UNITED STATES :PARTMENT OF OMMERCE

UBLICATION

-vi- /*

NBS TECHNICAL NOTE 619

U.S.

PARTMENT

OF

OMMERCE

National

Us 753

to. &/9

Millimeter Attenuation

and Reflection Coefficient

Measurement System
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards1 was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and

technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measure- ment system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Center for Computer Sciences and

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2 Part of the Center for Radiation Research.

3 Located at Boulder, Colorado 80302.
lational Bureau of Standards OCT 1 8 1972 P^Crf- OCC

Qc loo

c, &—

UNITED STATES DEPARTMENT OF COMMERCE

Peter G. Peterson, Secretary

(j.% NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

NBS

tTECHNICAL NOTE 619

ISSUED JULY 1972

Nat. Bur. Stand. (U.S.), Tech. Note 619, 175 pages (July, 1972) CODEN: NBTNAE

Millimeter Attenuation

and Reflection Coefficient Measurement System

B. C. Yates and W. Larson

Electromagnetics Division National Bureau of Standards

Institute for Basic Standards

Boulder, Colorado

"*f*u of

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide

a means for making available scientific data that are

of transient or limited interest. Technical Notes may

be listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D. C. 20402

(Order by SD Catalog No. 03.46:619). Priced, ,-£)

Contents

Page

Abstract 1

1. Introduction 1

2. System Description and

Measurement Procedures 2

2.1 Magnitude of reflection coefficient 2 2.1.1. Subsystem description 3 2.1.2. Measurement procedure 4 2.1.3. Brief modified ref lectometer

theory and tuning procedure 9

2.2. Attenuation 13

2.2.1. Subsystem description 13

2.2.2. Measurement procedure 14

3. Systematic Measurement Errors 15

3.1. Ref lectometer errors 16

3.1.1. Tuning errors 16

3.1.2. Precision Section error 18

3.2. Attenuation errors 20

3.2.1. Mismatch error 20

3.3. System measurement errors - Attenuation and/or reflection

coefficient magnitude 22

3.3.1. Converter linearity error 22

3.3.2. System instability error 23

3.3.3. Leakage error 24

3.3.3.1 RF Leakage 24

3.3.3.2 Intermediate Frequency

Leakage 26

iii
3.3.4. Signal-to-noise error 27

4. Standards 28

4.1. Reflection coefficient magnitude

standards 28

4.2. Standard attenuator 31

4.3. Interlaboratory standards 32

4.3.1. Reflection coefficient 32

4.3.2. Attenuation 35

5. Measurement Results 37

5.1. Reflection coefficient magnitude 37

5.2. Attenuation 39

Figures 1-21 43-63

Appendix A. 64

Appendix B. Estimated systematic error limits for

WR15 attenuation measurements 66

Appendix C. Estimated systematic error limits for

WR15 reflection coefficient magnitude

measurements 67

Figures 22-27 68-96

Appendix D. Machine drawings for

11 stub tuner for 5 5-65 GHz, WR15 68

Appendix E. Machine drawing for sliding

load for WR15 waveguide 72

Appendix F. Machine drawing for sliding dumbbell

short for WR15 waveguide 74

Appendix G. Machine drawings for four piece brass and

invar precision waveguide for WR15 76

Appendix H. Machine drawing for quarter-wave short

circuit for WR15 waveguide 80

IV
Appendix I. Machine drawings for circular waveguide

below-cutoff attenuator for nominal

30 MHz operation

References

82

97

LIST OF FIGURES

Figure 1. Block diagram of the reflection coefficient

magnitude subsystem using an i-f receiver.

Figure 2. Detailed diagram of the reflection coefficient

magnitude subsystem.

Figure 3. Detailed diagram of the two-loop automatic

frequency control network.

Figure 4. Waveguide termination.

Figure 5. Diagram of a tunable, single -directional

coupler ref lectometer (modified reflectometer)

.

Figure 6. Block diagram of the i-f series substitution

attenuation subsystem.

Figure 7. Detailed diagram of the rf receiver of the

attenuation subsystem.

Figure 8. Graph for estimating the magnitude of 1/K

given a response variation R when sliding a load with return losses of 30 to 70 decibels.

Figure 9. Graph for estimating the equivalent generator

impedance for a given response variation

R x 10 when sliding a short-circuit termination

Figure 10. Change in reflection coefficient magnitude

versus dimension change in the nominal waveguide width of 0.148 inch.

Figure 11. Change in reflection coefficient magnitude

versus dimensional change in the nominal

waveguide height of 0.074 inch.

Figure 12. Graph for estimating mismatch error limits

when the attenuation and system VSWR are given.

Figure 13. Theoretical mixer power conversion non-linearity

versus master-local oscillator power ratio.

Figure 14. Quarter-wavelength short-circuited waveguide

standards

.

vii
Figure 15. Graph for estimating the change in reflection

coefficient of a quarterwave short circuit

versus conductivity confidence interval (the

relative error substracted from unity)

.

Figure 16. Current distribution for a rectangular

TE,

n mode short-circuited waveguide.

Figure 17. Graph for estimating the change in reflection

coefficient magnitude of a quarterwave short

circuit versus dimensional deviation from

height dimension of 0.074 inch.

Figure 18. Graph for estimating the change in reflection

coefficient magnitude of a quarterwave short

circuit versus dimensional deviation from

nominal width dimension of 0.148 inch.

Figure 19. Waveguide-Below-Cutoff attenuator.

Figure 20. Typical change in narrow dimension of

rectangular waveguide used for interlaboratory

reflection standards.

Figure 21. WR15 ref lectometer and associated support

hardware

.

Figure 22. Machine drawings for 11 stub tuner for 55-65

GHz, WR15.

Figure 23. Machine drawing for sliding load for WR15 wave- guide . Figure 24. Machine drawing for sliding dumbbell short for

WR15 waveguide.

Figure 25. Machine drawings for four piece brass and invar

precision waveguid'e for WR15.

Figure 26. Machine drawing for quarter-wave short circuit

for WR15 waveguide.

Figure 27. Machine drawings for circular waveguide belowcutoff attenuator for nominal 30 MHz operation.

vm
MILLIMETER ATTENUATION AND REFLECTION COEFFICIENT

MEASUREMENT SYSTEM

B.C. Yates and W. Larson

Abstract

This paper presents the details to implement a WR15 attenuation and reflection coefficient magnitude

measurement system. A discussion of precision and of

systematic error is given along with equations for

estimating limits of the error. Machine drawings are provided to fabricate the waveguide standards and

necessary hardware not commercially available.

Key words: Attenuation; Measurement system; Millimeter;

Reflection coefficient, VSWR.

1 . Introduction

In the Electromagnetics Division of the National Bureau

of Standards, Boulder, Colorado, work is proceeding toward

the establishment and extension of calibration services at

frequencies in the millimeter region. Among the work com- pleted at this time is a system for the measurement of

attenuation and reflection coefficient magnitude on waveguide

devices in WR15 waveguide. The purpose of this report is to

describe this calibration system and include the instrumentation,

measurement procedure, and error analysis employed in the

system development and evaluation.
2 . System Description and Measurement Procedures

The system can be conveniently broken into two parts for

the purposes of description and discussion. The part (subsystem) dealing with measurement of reflection coefficient

will be described first.

2 . 1 Magnitude of Reflection Coefficient 1

Immense improvements in reflectometer techniques over

the past few years have made this method most accurate for

the measurement of microwave and millimeter impedance (VSWR

and reflection coefficient) 2 [1,2] 3. In particular, the

: The reflection coefficient r at a single frequency, and for a single mode of propagation having a sinusoidal time variation,

is the ratio of the incident to reflected wave amplitudes at a given terminal plane in a uniform waveguide. The reflection

coefficient is a complex number having both a modulus (magnitude)

and argument (phase).

2 The voltage standing-wave ratio (VSWR), in terms of the

above -defined reflection coefficient, is given by the relation,

i + | r|

VSWR = a =

i -

| r|

The converse relation (i.e., |r| in terms of c) is

a - 1 r

+ 1 A more complete discussion of reflection coefficient and

VSWR is given by Beatty [2].

Note: The symbol a is widely used to denote conductivity,

but is used in this note only to designate VSWR.

3 Figures in brackets indicate the literature references at the

end of this paper.
tuned modified ref lectometer , a single directional coupler

with associated waveguide tuners, offers the best performance

and accuracy over a large dynamic range. Untuned reflectometer

techniques [3] have also been developed which provide a reasonable accuracy.

2.1.1 Subsystem Description

Figure 1 is a block diagram of the reflection coefficient

magnitude calibration subsystem presently in use at NBS

.

The measurement system incorporates two microwave oscillators

,

the master oscillator (MO) and the sawtooth-modulated local

oscillator (LO) . The MO is tuned to the calibration frequency

and controlled with an AFC circuit. The LO center frequency

is tuned to either 30 MHz above or 30 MHz below the MO frequency

MO energy is propagated to the reflectometer where it is

reflected from the item under test and is applied to a mixer.

LO energy is also coupled directly to this mixer to produce

an i-f response of 30 MHz. The i-f response is then transmitted through a monitor network, which also provides a ground return for the mixer diode, and into a 30 MHz

waveguide below-cutoff (WBCO) piston attenuator. Next, the

attenuator output is amplified, detected, and filtered.

The filtered voltage is then applied to a monitor scope and a strip chart recorder. For a dynamic range greater than 40 dB

,

the sawtooth audio modulation is amplified following the i-f

amplifier and synchronously detected.

3
Figures 2, 3, are more detailed diagrams of the system.

In order to provide a coherent scope response, system

stability, and wide dynamic range, a sawtooth voltage is

superimposed upon the LO repeller voltage to frequency

modulate (± 2 MHz) the LO. If better system stability than

the modulated method provides is required, the LO can be con- trolled by an AFC circuit to maintain the i-f center frequency

at a fixed 30 MHz. This can be accomplished by employing

a separate AFC loop such as shown in figure 3. For more detail on system stability see section 3.3.2.

2.1.2 Measurement Procedure

The measurement is performed by: 1) attaching the unknown

test item, V , to the ref lectometer , 2) adjusting the gain

of the amplifier to obtain a convenient reference response on

a recorder (meter) , 3) replacing the test item by a reflection

coefficient standard (|r | - 1), and 4) adjusting the 30 MHz

standard attenuator to obtain the original output on the

recorder. The reflection coefficient magnitude can then be

calculated by using the formula,

L R

= 20 lo §10 T^T'

TM

' u

'

where L„ is the measured relative return loss (the attenuation

difference between |r1

I and |r I). Tables are available to

s ' ' u 1 J
facilitate the calculation of |r [41. Alternately, |r

can be calculated from the equations,

L R

= -20 log

10

|T| (2)

and

r u l = |r s

| • I r I - (3)

When measuring terminations having a sliding load (fig. 4)

as a terminating element, both the maximum and minimum reflection coefficients are measured. Usually the reflection coefficient of the termination is taken as the average of these

measurements

.

Terminations having a small reflection coefficient

(|r| _< 0.01) and a sliding load | I", | as a terminating element

are difficult to measure. Since both reflections are small,

it is not possible to immediately identify whether the average

reflection coefficient Irl i i belongs to the sliding load or ave & 6

to a discontinuity (fig. 4) associated with the termination.

(For «. the case (Irl vii > 0.011,j , iIrli is equal to the reflection

ave I coefficient of the discontinuity |r„| (to an order of |r

T

| 2

) provided that | F„ | > | I\ | ) . This is because the average value

of reflection coefficient is associated with that element

which has the largest reflection (see Appendix A).

The usual method to separate the two reflection coefficients is to insert a low-loss discontinuity either inside

the termination or attached to the waveguide flange of the
termination in order to provide a reflection which is large

compared to that of the sliding load. A flat metal plate with

dimensions smaller than nominal waveguide dimensions and which

has a VSWR - 1.2 can easily be attached to the termination

and also provide the necessary discontinuity. An alternate

method is to use two different, sliding loads inside the termination if it is physically practical.

The measurement procedure is to attach the plate to the

termination, measure the maximum and minimum reflection

coefficients as a function of the sliding load, and calculate

the respective ^ VSWR's, o and o . . (The d superscript ' max mm v r r

is used here to denote the VSWRs measured with the discontinuity

(plate) attached.)

The VSWR of the load a

T is calculated from the equation

[5]

a T =

A /

d

a /

d

U mov' a mm. . (4) *• -* L y max' min'

Next, measurements of the maximum and minimum reflection

coefficients are made with the discontinuity (plate) removed,

and the maximum and minimum VSWRs (a and a ) are calcu- max mm

lated. Here, a and a . are not to be confused with the ' max mm

VSWRs in eq. 4 but pertain only to the VSWRs with the discontinuity (plate) removed. Substitution of a and a . ' r max mm

into the equations,

o-. = o /o . , (5) 1 a / max mm

v *"
and

o n =Ja a '. , (6)

2 v max mm' v J

yields the VSWRs of the termination discontinuity and the

sliding load where a, and o

? are the VSWRs of the elements

with the smallest and largest reflection, respectively.

Comparison of eq. 5 and eq. 6 with eq . 4 removes the ambiguity

as to which VSWR is associated with the sliding load and

which VSWR is associated with the termination discontinuity.

When measuring terminations or nominally nonreflecting

one-ports'* which have a return loss greater than the dynamic

range of the measurement system, other measurement procedures

must be used. Four suitable techniques are described below.

The last two methods to be described (rf and i-f substitution)

can be also implemented for measuring attenuators over an extended attenuation range. Details on direct substitution

attenuation measurements are given in reference [6]. All

methods assume that adequate signal power is available.

The first method is to measure the return loss in two

steps , first calibrating the reflection coefficient of a transfer standard having a return loss of about 32 dB (|r| =

0.025) by the method described previously. Then, with the

power level at the measurement port increased to compensate

4 A nominally nonreflecting one-port is a termination which

is intended to produce no reflection or nearly no reflection (| T

| < 0.001) .
for the return loss of the transfer standard (32 dB) , the

unknown |r is compared to the transfer standard. I r i is i u i f i u i calculated from eqn . 1 where |ri is the reflection coefficient

s

i magnitude of the transfer standard. Alternately, the return

loss of the transfer standard can be added to the measured

return loss to obtain the return loss of the unknown.

The second method utilizes a reflection coefficient

standard that is fairly close in magnitude to the unknown

termination. In this case only a relatively small return

loss measurement which is within the dynamic range of the

system need be measured. Some excellent possibilities of

reflection coefficient standards of low VSWR are discussed

in section 4.1.

The third method utilizes a calibrated rf attenuator

isolated from and located between the generator and reflectometer. This method makes a direct comparison between the

standard of reflection coefficient (|r - 1) and the unknown.

When the unknown is compared to the standard, a portion of

the substituted return loss is placed in the rf attenuator

and a portion in the i-f 30 MHz standard attenuator and the

losses summed. The unknown is calculated from eq. (1).

Since the rf attenuation in the third method is not

always accurately known, the fourth procedure makes use of

the i-f attenuator to determine the attenuation in the rf
attenuator. To do this the i-f attenuation is transferred to

a second auxiliary rf attenuator. Next, the attenuation in

the original (third method) rf attenuator is measured with

the i-f attenuator. The sum of the two i-f attenuator losses

is then used in eq . (1) to calculate |r | . Although this

method is tedious, it has been found by experience to be more accurate than the third method.

2.1.3 Brief Modified Ref lectometer Theory and Tuning Procedure

For the measurement procedures outlined previously to

be valid, the output response from the modified ref lectometer

must be proportional to the reflection coefficient of the

device located at the measurement plane. In order to obtain

this output response, the imperfections in the directionalcoupler- tuner assembly and the reflections from the

equivalent generator are eliminated or minimized by appropriate tuning adjustments as will be described.

When a signal originating from the generator is incident

on a device presenting a reflection coefficient, r , at

terminal surface T_ (fig. 5) in a reflectometer , a portion

of the reflected signal is coupled to the output arm of the

coupler. The output response b-, can be expressed by the

equation [1 ] ,

1 b (7)

3 = c

, K

+ F L

i - r . r T 2i L
where r o . is the reflection coefficient of the equivalent 2i n source impedance looking back from T„ and

|K| - |S 21 | 10 D/2 ° (8)

D is the directivity of the reflectometer and the

transmission coefficient, S~, , is defined as the ratio of

the wave amplitude at T~ to that at T-. when T

? is terminated

by a nonreflecting device. S~, has magnitude values of

approximately 0.707, 0.95, and 0.995 for a 3 dB , 10 dB , and

20 dB coupler, respectively. Thus, when employing a coupler

with a directivity of 40 dB , is approximately 0.01 to

1*1 1 0.014 (3-20 dB coupler). These values of can be equal

|K|

to or larger than | I\ | so that from eq. (7) it can be seen that

considerable error could result if the assumption were made

that b, was proportional to I\ . In the denominator of eq. (7),

the magnitude of r

? .r, is relatively small but still gives an appreciable error which will be discussed later.

Since both the directivity and T . errors are significant

in the detected reading of the reflectometer , it is necessary

to reduce their effects by appropriate tuning operations which

are to raise the directivity of the reflectometer and to

reduce r„. to a negligible value. Reduction of T~. to zero implies the elimination of multiple reflections at terminal

plane, T~. If one could make the directivity infinite and

10
r„. = 0, eq. (7) would become

b

3

= c'f

L

(9)

In other words, the output would be directly proportional to

the reflection coefficient of the device connected to T~ , and

the ratio of the |b,| response from the device to the

response from a standard of reflection coefficient would

give the proper value of T, (see eq. (1)). Although in

principle these conditions are realizable, in practice it

is possible only to approach them. However, one can approach

them so nearly that only a small residual error remains.

This deviation from perfect tuning conditions causes what is

called the tuning error. The section on measurement errors

gives the formulas to calculate the limits of tuning error. For a more detailed discussion of tuning theory see [1,2].

Various techniques can be employed in raising the

directivity of the ref lectometer and reducing r„. to a negligible value. The individual techniques which are preferred by most metrologists are reviewed here.

The directivity of the ref lectometer is raised by

inserting a sliding load of small reflection coefficient

(VSWR of 1.01 to 1.001) into the uniform precision waveguide

(fig. 5) and adjusting tuner A for a null response at the

detector. (It is possible to obtain a false tuning adjustment

11
if the null is not obtained first). Next, while the sliding

load is moved (at least a half wavelength) to obtain the

maximum- minimum variations, tuner A is adjusted to make these

variations as small as possible. Usually a variation of 0.5

to 1 dB is considered satisfactory.

After making the directivity adjustment, a sliding

short circuit is substituted for the sliding load in the

precision waveguide to make the T~. adjustment. Tuner B is

adjusted to minimize variations in |b,| in the same manner as tuner A except that a detector null is not obtained originally.

The adjustment is usually continued until the T

?

. variation is

less than 0.005 dB . An automated carriage has been devised

to facilitate the tuning procedures [7] and its use or a similar device is highly recommended for tuning at millimeter

frequencies

.

It is always necessary to repeat the directivity adjustment (tuner A), after adjusting tuner B, but the r_.

adjustment (tuner B) usually need not be repeated again if the

output variation is reduced to 0.002 dB or less originally.

These adjustments should provide the necessary conditions that

the output signal is proportional to the reflection coefficient

of the device at T«, so that the measurement methods outlined

can be used.

12
Machine drawings for fabricating the tuners, sliding

load, and sliding short are given in Appendices D, E, and

F respectively.

2 . 2 Attenuation 5

The i-f substitution technique is most widely accepted

as the most accurate and most versatile method of performing

attenuation measurements over a wide range of frequencies

.

Several system configurations are possible with this measurement technique [6]. The most commonly used is the series i-f

substitution system shown in figure 6 and described below.

2.2.1 Subsystem Description

The basic series i-f substitution system for measurement

of attenuation incorporates the hardware of the reflection

coefficient subsystem; the insertion point for attenuators

being located at the terminal plane for reflection coefficient measurements. The reflectometer provides a "matched

generator" and is also used to tune the receiver port so that

there are no multiple reflections between the input and output ports of the device -under- test and the system into which

it is inserted.

5 Attenuation is a general transmission term used to denote a decrease of signal magnitude, usually resulting from either a dissipative or reflective loss. In this note, the term

attenuation also implies a non-reflecting system at the place

where the attenuator is inserted.

13
A signal from the MO is propagated through the reflectometer and device-under- test (insertion point) and frequency

converted (heterodyned) to 30 MHz by mixing with the LO

.

After the 30 MHz signal is attenuated by the WBCO standard

attenuator, it is amplified, detected and displayed on a monitor scope and chart recorder.

With this system configuration a change in attenuation

(e.g., an increase) in the device-under- test requires a corresponding change (decrease) in the WBCO attenuator. Thus,

this configuration is called a series i-f substitution system.

2.2.2 Measurement Procedure

Preparatory to making a measurement the ref lectometer

in the RF source portion of the waveguide system is tuned

by the procedures outlined in section 2.1.3 in order to

present a matched generator to the test device. The RF detector section (fig. 7) contains a precision waveguide and a waveguide tuner which is the output port of the insertion point.

After the ref lectometer is properly tuned, the insertion point

is closed and aligned. The waveguide tuner in the RF detector

section is then adjusted for a ref lectometer null response

(i.e., no i-f detector response). This completes the tuning

adjustments necessary to present the device -under-test with a matched insertion point.

14
The measurement is performed by: 1) inserting the device

under test into the system at the insertion point, 2) adjusting

the gain of the i-f amplifier to obtain a convenient detected

reference response on a recorder (meter) (Note: when measuring

variable attenuators, the gain is adjusted with the rf attenuation inserted), 3) removing the rf attenuation, and 4) substituting i-f attenuation from the WBCO standard to restore the

detected response to the reference value to obtain a direct

measure of the rf attenuation.

When setting either the standard or a rotary vane attenuator, the dial should always be turned in the direction

of increasing attenuation to avoid backlash effects from the

gear mechanisms.

Alternate methods for making attenuation measurements

when the dynamic range of the detector system is exceeded are described in section 2.1.2.

It should be noted that alignment of the flanges between

the device-under- test and the insertion point should be as exact as possible in order to obtain repeatable measurements.

3 . Systematic Measurement Errors

The discussion of the limits of systematic measurement

errors encountered is divided into three parts . The first

part deals with errors in the measurement of reflection

coefficient. The second part deals with errors due to mismatch

15
in measuring the attenuation. And the third part deals with

errors common to the measurement of both attenuation and

reflection coefficient. Estimated systematic error limits

for NBS WR15 components and systems are summarized in appendices

B and C.

3 . 1 Reflectometer Errors

3.1.1 Tuning Errors

Evaluation of the tuning errors in a tuned reflectometer

is very important. Since the ideal conditions of K = °° and

T„ . = will not be realized in practice, the relation 2i ft

b, = c'I\ will not be exact, and a residual error is present

in the measurement.

The maximum relative error in an unknown test item,

|r | , due to K f

°° and T

?

. = is given by the equation, 6

I dr I , I

r

e | + I r I (10)

r k r r u ' ' ' ' u s

r u

K

where |K| is approximated by eq . 8 and | T | is the reflection

coefficient magnitude of the standard.

To obtain the approximate magnitude of K, a load of

small known reflection coefficient, r. , is placed in the

precision waveguide section and its phase is varied by sliding

it more than one-half wavelength. Next, the attenuation

difference, R, in decibels between maximum and minimum output

6 Equation (10) contains a typographical error in reference [2]

16
signal variation is noted. This is the variation observed

when raising the directivity of the ref lectometer (section

2.1.3). Then, |K| is calculated from the equation,

in R/20

|K| = ^ U . (11)

(io R/2 ° - i) |r L

| The estimation of 1 /

| K | is facilitated by figure 8.

A typical value that can be obtained when sliding a load

(|r

L

| = 0.001) is R = 0.5 dB so that |K| * 3.5 x 10

1*. This

corresponds to raising the directivity of the ref lectometer

to greater than 90 dB . At millimeter wave frequencies 80 dB

is usually the upper directivity limit that can be maintained

for a three to four hour time interval without readjustment,

while 90 dB can be maintained over the same interval for

microwave frequencies

.

The maximum relative error due to r.. ^ but K = °° is 2i

given by the relation, 7

I dr I fir I + I r I) I r„. i

i u ' , v ' u ' ' s ' J ' 2i

in R/20

r 2i | = - (13)

: S 2 Si-, (12)

I r I l - |r,. r I

1 u

' 2i u

where \T n . is obtained from the equation. 2i

n '

10

R / 20

- 1

(io R/20

+ i) I

r

L in which R is now the output dB variation observed when a short circuit (

| r. | - 1) is slid more than one-half wavelength

Typical values are |r | = 0.996, and R = 0.003 so that

'Equation (12) contains a typographical error in reference [2]

17
|r_. - 0.0002. The estimate of |r 1 o .| is facilitated by

2 x

'

' 2i

'

3 figure 9

.

The above results should not be difficult to obtain

provided good tuners and reasonable system stability are available. As a word of caution, the tuning conditions are sharply frequency sensitive and cannot be accurately maintained

unless the master oscillator is frequency controlled.

Equations (10) , (11) , (12) , and a form of (13) were

presented in reference [2].

3.1.2 Precision Section Error

Although the precision section of waveguide used in the

reflectometer is carefully constructed and considered to be a standard transmission line, and thus could be discussed in the

section on standards, it is also an integral part of the reflectometer. Thus, the errors associated with that waveguide section

are presented here.

A major portion of the ref lectometer error is caused by

the cross -sectional deviation of the precision section from

standard waveguide dimension. It should be noted that this

particular error is the limiting factor in obtaining better

accuracy in waveguide impedance measurements , because it is

possible to reduce the tuning errors to a value much smaller

than the precision section error. Although present fabrication techniques make possible a waveguide tolerance of ± 50

microinch, this error can be significant. The quoted limit of
error from this source may be actually too conservative, and

a future reduction may be possible if and when a more rigorous

mathematical analysis of this type of problem can be performed

The residual reflection coefficient magnitude caused

by dimensional deviations Aa and Ab in the a and b dimensions

respectively, is given by the formula,

Af = 2 A

c

J

Aa

4a

Ab

(1 + o)

(14)

where

a = the broad waveguide dimension,

b = the narrow waveguide dimension,

X = the guide wavelength,

A = the cutoff wavelength,

o = the measured VSWR of the item under test. (Not to be

confused with conductivity of the metal)

.

This formula considers only the change in characteristic

impedance of the waveguide. Also, the respective error terms

are derived while holding the other waveguide dimension constant

at the nominal dimension. The "a" dimension error term is

believed correct to 2 percent. The "b" dimension is correct

to 1 percent for VSWR's less than or equal to 1.1 and varies

to 101 for VSWR's of 2. Graphs of the respective errors for

WR15 waveguide are given in figure 10 and figure 11.

Another possible error is due to the fact that the inside

corners of the waveguide are filleted and not sharp.

19
The reflection from the junction of standard rectangular waveguide to filleted waveguide has been derived [8] and is given

by the expression,

'A R

AT =

4 - TT 8ab I a j where R is the radius of curvature of a filleted corner

and the other parameters are as given for the previous

equation

.

Machine drawings for fabricating brass and invar

precision waveguide sections are given in Appendix G.

(15)

3 . 2 Attenuation Error

3.2.1 Mismatch Errors

The error due to mismatch must be considered in making

attenuation measurements because the attenuator is not

always inserted in a perfectly matched system.

The attenuation difference of a variable or rotary-vane

attenuator is measured by moving the vane from a zero or reference angular position to the desired vane angle or attenuation. The mismatch error [9] is expressed for the

attenuation difference measurement by the equation,

e(dB) = 20 log

1(

(i - (£) r.r ) (i - ^s^r,

)

fi - t^r.r ) ri -

( f)

i g

(16)

S 22V

20
where the frontscripts (i) and (£) , refer to the initial and

final values, respectively, and V. is the input voltage reflection coefficient of the variable attenuator when the attenuator is terminated with a load (receiver) of reflection

coefficient, I\ . r is the reflection coefficient of the

L g generator, and S~~ is the reflection coefficient at the output

port when the input port is terminated with a load | I\ | =0.

For insertion loss measurement of a fixed attenuator

the mismatch error [6] is given by the equation,

Id - s r )(i - s r ) - s s r r | e(dB) = 20 log 1f1 ±±-& ±L± iZ Z1 L g » (17)

1 1 - r r T

I

1 g l

1

where S, , is the attenuator input reflection coefficient, and

S, „ and S^-, are the attenuator transmission coefficients.

Figure 12 can be used to quickly estimate the mismatch error

for fixed attenuators having attenuation of 20 dB or more.

A typical value of mismatch error is approximately 0.008 dB for

WR15 attenuators (fixed or variable) with a system VSWR of 1.02

at the insertion point. The magnitude of this error is

approximately 50 percent of the total systematic error for

attenuation measurements from zero to 30 dB, and approximately

20 percent for a 50 dB measurement (see also Appendix 3)

.

21
3. 3 System Measurement Errors -- Attenuation and/or

Reflection Coefficient Magnitude

3.3.1 Converter Linearity

A knowledge of the degree of linearity of the power

conversion of the mixer is essential in the i-f measurement

system. When using a diode mixer in heterodyne receivers,

nonlinearity is always present. This nonlinearity is a function of the ratio of the local oscillator power to the

master oscillator power. Empirically, it has been shown in

the NBS WR15 waveguide system that a 27 dB ratio (i.e.,

the MO power 27 dB down from the LO power) will give a non- linearity less than 0.003 dB over the measurement range of

0-50 dB when the LO power is set at 2-3 mW at the mixer.

The deviation from linearity is reduced when the signal power

in the mixer is decreased relative to the local oscillator

power. These results are in good agreement with the theory

[10] (see figure 13)

.

In practice, the degree of linearity is established by

measuring the same known attenuation step (e.g., 5 or 10 dB)

at various power levels over the required measurement range.

The difference between the measured value at the higher

level and the value of attenuation at low levels, AdB (decibel),

is the converter nonlinearity.

22
The relative error in reflection coefficient magnitude

due to nonlinearity is calculated from the formula,

I Ar l = 0.115 AdB (18)

where AdB (decibel) is the deviation from linearity. The error for an attenuation measurement is AdB.

3.3.2 System Instability

Instability errors caused by power or frequency fluctuations are dependent on the particular generators, amplifier,

detectors, power supply, and frequency stabilizer used and

cannot be predicted in advance for a particular system. The

variation of the output signal from an average power level can be held to less than ± 0.1 dB with a stable power

supply and water cooling of the rf source (klystron). Phase

locking the signal klystron to a stable source operating at a lower frequency (fig. 3) can hold the i-f output level fluctuations to approximately ± 0.005 dB for a 30-60 second interval.

The two-loop AFC used here accomplishes this stability with

only a water-cooled LO. When the two-loop AFC was applied to

the LO also, the stability was held to better than ± 0.002 dB

for a 1-2 minute interval. Frequency stability of this

system (WR15) is approximately 1-2 kHz short-term and 5-10 kHz

daily drift.

23
Instability errors are usually treated as random errors

of measurement, a value being assigned after several hundred

random measurements are made. When only a few measurement

data are available, the error is formulated from eq . (18).

Connect-disconnect instabilities and repeatabilities of

flanges , attenuators , and terminations are discussed in Section

5 . 1 and 5.2.

3.3.3 Leakage

3.3.3.1 RF Leakage

The effect of rf leakage becomes noticeable and increases

the measurement error when measuring an attenuation ratio of

35-40 dB or more. This applies to a typical system where no special precaution has been made to control the leakage.

The maximum attenuation error can be computed from the

equation [11]

,

AdB = 20 log. (19)

where P„ and P, represent the signal power and leakage

power, respectively. The reflection coefficient error is

given by applying the results of eq. (19) to eq . (18).

In practice eq. (19) is not easily utilized, because

an accurate measure of the leakage power cannot be made, but

it can be applied to yield approximate error limits. A

suggested method is to use a RF receiver (e.g., the attenuation

24
LO receiver) with an incorporated dial readout attenuator

attached. This receiver is mobile enough to be placed near possible sources of leakage and can give an indication of

the leakage signal. The receiver can be "calibrated" by the

usual attenuation measurement system.

The leakage can be eliminated or minimized by several

trial - and-error techniques. Placing the signal sources in

shielded containers will usually sufficiently reduce this leakage source. Waveguide joints can be wrapped with steel wool

or metal foil, and polytetrafluoroethylene-metal gaskets [12]

have been used at microwave frequencies. Also, if the system

is of a permanent nature, painting joints with a solution

containing a high silver content will eliminate the leakage.

Unfortunately, a major source of leakage may be the test item

(e.g., a rotary vane attenuator). In the case of some commercial attenuators, the leakage power is down only 40 dB

from the incident power in the waveguide and it is rarely

down more than 60 dB. Fabrication techniques for NBS rotaryvane attenuators using absorbing material have been devised

to reduce the leakage to more than 120 dB below the incident

power [13] . Leakage in an NBS fabricated WR15 rotary-vane

attenuator was shown to be at least 80 dB below the incident

power

.

25
3.3.3.2 Intermediate Frequency Leakage

I-f leakage is present around the standard attenuator,

i-f amplifier, converter, and the associated i-f coaxial cables.

The leakage from the standard attenuator can be contained

by proper fabrication techniques. The i-f amplifier should

be placed in a shielded container which has filtered power

input connectors. The coaxial cable connector leakage can be

reduced by wrapping the joint with lossy cloth and metal foil,

but the suggested procedure is to use a conductive silver paint

on threaded connectors and pack metal foil around the outer

walls of BNC type connectors.

A field strength meter and probe or alternately an additional i-f receiver can be used to detect this type of

leakage . If the i-f leakage cannot be controlled adequately (30-50 dB

range), a rf substitution in conduction with the i-f substitution (similar to the method used for nonre fleeting terminations (see Section 2.1.2)) will usually overcome the problem,

since the signal power will be much larger than the leakage

power. Although this method requires an additional calibration,

it may yield a more accurate attenuation measurement. The

technique is to remove approximately 20-25 dB of attenuation

from the attenuator which holds the MO-LO 30 dB ratio (for

power linearity) to an auxiliary attenuator. The unknown item

is then calibrated by using the attenuations of the rf and

i-f attenuators.

26
At least 20-25 dB (the amount removed previously) must be

measured by the rf attenuator. If the i-f leakage cannot be

reduced to a negligible amount, an estimate of its AdB

attenuation change can be treated as a systematic error as

in the case of rf leakage.

3.3.4 Signal- to-Noise Error

In the series i-f substitution system used at NBS , it has

been demonstrated experimentally that attenuation measurement

error due to noise is not significant. This is because the

principal noise present in the 30 MHz detection system originates from the i-f amplifier and not the mixer. Thus, since

the i-f amplifier receives a constant signal level from the

30 MHz attenuator, as is the case with the series i-f substitution, no apparent signal-to-noise error arises. The latter

statement assumes a 50 dB range only. (There may be some range greater than 50 dB where the mixer noise dominates).

An error due to noise that may be significant is that due

to loss of readout resolution (i.e., the true signal level is

not readily determined from the random variations caused by

noise) . This problem can usually be corrected by using a long

time-constant filter after the amplifier detector when measuring over a dynamic range of 0-50 dB . Also, the resolution can

be improved by increasing the signal power and using the i-f

and rf substitution technique described previously.

27
The measurement error from random variations due to a

small signal-to-noise ratio is the observed readout variation

in decibels for attenuation measurements, and the associated

reflection coefficient error is given by eq. (18).

4. Standards

4 . 1 Reflection Coefficient Magnitude Standards

The standard of reflection coefficient used for impedance

measurements at NBS is the quarter-wavelength short-circuited

waveguide, more commonly called the quarter-wave short

circuit (fig. 14) . The main advantages of this type of standard are: 1) the

reflection coefficient magnitude can be calculated from

derived formulas given in references [14], [15] if conductivity

or attenuation measurements [16], [17] of the waveguide are available. Relatively crude measurements of conductivity

will suffice to obtain the reflection coefficient to excellent

accuracy (fig. 15). For example, a 20 percent error in the

conductivity measurement will result in only a 0.015 percent

error in the standard; 2) the axial component of current

vanishes a quarter-wavelength from the shorting plate (fig. 16)

which makes the dissipative loss in the waveguide joint negligible; and 3) small dimensional variations in the waveguide cross section have a negligible effect on the reflection coefficient. An increase in height of 0.001 inch causes 0.0008

28
percent change in reflection coefficient (fig. 17) at

62.5 GHz; an increase in width of 0.001 inch causes approximately a 0.001 percent change at the same frequency (fig. 18).

NBS short circuits are fabricated from electroformed silver

or copper to a tolerance of ± 0.0002 inch for the narrow and

wide waveguide dimensions.

The critical dimension of a short circuit is the length

(ideally a quarter wavelength) . The length of the short

circuit must be accurately dimensioned in the fabrication

process in order to achieve the vanishing of the axial component of current at the connector surface. If the electrical

length is different from that at the design frequency, current

will flow across the discontinuity and result in a loss of

power, so that the reflection coefficient will be less than

the calculated value

.

The proper length of the short circuit corrected for

the change in phase factor due to guide attenuation [18] is

given by the equations

,

A a

I = (1 + a /3) 4 3 ep

(20)

and

where

b(A/U

ep [2(b/a)(A/A

c

) + e r

] (21)

a = the measured waveguide attenuation constant,

m

& '

29
and

2tt 3 = t— = the wave phase factor,

g

A = the guide wavelength,

A = cutoff wavelength,

A = free space wavelength,

b = narrow inside dimension of waveguide,

a = broad inside dimension of waveguide,

e = relative dielectric constant of the laboratory

environment

.

The reflection coefficient magnitude (|r |) is given

by the equation,

r = 1 - 2a(i + I ) s

^ ep y (22)

The attenuation constant is obtained by comparing the

change in attenuation between a quarter-wave short circuit

and a five-quarter-wave short circuit which is designed to

operate at mid-frequency (mid-frequency is not essential) of

the particular waveguide band. The attenuation at other

frequencies in the particular waveguide size is given by the

equation

,

a = a

1 1 3/2 r f

f .

e r

+ 2(b/a)(A/A

c

) 2 1

e + 2(b/a) (A /A ) 2 r

y

' J y w cnr ;

U ) 2

»> gm

(23)

where the m-subscripted parameters correspond to the parameter

wavelength values at the mid-frequency f . The reflection coefficient magnitude measurement error

due to the quarter-wave short circuit is directly related to

the error of the standard. In other words,

30
dr ar

J

' ' s

'

r iiI I r I

i si

The fractional error in the reflection coefficient of the

NBS quarter-wave short circuits is estimated to be less than

± 0.03 percent

.

Machine drawings for fabricating quarter-wave short

circuits are given in Appendix H. The previous discussion on quarter-wave shorts does not

mean to imply that other reflection coefficient standards

could not be fabricated in WR15 waveguide. Examples of several

possibilities are half-round inductive obstacles [18, 19],

waveguide irises, inductive and capacitive posts [20, 21] and

waveguide holes [22].

4 . 2 Standard Attenuator

The IF substitution method has been used at NBS for com- parison of attenuation difference and insertion loss in waveguide sizes WR2 8 to WR4 30 for many years. This method employs

a waveguide below- cutoff (WBCO) attenuator operating at the

selected frequency of 30 MHz. The WBCO is a continuously

variable attenuation standard whose incremental attenuation

may be closely predicted from a knowledge of its waveguide

dimensions [23]. If the waveguide section is uniform, nearly

lossless, and excited sinusoidally in only one mode, the field

decays exponentially along the waveguide in a predictable manner

31
Thus , a probe or pickup coil which is moved a known distance

(with respect to an excitation coil) along the waveguide axis causes a calculable change in insertion loss. If certain

constraints are applied regarding frequency of operation,

resistivity of the waveguide, and the waveguide dimensions,

the attenuator will constitute a nearly ideal standard.

Grantham and Freeman have published detailed theoretical

factors affecting the design of the WBCO attenuator and its

use as a standard attenuator [24]. The NBS Monograph 97 [6]

treats the WBCO for general considerations, dimensional

tolerances and accuracy of measurement of displacement, skin

depth corrections, loading effects, and mode purity.

The errors in the NBS WBCO attenuator is estimated to

be within 0.002 dB + 0.002 dB/20 dB. The error in reflection

coefficient magnitude is given by application of eq . (18).

The machine drawings required to reproduce the NBS model

VII WBCO standard attenuator are included in Appendix I. Figure 19 is a photo of an NBS WBCO attenuator.

4 . 3 Interlaboratory Standards

4.3.1 Reflection Coefficient

The most frequently encountered type of interlaboratory

standard (fig. 20) uses a change in height of the narrow wave- guide dimension to achieve a calculable reflection coefficient.

The ratio of waveguide heights is closely equal to the VSWR for

32
ratios less than 1.5. The frequency characteristic of this

type of device is dependent on the capacitive effect of the

waveguide discontinuity, but it is of second order. Formulas

are available [20] for the capacitive correction terms. Thus,

this type of standard has the desirable qualities of being

more broadband than most types and having a calculable

reflection coefficient. This type of device usually incorporates a low-reflection sliding load to terminate the

structure

.

Caution should be observed when selecting interlaboratory

standards for measurement purposes. Two of the main sources

of trouble in a poor quality standard are nonflatness of the

connector (flange) surface (see fig. 4) and mechanical and

electrical instability of the sliding load incorporated in

the reflector.

A connector (flange) surface which has protrusions, bent

surfaces or separated seams (where the device is fabricated

from 2-4 separate pieces) does not mate properly so that there

is excessive joint loss and leakage which will change with

use of the standard, thereby changing the measured value.

Another disadvantage of joint loss is the increased leakage

signal which can effect the measurement accuracy. Also, protrusions on the connector (flange) surface can damage the fine

surface finish of a precision waveguide section which will

degrade the accuracy of the measurement system.

33
The electrical instability of the sliding load is the

most common flaw in an otherwise good standard. It is

possible to overcome this fault by improving the mechanical

fit between the shaft and the shaft hole, or by providing a better sliding fit between the load supporting mechanism and

the waveguide. The recommended procedure is to mount a pyramidal taper on a block which has teflon guides that provide

a close fit with the waveguide walls. Both the taper and the

block should be made from an rf absorbing material. If

properly constructed, the electrical instability is virtually

eliminated

.

Other qualities to be considered in selection of a standard are: 1) accessibility to the reverse side of the

connector (flange) surface to provide fast connect/disconnect,

and 2) sturdy construction to eliminate flexing of the flange

and associated waveguide.

Cautions to be observed before and after calibration

are: 1) Inspect for flat front and reverse connector (flange)

surfaces. This includes removal of paint and uneveness on

the reverse side which can cause different pressures to be

applied to the mating surface, 2) inspect interior waveguide

walls for freedom from dust and lint, and 3) inspect connector

surfaces for freedom from grease and corrosion.

34
4.3.2 Attenuation

There are two basic types of rf attenuation interlaboratory standards, the fixed attenuator [25] for insertion

loss and the variable attenuator for attenuation difference.

There are two designs of variable attenuators that are suitable for calibration. One type has a resistive vane which

moves into the waveguide field from a side wall. The other

type is the rotary-vane attenuator. Both types of attenuators

have good resolution at low values of attenuation, but the

rotary-vane attenuator has superior resolution at high values

as compared to the first type. The rotary-vane attenuator is

less frequency-sensitive and has less incremental phase

change than the other type

.

The rotary-vane attenuator which basically consists of

a dissipative vane rotated in a circular waveguide is the

preferred variable attenuation interlaboratory standard. It

has the property that the "ideal" attenuation can be calculated

by the expression

A = -40 log cos 6 + c (25)

where 6 is the angle between the rotating vane and the polarization of the circular TE, , mode, and c is the residual

attenuation when 0=0.

Equation (25) is ideal because fabrication imperfections

can cause deviations in actual attenuation for a known vane

angle 6. Among the factors causing these deviations are

35
mismatch, misalignment of the rotating vane, insufficient

attenuation of the vane, imperfections in the gear drive

mechanisms, readout parallax, and a warped vane. Vane alignment techniques have been developed to reduce the errors from

stator and rotating vane misalignment [26, 27, 28]. Likewise,

fabrication techniques have also been improved so that the

mechanical and physical imperfections are minimized [13].

Two main types of single-value attenuators are the fixed

pad and the single-step attenuator. The disadvantage of the

fixed pad is that it must be inserted and removed during a calibration, thus requiring good system stability and a repeatable connect-disconnect system assembly (see Section 5.2

for measurement results).

The step attenuator can remain in the system during its

operation and thus overcomes the disadvantage of the fixed

pad if its mechanical characteristics are stable and repeatable.

The step attenuators usually consist of a movable resistive

vane located between the two sets of coupling holes of an in-line directional coupler. When the vane is located in the

center of the waveguide, energy is transmitted through the

device via the coupling path, thus being attenuated in

proportion to the design coupling factor. When the vane is

located in the minimum electric field (against the wall) only

a small residual attenuation results. Thus, with this device

a fixed attenuation step can be measured without insertion

and removal of the device. Other advantages of this device

36
are low VSWR and minor frequency sensitivity.

Precision calibrated attenuators used as interlaboratory

standards require careful handling and should meet the

following criteria to give satisfactory results. They should:

1) be electrically stable over several years time,

2) be mechanically rugged so that the electrical characteristics do not change through handling,

3) be electrically stable under environmental changes

such as temperature, humidity, etc.,

4) be electrically stable for reasonable overloads (power)

,

5) have a VSWR of less than 1.2 (the nearer to 1.00, the

better)

,

6) have input and output waveguide ports that are axially

in line,

7) have a small to negligible leakage power, and

8) have excellent flanges or connector surfaces.

A more complete discussion of the above is found in reference

[6].

5. Measurement Results

5 . 1 Reflection Coefficient Magnitude

Measurements were performed on two WR15 waveguide reflectors which were manufactured at the NBS . The reflection coeffi

cient magnitudes were approximately 0.1 and 0.024. The devices

37
were measured each day for 10 days in order to obtain preliminary information on the standard deviations of individual

runs (flange repeatability) and of day to day measurements

(system random error)

.

The 0.024 device was made with a standard UG-385/U flange

and the 0.1 device was made with a flat (non-bossed) mating surface. The waveguide precision section to which the devices

were joined is a flat surface. Alignment pins were used on both flanges.

The results show that the device with the flat flange

is more stable and repeatable. For the 0.1 device (flat

flange) the standard deviation within runs (based on 4 individual determinations per run) was 0.02 percent of the

reflection coefficient magnitude, and the standard deviation

between daily averages was 0.015 percent giving a quadrature

sum of 0.025 percent.

The 0.024 device exhibited some instability, and a plot

of the results displays a "learning curve" (the standard

deviation values decreased by an order of magnitude from start

to finish) so that a components of variance analysis is not

possible at present. Since the standard deviation of the daily

averages for the 0.1 device is small (which implies that the

measurement system is stable) , the conclusion is that the

UG-385/U flange is the contributing factor to the reflector

instability and is indeed inferior in respect to measurement

repeatability

.

38
Additional measurements on the 0.024 device which

consisted of tightening the flange bolts by proceeding in either

a clockwise or counter clockwise direction around the flange

by one operator reduced the standard deviation from 0.8 percent

to 0.07 percent. However, when operators were changed,

different values of reflection coefficient were obtained.

At present, measurements using this type of flange are unstable, and until further research on flange repeatability

and the development of procedures to torque the flange bolts,

no definite limits of the repeatability of reflection coefficient measurements using the UG-385/U flange can be reached.

5 . 2 Attenuation

The measurement of attenuation difference with a rotary- vane attenuator involves angular rotation of the center vane

by a dial mechanism being set on several prescribed marks.

The repeatability of such a measurement of attenuation involves these factors: (1) ability of the rotor vane to

repeat the same angular displacement for a given dial setting,

(2) the ability of the operator to set and read the same mark,

and 3) system stability. Thus, the lack of repeatability

introduces a random error in the process of several measurements

,

(A precise high resolution WR15 rotary-vane attenuator with

a repeatability of .011 dB at a dial setting of 50 dB has

been designed and constructed at the NBS .

)

39
The procedure for an insertion loss measurement requires

that the waveguide assembly be opened to accept the deviceunder-test. In both the closed and receptive position, the

waveguide holes must be maintained in exact axial alignment

to make precision measurements. The connect-disconnect and

bolting of the flanges should be done with great care,

especially in WR15 and smaller waveguide sizes. Laboratory

benches are commercially available for holding waveguide assem- blies in a stable and rigid position. The present NBS developed

millimeter measurement system- (fig. 21) for attenuation and

impedance uses a commercial laboratory bench with moderate

modifications. The attenuation calibration system is arranged

in such a manner that fixed pads, inline multi-hole attenuators,

directional couplers , and variable attenuators all can be

inserted into the system with minimum effort.

At this time the estimate of the attenuation measurement

system random error limits have not been completed, but some typical measurement results are presented in the following

paragraphs

.

Several commercially available waveguide devices were

measured as fixed interlaboratory standards for insertion

loss in WR15 waveguide measurement system at 62 and 64 GHz.

One device, a directional coupler terminated with a matched load at one output port, was used as an inline fixed

attenuator with a nominal value of 1 dB. The directional

40
coupler was measured in the condition that it was received

in the laboratory, that is, with a slight bend in the flange

of one port. The estimated value of 3S (three times the

calculated standard deviation of the mean) for six determinations taken in this circumstance was 0.129 dB . After the

flange of the damaged port was realigned by machining, the

calculated values of 3S for five determinations was 0.009 dB.

Thus, the above measurements of insertion loss illustrate

that excellent alignment of the output flanges is a must for

precision measurements in millimeter waveguide.

Two fixed attenuators in WR15 waveguide measured

at 62 and 64 GHz were of nominal values of 10 and 20 dB. The

calculated values of 3S for five determinations of the 10 dB

attenuator at 62 GHz and of a 20 dB attenuator at 64 GHz was 0.023 dB and 0.012 dB , respectively. The measurement precision

was better with the 20 dB attenuator due to better flange

alignment

.

The insertion loss or attenuation of a twenty-eight inch

section of commercial silver WR15 waveguide was measured at

64 GHz. The value of 3S for five determinations was 0.012 dB.

The nominal value of attenuation of the twenty-eight inch

section was 1.5 dB , or about 0.05 dB/inch.

41
The authors extend their appreciation to R.W. Beatty for

his helpful suggestions regarding this paper and to G.C. Counas

and R.D. Hunter for their help in the system instrumentation

and measurements.

42
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0.1 1 .0 SIGNAL VARIATION R IN DECIBELS

Figure 8. Graph for estimating the magnitude of 1/K

given a response variation R when sliding a load with return losses of 30 to 70 decibels

50

0.1

o

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as

C3

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NOTE:

N EQUALS ANY

POSITIVE INTEGER

J I

1 .0 5 NORMALIZED SIGNAL VARIATION R X 10'

IN DECIBELS

N

Figure 9, Graph for estimating the equivalent generator

impedance for a given response variation

-N R x io when sliding a short-circuit termination.

51

1000

o

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CO

~ 400

0.074 INCH

0.001 0.002 0.003 0.004 0.005 0.006 0.007

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Figure 10. Change in reflection coefficient magnitude

versus dimension change in the nominal wave

guide width of 0.148 inch.

52

1 000

Figure 11

0.001 0.002 0.003 0.004 0.005 0.006 0.007

AT

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versus dimensional change in the nominal

waveguide height of 0.074 inch.

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CALCULATED FOR WR 1

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OPERATING AT 62.5 GHz

CONDUCTIVITY

mhos/METER

1 .0

CONDUCTIVITY RATIO DECREASE

Figure 15. Graph for estimating the change in reflection

coefficient of a quarterwave short circuit versus conductivity confidence interval (the

relative error substracted from unity)

.

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63

APPENDIX A

To illustrate the statement in section 2.1.2 that the

average& reflection coefficient magnitude 6iiIrl is associated

ave with that element which has the largest reflection, consider

the following lossless case (for definitions of losslessness

see [29], p. 48) of a termination with a fixed discontinuity

r„ and a sliding load r. .

It can be shown [30, 31] that

I r D

l +

l r L max

1 + IVl

and

mm l - r r 1 D L or

mm 1 - r r I D L

> I r,

> r,

where Irl 1 and Irl . correspond to the measured maximum ' max '

' mm r and minimum reflection coefficients. Then, the average

reflection coefficient magnitude

r = — I I r I + ir, 1 ave i

' max Hi mi

or

(1 r L n

l - I r r 1 2 1

! D L

1

r > r D

1 I L

64

t 1 - l r pl

2

)

1 - IVJ 2 r > r

is in either case a first order approximation to the largest

reflection coefficient.

65

/

APPENDIX B Estimated Systematic Error Limits for WR15 Attenuation Measurements

The following estimated error limits are based on tolerances for the NBS WR15 components and systems.

Converter (Mixer) Error ±0.003

xt . . f40 dBI measured ±0.004 Noise up to J I \cn j-dJ attenuation ±0.020 dB

30 MHz Standard Attenuator

Loading effects ±0.001 dB

Mode purity ±0.001 dB

Dimensional Tolerance ±0.002 dB/20 dB

Mismatch Error vs. Attenuator VSWR

(System VSWR at insertion point = 1.02)

Attenuator VSWR Mismatch Error (dB)

1.05 ±0.005

1.10 ±0.008

1.15 ±0.013

1.20 ±0.017

Total Systematic Error (dB)

Attenuator VSWR

ial Setting

(dB) 1 05 1 .10 1 15 1 20

10 ±0 .012 ±0 .015 ±0 .020 ±0 024

20 ±0 012 ±0 .015 ±0 .020 ±0 .024

30 ±0 .014 ±0 .017 ±0 022 ±0 .026

40 ±0 .018 ±0 .021 ±0 .026 ±0 .030

50 ±0 .036 ±0 .039 ±0 .044 ±0 048

APPENDIX C Estimated Systematic Error Limits (AT) for

WR15 Reflection Coefficient Magnitude (|r|) Measurements

The following estimated error limits are based on tolerances for the NBS WR15 components and systems.

> 0.025

Tuning Error

Directivity

2i

Converter Error

30 MHz Standard Attenuator

Reflection Coefficient

Magnitude Standard

Precision Section

Total Error

Reported Estimated Error

±0.00015 (1 + |r|

)

±0.00012 (i + | r]

)

±0.00035 |r|

±0.00046 |r|

±0.0003 |r|

±0.0006

±0 .00087 + .00138 | r|

AT = ±(1 + i.5|r| )x 10

-3

I T| < 0.025

Converter Error

30 MHz Standard Attenuator

Total Error

Reported Estimated Error

±0.00105 |r|

±0.00138 |r|

±0.00087 + 0.0030 | r|

AT = ±(1 + 3|T| ) x 10

67

APPENDIX D

Machine drawings for 11 stub tuner

for 55-65 GHz, WR15.

Figures 22(a), 22(b), 22(c).

Certain commercial equipment and materials are identified

in this paper in order to adequately specify the experimental

procedure. In no case does such identification imply

recommendation or endorsement by the National Bureau of

Standards , nor does it imply that the material or equipment

identified is necessarily the best available for the purpose.

68

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71

APPENDIX E

Machine drawing for sliding load

for WR15 waveguide.

Figure 23

72

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Figure 27(n) 96

References

[1]

[2]

[3]

[4]

R.W. Beatty, Microwave impedance measurements and standards,

NBS (U.S.) Monogr. 82, 32 pages (August 1965).

W.J. Anson, A guide to the use of the modified reflectometer technique of VSWR measurement, J. of Res. Eng. and

Instr., Vol. 65C, No. 4, pp. 217-222, Oct. -Dec. 1961.

W.E. Little and D.A. Ellerbruch, Precise reflection

coefficient measurements with the untuned ref lectometer

,

J. Res. NBS, (U.S.) Vol. 70 C, (Eng. and Instr.) 165-168

(July-Sept. 1966).

R. W. Beatty, and W. J. Anson, Table of magnitude of

[5]

[6

[7]

[8]

reflection coefficient versus return loss L

R

= 20 log,.,

NBS Tech. Note 72, Sept. 19, 1960.

M. Sucher and J. Fox (editors), Handbook of Microwave

Measurements, Vol. I, pp. 103-105 (Polytechnic Press of the

Polytechnic Institute of Brooklyn, 1963).

R. W. Beatty, Microwave attenuation measurements and standards, NBS (U.S.) Monogr. 97, 48 pages (April 3, 1967).

M.H. Zanboorie, A semi-automatic technique for tuning a reflectometer , IEEE Trans, on Microwave Theory and Techniques

(correspondence), Vol. MTT-13, pp. 709-710, Sept. 1965.

D.M. Kerns and W.T. Grandy, Jr., Perturbation theorems

for waveguide junctions, with applications, IEEE Trans, on Microwave Theory and Techniques, Vol. MTT-14, pp. 85-92,

Feb. 1966.

97
[9] R.W. Beatty, Mismatch errors in the measurement of ultra-high

frequency and microwave variable attenuators, J. of Res.,

NBS, Vol. 52, No. 1, pp. 7-9, Jan. 1954.

[10] D. Russel and W. Larson, RF Attenuation, Proc. of IEEE,

Vol. 55, No. 6, pp. 942-959, June 1967.

[11] C.G. Montgomery (editor), Technique of Microwave Measurements, MIT Rad. Lab. Series 11, p. 830 (McGraw-Hill Book

Co., Inc., New York, N.Y., 1947).

[12] M.B. Hall, N.T. Larsen, and W.E. Little, Combination rf

radiation and fluid pressure seal, Proc. IEEE, Vol. 54,

No. 11, pp. 1585-1586, Nov. 1966.

[13] W.E. Little, W. Larson, and B.J. Kinder, Rotary-vane

attenuator with an optical readout, J. of Res. NBS (U.S.),

Vol. 75C, (Eng. and Instr.) No. 1, 1-5, (Jan. -March 1971).

[14] R.W. Beatty and D.M. Kerns, Recently developed microwave

impedance standards and methods of measurement, IRE Trans,

on Instr., Vol. 1-7, pp. 319-321, Dec. 1958.

[15] R.W. Beatty and B.C. Yates, A graph of return loss versus

frequency for quarter-wavelength short-circuited waveguide

impedance standards, IEEE Trans, on Microwave Theory and Tech

MTT-17, No. 5, pp. 282-284, May 1969.

[16] T.Y. Otoshi, C.T. Stelzried, B.C. Yates, and R.W. Beatty,

Comparisons of waveguide losses calibrated by the dc

potentiometer, AC ratio transformer, and reflectometer

techniques, IEEE Trans, on Microwave Theory and Tech.

MTT-18 No. 7, pp. 406-409, July 1970.

98
[17] R. W. Beatty, A two-channel nulling method for measuring

attenuation constants of short sections of waveguide

and the losses in waveguide joints, Proc. IEEE, Vol. 53,

No. 6, pp. 642-643, June 1965.

[18] B.C. Yates and W.E. Little, Complex reflection coefficient

standards, to be published.

[19] D.M. Kerns, Half-round inductive obstacles in rectangular

waveguide, J. Res. NBS (U.S.), Vol. 64B (Math. Sci.),

113-130, (Apr. -June, 1960).

[20] N. Marcuvitz, Waveguide Handbook, MIT Rad. Lab. Series 10,

New York, (McGraw-Hill Book Co., Inc., 1951).

[21] L. Lewin, Standard Mismatch-the Production of Controlled

Small Reflections in Waveguides, J. Res. NBS (U.S.), 72C

(Eng. and Instr.), No. 4, 197-201 (July-Sept. 1968).

[22] R.W. Beatty, Impedance of Uniconductor Waveguide, Proc.

of IEEE, Vol. 55, No. 6, pp. 933-941, June 1967.

[23] D.E. Harnett and N.P. Case, The design and testing of

multirange receivers, Proc. IRE 23, 578-593, June 1935.

[24] R.E. Grantham and J.J. Freeman, A standard of attenuation

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1948.

[25] W. Larson, Inline waveguide attenuator (correspondence),

IEEE Trans, on Microwave Theory and Tech. MTT-12, pp. 367-

368, May 1964.

99
[26] W. Larson, Analysis of rotation errors of a waveguide

rotary vane attenuator, IRE International Convention

Record, Pt. 3, pp. 213-219, 1962.

[27] W. Larson, Table of attenuation error as a function of

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Tech. Note 177, 154 pages, (May 1963).

[28] P.F. Mariner, An absolute microwave attenuator, Proc. IEEE

(London) 109, Pt. B, pp. 415-419, Sept. 1962.

[29] D.M. Kerns and R.W. Beatty, Basic Theory of Waveguide

Junctions and Introductory Microwave Network Analysis

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[30] J.L. Altman, Microwave Circuits, pp. 393-395 (D. Van

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Coefficient and Impedance in Waveguides and Transmission

Lines, to be published by NBS.

100
FORM NBS-114A (1-71) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. Technical Note 6192. Gov't Accession No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE Millimeter Attenuation and Reflection Coefficient

Measurement System

5. Publication Date July 1972

6. Performing Organization Code

7. AUTHOR(S) B. C. Yates and W. Larson

8. Performing Organization

10. Project/Task/Work Unit No. 2724203

9. PERFORMING ORGANIZATION NAME AND ADDRESS NATIONAL BUREAU OF STANDARDS, Boulder Labs

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16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or literature survey, mention it here.) This paper presents the details to implement a WR 15 attenuation and

reflection coefficient magnitude measurement system. A discussion of precision and of systematic error is given along with equations for estimating

limits of the error. Machine drawings are provided to fabricate the waveguide

standards and necessary hardware not commercially available.

17. KEY WORDS (Alphabetical order, separated by semicolons) Attenuation; Measurement system; Millimeter; Reflection coefficient, VSWR.

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