRADE A^'D 40 PERCE^'T

RELATIVE HU^MDITY. T'-IE °0-vER PRESENTED TO THE ATTEMUATOR WAS LESS

THAN 2-30 >'ILLIVATT^, THE ATTEMUATOR WAS TERf^ ! AT ED AT EACH E^''D APPROXIMATELY 50 + J 0 OH^'S, THE CALISRATIO'! FREQUENCY OF 53 '^MZ

•JAS ACCURATE TO O'lE PART 1, 302,000. THE CHA^^GE IV. IMSERTIO^

LO-^ WHE'J THE COU'JTER IS I\^CREASED FRO^' A 00^00 REFERENCE SETTING

a:)o the dial is increased fro^ a 3.0^0 refere^'Ce setting IS DDICATED in THE ATTACHED TARLE,

THE INSERTIO'] LOSS OF THIS ATTENUATOR WITH T'-E C^J'T"-; ""T .T

A'lD THE DIAL SET AT 0.000 IS AP^^ROXlf^ ATELY 33.4 '^ECI^ZL".

Figure 4.3. Report of calibration on variable attenuator,

PAGE 1 OF 3

' I'

' 1 , 10 0'"'"

^MV 0- CALI 3RATI0>': . 'GUST 23, 197o

4-13
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U A 1 : 1 T V

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jjc * * >k 5< >k i ^ >^ >^ ^ >^ >ir

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'", ' 91 1 ' ~ ^ » J J T I ^ 1 'j I • y J -i

' '1 ~i c

J . :3 T , , 1 0 c 1 7 1^ T "Tl ;

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a ' -1 , 1 0 1 ^ • J 3

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HATE OF C AL I : .^^.TI O'':

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AUGUST -^.^ 197'

°.^OJFCT ^^0, 07^544^

4-14
VARIABLE WAVEGUIDE SELOW-CUTOFF ATTENUATOR,

COAXIAL CONNECTORS

NATIONAL BUREAU OF STANDARHS

MODEL VII, SERIAL rJO. 3

THIS CALIBRATION IS VALID QfJLY WHEV THE ATTEMUATOR IS SET BY

APPROACHING THE INDICATED VALUE FRO^ A LOWER VALUE OF ATTENUATION,

THREE MEASUREMENTS WERE !^ADE AT EACH ATTEMUATOR SETTING TO FIND THE

MEAN VALUE OF "CHANGE IN riSERTION LOSS" AMD TO ESTIMATE THE STANDARD DEVIATION (S.D.) OF THIS MEAN. EXCEPT AS NOTED aELOW,- A COMBINED ESTIMATE OF S.D. (RMS VALUE OF ALL THE S.C.'S ABOVE) HAS BEEN

ASSIGNED TO EACH MEAN. THE MAXIMUM UMCERTAINTY IS THE SUM OF THE

LIMIT OF SYSTEMATIC ERROR AMD THE RAMDO^^ ERROR WHERE THE LATTER IS

DEFINED AS THREE TIMES THE ESTIMATE OF THE S.D. OF THE MEAN.

FOR CONVENIENCE, USUALLY O^JE OR MORE I MTER^iEDI ATE REFERENCE SETTINGS

ARE USED DURING CALIBRATION^ TO DETERMINE THE ESTIMATE OF STANDARD

DEVIATION OF THE MEAN FOR A SPECIFIC PISERTIO" LOSS SETTING WHICH

WAS MEASURED WITH RESPECT TO AN INTERMEDIATE SETTIMQ, THE S.D. OF

THE INTERMEDIATE SETTT^IG AND THE S.D. OF THE SPECIFIC SETTING WERE

POOLED (VARIANCES ADDED).

FOR THE DIRECTOR,

THE INSTITUTE FOR BASIC STANDARDS

ROBERT A. KAMPER, ACTING PROGRAM CHIEF

GUIDED WAVE METROLOGY

ELECTROMAGNETICS DIVISION

PAGE 3 OF 5

TEST NO.

DATE OF CALI3RATI0NJ

REFERENCE:

AUGUST 20, 197S

PROJECT NO. 2763446

4-15

5. CONCLUSIONS

This RF Attenuation Measurement System meets the original performance goals. The

system has a measurement range of nominally 80 dB including any minimum insertion loss

associated with the Device Under lest (DUT) . The system is quite accurate for calibrating

attenuators over a 50-dB range above their minimum insertion loss.

The optimum use of this system lies in calibrating waveguide below-cutoff attenuators

when the best accuracy attainable is desired. Phase shift and mismatch errors may occur when it is used to calibrate fixed resistive attenuators or step resistive attenuators, if a buffer pad is not used at the input (as shown in figure 3.10). A thorough investigation

of these errors should be performed before this system is used to calibrate attenuators

other than the types discussed in this report.

We have used the SQUID system to calibrate a high quality piston attenuator. Our

results consistently show deviations of 0.003 dB (rms) or less. The reproducibility of a given zero of Jq is 0.001 dB or better for a fixed set of operating parameters. It appears

that the deviations are systematic in nature, depending in part on microwave frequency,

phase of the mixer reference signal, etc.

We want to emphasize that in utilizing the detailed shape of the interference pattern

of the rf-biased SQUID, extreme care must be exercised in both the signal handling and the

fabrication of the junction. A close study of eq (2.4) clarifies the nature of a number of

possible error-causing interferences. An awareness of these problems provides guidance in

the design of the readout system. A study of the equation also shows how one can reduce errors due to harmonic distortion of the interference response, ^/hile these error-reducing

methods are a necessary part of the system operation, it should be recognized that best

results will be obtained when the harmonic distortion of the interference response is

minimized. That is, the proper setting of bias levels can only provide a certain reduction

in errors due to distortion, and thus such distortions should be minimized. We therefore

conclude that the contact parameters are crucial to the concept and that further improvements will require a deeper understanding of the junction operation.

The fact that the junction in our system operates in the nonhysteretic mode means that

the SQUID response is derived primarily from a modulation of the phase of the microwave

signal. This makes the frequency response of the entire system a rather important part of

the detection linearity. Reflections in the microwave components, phase of the doublebalanced-mixer reference, and SQUID resonances each contribute to a nonlinear frequency

response which in turn affects the linearity of detection. W^e suggest that this is at

least partly responsible for the systematic deviations in our calibration results. We

believe that the calibration accuracy of such systems will be improved to better than

0.001 dB when these problems are resolved. One step in this direction would be the use of a cold microwave amplifier in close proximity to the SQUID, which would eliminate the

effect of microwave reflections. Another approach might be to operate in the hysteretic

mode where the phase modulation is a minimum, and thus reduce the importance of frequency

response. To date we have been unsuccessful in this type of operation for reasons which

we do not understand.

5-1
As a final demonstration of the usefulness and simplicity of the technique, we have

turned the system over to a technician who was not at all familiar with the principle of

operation. After some coaching In the use of the system, quite satisfactory results were

obtained. Our Intention is to put this system into routine calibration use and thus gain

long term experience in its operation.

This RF Attenuation Measurement System, using a SQUID, was designed and constructed

under CCG Project Number 72-72C. The project objectives are successfully met.

5-2
6 . ACKNOWLEDGMENTS

The work reported here was performed for the Department of Defense, Calibration

Coordination Group, under CCG Project No. 72-72C.

The authors would like to acknowledge the assistance of the following people in

the design and construction of the RF Attenuation Measurement System, and in the preparation of this document.

R. N. Jones

R. A. Kamper

V. Lecinski

E. V. Rivera

J. E. Zimmerman.

The diligent efforts of Vergie Fudge, Sharon Foote, and Sheila Aaker in typing this

document were especially valuable.

6-1

7. REFERENCES

[I] Kamper, R. A., Simmonds, M. B., Hoer, C. A., and Adair, R. T., Measurement of rf power

and attenuation using superconducting quantum interference devices, Nat. Bur. Stand.

(U.S.), Tech. Note 643, 12-63 (Aug. 1973).

[2] Kamper, R. A., Simmonds, M. B., Adair, R. T. , and Hoer, C. A., Advances in the measurement of rf power and attenuation using SQUIDS, Nat. Bur. Stand. (U.S.), Tech. Note 661,

27 pages (Sept. 1974)

[3] Adair, R. T. , Simmonds, M. B. , Kamper, R. A., and Hoer, C. A., RF attenuation measurement using quantum interference in superconductors, IEEE Trans. Instrum. Meas.,

Vol. IM-23, No. 4, 375-381 (Dec. 1974).

[4] Kamper, R. A., Superconducting Devices for Metrology and Standards, Chapter 5 in

Superconductor Applications: Squids & Machines (Plenum Publishing Corp., N.Y.,

N.Y, 1977).

[5] Petley, B. W. , Morris, K. , Yell, R. W. , and Clarke, R. N. , Moulded microwave SQUID

for rf-attenuator calibration, Electronics Letters, Vol. 12, 237-238 (1976).

[6] Strait, S. F. , Development of mechanically stable, thermally cyclicably point contacts for use in superconducting devices. Report //1636, Cornell Materials Science

Center, Ithaca, New York (1971).

[7] Simmonds, M. B. , private communication (unpublished).

[8] Zimmerman, J. E. , Thiene, P., and Harding, J. T., Design and operation of stable rfbiased superconducting point-contact quantum devices, J. Appl. Phys, Vol. 41,

1572-1580 (1970).

[9] Silver, A. H. and Zimmerman, J. E., Quantum states and transitions in weakly connected

superconducting rings, Phys. Rev., Vol. 157, No. 2, 317 (1967).

[10] Sullivan, D. B. , Superconducting quantum interference devices: An operational guide for

rf-biased systems, Nat. Bur. Stand. (U.S.), Tech. Note 629, 3-10 (Nov. 1972).

[II] Abramowitz, M. and Stegun I. A., Handbook of mathematical functions, Nat. Bur. Stand.

(U.S.), Applied Math Series 55, 409 (June 1964).

[12] IEEE Standard Dictionary of Electrical and Electronics Terms, IEEE STD 100-1972

(Wiley and Sons, N.Y. , N.Y. , 1972).

7-1

8. COMPONENT INFORMATION

The components listed in tables 8.1 through 8.6 are the major electrical and mechanical

components used in this RF Attenuation Measurement System.

Commonly available stock items such as connectors, switches, interconnecting cables,

and miscellaneous hardware are not listed in detail. Critical items are detailed on the

appropriate circuit diagrams.

8-1
Table 8.1. Components contained in SQUID readout unit mainframe.

Component

Mainframe

Oscilloscope

Digital Counter

Readout Unit

Description

AMCO Engineering Co.

APDM 14-WA-C-H

HP Model 1200B

HP Model 5301A

NBS Model 3

Quantity

1

1

1

1

Component

Helium Dewar

(30 litre)

SQUID

Dip Tube

Table 8.2. Cryogenic Components.

Description

Minnesota Valley

Engineering

Model USHE-30A

NBS Model CTG-30

See Appendix B

Figures 10(b), (c), & (d)

NBS Model 3

See Appendix B

Figure 10(o)

Quantity

1

8-2
Component

Table 8.3. Major Components in SQUID readout unit,

Description

Mainframe with ±15V dc, lA

Power Supply

Plug-In Module

Hardware & Connectors

RF Source Plug-In

Power Supply

±15V dc, 90 mA

Power Supply

±15V dc, 150 mA

Coaxial Switch

Termination

Null Indicator

(100-0-100 yA)

Phase Sensitive

Detector Circuits

Burr-Brown

Model 506/16A

Burr-Brown

Model/16

NBS (See Table 8.4)

Lambda LZD-22

Lambda LZD-23

HP 8761A with

SMA Connectors

SMA 50 ohm

API Instruments Co.

Model 447-101R3

See Appendix B

Figures 10(e) and (j)

Quantity

1

8-3
Table 8.4. Components in rf source plug-in.

Component

Amplifier

Attenuator

Capacitive Termination

and RF Output Level

Control

180* Hybrid Junction

Signal Source

Termination

Assorted Cables

Description Quantity

Greenray Industries, 1

Model X-133A

3 dB, 2 watts, Narda, 1

Model 4778-3

Variable Piston Capacitor

Johanson Type JMC 190C

0.7 - 30 pF 2

Merrimac Model CHTM-30/13291 1

CTS Knights, Inc. Model VCXO 1

Part No. 970-3367-0

SMA 50 ohm 1

Appropriate Lengths of 0.358 cm 4

diameter semi-rigid cable with

SMA Connectors on Each End

Assorted Connectors

and Adapters

SMA as Required

8-4
Table 8.5. Major

Component

Master Circuit Board

Directional Coupler

1 GHz, 20 dB

RF Detector

1 GHz Phase Shifter

Coaxial Low

Pass Filter

SMA Tee

SMA Adapters

Coaxial Cables

components in SQUID control unit.

Description

DC & 1 kHz Bias Circuits

See Figures 3.7 and 10 (e)

OMNI Spectra

Model 20063-20

Merrimac Double Balanced

Mixer Model DMM-2-500

Merrimac Model PSM-2/22401

NBS Fabricated

See Appendix B, Figure 10 (n)

OMNI Spectra Model 20200-2

SMA Double Male

SMA Elbow

Semirigid With SMA Connectors

(Length As Necessary)

Qxiantity

1

DC Bias Voltage Ultra Stable DC Bias 1

Reference Circuit Board Supply, See Figure 10 (g)

1 GHz Oscillator AVANTEC VTO 8090 1

& Voltage Variable AVANTEC UTF 015 1

Attenuator AVANTEC CASE TC2M 1

1 GHz Amplifier AVANTEC UTO 1011 (12 dB Gain) 1

40 dB Gain AVANTEC UTO 1521 (28 dB Gain) 1

AVANTEC CASE UCS2M 1

1 GHz Amplifier AVANTEC UTO 1511 (10 dB Gain) 1

10 dB Gain AVANTEC CASE USCIM 1

1 GHz Oscillator Midwest Microwave

Output Attenuator Model 205-60 dB 1

1 GHz OSC REF Midwest Microwave

Output Attenuator Model 205-3 dB 1

8-5
Table 8.6. List of suggested external coaxial cables & adapters.

Component

RF Cable

(CBL-1)

RF Cable

(CBL-2)

Microwave Cable

(CBL-3)

DC Power & AC

Signal Cable (CBL-4)

Digital Counter

Input Cable (CBL-5)

Oscilloscope Vertical

Input Cable

(CBL-6)

Description Quantity

1.5 Meters RG-9B/U With 1

Male Precision Type N

Connector on Each End

(Input to DUT)

2 Meters RG-9B/U With 1

Male Precision Type N

Connector on Each End

(From DUT to SQUID RF Port)

8 Centimeters 0.358 cm diameter 1

Semirigid Coax With a Male

SMA Connector on Each End

See Appendix B 1

Figures 10(k) and (q)

0.5 Meter RG-55/U With a 1

BNC Male Connector on Each End

2 Meters RG-55/U With a 1

BNC Male Connector on One End

& Rear Panel Input Connector

Supplied With Oscilloscope on One End

Oscilloscope Sync

Signal Cable

(CBL-7)

Assorted Adapters

2 Meters RG-55/U With a BNC Male Connector on Each

End

Precision 14 mm to Precision

Type N Male

Precision 14 mm to Precision

Type N Female

Precision 7 mm to Precision

Type N Male

Precision 7 mm to Precision

Type N Female

Other Adapters As Appropriate

For Calibrating Various Devices

Under Test

8-6
9. APPENDIX A

FREQUENCY SPECTRUM FROM THE SQUID

The SQUID response given by eq. (2,8) (including harmonic distortion) is

00

V((}>) =

J V co8(2TTn(j)/4> ) . (9.1)

n"l

The flux applied to the SQUID consists of a signal at o) , a low frequency bias at to,, and m a

a dc bias, the sum of which is

<t> = i> sin(aj t) + (\>j sin(aj,t) + <t>, . (9.2) ^m m ^d d ^b

Using notation introduced in section 2, the argument in eq. (9.1) is written

2Tr4 n — = n

277(1) 2tt(1)j 2iT(i). *" d . , ^. b

sin(a) t) + —— sin(aj,t) +

m 9 a

= nM sin(cj t) + nD sin(tD,t) + nB . (9.3) m a

To simplify notation let Msin((i)^t) * m and Dsin(aj^t) = d. Expansion of the cos term in

eq. (9.1) then gives

cos(nm+nd+nB) = cos(nB) [cos(nm)cos(nd) - sin(nm)sin(nd)

]

- sin(nB) [sin(nm)co8(nd) + cos(nm)sin(nd) ] . (9.4)

The following Bessel function identities are required to complete the derivation.

00 co8(Z sin e) = J (Z) + 2 J J (Z)cos(2ke)

8in(Z sin 6) = 2 J (Z) sin(2k+l) 6 . (9.5)

Note that, if m and d are replaced by their sinusoidal values, all 8 terms in the

brackets in eq. (9.4) have the form of the identities in eq. (9.5). Eq. (9.4) thus

becomes

00 f

00 00 V » y V • co8(nB) [J„(nM) + 2 T J_, (nM)co8(2ka3 t)][J (nD) +21 J- , (nD)cos(2Ja) -t) ]

, n U , . ZK m o . - zi a n=l k-1

^ - w

00 r 00 00 - I V Jsin(nB)[jQ(nM) + 2 J J2j^(nM)cos(2ku3^t) ] [2 I J2,^j^(nD)sin(2j+l)aj^t]

[ n"l ^ k=l j=0

00 ^ 00 00 ^ -

I V^|sin(nB)[2 I J2j^_^^(nM)sin(2k+l)a)j^t] [ J^(nD) + 1 I (nD)cos(2ja)^t) ]|

00 00 00 N -

I V^Jco8(nB)[2 I

J,, .,(nM)sin(2k+l)a) t][2 I J,, . . (nD)sin(2J+l)a) ,t] i , (9.6)

n-1 k-0 ^^^^ " j-O ^^^^ ^ ^ 9-1

10. APPENDIX B CIRCUIT DIAGRAMS AND COMPONENT DETAILS

A detailed, itemized list of parts is not included in this document since its primary

use is to aid in the operation and maintenance of the system. The critical parts necessary

for the fabrication of this system are listed on the drawings in figures 10(a) through 10(q).

Non-critical common stock items, such as machine screws, are not listed here.

10-1
< C/3 X

COA MHz OAD C

CO C in

m

c/3 CO

C/)

rnrrrsAAAi

N

U3

•H

fX4

o

I

13 O

o fo

1^Q

O CO H !z: a

u

M

H

S3O

10-2
son TERMINATION SIGNAL COIL

SIGNAL INPUT

O. \

READOUT COIL

SQUID SIGNAL

READOUT INPUT

3^

Figure 10(b)

DIAGRAM OF MICROWAVE BIASED SQUID NBS

MODEL CTG-30 WITH PERMANENT POINT CONTACT

CARTRIDGE

«NOTE = NOT SHOWN ARE CAPS OVER BOTH ENDS WHICH SERVE TO SEAL THE SYSTEM

AGAINST MAGNETIC FLUX LEAKAGE

10-3

10-5

10-7

INPUT FROM \m PSO

P7(H)

INPUT FROM I KHZ PSD

NULL COUNT

OUTPUT

(TO COUNTER)

METER

AMPLIFIER

ABSOLUTE VALUE

CIRCUIT

BLOCK DIAGRAM

HOT CARRIER

DIODES .... . HP 5082 - 2811 100 - 0- 100 /iA NULL INDICATOR

P7(ll) P7(J) TO METER SELECTOR SWITCH

ON 2 KHZ PSOPLUC-IN SCHEMATIC DIAGRAM

0 V

ISV -I5V P 9

P7(A) P7(C) P7{D) P7{L)

NULL INDICATOR AND NULL COUNTING TRIGGER CIRCUITS (CONTAINED IN NULL INDICATOR PLUG-IN)

Figure 10(h)

10-9
CAPACITIVE TERMINATION (TMCi)

L.

30 MHz

SI6NAL SOURCE

RF OUTPUT LEVEL CONTROL

(TMCt)

30 MHz AMPLIRER Ut ATTENUATOR

BLOCK DIAGRAM

3) HYBRID (T

JUNCTION^

®

RF OUTPUT

P8

r

-T~ IN 5255 _2jT

1 30 MHz

15 V VCXO

J +

SET UP RUN

SCHEMATIC DIAGRAM

RF SOURCE PLUG-IN

Figure 10(i)

10-10 177X2610 )
Jo

o

10-11
AXIS OF STMttETRT FOR 90IH CABLE ENDS

OUTER BRAID ^ BlA ®®®

©® ® ©

® ® ®

H5V

F o

SIGGHO

-©_BRO»N_ -(o) RED

SIC OUT r

VIDEO

BfHOIX PTCKT CONNECTOR

Ic-lOP REAR VIEf (FENALE)

C

J <^

0 ° j^-ISV

E

-I5V

BENOIX PTCKT IMOP KALE TTPE CONNECTOR THIS END OF CABLE

C REEN

BROWN

RENDU PTCMT CONNECTOR

IZ-lOP FEMALE TYPE -DC PO«ER AND AC SIGNAL CABLE CONTAINS 4(F0UR) RC-IT4 COAX CABLES AND 6(SIX)#26 STRANDED

HOOR OP HIRES ALL WITH PVC INSULATION ALL fITHIN A SHIELD. CABLE LENGTH TO BE 5 KETERS

DC POWER AND AC SICNAL CABLE DIAGRAM

TTP PIN SCHEDULE

CONNECTORS JB.JT.JB.JS

ii

(IF OUTPUT

0.359 cm DIA SEMI-RICID 6 4CIII LONG

IITH SNA MALE CONNECTOR ON EACH END

SQUID READOUT UNIT MAIN FRAME WIRING DIAGRAM

Figure 10 (k)

10-12
3Cin LENGTH

OF N0.22 STRANDED HOOR-UP WIRE

ASSEMBLY OF COMPONENTS

VARIABLE PISTON CAPACITOR JOHANSON ,7-30 /i/iF

^36.69min (1.562

) ^

(*540")DIA t

1 l2.7mni(.500")0IA

1

r

3.17 mm (.125")

1.59 mm (.062")

13.72mm (.540")0IA 1

I 12.7 mm (.500") DIA J

1

9.9! mm (.390") DIA

f

NOTES

A) ALL DIMENSIONS IN MILLIMETERS - DIMS. IN BRACKETS DENOTE EQUIVALENT VALUES IN INCHES

B) 12.7 mm (.500") D. IN BOTH COMPONENTS IS NOMINAL - ASSURE APPROX. 0.05 mm (.002") CLEARANCE

TO ALLOW CAPILLARY FLOW OF SOLDER (USE LOW MELTING POINT SOLDER)

C) FABRICATE COMPONENTS SHOWN IN DETAIL FROM BRASS

D) INSTALL CONNECTOR IN ONE END OF TUBING AS SHOWN ON ASSEMBLY DRAWING AND SOLDER

IN PLACE USING LOW MELTING POINT SOLDER - FILL ALSO GAPS BETWEEN INNER SURFACE

OF TUBE AND SIDES OF HEXAGONAL NUT OF CONNECTOR

DETAILS OF COMPONENTS TO BE FABRICATED

CAPACITIVE TERMINATION TMC,

FOR USE ON PORT 1 OF 180" HYBRID JUNCTION

(RF OUTPUT MINIMUM ADJUST)

Figure 10(1)

10-13

I7?x m I
~1

s; e —

1

1 1 ^ — IT

1- ^ r T

1

i S is

3

ii o

1— C3 H

««: Q <U

LlJ to ^ U

or —

1

M

oo ^ •H

LU Q_ CO O

10-14
NOTES

A) ALL DIMENSIONS IN MILLIMETERS - DIMENSIONS IN BRACKETS DENOTE EQUIVALENT VALUES IN INCHES

B) TURN DOWN ON LATHE HEX. PORTION OF FEED-THROUGH CAPACITOR TO 7.25mm (.285") OIA ; MODIFY SOLDERING

PINS ON BOTH ENDS AS INDICATED - DEPTH OF 0.7 mm (.028") DIA HOLE TO BE 1.6 mm (.063")

C) TRIM WIRES OF RF CHOKE AS NECESSARY

D) MODIFY LENGTH OF DIELECTRIC IN SMA CONNECTOR TO NOTED LENGTH - CUT ALSO LENGTH OF CTR. PIN TO CORRECT

CORRESPONDING LENGTH; HOLE IN CTR.PIN TO BE 0.7mm (.028") DIA « 2.5nim(.098") DEEP

E) SOLDER ALL COMPONENTS USING LOW MELTING POINT SOLDER

LOW PASS FILTER

Figure 10 (n)

10-15
I246.l9inin{49.062")

1270.0 mm (50.000")

NOTES:

3.17mm (.125")

CUT NOTCH IN TUBE AS SHOWN (TO CTR.OF DIA.)

STAINLESS STEEL TUBE

3.17mm (.125") O.D.x 0.38mm (.015") WALL

1246.19mm (49.062") LONG

^8.89mm(.350")DIA

[*-6.35mm(.250")DIA

-*tt|!W-3.l7mm(.l25")()IA^—BRASS COLLAR

9.14mm (.360")

31.75mm (1.250")

^STANDARD COPPER REDUCER (FOR SOLDERING)

H— 15.87mm (.625") DIA - 17.78mm (.700")DIA

A) ALL DIMS. IN MILLIMETERS - DIMS. IN BRACKETS DENOTE EQUIVALENT VALUES IN INCHES

B) DIMENSIONS INDICATING RESPECTIVE DIAMETERS OF COMPONENTS WHERE SOLDERED

ARE NOMINAL - ALLOW ENOUGH CLEARANCE FOR CAPILLARY aOW OF SOLDER

C) SOFT SILVER SOLDER ALL COMPONENTS

DIP TUBE

FOR DETERMINATION OF LIQUID HELIUM LEVEL IN STORAGE DEWAR

Figure 10 (o)

3078

10-1'6
10-17
CBL-4

Figure 10 (q)

CABLES USED IN OPERATING SQUID SYSTEM

10-18
11. APPENDIX C SYSTEM OPERATION AT OTHER FREQUENCIES

This SQUID Attenuation Measurement System can be used quite satisfactorily at any frequency from 10 KHz to 100 MHz. A good quality signal source must be substituted for the

30 MHz signal source contained in the system. The signal source to be used must have good

amplitude stability and must be used with a good quality low pass filter on its output.

Any harmonic of the measuring signal frequency which is allowed to reach the SQUID will

cause a SQUID response which is not ideal and this will produce erroneous measurement results.

A detailed discussion of these effects appears in Section 2.3.

The total system accuracy and precision should not be significantly affected by operating

at other frequencies provided the above procedure is followed.

Procedure for Substitution of an Alternate Frequency Source

1. Switch the 30 MHz Setup-Run switch to Setup. (This connects a 50 ohm load to

the output of the 30 I-IHz source.)

2. Disconnect the RG9B/u cable from the "rf output" jack J4.

3. Perform the system setup procedure as presented in Section 3.5.

4. Attach the appropriate low pass filter to the alternate frequency signal source output.

5. Adjust the signal level to 300 milliwatts (nominally) at the filter output.

6. Connect the RG9B/u cable (removed from J4) to the filter output.

7. Proceed with the attenuation measurement as outlined for 30 MHz in Section 3.6.

Caution: The rf signal source should not be connected to the SQUID during the setup

procedure. Improper setup conditions can result and this will cause incorrect attenuation

measurement results.

11-1

NtS-lUA (NCV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOCRAPtHIC DATA

SMCET

1. PLMLK-AllUiN UK Kr,KUKl riU. NBSIR 77-863

A* \Joy t Accession

No.

J. Kecipient s Acces.sion No.

4. TITLE AND SUBTlTLt

RF Attenuation Measurement System Using a SQUID

5. Publication Date Septenber 1977

4. Perfofming Org&nizfttioQ Code

276 and 275

7. AUTHOR(S)

Robert T. Adair, Nolan V. Frederick, and Donald B. Sullivan

1. Performing Organ. Report No.

PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2761446

11. Contract/Grant No.

CCG Project No.72-72C

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Army/Navy/Air Force

Calibration Coordination Group

13. Type of Report ft Period

Corered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

1i. ABSTRACT (A 200-word or leaa factual aummary of moat ai^tiflcant Infomatlan. If docunwnt includea a al0tlficant bibliography or literature survey, mention it here.)

This report describes a unique portable system for measuring attenumtion at

30 MHz over a range of 50 dB to an accuracy of 0.005 dB per 20 dB. This system

does not require any reference standard. A SQUID (Superconducting QUantum

Interference Device) vith its associated instnuaentation is used to determine

attenuation in terms of Bessel Function Zeros. A SQUID is a loop of superconducting metal closed by a weak point contact called a Josephson junction,

operating in liquid helium.

The system specifications, description, and theory of operation are presented. A complete system operating procedure including data reduction techniques is given along with a discussion of sources of errors. Considerable additional information and diagrams are presented as an aid to

the user in understanding and operating the system.

17. KEY VORDS (six to twelve entries; alphabetical order; cepitaUMC only tfie firal letter of Ae ffrat key word unleaa a proper name; separated by aemicolons)

Josephson junction; quantum interference; rf attenuation; superconductivity.

U. AVAILABILITY [X, Unlimited 1». SECURITY CLASS

(THIS REPORT)

21. NO. OF PAGES

1

' For Official Distribution. Do Not Release to NTIS

UNGL ASSIFIED 160

1

' Order From Sup. of Doc, U.S. GoTcrnment Printing Office Waahin.ton. D.C. 20402. SO Cat. No. CH20. SECURITY CLASS

(THIS PAGE)

22. Price

Order From National Technical Information Serrice (NTIS)

Springfield, Virginia 22151 UNCLASSIFIED

$8.00

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