4

The Rotary-Vane Attenuator as

an Interlaboratory Standard

NatfoMj Surew of Stedfir^

JAN 2 7 t976

761546-/^3^

GiC lOO

no. 144

n"73

Wilbur Larson

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

U.S. DEPARTMENT OF COMMERCE, Rogers C. B. Morton, Secretary

James A. Baker, III, Under Secretary

Dr. Betsy Ancker-Johnson, Assislani Secretary for Science and Technology

IJI.SNATIONAL bureau of standards, Ernest Ambler, Acting Director

Issued November 1975
Library of Congress Cataloging in Publication Data

Larson, Wilbur.

The Rotary-Vane Attenuator as an Interlaboratory Standard.

(National Bureau of Standards Monograph; 144)

Bibliography: p.

1. Attenuators, Rotary-Vane. 2. Microwave Measurements. I. Title. II. Series: United States. National Bureau of Standards. Monograph; 144. QC100.U556 No. 144 [TK7871.65] 389'.08s [621.381'371

75-619099

National Bureau of Standards Monograph 144

Nat. Bur. Stand. (U.S.), Monogr. 144, 70 pages (Nov. 1975)

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Contents

Page

1. Introduction 1

2. Theory of operation 1 2.1. Zero setting 2

2.2. Stator alignment 2

2.3. Transmission error or insufficient

attenuation in the rotor 4

3. Dial readout of rotary-vane attenuator 5

4. The measurement of the rotary-vane at- tenuator by different methods 8

4.1. NBS developed attenuation

systems 8

4.2. Comparison of modulated subcarrier and dc substitution

methods 10

4.3. Comparison of modulated subcarrier and i-f substitution

methods 10

4.4. Simultaneous measurement by

modulated sub-carrier and dc substitution methods 11

4.5. Measurement of precision optical

rotary-vane attenuator by dc and

i-/substitution methods 11

4.6. Power ratio (dc) versus off-null

measurements 11

5. Procedures for evaluating the rotary-vane

attenuator 14

5.1. Determination of average vane

angle error and eccentricity from

calibration data 15

5.1.1. Analysis of caHbration

data 15

5.1.2. Cyclic pattern of angular

displacement 15

5.2. Gearing errors related to rotary- vane attenuator 16

5.2.1. Effects of a on ey 17

5.2.2. Effects of pitch diameter on error of attenuation... 19

6. Compensation for transmission error of

rotary-vane attenuator 21

6.1. Transmission error versus dial

setting in decibels 21

6.2. Stator realignment 21

6.3. Illustration of transmission error and compensation for 110-dB

maximum 22

6.4. Mechanical compensation and

measured results 24

7. Measurement of precision rotary-vane

attenuators with high resolution readouts. 24

7.1. Measurement of rotary-vane at- tenuator with a gear driven

readout 24

7.1.1. Measurements of precision gear driven rotary- vane attenuator 25

iii

Page

7.1.2. Angular resettabihty of

attenuator 25

7.2. Mounting the gear drive 25

7.3. Optical rotary-vane attenuator 26

7.3.1. Measurements on optical rotary-vane attenuator 26

7.3.2. Measurement after rotor

repair 27

8. Resolution and resettabihty 27

9. Resolution of rotary-vane attenuator in

percent of dial setting 28

10. Frequency sensitivity of the rotary-vane

attenuator 28

10.1. Spectrum of microwave attenuation cahbration systems 2.6 to 40 GHz 29

10.2. Statistical analysis of the frequency sensitivity from calibration data at 30, 40, and 50 dB 33

10.3. Frequency sensitivity of rotary- vane attenuators for eight waveguide frequency ranges 35

11. Evaluation of the rotary-vane attenuator

by "bootstrapping" and check standards 35

11.1. Errors in attenuation for the

initial and the final setting of the

rotary-vane attenuator for an at- tenuation difference measure- ment 36

11.2. Graphical presentation 36

11.2.1. Deviations in attenuation due to rotor-vane

alignment error 36

11.2.2. Attenuation versus 6

in degrees 36

11.2.3. ^'i versus dial

setting (in degrees and

decibels) 38

11.2.4. Minimal value of e' 38

12. Evaluation of precision rotary-vane at- tenuator with waveguide fixed-step

attenuator 40

13. Attenuation measurement with the

rotary-vane attenuator as the standard. 40

13.1. Introduction 40

13.2. The Measurement system 40

13.3. Errors of microwave measure- ment system 42

13.3.1. Systematic and ran- dom errors 42

13.3.2. Insertion point of the

device under test 42
Page Page

13.3.3. Mismatch error in at- tenuation measure- ment

13.4. Externalleakage

14. Conclusion

List

Figure 1. Pictorial diagram of the rotary- vane attenuator

Figure 2. Illustration of the determination

of b' with measured distances bi

and 62 from the reference plane

as viewed from the rectangular

waveguide input flange

Figure 3. Rotor index or zero coincident

with first (or second) stator Figure 4. Rotor index or zero coincident

with average position of stators__

Figure 5. Type B aUgnment: first attenuation maximum. Mi, at 6' 12 prior

to 90°; saddle minimum, Mg, at 90°; and second maximum, M2,

at 612 beyond 90°

Figure 6. Type A alignment, rotor advanced to d'l2: first attenuation

maximum. Mi, at 90°— 6'; saddle

minimum, Ms, at 90° — ^72; and

the second maximum, M2, at 90°

Figure 7. Type /4 alignment, rotor retarded:

first attenuation maximum. Mi,

at 90°; saddle minimum, Ms, at 90°+ 072; and the second maximum at 90°+ 0' Figure 8. Rotary-vane attenuator dial readout in decibels — spiral — 3 cycle__

Figure 9. Rotary-vane attenuator dial readout in decibels — cylindrical —

6

cycle

Figure 10. Rotary-vane attenuator dial readout in decibels — cylindrical —

9

cycle

Figure 11. Graph of the deviation in attenuation from nominal versus dial

setting in degrees which corre- sponds to a linear deviation of

0.020" for three rotary-vane

attentuators

Figure 12. Dial readout in units, tenths,

hundredths and thousandths

of degrees for rotary-vane

attenuator

Figure 13. Pictorial view of drive unit for

rotary-vane attenuator

Figure 14. Machine drawing of drive

unit gearing for rotary-vane

attenuator

15i References 50

16. Appendices

42 A. Definitions and Terms 51

44 B. Machine Drawings for Optical

50 Rotary-Vane Attenuators 51

of Figures

Figure 15. Illustrated deviation of the

1 rotor vane of an attenuator calibrated by different methods:

power ratio (I960), off-null, and

power ratio (1968) 13

Figure 16. Apparent deviation of rotor vane

3 in degrees from nominal at each

dial setting in degrees. The

3 indicated vane angle correction

has been applied to each result 13

3

Figure 17. Graphs of deviations in attenuation from nominal versus dial

setting in decibels and degrees.

a. Measured deviation (circles)

4, and computed deviation for

+0.064° vane-angle error __ 16

b. Measured values after applying —0.064° vane angle cor- rection 16

4 Figure 18. Graphs of the cyclic pattern of

angular displacement curve,

d'r, with average vane-angle error

of +0.064° and d'r with -0.064°

correction 16

4 Figure 19. Variations in gear eccentricity

error 17

5 Figure 20. Attenuation as a function of vane

angle, variation in the indexing

error for the three cycles, and the

6 error in attenuation from nominal

for the dial settings of 0 to 90P 17

Figure 21. Errors in attenuation at the dial

6 setting of 10 dB versus the angle

a for different pitch diameters _ . 18

Figure 22. Errors in attenuation at the dial

setting of 20 dB versus the angle

a for different pitch diameters __ 18

Figure 23. Errors in attenuation at the dial

6 setting of 30 dB versus the angle

a for different pitch diameters _ _ 18

Figure 24. Errors in attenuation at the dial

setting of 40 dB versus the angle

7 a for different pitch diameters _ _ 18

Figure 25. Errors in attenuation at the dial

8 setting of 50 dB versus the angle

a for different pitch diameters 19

Figure 26. Errors in attenuation at the dial

9 setting of 10 dB versus pitch

iv
Page

diameter for the angular displacement error 19

Figure 27. Errors in attenuation at the dial

setting of 20 dB versus pitch

diameter for the angular displacement error 20

Figure 28. Errors in attenuation at the dial

setting of 30 dB versus pitch

diameter for the angular displacement error 20

Figure 29. Errors in attenuation at the dial

setting of 40 dB versus pitch

diameter for the angular displacement error 20

Figure 30. Errors in attenuation at the dial

setting of 50 dB versus pitch

diameter for the angular displacement error 20

Figure 31. Estimate of the transmission error versus dial setting in decibels for

maximum attenuation values of

60 to 160 dB 21

Figure 32. Illustration of stator rotation and

rotor alignment to induce the type

B error 21

Figure 33. Estimated angular displacement

of staters in degrees versus the

maximum attenuation value of

rotor vane in decibels for the

compensation required to approach theoretical cos^ 6 law 22

Figure 34. Deviation in attenuation caustd

by misalignment of the stators,

6' equals 0.2°, and insufficient

maximum attenuation of 110 dB

for the dial setting of 20 to 70

dB 23

Figure 35. Deviation of attenuation from

nominal versus dial setting in

decibels for rotary-vane attenuator with 72-dB maximum: (a)

Curve of calibration points, (b)

Curve of correction induced by

misaligning the stator 0.87°, and

(c) Plot of calibrated values after

stator misalignment 24

Figure 36. Angular error, d'r, in degrees from

nominal (theory) versus the dial

setting, 6, in degrees, determined

from measurements by the power

ratio, modulated subcarrier, and

i-f substitution methods 25

Figure 37. Angular error caused by binding

effect between the drive gear and

the driven gear (concentric to the

rotor section) 26

Figure 38. Angular error, 6', in degrees

versus dial setting in degrees, 6,

after precise machining was

applied 26

Figure 39. Deviation in decibels and degrees

versus dial setting in degrees 26

Figure 40. Deviation in decibels and degrees

versus dial setting in degrees,

after repair of the rotor section 27

Figure 41. (a) Deviation of measured atten- uation and equivalent angular

deviation from theoretical values

for a vane angle correction of — 0.033° versus dial setting of 0

to 45° 27

(b) Deviation of measured atten- uation and equivalent angular

deviation from theoretical values

for a vane angle correction of — 0.033° versus dial setting of

45 to 87.5° 27

Figure 42. Resolution error in decibels ver- sus dial setting in decibels 28

Figure 43. Resolution of the dial in percent

of attenuation versus dial setting

in decibels for an attenuator with

angular resolution of 0.01° 28

Figure 44. Deviation of attenuation for aver- age vane-angle errors of 0.098,

0.080, and 0.036° versus dial set- ting in decibels at 9.0, 9.8, and

11.2 GHz 29

Figure 45. Deviation of attenuation for aver- age vane-angle errors of — 0.032,

-0.042 and -0.054° versus dial

setting in decibels at 9.0, 9.8,

and 11.2 GHz 30

Figure 46. Deviation of attenuation for aver- age vane-angle errors of 0.024,

0.035 and 0.049° versus dial set- ting in decibels at 29, 33, and 37

GHz 30

Figure 47. Deviation of attenuation for aver- age vane-angle errors of 0.008,

-0.014, and -0.042° versus dial

setting in decibels at 29, 33, and

. 37 GHz 31

Figure 48. Deviation of attenuation for aver- age vane-angle errors of —0.031,

-0.010, and 0.013° versus dial

setting in decibels at 2.85, 3.25,

3.55 GHz 31

Figure 49. Deviation of attenuation for aver- age vane-angle errors of 0.128,

0.105, and 0.120° versus dial set- ting in decibels at 2.85, 3.25. and

3.55 GHz 32

Figure 50. Deviation of attenuation for aver- age vane-angle errors of —0.070,

V
Page

Figure 51.

-0.067, and -0.032° versus dial

setting in decibels at 2.85, 3.25,

and 3.55 GHz

Limits of magnitude of one- sigma error in attenuation versus frequency in GHz for twenty

WR284 rotary-vane attenuators

at 30, 40, and 50-dB dial set- tings

Figure 52. Limits of magnitude of one- sigma error in attenuation versus frequency in GHz for twenty-one

WR187 rotary-vane attenuators

at 30, 40, and 50-dB dial set- tings

Figure 53. Limits of magnitude of one- sigma error in attenuation versus frequency in GHz for eighteen

WR137 rotary-vane attenuators at 30, 40, and 50-dB dial settings __ Figure 54. Limits of magnitude of one- sigma error in attenuation versus frequency in GHz for twentythree WR112 rotary-vane attenuators at 30, 40, and 50-dB dial

settings

Figure 55. Limits of magnitude of one- sigma error in attenuation versus frequency in GHz for fifty-one

WR90 rotary-vane attenuators at 30, 40, and 50-dB dial settings _ _ Figure 56. Limits of magnitude of one- sigma error in attenuation versus frequency in GHz for seven WR62

rotary-vane attenuators at 30, 40,

and 50-dB dial settings

Figure 57. Limits of magnitude of one- sigma error in attenuation versus frequency in GHz for seven WR42

rotaiv-vane attenuators at 30, 40,

and "^-dB dial settings

Figure 58. Limi of magnitude of one- sigma error in attenuation versus frequency in GHz for seven WR28

rotary-vane attenuators at 30, 40,

and 50-dB dial settings

Figure 59. (a) e' error from nominal (10 dB)

increments versus dial setting in

decibels for rotor misahgnment,

e', equal to 0.100, 0.200, and

0.300°

(b) Attenuation in decibels versus

6 in degrees, and angular hmits

in degrees for attenuation differ- ence oflOdB

Figure 60. e' error in decibels versus 6', from 0 to ±0.300° for 10-dB

increments as follows: 0 to 10

33

33

33

33

dB, 3 to 13 dB, 6 to 16 dB, 10 to 20 dB, and 15 to 25 dB

32 Figure 61. (a) e' error from nominal (6 dB)

increments versus dial setting in

decibels for rotor misahgnment,

e;, equal to 0.100, 0.200, and

0.300°

(b) Attenuation in decibels versus

d in degrees, and angular hmits

in degrees for attenuation differ- ence of6dB

Figure 62. e' error in decibels versus d'l from 0 to +0.300° for 6-dB increments as follows: 0 to 6 dB, 3 to 9 dB, 6 to 12 dB, 9 to 15 dB, 12 to 18 dB, 15 to 21 dB, and 18 to 24 dB

Figure 63. (a) e' error from nominal (3 dB)

increments versus dial setting in

decibels for rotor misahgnment,

e;, equal to 0.100, 0.200, and

0.300°

(b) Attenuation in decibels versus

d in degrees, and angular hmits

in degrees for attenuation differ- erence of 3 dB

Figure 64. e' error in decibels versus d'l from 0 to +0.300° for 3-dB increments as follows: 0 to 3 dB, 2 to 5 dB, 3 to 6 dB, 6 to 9 dB, 9 to 12

dB, 15 to 18 dB, 18 to 21 dB, and

21 to 24 dB

Figure 65. (a) e' error from nominal (1 dB)

increments versus dial setting in

decibels for rotor misahgnment

d'l, equal to 0.100, 0.200, and

0.300°

(b) Attenuation in decibels versus

6 in degrees, and angular hmits

in degrees for attenuation differ- ence ofl dB

Figure 66. e' error in decibels versus d'l from 0 to +0.300° for 1-dB increments as foUows: 0 to 1 dB, 5 to 6 dB, 9 to 10 dB, 29 to 30 dB, and

39 to 40 dB

Figure 67. e' error from nominal (0.1 dB)

increments arsus dial setting in

decibels for rotor misahgnment,

d'l, equal to 0.100, 0.200, and

0.300°

(b) Attenuation in decibels versus

6 in degrees, and angular hmits

in degrees for attenuation differ- ence of 0.1 dB

Figure 68. e' erroi in decibels versus 6]

from 0 to +0.300° for 0.1-dB

increments as follows: 0 to 0.1

34

34

34

35

37

37

VI
Page Page

dB, 6.0 to 6.1 dB, 10 to 10.1 dB,

30 to 30. 1 dB , and 50 to 50. 1 dB„.. 46

Figure 69. Deviations in attenuation from

nominal in decibels versus dial

setting in degrees and decibels,

for d', equal 0.100, 0.200, and

0.300°, and d^, equal ± 0.010 46

Figure 70. Deviations in attenuation from

nominal in decibels versus dial

setting in degrees and decibels

(for 5 to 6 dB) when d'l equal

±0.100, ±0.200, and ±0.300°,

and 6»; equal ±0.010° 47

Figure 71. Block diagram of microwave at- tenuation measurement system __ 48

Figure 72. Detailed block diagram of microwave attenuation measurement

system 48

Figure 73. A recording showing the system

stabihty at a 30-dB measurement

level 49

Figure 74. Photo of the open rectangular

waveguide at the insertion point

for devices under test 49

Figure 75. Photo of a fixed waveguide

attenuator under test being in- serted into the rectangular waveguide at the insertion point 49

Figure 76. Photo of the rectangular waveguide with adapters to admit

coaxial devices at the insertion

point 50

Figure 77. Photo of a fixed coaxial attenuator

under test being inserted into the

line at the coaxial insertion

point 50

Figure 78—87. Machine drawings for optical

rotary-vane attenuator 52—61

Figure 88. Exploded view of a rotary-vane

attenuator utilizing a Spiroid gear

set in WR15 waveguide 62

List of Tables

Table 1. Angular displacement of rotor

corresponding to a linear displacement of 0.020 inches on the

readout scale for 3, 6, and 9 cycle

readouts

Table 2. Comparison of measurements obtained by modulated subcarrier

and dc substitution methods

Table 3. Comparison of measurements obtained by modulated subcarrier

and i-f substitution methods

Table 4. Differences between measure- ments made simultaneously by

modulated subcarrier and dc substitution methods

Table 5. Cahbration data of optical rotary- vane attenuator in power ratio

and {-/substitution systems at 9.0

GHz

Table 6. Comparison of calibration data

for the same attenuator at 9.39

GHz using two independent methods (power ratio 1960 versus off- null)

Table 7. Comparison of calibration data

for the same attenuator at 9.39

GHz using two independent methods (power ratio 1968 versus off- null)

Table 8. Comparison of deviation from the

average values with vane-angle

correction applied

Table 9. Comparison of calibration data

with average vane-angle error correction applied

12

12

14

14

Table 10. Summary of data for determining

average vane-angle error of a rotary-vane attenuator 15

Table 11. Angular values of a for maximum

and minimum ey at 10, 20, 30, 40,

and 50-dB dial settings 17

Table 12. Angular values of 6 where maximum (+ or —) deviations of at- tenuation occur due to indexing

error in 3-cycle drive and the

corresponding theoretical attenuation values 19

Table 13. The angular correction required

for different values of maximum

attenuation and the distance b' necessary to produce the angular

correction for various waveguide

sizes 22

Limits of magnitude of one-sigma

error in attenuation in decibels

per GHz for rotary-vane attenuators in WR28, WR42, WR62,

WR90, WR112, WR137, WR187,

and WR284 waveguide at 30, 40,

and 50-dB dial settings 35

Table 15. Deviations from nominal 1-dB in- crement of attenuation (dial set- ting changed from 5 to 6 dB) for

61^ = ±0.010° and d', = 0, ±0.100°,

±0.200°, and ±0.300° 47

Table 16. Attenuation difference measure- ments of a waveguide step atten- uator at 10 GHz with initial dial

settings of the standard RVA from

0 to 60 dB 47

10

10

11

12 Table 14.

vu

The Rotary-Vane Attenuator as an

Interlaboratory Standard

Wilbur Larson

This paper presents a comprehensive report on the measurement and the use of the rotary-vane

attenuator as an interlaboratory standard. Methods of attenuation measurement developed at NBS are used to supply data for the evaluation of the deviations from theoretical cos^lavv' due to rotor misalignment, gear eccentricity, resettabiUty, resolution, and insufficient maximum attenuation. A precision rotary-vane attenuator with an optical readout capable of 1 second of arc angular

resolution has an effective attenuation resolution of 0.00005 dB at a 3-dB dial setting, and 0.0005 dB at a 30-dB dial setting. This type of precision attenuator is an effective standard for use in the dual detection

microwave bridge measurement system.

Key words: Attenuation; interlaboratory standard; measurement; rotary-vane attenuator.

1. Introduction 2. Theory of Operation

In the past decade a considerable amount of

material has been published on use of the rotary- vane attenuator for attenuation measurements in

the microwave region. During this period an effort

has been made to estabhsh an improved standard for

attenuation that would be useful and adaptable to calibration of commercial attenuators over the entire

microwave frequency range.

The dial readout of the rotary-vane attenuator

indicates either the angular displacement in degrees

or the corresponding value of attenuation in decibels.

The purpose of this report is to discuss the work

and experiments employed in the development and

evaluation of the rotary-vane attenuator as an interlaboratory standard.

The rotary-vane attenuator has the properties

essential for a standard attenuator. This type of

attenuator is a device that has a dissipative resistive vane which can be rotated in a circular section of

waveguide. The attenuation produced follows very

nearly the cosine squared 6 law where 6 is the an- gular displacement of the vane from the polarization

of the TEi^i mode of the waveguide.

Intrinsically, the rotary-vane attenuator consists

of three sections of waveguide, two ends which are rectangular/circular transitions and the circular

center section. These three sections are placed in

tandem on the longitudinal axis as shown in figure 1. A resistive vane is mounted across the center of

each circular section of waveguide. In the minim.um

ROTARY VANE ATTENUATOR

ESINS

Ecose /Ecose

.ECOS 0

1 1 Ecos^e

ECOSfiSINS

ATTENUATION = -20 LOq^COS^^ = -40 LOG^COS^

Figure 1. Pictorial diagram of the rotary-vane attenuator.
attenuation position, the vanes in the three sections

are parallel to each other and the wide side of the

rectangular waveguide (i.e., perpendicular to the

electric E field). The entire center section, the rotor, can be rotated about the longitudinal axis of the

waveguide, thus putting the vane parallel to a portion {E sin 6) of the E field. The resistive film

absorbs the component E sin 6, while the component

E cos 6, normal to the center vane, passes through

unattenuated to the vane in the second stator. The

E cos 6 component upon entering the second stator

splits into two components. The resistive film

absorbs the E cos 6 component, and the E cos 6^

component emerges in a plane normal to the original.

Thus, the attenuation. A, stipulated from this

relationship can be written as ^=-20 logio cos2 0 + C (1)

where 6 is the angle of the rotating vane relative to the stator vane of the input section, C is the residual

attenuation, and A is the corresponding attenuation

in decibels [1].^ The center section is mounted concentrically

with either a driven gear mechanism, an optical

device [3], or an electrical transducer [4] for translation of angular rotation to a suitable display.

Each of the above methods of displaying the angular

rotation will be discussed later in detail, which will

include their respective desirable features or disadvantages.

2.1. Zero Setting

The variable attenuator can be used for attenuation difference with a known reference level.

Usually, this reference is zero dial setting, cor- responding to minimum insertion loss. The value of

minimum insertion loss appears to be the most

logical position to aUgn the rotor and the stator vanes to correspond to zero dial setting. However,

if achieved electrically, the angular displacement

of the rotor section from 0° requires more than 0.6°

to correspond to a 0.001 dB in attenuation. But,

when the rotor vane approaches a right angle with

the stator vane, the same 0.6° of angular rotation

corresponds theoretically to a change greater than

100 dB. Although the maximum attenuation is much

less than the theoretical value (approaches a limit

of 110 to 120 dB) the loss of sensitivity in measuring

such large values of attenuation more than offsets

the advantage of high angular resettabihty for a given value of attenuation. Therefore, an equal angle

technique of approximately 10° either side of 90°

appears to be a good compromise. Using this technique, the attenuator is set to an angle of approximately 100° so that its output is equal to the output

' Figures in brackets indicate the literature references on page

at 80°. The midpoint of these two angles represents

the true electrical plane of the attenuation vane. This technique is only valid for direct driven dial

mechanisms, where the angular displacement due

to gear eccentric or run out is not present [5]. The

misalignment encountered by eccentric gearing

has been evaluated at NBS [6]. Some commercially available attenuators have

stops to prevent angular rotation beyond zero, and/or 90° the theoretical maximum for attenuation. This type of mechanical stop makes it impossible to ahgn the rotor vane by the equal angle

technique. In addition, striking the stop a severe blow during rotation at either end could reorient

the center rotor vane due to gear or shaft slippage

and cause undesirable deviation from the cos^ law

at the high angle setting.

2.2. Stator Alignment

In the fabrication of a precision rotary-vane

attenuator it is not only essential that the zero of

the dial readout be oriented with the reference

plane of the vane in the rotor section, but the vanes

of the end sections or stators should He in the same

plane. If the end vanes are not parallel the insertion

loss will increase slightly, but more important, the

rotor to stator alignment will be impaired, and cause

an angular misalignment about the longitudinal axis, as shown in figure 2. Here, the distances to the stator vanes from the reference plane are indicated as

bi and 62, and the difference as b'

.

Figures 3 and 4 illustrate two methods of initially

aligning the rotor vane with reference to the stator vanes. Two types (Type A and Type B) of errors are

possible for rotary-vane attenuator with rotationally

misaUgned stators [6]. The Type A occurs when the

rotating section index or zero is coincident to the

first (or second) stator vane, and the Type B occurs when the rotating section index or zero is coincident

to the average position (or bisection) of the stator vanes. The error, in decibels, for Type A misalignment is

cos(g+g')

ea = -201ogio (2) cos 0

and the error, in decibels, for the Type B misahgnment is

e6 = -201og,o — . (3)

cos"' 0

With the use of trigonometric identities the Type

B error can be written [7] as

€6 = -2Olog(^cos2|--tan2 0sin2-|- j dB (4)

2
RECTANGULAR

WAVEGUIDE

FLANGE

REFERENCE PLANE

Figure 2. Illustration of the determination ofh' with measured distances bi and b2 from the reference plane as viewed from the rectangular waveguide input

flange.

Regardless of the type of alignment with reference

to the dial zero, the entire range of attenuation is affected by any misalignment of the stators. For

example, in a Type B alignment, a 90° rotation of the

rotor vane will coincide with the saddle portion of a double hump maximum attenuation, figure 5. Figure

5 shows that the first maximum attenuation will be

reached to coincide with 6' 12 prior to 90° on the dial,

while the second maximum will occur at 6' 12 beyond

90° on the dial.' However, the Type A alignment gives

rise to two possible situations, an advanced rotor vane or a retarded rotor vane with reference to either

stator vane. In figure 6, the rotor vane is assumed to be advanced d'l2. The first maximum attenuation occurs at 90° - 0', the saddle minimum at 90° - 6' 12,

and the second maximum attenuation at 90° of the

3
Figure 7. Type A alignment, rotor retarded: first attenuation

maximum. Mi, at 90°; saddle minimum, Mj, at 90°+ 6' 12; and the second maximum at 90° + 6'.

DIAL e, (DEGREES)

STATOR

#2

Figure 6. Type A alignment, rotor advanced to 6' 12: first attenuation maximum. Mi, at 90° — d'; saddle

minimum, Ms, at 90° — 6' 12; and the second maximum, M2, at 90°.

dial setting. To observe the conditions for a retarded

rotor vane of 6' 12 refer to figure 7. In this case the

first maximum attenuation occurs at 90°, the saddle

minimum at 90°+ 072, and the second maximum

attenuation at 90°+ 0' of the dial setting.

The double-humped attenuation curves shown in

figure 5, 6, and 7 only occur when end vane misalignment and insufficient attenuation are simultaneously present. With perfect vanes, attenuation

would tend to infinity at two angles.

2.3. Transmission Error or Insufficient

Attenuation in the Rotor

The ideal characteristics of the cos^ law is not

obtainable with the rotary-vane attenuator at the

high setting of 6 due to the transmission error. Although one may argue that any error occurring during transmission of a wave through a rotary-vane

attenuator could be called transmission error, the

author here follows the common practice of many

writers on the subject and assigns the transmission

error entirely to the error resulting from insufficient

maximum attenuation in the center vane. Of course,

the theoretical cos^ 6 law assumes infinite attenuation in the center vane. In addition to large trans- mission error, the lack of sufficient maximum atten- uation shows increased phase shift and frequency

sensitivity at the higher setting of 9.

4
The error related to the transmission error and

phase shift of the rotary-vane attenuator has been

treated by James [8], Otoshi [7], and Mariner [5]. The transmission error is given by

€f = -201og (l + e-«'tan2 0) dB (5)

where the term e~"' can be determined experimentally by setting 6 to 9(f and then measuring A

(maximum attenuation)

logio^

A_

20

7 = 10^) (6)

Where / is the distance the wave travels in the

rotor section of the attenuator and a is equal to the

difference between the attenuation constants of

the tangential and normal electric field components

in the rotor. The calculated error from eq (5) and a measured

value of 90 dB for 0=7r/2, shows that = 0.086

dB at a dial setting of 50 dB.

The phase shift of the transmitted signal as a function of 6 is given by

_ _j e-"^sin pi sin^ d

cos2 0 + e-«'sin2 0cos/3/

(7)

where ^ = /3o — jSi. The quantity fil can be found

experimentally. Where 13 is equal to the difference

between the phase shift constants of the tangential

and normal electric field components in the rotor.

If /3/ equals 90°, the phase shift (f> wiU be less than

0.2° between 0 to 40 dB.

For use in the deep space project a compact

rotary-vane attenuator was developed. Any compactness, especially in the rotor section of the

attenuator would affect its cos^ response in relation

to maximum attenuation, phase shift and frequency

sensitivity. However, at a fixed frequency and low

values of attenuation, this device can be a standard.

A shorter rotor section provides less maximum

attenuation, thus increasing transmission error. A modified law derived by Otoshi [9] corrects for

this effect of transmission error. His treatment of

the transmission error is similar to James [8] but

does not assume that the transmission error signal

effect is of a known magnitude or phase.

The attenuator's physical length need not be long

as the modified law does not require a zero transmission error. This permits a marked decrease in

physical length where this is a physical factor.

In addition, the modified law can be used for

corrections, that are necessary to extend the

dynamic attenuation range of the present precision

rotary-vane attenuator. A mechanical technique for

compensating for insufficient attenuation will be

discussed in a later section of the text.

3. Dial Readout of Rotary-Vane

Attenuator

The readout scale indicates the value of attenuation in decibels for most rotary-vane attenuators.

Let us consider several of the methods that can be

used for presenting a decibel scale of the attenuation, such as the 3 cycle spiral, and 6 and 9 cycle

cylindrical readouts as illustrated in figures 8, 9, and

10 respectively.

X-band (WR90) rotary-vane attenuators were

used in the evaluation of 3 and 6 cycle readouts and

an S-band (WR284) attenuator was used to evaluate

a 9 cycle readout. It is estimated that setting the

indicator line of the readout on either edge of a given

mark on the scale corresponds to a linear deviation

of about 0.020". The angular displacement of the

rotor section, that is equivalent to 0.020" hnear displacement on the dial, was calculated for each of

three types of scales. The results of these calculations are summarized in table 1. Column five in the

table shows the calculated angular displacement of

the rotor in degrees which corresponds to a linear

deviation of 0.020" (the nominal width of a scale

Une) on the scale readout. Note that the value of

angular displacement of the rotor changes with each

spiral in the 3 cycle readout for a given linear deviation, but remains constant for all parts of the cyUndrical readouts. Graphs of the deviation of attenuation from nominal in decibles versus the dial setting

in degrees, 0 to 86.5 (0 to 50 dB), are shown for each

of the three types of readouts in figure 11. The deviao

f o :

rr>~z

CO .

A

'A *

Figure 8. Rotary-vane attenuator dial readout in decibels

spiral— 3 cycle.

5
Cylindrical —6 cycle.

tion of attenuation from nominal in decibels is very

nearly the same for the 3 cycle spiral, and the 6

cycle cylindrical readout, in WR90 waveguide. However, the deviations are considerable less for the

9 cycle cylindrical readout in WR284 waveguide.

NBS has designed a drive unit for a commercial

rotary-vane attenuators that have a gear mechanism

ratio of 12. The use of the drive unit modifies the

attenuator to give the angular rotation of the rotor

section in decimal parts of a degree. Figure 12 shows

Table 1. Angular displacement of rotor corresponding to a linear displacement of

0.020 inches on the readout scale for 3, 6, and 9 cycle readouts

Type of scale Gear

ratio

Diameter of scale readoutDiameter

of driven

rotor gear

Rotor angular

displacement

degree

3 cycle

(spiral)

12:1 1.75" (0-2.5 dB)

2.75" (2.5-12 dB)

3.80" (12-max)

1.59"

1.59"

1.59"

0.021°

.014° .009°

6 cycle

(cylindrical)

24:1 1.27" 2.17" .010°

9 cycle

(cylindrical)

36:1 2.25" 4.5" .002°

g 0.030 --

TYPE OF READOUT WAVEGUIDE

SIZE

! 3 CYCLE SPIRAL

.2 6 CYCLE SPIRAL —2- 9 CYCLE CYLINOERICAL

UR 90 UR 90

UR 284

30 40 50 60

DIAL SETTING IN DEGREES

the three dial readout of the rotor in units, tenths,

hundredths and thousandths of a degree. The use

of a three dial readout is an appropriate method to increase the resolution of the angular displacement

dial to thousandths of a degree. In order to convert an angular displacement to decibels for increments

of 0.001° refer to NBS Technical Note 229. Figure

13 and 14 show the machine drawings of the drive

mechanism and scale used to display the angular

displacement of the gear driven rotor (ratio of 12)

Figure 11. Graph of the deviation in attenuation from nominal versus dial setting in degrees which corresponds

to a linear deviation of 0.020" for three rotary- vane attenuators.

6
in 0.001° increments from 0 to 90°. A simplified

gear drive for rotary-vane attenuators was developed

recently at NBS in WR15 waveguide size [10]. This

one-step drive consists of a 180:1 precision spiroid

gear set which provides an accurate and repeatable

readout an order of magnitude better than commercial attenuators. This drive mechanism permits

readout of 0.01° increments of vane angle displacement. To convert this readout to decibels, refer to NBS Technical Note 229.

A rotary-vane attenuator with an optical readout

[3] was designed at NBS, Boulder, that provides an

angular displacement and readout with a resolution

of ± 1 second of arc. A table is very useful for

determining the attenuation in decibels for angular

displacements in degrees, minutes, and seconds as

would be obtained from the above attenuator

readout. Three computer tapes have been run off

for the function (/4 = — 40 logio cos 6) versus degrees,

minutes, seconds as follows:

Tape Attenuation (9

(1) (0.000000-2.498726 dB) (0°0'0' to29°59'59")

(2) (2.498775-12.041054 dB) (30°0'0' to59°59'59")

(3) (12.041200-212.577005 dB) (60°0'0' to89°59'59")

The computer tapes provide 324,000 values of

attenuation to six decimal places from 0 to 212.577005 dB for every second of arc from 0 to 89°59'59".

TENTHS

Figure 12. Dial readout in units, tenths, hundredths and

thousandths of degrees for rotary-vane attenuator.
S»£€T I OF ^

Figure 13. Pictorial view of drive unit for rotary-vane attenuator.

4. The Measurement of the RotaryVane Attenuator by Different

Methods

In most of the microwave standards laboratories

several methods are available for the measurement

of waveguide attenuation devices. At NBS several

excellent methods were developed to calibrate

rotary-vane attenuators. The inherent properties

of the rotary-vane attenuator make this device an

excellent standard for intercomparison of calibration systems. In order to obtain the best results from

any measurement data, it is essential that the interlaboratory standard used meets the criteria of a

desirable standard [11].

The purpose of this section of the report wiU show

that the calibration data of the rotary-vane attenuator

used in several systems enables one to evaluate both

the systems and the interlaboratory standard,

simultaneously.

4.1. NBS Developed Attenuation Systems

The power ratio method was developed in 1959 at NBS/Boulder for microwave attenuation measure- ments and the error affiliated with this technique

has been carefully evaluated [12]. The application of

this method resulted in a significant improvement in

the resolution and stability of attenuation difference

measurements, especially for small attenuation

values, over a broad frequency range. Other systems were developed at NBS in the microwave attenuation measurement area, namely, the modulated subcarrier [13] and off-null [14] methods. In addition to these highly accurate and precise measurement

systems, the i-f substitution method for attenuation

measurement has been developed to a high degree of

excellence [15, 16]. The i-f substitution method is the most commonly used in both waveguide and

coaxial systems at NBS. At present the i-f substitution waveguide systems are used over the frequency

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Figure 14. Machine drawing of drive unit gearing for rotary- vane attenuator.

range from 1.7 to 65 GHz in the waveguide sizes

from WR430 to WR15. The other systems mentioned

above were developed predominantly in the X-band

region.

During the past 15 years NBS/Boulder has calibrated many rotary-vane attenuators in nine

different waveguide sizes. Most of these attenuators

have been commercially purchased for use as interlaboratory standards in pubUc, military, and government agencies.

A commercially available X-band rotary-vane

attenuator ^ was calibrated by the NBS power

ratio method [12]. This work revealed the limitations of commercial rotary-vane attenuators for

values greater than 1 dB; it was shown that the reso- lution and repeatability deteriorate rapidly at the

higher values of attenuation. In other words, the

power ratio calibration system challenged the preCertain 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 simply that the material or equipment identified is necessarily the best availalbe

for the purpose.

cision and resolution that could be obtained with the

present available rotary-vane attenuator.

A short time later another method of measuring

microwave attenuation was developed at NBS.

This new method known as the modulated subcarrier technique [13] utilized commercially available components to provide resolution and accuracy

comparable to the power ratio method.

In the evaluation of this new method, attenuation

measurements were compared with those obtained

by the power ratio or (dc-substitution) and the

J-/ substitution (30 MHz standard) techniques. The

same commercial rotary-vane attenuator of WR90

waveguide size was calibrated at specific dial

settings by each of the above methods at about 9.4

GHz. Although the measurement data was taken

some years ago, recent additional evaluations have

been made regarding the properties of the rotary- vane attenuator. Also, a recently discovered defect

in the fabrication of the interlaboratory standard

used in the above measurements sheds new light on this caUbration data.

9
4.2. Comparison of Modulated Subcarrier

and dc Substitution Methods

Table 2 shows a comparison of the modulated

subcarrier with those of the dc substitution method

(power ratio). The dial setting of the attenuator

in decibels is given in column one. In columns two

and three the measured values for each dial setting

by the modulated subcarrier and dc methods are hsted, respectively. Column four gives the discrepancy between the dc and subcarrier methods.

This discrepancy between the two methods is shown

to be less than 0.0020 dB from 0.01 to 1-dB values,

while the discrepancy increases to 0.03 dB at the

30-dB value. A large portion of these discrepancies

are due to attenuation resettabihty and operator

performance.

Table 2. Comparison of measurements obtained by modulated

subcarrier and dc substitution methods

Measured attenuation (with attenuator vertical)

Attenuator Modulated Discrepancy

dial reading subcarrier dc method between dc

method and subcarrier

methods

dB dB dB dB

0.01 0.0111 0.0107 + 0.0004

.02 .0218 .0214 + .0004

.03 .0308 .0303 + .0005

.04 .0413 .0407 + .0006

.05 .0532 .0521 + .0011

.06 .0626 .0609 + .0017

.07 .0718 .0700 + .0018

.08 .0814 .0802 + .0012

.09 .0918 .0909 + .0009

.10 :1037 .1021 + .0016

.12 .1206 .1191 + .0015

.14 .1388 .1375 + .0013

.16 .1590 .1573 + .0017

.18 .1796 .1783 + .0013

.20 .2023 .2007 + .0016

.25 .2482 .2471 + .0011

.50 .4994 .4979 + .0015

1 1.004 1.004 .0000 2 1.999 1.996 + .003 3 3.000 2.998 + .002 5 4.991 4.990 + .001 10 9.971 9.965 + .006 15 15.01 14.99 + .02 20 19.97 19.95 + .02 25 25.00 25.01 -.01

30 30.10 30.07 + .03 40 40.44 40.33 + .11 50 52.39 52.24 + .15

4.3. Comparison of Modulated Subcarrier

and i-/ Substitution Methods

Table 3 shows the similar comparison between

the modulated subcarrier and i-f methods with the

same rotary-vane attenuator as the interlaboratory

standard. A change of position of the attenuator

caused a deviation of about 0.5 dB between the two

different subcarrier measurements at the 50 dB

dial setting.

The discrepancy between the subcarrier and i-f

methods was about 0.004 dB at 1-dB dial setting

(greater than for the subcarrier and dc methods),

while the discrepancy was 0.02 dB at the 30-dB

dial setting (less than for the dc and subcarrier

methods). In addition, table 2 shows the measured

values of attenuation to be less than in table 3 for

dial settings of 40 and 50 dB. This change could be

caused by the vertical and/or the horizontal positions

of the attenuator under caUbration [13], as indicated

in table 2 and table 3.

Table 3. Comparison of measurements obtained by modulated

subcarrier and i-f substitution methods

Attenuator

dial reading

Measured attenuation (with attenuator

horizontal)

Modulated

subcarrier

method

i-f method

Discrepancy

between i-f and subcarrier

methods

dB dB dB dB

0.1 0.1026 0.101 + 0.0016

.2 .2010 .199 + .002

.5 .4978 .498 - .0002

1 1.002 .998 + .004 2 1.997 1.999 -.002

3 2.998 2.997 + .001

5 4.989 4.980 + .009 10 9.958 9.965 -.007

15 14.98 14.99 -.01

20 19.94 19.95 -.01

25 24.95 24.95 .00 30 30.02 30.00 + .02 40 40.24 40.15 + .09 50 51.70 51.66 + .04

The data from each comparison shows that the

dial of the attenuator agrees rather closely with the

measured values for the range from 0.01 to 30 dB.

However, this is not true for the dial settings of 40

and 50 dB. At 50dB the deviation is greater than

2 dB as shown in table 2. An increase in attenuation

of this magnitude is not a normal characteristic of a rotary-vane attenuator, especially since it has good

agreement to 30 dB. The usual indication is a decrease in attenuation from nominal at the higher

values. This older type rotary-vane attenuator has a low maximum attenuation value of about 80 dB. The

deviation in attenuation below nominal caused by

this low value of maximum attenuation is. about

0.3 dB at 50 dB.

Concentric Rotor Gear Sector

At a later date, the drive mechanism of this

attenuator was disassembled. This revealed that the

gear concentric to the rotor was a sector of about

120°. This gear sector was welded to the outer case

10
of the rotor section. A slight tilt of the gear sector

during the welding process would cause an angular

displacement. It has been shown that an error in the

driven gear of 0.36° will produce a deviation in

attenuation of more than 2 dB at the 50-dB dial

setting [17].

The physical orientation of the attenuator under

test can cause deviations in measurements as shown

in tables 2 and 3. The measured values at the 50-dB

setting deviate by about 0.7 dB between vertical and

horizontal positions of the attenuator. End play in

the bearings of the rotor section, and backlash in the

gearing can cause angular displacement in the

cylindrical dial readout. A change of angular displacement equal to 0.13° causes a change of 0.7 dB

at 50 dB [17].

4.4. Simultaneous Measurement by Modulated Subcarrier and dc Substitution

Methods

In order to more truly compare the subcarrier and

dc substitution methods, the rotary-vane attenuator

was measured in a special situation. A three channel [13] system was devised so that simultaneous

measurements could be made by the dc and subcarrier methods for a given dial setting. The results

of these measurements are shown in table 4. The

deviations between the two methods are 0.0005 dB

up to 0.5-dB measurements, and slightly over

0.001 dB up to 10 dB. While the deviation increased

to 0.006 dB at 20 dB, this confirms that the larger

deviations shown in tables 2 and 3 are due to mismatch error, resettability, and operator performance.

Table 4. Differences between measurements made simultaneously

by modulated subcarrier and dc substitution methods

Attenuator Difference

dial reading (with attenuator vertical)

dB dB

0.01 +0.0002

.02 -.0002

.05 -.0001

.10 +.0005

.50 +.0001

1.0 -.0012

2.0 -.0003

5.0 -.0011

10.0 +.0012

20.0 +.0066

4.5. Measurement of Precision Optical

Rotary-Vane Attenuator by dc and i-f

Substitution Methods

The X-band optical rotary-vane attenuator [3]

developed at NBS/Boulder increased the resolution

and resettability of the RVA to 2 seconds of arc. In

addition, the optical readout feature eliminates

angular displacement errors due to gear eccentricity. This precision attenuator was measured over a

dial range of 0 to 87.5° in 2.5° increments. The

measurements were made using the power ratio

method for attenuator dial readings of 0 to 60° and

using the i-f substitution method for dial settings of

62.5 to 87.5°. In table 5, the calibration of the

optical attenuator is shown for the frequency of 9.0

GHz. Column one lists the dial setting in degrees

(d). Column two gives the theoretical value of

attenuation in decibels corresponding to the angles

of column one. Column three shows the calibrated

value of attenuation at each dial setting. From this

data the average apparent vane angle deviation was

determined [18] to correspond to a retardment of

the rotor vane of 2 minutes of arc or 0.033°.

The attenuator was recalibrated with a correction

of 2' applied to each dial setting. The results are recorded in column four. The application of the

correction to the dial reading enabled the measured

attenuation values to follow the cos^ law more

closely. The deviation of these measurements from

the corresponding theoretical values of attenuation

in decibels are listed in column five. The deviations

from the theoretical value are shown to be less than

0.001 dB for measurements up to 60° (12 dB), and

vary from 0.001 to 0.012 dB; from 62.5 to 87.5°

(13 to 54 dB). The values of the discrepancy of the

measurements that were made simultaneously

between the subcarrier and the dc methods are in

close agreement with those made with the high

resolution optical attenuator (see tables 4 and 5).

This illustrates the excellent,agreement of attenuation measurements between systems and that a high

resolution attenuator eliminates the need for

simultaneous measurement to obtain precise data

for intercomparison of systems.

4.6. Power Ratio (dc) Versus OiT-Null

Measurements

A two-channel off-null technique for measuring

small values of attenuation was developed at NBS

[14]. The interlaboratory standard chosen for

intercomparisons of this measurement system was

the X-band rotary-vane attenuator that was calibrated by the power ratio (dc) method eight years

previously [12].

The rotary-vane attenuator exhibits very little phase shift and provides high resolution at small

values of attenuation; thus these inherent characteristics make the attenuator an excellent device for

this intercomparison. The attenuation range for the

intercomparison was 0.01 to 0.1 at 0.01-dB intervals.

It is estimated that the resettability of this type of

rotary-vane attenuator corresponds to an angular

displacement of the rotor of about 0.006°. Then the

limits of error of resettability for the attenuation

from 0.01 to 0.10 dB are about 0.00006 to 0.00020 dB,

respectively.

11
Table 5. Calibration data of optical rotary-vane attenuator in power ratio andi-{ substitution systems at 9.0 GHz

Calibrated Deviation

Theoretical Calibrated value from

value of value of attenuation theoretical Dial setting attenuation of attenuation with 2' value

in degrees in decibels in decibels correction in decibels

2.5 0.0165 0.0161 0.0166 +0.0001

5.0 .0662 .0653 .0662 +.0000

7.5 .1493 .1478 .1491 -.0002

10.0 .2659 .2640 .2658 -.0001

12.5 .4167 .4145 .4166 -.0001

15.0 .6022 .5996 .6022 -.0000

17.5 .8232 .8203 .8233 +.0001

20.0 1.0805 1.0772 1.0806 +.0001

22.5 1.3754 1.3715 1.3755 +.0001

25.0 1.7089 1.7046 1.7091 +.0002

27.5 2.0828 2.0779 2.0830 +.0002

30.0 2.4987 2.4931 2.4989 +.0002

32.5 2.9588 2.9526 2.9587 -.0001

35.0 3.4654 3.4586 3.4657 +.0003

37.5 4.0213 4.0136 4.0214 +.0001

40.0 4.6300 4.6218 4.6303 +.0003

42.5 5.2948 5.2858 5.2957 +.0009

45.0 6.0206 6.0108 6.0203 -.0003

47.5 6.8127 6.8018 6.8135 +.0008

50.0 7.6773 7.6653 7.6771 -.0002

52.5 8.6221 8.6094 8.6231 +.0010

55.0 9.6563 9.6419 9.6569 +.0006

57.5 10.7913 10.7750 10.7908 -.0005

60.0 12.0412 12.0226 12.0414 +.0002

62.5 13.424 13.406 13.425 +.001

65.0 14.962 14.942 14.967 +.005

67.5 16.686 16.662 16.692 +.006

70.0 18.638 18.611 18.640 +.002

72.5 20.874 20.843 20.876 +.002

75.0 23.480 23.443 23.479 -.001

77.5 26.586 26.543 26.587 +.001

oU.O 30.413 30.357 30.413 .000 82.5 35.372 35.296 35.367 -.005

85.0 42.388 42.266 42.379 -.009

87.5 54.413 54.178 54.401 -.012

Table 6. Comparison of calibration data for the same attenu- ator at 9.39 GHz using two independent methods (power

ratio 1960 versus off-null)

Dial

setting

(dB)

Measured attenuation

difference (dB) Discrepancy between

1960 power ratio and 1968 off-null methods (percent)

1968

Off-null method [1]

1960

Power ratio method [2]

0.01 0.0103 0.0107 -3.7

.02 .0208 .0214 -2.9

.03 .0294 .0303 -3.0

.04 .0397 .0407 -2.2

.05 .0513 .0521 -1.5

.06 .0598 .0609 -1.8

.07 .0695 .0700 -.7

.08 .0792 .0802 -1.2

.09 .0896 .0909 -1.4

.10 .1008 .1021 -1.3

Average 2.0

Table 7. Comparison of calibration for the same attenuator at 9.39 GHz using two independent methods (power ratio 1968

versus off-null)

Dial

setting

(dB)

Measured attenuation

difference (dB) Discrepancy between

1968 power ratio and off-null methods (percent)

1968

off-null method [1]

1968

power ratio method

0.01 0.0103 0.0101 + 2.0

.02 .0208 .0205 + 1.5

.03 .0294 .0290 + 1.3 .04 .0397 .0394 + .8 .05 .0513 .0507 + 1.2 .06 .0598 .0595 + .5 .07 .0695 .0687 + 1.2

.08 .0792 .0786 + .8 .09 .0896 .0890 + .7 .10 .1008 .1003 + .5

Average 1.0

12
The results of the measurements made by the

power ratio methods in 1960 and the off-null method

in 1960 are compared in table 6. Column four shows

the discrepancy between the two methods in percent of the measured value. The greatest percent

discrepancy, 3.7, occurs at the 0.01 dB-dial setting;

however the largest deviation in attenuation is 0.0013 dB and occurs at the dial setting of 0.10 dB.

But more significant is the negative sign common to

all values in column four. Two factors suggest a systematic error, the common minus sign in the

discrepancy column, and the 0.0013-dB difference

at the 0.10-dB measurement. Table 4 shows that the

greatest deviation in measurement for the range of

0.01 to 0.10 dB between the subcarrier and dc substitution method was 0.0005 dB at a dial setting of

0.10 dB. These above factors led us to further

measurement and evaluation.

The rotary-vane attenuator was calibrated later

in 1968 by the power ratio method. The results of

these measurements were compared with those

taken with the off-null method, and are shown in

table 7. The discrepancy between the 1968 power

ratios and off-null methods are listed in column

four. The greatest percent discrepancy, 2, occurs at the 0.01 dB-dial setting, as was the case in table 6,

but the value of the percent of discrepancy was

reduced almost one half. Also, the average value

of the percent of discrepancy for all measurements

of the latter measurements was decreased by one

half.The measured values of attenuation difference for

both the power ratio and the off-null methods were

analyzed for apparent angular deviations [18, 19].

The dial setting of the attenuator was assumed to be

the true value for this analysis. Figure 15 illustrates

the apparent deviation of the rotor from nominal dial

setting in degrees, which correspond to attenuation

values of 0.01 to 0.10 dB. The average vane angle

error representative of each measurement is shown

as a straight line with the angular deviation in

degrees indicated as follows: the power ratio method

of 1960, +0.044°; the off-null method of 1968,

+ 0.008°; and the power ratio method of 1968,

—0.012°. Note, the average vane angle error line

shows a decease from +0.044° in 1960 to a -0.012°

in 1968 for the power ratio method. This shift in the

average vane angle error line indicates that the rotor- vane changed 0.056° during the eight year period.

Angular slippage is very possible when the zero reference of the dial readout is on the shaft of the

drive mechanism geared to the rotor section. This

is not uncommon if either end stop is struck sharply.

When a correction equal to the shppage for each

method is applied, the average vane angle error lies on the zero deviation line, as shown in figure 16. This

figure more clearly illustrates the random point to point deviation which indicates the random error in

the measurement process. Table 8 shows the deviation in decibels from nominal after the correction was apphed to the angular deviation. In addition,

0 12 3 4 5 6

Dial Setting in Degrees

Figure 15. Illustrated deviation of the rotor vane of an at- tenuator calibrated by different methods: power

ratio {I960), off-null, and power ratio {1968).

r ^— POWER RATIO 1960

„,„„ OFF NULL 1968 ~ __0__POWER RATIO 1968

.060° -

-.050° -

-.060° ^ 1 1 1 1 1 1

1 2 3 4 5 6 7

DIAL SETTING IN DEGREES

Figure 16. Apparent deviation of rotor vane in degrees from

nominal at each dial setting in degrees.

The indicated vane angle correction has been applied to each result.

the application of the correction reduced the discrepancy between each comparison. The average

discrepancy is improved from 2 to 0.17 percent and

from 1 to 0.08 percent, respectively, as shown in

table 9, columns five and six. In figure 16 the large apparent angular deviations

are caused by internal reflections and irregularities

within the rotary-vane attenuator. The phenomena

will be noted in evaluating the low values of attenuation in the optical rotary-vane attenuator. There is a

slight indication of a haff cycle of eccentricity present, but the 2 degree cycling shown is not caused by

eccentricity.

13
Table 8. Comparison of deviation from the average values with vane-angle correction applied

Dial

setting

Average deviation from

nominal after correction

for rotor slippage

Spread of measured values

after correction

Deviation from average value

1960 rower ratio

1968

/^CC 11 Uii-nuU

1968

Power ratio

U.Ui U.UUUZ'* U.UUUUo +0.00001 -0.00002 +0.00001

.02 .00073 .00007 +.0000

1

— AAAA.1 .UUUU4 1 AAAAQ +.UUUUa

.03 .00066 .00021 —.00012 +.00011 1 AAAAO +. UUUUo

(\A .U'+ AAAOn

. uuuzu . uuuuo —.UUUUl AAAA/; +1 AAAA"? .UUUU/

.UO .UUUll .UUUiU .00000 1 AAAAT +.00001 — AAAA/I .UUUU4

U.UO u.uuuzo u.uuuzu -0.00001 +0.00015 -0.00010

.07 .00096 .00047 +.00025 -.00022 -.00004

.08 .00104 .00009 +.00004 +.00001 -.00005

.09 .00054 .00021 -.00008 .00011 +.00005

.10 .00066 .00022 -.00001 -.00010 +.00012

Table 9. Comparison of calibration data with average vane-angle error correction applied

Discrepancy between

off-null and each power

Deviation (in decibels) from nominal after ratio method (in percent) with

correction for rotor slippage correction applied

Dial

setting 1960 1968 1968 1960 1968

(dB) Power ratio Off-null Power ratio Power ratio Power ratio

0.01 -0.00024 -0.00022 -0.00025 -0.2 -0.3

.02 -.00074 -.00069 -.00076 -.25 -.35

.03 +.00048 +.00077 +.00074 + 1.0 +.1

.04 +.00019 +.00014 +.00027 -.1 -.3

.05 -.00109 -.00114 -.00104 +.1 +.2

.06 +.00020 +.00040 +.00015 +.3 +.4

.07 +.00121 +.00074 +.00092 +.7 -.3

.08 +.00108 +.00105 +.00099 -.03 +.07

.09 +.00046 +.00065 +.00059 +.2 -.07

.10 -.00065 -.00056 -.00078 -.1 -.2

Average 0.17 0.08

5. Procedures for Evaluating the

Rotary-Vane Attenuator

One of the factors affecting the closeness with

which the rotary-vane attenuator follows the cos^

law is the alignment of the rotor and stator vanes. The ideal properties of this device can be approached when the zero of the dial coincides with

the alignment of these vanes. (The limit of idealism

is also affected by the maximum attenuation of the

rotor section, which will be discussed later.)

Several methods are available for the adjustment

of the vanes in the rotary-vane attenuator. Optical

equipment may be used for a mechanical alignment of the vanes. The electrical method utilizes a waveguide measurement system, where the same

energy level is maintained at the detector during

the positioning of scale at equal angular marks

either side of the 90° position of the rotor vane [5].

Any incorrect alignment of the rotor vane with

reference to the scale readout (degrees or decibals) causes a systematic error that is inherent

[6] to the rotary-vane attenuator. During the calibration of an attenuator, the operator induces a random error in setting the dial readout on a mark.

In making an attenuation difference measurement

of a rotary-vane attenuator, the errors at the

final setting may be written as

, 1 cos jdf+efo + dfi)

€/0 + 6// = - 40 logio (8) cos df

where 6/ is the vane angle at the final setting to obtain the calculated attenuation, dj^ is the vaneangle error made by the operator at the final setting,

and 6fi the inherent vane-angle error caused by

misalignment.

A table of attenuation error as a function of vaneangle error for rotary-vane attenuators is given in

NBS Technical Note 177. The table gives the error,

e, for a given value of attenuation (/i= — 40 logio cos 6) according to the relationship

, cos {6 + d')

e = - 40 logio . (9) cos 6

14
where 6 is the true vane angle and 6' is the angle of vane misalignment. Thus, the angle 6' is the differ- ence between the indicated vane angle and the cor- rect vane angle. The table is divided into the following intervals of attenuation value increments:

0.01 to 0.1 dB in 0.01-dB increments; 0.1 to 1.0 dB

in 0.1-dB increments; 1 to 20 dB in 1-dB increments; and 20 to 70 dB in 5-dB increments. The

attenuation errors corresponding to vane-angle

error ranging from 0 to ±0.499°, in increments of

0.001°, are presented for each value of attenuation given above.

5.1. Determination of Average Vane-Angle

Error and Eccentricity from Calibration

Data

With the aid of the table of Technical Note 177,

the calibration data of the rotary-vane attenuator can

be analyzed for numerous characteristics, such as misalignment of the scale readout with reference

to the rotor and stator vanes, gear-eccentricity

related runout and backlash, reahgnment techniques, and resettability.

The equal angle technique of rotor vane aUgnment

was assumed to be without error, but NBS has

reported that eccentricity in the gear mechanism

induces an error of ahgnment when the above technique is analyzed [6].

S. 1 . 1 . Analysis of Calibration Data

Let us evaluate the cahbration data at specific

dial settings of the rotary-vane attenuator for the

presence of an alignment error and eccentricity.

A range of attenuation from 10 to 50 dB requires a

httle more than one cycle of the 3-cycle gear drive

and scale readout. Table 10, columns one and two,

show the dial settings and measured values of

attenuation in decibels. The dial error or the deviation of the measured values in decibels from

nominal are shown in column three. The estimated vane angle for each dial setting is determined by

use of NBS Technical Note 177 and is recorded in

column four. (An example of the use of Note 177: on page 90, for a nominal setting of 10 decibels, the

measured dial error of 0.038 dB is found in row

nine, column six, to correspond to a vane-angle

error of 0.085°.) Column five shows the attenuation

error corresponding to the average vane-angle

error of 0.064° for each dial setting. The estimated

vane-angle error (column four) minus the average

vane-angle error (0.064°) yields the values in column

six. Column seven shows the error in decibels after

correcting for the average vane-angle error. In

figure 17a the circles are a plot of column three and

the solid curve represents the values from column

five. In figure 17b, the circles are a plot of column

seven. The deviations around the zero reference line

indicate the appropriateness of applying an average

vane-angle correction to all the readings.

5.1.2. Cyclic Pattern of Angular Displacement

In order to illustrate the magnitude of the apparent

angular displacement in degrees, the values of

column four and six (table 10) are plotted in figure 18.

The curve d'c is a plot of column four with the aver- age vane-angle error value, 0.064°, as a reference.

The cyclic pattern of the angular displacement

indicates the presence of an indexing error [6]. The

curve dy is a plot of column six, and indicates the

reference line shift when the 0.064° correction is appUed to the rotor alignment.

Table 10. Summary of data for determining average vane-angle error of a rotary-vane attenuator

Dial setting

in decibels

Measured

value in decibelsDial error

in decibels

Estimated

vane-angle

error

Attenuation

error in decibels for the average of the estimated

vane-angle

error in degrees

Deviation

from average

estimated

vane-angle

errors in degrees

Error in decibels with

correction

for average estimated

vane-angle

applied

10 10.038 0.038 + 0.085 0.028 + 0.021 + 0.009

12 12.050 .050 + .096 .034 + .032 + .017 14 14.04S .048 + .079 .039 + .015 + .009 17 17.046 .046 + .061 .048 -.003 -.002

20 20.026 .026 + .029 .058 -.035 -.032

25 25.034 .034 + .027 .080 -.037 -.046

30 30.072 .072 + .043 .107 -.021 -.035

35 35.160 .160 + .071 .145 + .007 + .016 50 50.475 .475 + .087 .348 + .023 + .127

Average + 0.064

15
s 0.10 -

(b)

1 2 1 4 _1_

35l_ 50dB — _J r

60° 70° 80° 90°

DIAL SETTING IN DEGREES 6, AND DECIBELS

Figure 17. Graphs of deviations in attenuation from nominal

versus dial setting in decibels and degrees.

a. Measured deviation (circles) and computed deviation for +0.064° vane-angle

error.

b. Measured values after applying —0.064° vane angle correction.

5.2. Gearing Errors Related to Rotary-Vane

Attenuator

The equations related to the angular errors in

gears [20, 21] have been applied to the angular

motion of the rotating section of the rotary-vane

attenuator [6]. The angular rotation of the driven

gear concentric about the rotor section of the at- tenuator is represented as the angle 9. With a gear

ratio of 12 to 1, the angle of the drive gear 8' equals

126. Let a be the angular difference between the

zero point of the drive gear eccentricity and the

zero point of the scale on the dial in degrees.

The angular displacement of the rotor vane in

degrees caused by the indexing error is written as

180 TCE

ttD

sin(120+a) (10)

where D is the pitch diameter and TCE is the total

composite error. The angular displacement of the rotor vane in

degrees caused by backlash error is written as

360 TCE

ttD

[l-cos(120+Q!)] tan(/) (11)

where (j> is the pressure angle.

The angular displacement of the rotor vane caused

by the total angular error is

180 TCE

ttD

[sin(120 + a)

+ 2{l-cos(12e + a)} tan</)].

(12)

The total angular displacement, r, is equal to the

sum of the backlash error, /3, and the indexing error,

y. A relationship of these angular displacements in

degrees versus the drive gear rotation is plotted

for 360° in figure 19. With a gear ratio of 12, a rotation

of the drive gear of 360° {126, or 8') is equal to a

rotor section rotation of 30° (0). Thus, the drive

gear rotation equals 1080° for a 90° rotation of the

rotor section.

Figure 18. Graphs of the cyclic pattern of angular displacement curve, d'^, with average vane-angle error of + 0.064 ° and 0'^ with — 0.064 ° correction.

16
UJ

<

I \ \ \

I

0° 90° 180° 270° 360°

DRIVE GEAR ROTATION

IN DEGREES

Figure 19. Variations in gear eccentricity error.

<

VANE ANGLE IN DEGREES. B

Figure 20. Attenuation as a function of vane angle, variation in the indexing error for the three cycles, and

the error in attenuation from nominal for the dial

settings of 0 to 90°.

The curve of angular displacement for dy (fig. 18)

shows the maximum value to be ±0.040° between

dial setting of 10 to 50 dB (55° to about 85°). Let us assume that the pitch diameter of the driven gear

(rotor section) is about 1.59" and a equals zero. Using eq (10) the TCE is calculated to be about 0.001"

for this attenuator.

We can best illustrate the effect of the indexing

error relative to the error in attenuation by plotting

the values obtained in eqs (1), (10), and (9) versus the vane angle rotation, 6, in degrees, as shown in figure

20. The curve (a) is a plot of eq (1) showing the

increase of attenuation from 0 to greater than

80 dB as 6 increases from 0 to about 90°. The curve

(b) is a plot of eq (10) displaying the indexing error from maximum to minimum for the 3 cycles of

the drive gear (6'), or as d increases from 0 to 90°.

The curve (c) is a plot of eq (9) representing the error

in attenuation in decibels for the values of d from 0

to about 90°. The curve of the error in attenuation

shows the cychc pattern similar to the indexing

error but the magnitude of the attenuation error increases at the larger values of 9. For example, the

attenuation error is less than 0.005 dB during the

first cycle of the gear drive, ^ = 0 to 30°; increases to about 0.015 dB in the second cycle, 6=30 to 60°;

and reaches a maximum of 0.140 dB in the last cycle,

0 = 60 to 90°. In figure 20 the insert (d) shows that

the maximum error occurs at about 88° for the vane

angle 6, which is about 5i degrees from the maximum

indexing error during the third cycle.

5.2.1. Effects of a on €r The zero point on the scale of the readout does

not usually coincide with the zero point of drive

gear eccentricity. Nor does the manufacture attempt

to control this phenomenon. Therefore the value of

the angle a may vary from 0 to ±180°. Table 11

shows the values of the angle a where the maximum

and minimum deviations in attenuation, ey , occurs

for the dial settings of 10, 20, 30, 40, and 50 dB. It can be seen that the difference between the two

values of a at any setting of 6 is always 90°.

Table 11. Angular values ofafor maximum and minimum

€y at 10, 20, 30, 40, and 50 dB dial settings

Dial

setting

in decibels 0

a

max Cy. min €y

10 55.7821° -39.3852° + 50.6148°

20 71.5650° -48.7800° + 41.2200°

30 79.7567° + 32.9196° - 57.0804°

40 84.2608° -21.1296° + 68.8704°

50 86.7763° -51.3156° + 38.6844°

The graphs in figures 21, 22, 23, 24, and 25 show

the error in attenuation for different pitch diameters

of the driven gear for dial settings 10, 20, 30, 40, and

50 dB, respectively. These errors were determined

by calculating d'y for the changes in a. In figure 21,

at a dial setting of 10 dB, the changes in a vary from

-39.3852 to +50.6140". The dotted fine indicates

the values of the error in attenuation when a equals

zero, and 8' indicates the number of degrees rotation

of the drive gear to obtain a dial setting of 10 dB.

In order to change the value of attenuation from

10 to 50 dB, the drive gear has an angular rotation

(669.352 to 1041.3156°) of about 372°, or a few degrees beyond one cycle of the possible 3 cycles

range of the attenuator. The driven gear has a angular rotation (55.7821 to 86.7763°) of about 31° or

17
a IN DEGREES a IN DEGREES

99

LJo

o

0,0125

0,025

0.0375

0.050

+50.6148° -57.0804

0

32.9196

Figure 21. Errors in attenuation at the dial setting of 10 dB

versus the angle a for different pitch diameters.

COo

o

<3

<Z

ITO

tr

tr

0.050 —

0.100

0.150

o

<

UJ

O

tr

tr

0.075

0.0625

0.050

0.0375

0.025

0.0125

DIAL SETTING 20 db

a--o 9= 71.5650° ICE =0.001"

S'-- 058. 7800°

1 PRESSURE ANGLE = 20° a (-48.78° to-'4l.22°) —

-A 1 PITCH DIAMETER

A : 0.6388

B = 0.9583

C = 1.2777 ~

D = 1.5972

E = 2.2222

B \

F = 3.1805

D ^v,^^ I

E

"""^--MAXIMUM ERROR

Figure 23.

-21.1296

Errors in attenuation at the dial setting of 30 dB

versus the angle a for different pitch diameters. a IN DEGREES

68.8704°

3

o

0.050

0.100

0.150

0.200

0.250 —

0.300 —

-48.78' -41.22"

a IN DEGREES

Figure 22. Errors in attenuation at the dial setting of 20 dB FIGURE 24. Errors in attenuation at the dial setting of 40 dB

versus the angle a for different pitch diameters. versus the angle a for different pitch diameters.

18
a IN DEGREES 5.2.2. Effects of Pitch Diameter on Error of Attenuation

-51.3156

0.050

0.100

0.150 —

0.200

0.250

0.300

0.350

0.100

0.450

0.500

Figure 25. Errors in attenuation at the dial setting of 50 dB

versus the angle ot for different pitch diameters.

one third of the 0 to 90° possible displacement of

the rotor section. As shown in figure 20, the indexing

error goes through three positive and three negative

maximums from 0 to 1080° rotation, 6', of the drive

gear. The maximum positive and negative indexing

errors occur at fixed angular displacements of d. Table 12 shows the angular values of 6 where these

maximums occur and their respective theoretical

values of attenuation in decibels.

The pitch diameter of the driven gear affects the

angular displacement errors as indicated by eqs (10),

(11), and (12). The waveguide size usually is the

determining factor for the value of the pitch diameter used as the driven gear. The rotary-vane at- tenuators in the millimeter range require smaller

waveguide components and normally a driven gear

having a smaller pitch diameter is mounted on the

rotor section. The graphs of figures 26, 27, 28, 29,

and 30 indicate the maximum error in attenuation

for the displacement angles d'y, 6'^ and 6'^ for

changes in pitch diameter at 10, 20, 30, 40, and 50-

dB dial settings, respectively. The pressure angle (/> appears in eqs (11) and (12) and curves are plotted

for 20° and 14.5° pressure angles to illustrate the

change in attenuation error for ^^ and 0^ . The

indexing error is not changed by the pressure angle

of the gears; thus, only one curve is needed to show

this error at each dial setting. All graphs show that an increase in pitch diameter of the driven gear

decreases the error in attenuation caused by any one of the displacement errors.

<Z

LlI I-h-<

o

cc

cc

0.600

0.500

0.400

0.300

0.200

1 \ \ \ r \—

r

DIAL SETTING 10 d b

Sji = TOTAL ANGULAR ERROR

B{ -- INDEX ERROR

9'g = BACKLASH ERROR

TCE= aool" PRESSURE ANGLES

(1) =20°

(2) = 14.5°

0 0.2 0.4 0,6 0.8 1.0 1.2 1,4 1,6 1,8 2.0 2.2

PITCH DIAMETER IN INCHES

Figure 26. Errors in attenuation at the dial setting of 10 dB

versus pitch diameter for the angular displacement

error.

e Max Decibels

7.5° + 0.149257

22.5° 1.375386

37.5° + 4.021334

52.5° 8.622115

67.5° + 16.686414

82.5° 35.372093

Table 12. Angular values of 0 where maximum (+ or —) de- viations of attenuation occur due to indexing error in 3-cycle drive and the corresponding theoretical attenuation values

19
Figure 27. Errors in attenuation at the dial setting of 20 dB

versus pitch diameter for the angular displace- ment error.

2

O

0.900

0,800 -

0.700

0.600

0.500

0.400

o 0,300

0.200

0.100

DIAL SETTING 30 d b

= TOTAL ANGULAR ERROR

= INDEX ERROR

Sb = BACKLASH ERROR

TCE= O.OOl" PRESSURE

(1) 20°

(2) 14.5°

ANGLES

J L

0 0.2 0.4 0,6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

PITCH DIAMETER IN INCHES

Figure 28. Errors in attenuation at the dial setting of 30 dB

versus pitch diameter for the angular displace- ment error.

PITCH DIAMETER IN INCHES

Figure 29. Errors in attenuation at the dial setting of 40 dB

versus pitch diameter for the angular displacement error.

m

UJQ

<

o

IX

C.900

0.800

0.700

C.600

0.500

0.300

0.200

0.100

T T T

DIAL SETTING 50 d b

= TOTAL ANGULAR ERROR

= INDEXING ERROR

= BACKLASH ERROR

TCE= O.OOl" PRESSURE ANGLES

(1) = 20°

(2) = 14.5°

_L

0 0.2 0.4 0.6 0,8 1.0 1.2 1.4 1.6 1.8 2,0 2.2

PITCH DIAMETER IN INCHES

Figure 30. Errors in attenuation at the dial setting of 50 dB

versus pitch diameter for the angular displace- ment error. 20
6. Compensation for Transmission

Error of Rotary-Vane Attenuator

The transmission error becomes less as the magnitude of the maximum attenuation is increased in

the rotor section of the attenuator. Otoshi [9] has

presented a modified law that provides a tool for

extending the useful dynamic range of the rotary- vane attenuator with low values of maximum at- tenuation. A mechanical technique of increasing

the dynamic range may be achieved by adjusting the

input stators of the attenuator.

6.1. Transmission Error versus Dial Setting

in Decibels

With a known maximum attenuation value at 6

equals 90°, the transmission error can be determined

from eq (5). In order to make quick estimates of the

transmission error, eq (5) was used to obtain figure

31. The graphs show that the transmission error is about 0.03 dB at the dial setting of 50 dB for an at- tenuator with a 100-dB maximum. The error in- creases to a value of 0.3 dB for a maximum attenuation of 80 dB at the same dial setting. However,

the error decreases to about 30 microbels if a 160-dB

maximum attenuation can be achieved in the center

section of the attenuator.

1 .0

0 .

1

0.01

0.001 - —

0.0001

0.00001

20 30 40 50

DIAL SETTING IN dB

70

Figure 31. Estimate of the transmission error versus dial

setting in decibels for maximum attenuation values of 60 to 160 dB.

6.2. Stator Realignment

The mounting holes of each stator are enlarged to enable angular rotation around the longitudinal

axis of the waveguide sections of the rotary-vane

attenuator. The stators may be rotated either direction with reference to the input port of the attenuator,

as shown in figure 32. The Type B error in part (A)

indicates that stator SI was rotated 1/2° clockwise

and stator S2 was rotated 1/2° counterclockwise;

and in part (B) indicates that the stators were rotated

conversely. From eq (3) the calculated deviation

was determined to be 0.066 dB for the dial setting of

40 dB. The measured attenuation difference

deviated from calculated attenuation by 0.009 and

0.015 dB for the conditions A and B, respectively,

at the dial setting of 40 dB. However, the 1/2° rota- tion of the stators induced an increase in the attenuation difference of about 0.08 dB in both cases at the 40-dB setting. In other words the Type B error of misahgnment increases the value of attenuation

for nominal dial settings. As will be shown later,

intentional misalignment of the stators can effectively compensate for insufficient maximum

attenuation.

-TYPE "B" ERROR -

ROTOR ZERO POSITION ALIGNED TO AVERAGE POSITION OF STATORS POWER

(A) (B)

1 s)'

- R s\z

1

c.w.

cc.w. ROTOR ROTOR

DIAL SETTING

40.075 db 40 db MEASURED VALUE

40.081 db MEASURED VALUE

Figure 32. Illustration of stator rotation and rotor align- ment to induce the Type B error.

Angular Displacements versus Maximum Attenuation

In figure 33 the smooth curve provides an estimate of the angular displacement, 6' 12, which the

stators require to compensate for the values of

maximum attenuation. The angular displacement

equals about 1.05° for 70 dB and decreases to an

angle of 0.018° for 140-dB maximum attenuation.

For example, the graph shows that the stators must

be rotated about 0.18° to compensate for the transmission error when maximum attenuation equals

100 dB. In order to determine the value of compensation in decibels, refer to NBS Technical Note 177.

Page 139 gives the attenuation deviation versus

21
angular deviation for the nominal value of 50 dB,

^ = 86.7763°. For example, column 1 and line 2 give

values of +0.997123 dB and -0.942820 dB corre- sponding to the angular deviation of 0.18°. The value

of compensation, e^,, equals 0.027515 dB, which is one-half of the algebraic sum of the attenuation

deviation in decibels. This result can be computed

from eq (3). Figure 31 shows that the deviation from

MAXIMUM VALUE OF ROTOR VANE ATTENUATION IN dB

Figure 33. Estimated angular displacement of stators in degrees versus the maximum attenuation value of rotor vane in decibels for the compensation re- quired to approach theoretical cos'' 6 law.

nominal attenuation in decibels equals about 0.027

dB for a dial setting of 50 dB and the maximum

attenuation line of 100 dB.

Realignment of the stators causes the end ports of

the rotary-vane attenuator to be out of alignment

with the ports at the insertion point of the measure- ment system. Therefore, a waveguide adapter with an angular twist equal to 6' 12 should be placed at the

ends of each stator. The twists becomes a part of the

attenuator after the angular displacement is determined by the maximum attenuation of each attenuator. Table 13 shows the angular correction, 6' j2,

required for maximum attenuation values of 90 to 160 dB in 10-dB intervals. The distance b' necessary

to produce the angular correction is given for eleven

waveguide sizes from WR15 to WR650. The angular

displacement has been converted to length in inches

or distance b' from a reference plane, as shown in

figure 2.

6.3. Illustration of Transmission Error and

Compensation for 1 10-dB Maximum

Figure 34 illustrates the deviations in attenuation

from nominal by giving both the increase in attenuation caused by misaligning the stators and the de- crease caused by insufficient maximum attenuation,

respectively. The deviations are plotted for dial set- tings from 20 to 70 dB. The solid curve indicates the

calculated (eq (5)) deviations in attenuation for an

attenuator of 1 10-dB maximum. (Fig. 31 can be used

for rapid estimates.) The dashed curve indicates

the calculated (eq (3)) deviation in attenuation for an

attenuator with 0.1° {d' 12) stator misalignment. In

other words the misalignment of the stator by 0.1°

induces an increase in the attenuation which closely

compensates for the decrease in the attenuation

caused by an insufficient maximum value of 110 dB.

Table 13. The angular correction required for different values of maximum attenuation and the distance h' necessary to produce

the angular correction for various waveguide sizes

ei

90 dB 100 dB llOdB 120 dB 130 dB 140 dB 150 dB 160 dB

0.320° 0.180° 0.100° 0.057° 0.032° 0.018° 0.010° 0.008° WR a b'

15 (0.148) 0.00080 0.00046 0.00026 0.00017 0.00008 0.00004 0.00003 0.000020

28 (.280) 0.00150 0.00088 0.00049 0.00031 0.00016 0.00009 0.00005 0.000038

42 (.42) 0.00227 0.00132 0.00073 0.00047 0.00023 0.00013 0.00007 0.000057

62 (.622) 0.00337 0.00195 0.00109 0.00070 0.00035 0.00020 0.00011 0.000084

90 (.900) 0.00488 0.00283 0.00157 0.00101 0.00050 0.00028 0.00016 0.00012

112 (1.122) 0.00608 0.00352 0.00196 0.00126 0.00063 0.00035 0.00019 0.00015

137 (1.372) 0.00745 0.00431 0.00239 0.00154 0.00076 0.00043 0.00024 0.00019

187 (1.872) 0.01015 0.00588 0.00327 0.00211 0.00104 0.00059 0.00033 0.00025 284 (2.840) 0.01541 0.00892 0.00496 0.00319 0.00158 0.00089 0.00050 0.00038

430 (4.300) 0.0233 0.01351 0.00750 0.00484 0.00240 0.00135 0.00075 0.00058

650 (6.500) 0.03527 0.02042 0.01134 0.00731 0.00362 0.00295 0.00113 0.00088

672 = a/2 tan d' 12

b' = atan 6' 12

22
MAX = IIOdB

Figure 34. Deviation in attenuation caused by misalignment

of the stators, 6' equals 0.2°, and insufficient maximum attenuation of 110 dB for the dial setting of

20 to 70 dB.

23
6.4. Mechanical Compensation and

Measured Results

In order to experimentally evaluate the compensation technique of stator realignment, a commercially

available rotary-vane attenuator was modified.

The stator flange bolt holes were enlarged to permit

rotation of the stators and the vane in the rotor section was decreased in length. The measured maximum attenuation (at 6 equals 90°) dropped from a previous 90 to 72 dB after the rotor section modification. In figure 35, the calibrated values of the

modified attenuator are plotted as X points on the

solid line curve at dial settings of 20, 30, 40, 50, 60, at 70 dB. The solid line curve indicates the calculated

deviation in attenuation for an attenuator with 72-dB

maximum attenuation. Referring to figure 33, the

angular displacement required for 72-dB maximum

is estimated to be about 0.87°. In figure 35, the calculated deviation in attenuation induced by misaligning the stators 0.87° is plotted as the dashed hne.

The calibration points plotted as <8> indicate that

the compensation caused the values of 10 to 40

dB to fall in a random manner about the zero deviation line. However, the larger deviation shown at 50

dB is within the limits of the system error and the

resettability of the commercial attenuator.

0.70

O60

050

0.40

030

O20

OlO

0

-OlO

-O20

-0.30

-0.40

-O50

-0.60

<z

S

o

o

<

LU

I-<

<

>

UJQ

(b) CORRECTION

INDUCED BY MISALIGNING

THE STATORS 0.87° ; (b)

(c)

- CALIBRATED VALUES AFTER STATORS MISALIGNMENT

(a) DEVIATION OF CALIBRATED VALUES WITHOUT REALIGNING

THE STATORS

-0.70

0 10 20 30 40

DIAL SETTING IN DECIBELS

Figure 35. Deviation of attenuation from nominal versus dial

setting in decibels for rotary-vane attenuator with 72-dB maximum: (a) Curve of calibration points,

{b) Curve of correction induced by misaligning

the stator 0.87°, and (c) Plot of calibrated values

after stator misalignment.

7. Measurements of Precision Rotary-Vane Attenuators With High

Resolution Readouts

A cahbrated high precision rotary-vane attenuator can be regarded as an ideal working or transfer

standard for making precise measurements in a microwave standards laboratory. Regardless of the

great care taken in the fabrication of the attenuator,

or the high resolution of the dial readout, the device

should be evaluated before it is used as a standard.

Though several attenuators may be built of identical

design and precise fabrication each has distinct

inherent characteristics [3, 18].

At present the commercially available rotary-vane

attenuators have a dynanic maximum range of 90 to 100 dB. This value of maximum attenuation provides

only one-half of the theoretical value attainable at 1 arc second less than 90° rotation of the rotor. The

usable scale of these attenuators are marked from

0 to 50 dB. Thus, about one-fourth of the total range

of attenuation is at present being used for calibrated

interlaboratory standards. Usually this type of

rotary-vane attenuator utilizes a spiral scale for the

dial readout of attenuation in decibels. The attenuator must be calibrated at nominal values, but even

then the resolution and scale readout usually are

too coarse for precise interpolation between points

of calibration.

At present several angular displacement readouts have been designed for use with precision

rotary-vane attenuators. A gear mechanism designed by NBS can be installed onto commercial

rotary-vane attenuators to give dial readings of

angular displacement of 0.001° from 0 to 90°. The

NBS optical rotary-vane attenuator provides an

angular displacement with a resolution of ± 1 sec- ond of arc. The Royal Radar Establishment of England has developed a digital angular readout for

rotary-vane attenuators. It utilizes a row of numerical indicator tubes and has a resolution of 0.001°.

7.1. Measurement of Rotary-Vane Attenuator With a Gear Driven Readout

The gear mechanism illustrated by the drawings

in figures 13 and 14 has been used successfully

with commercial rotary-vane attenuators in WR62,

WR90, and WR112 waveguide sizes, and adapts

to rotary-vane attenuators in waveguide sizes

WR137 and WR187 with minor modifications.

The modified attenuator, which now reads in

angular displacement of the rotor section, must

be calibrated in an attenuation measurement sys- tem for use as an attenuation device. The vaneangle error and gear eccentricity can be determined

from the calibration data as shown in 5.2. In

order to obtain the best possible evaluation of the

modified gear driven readout, three measurement

systems were used in the calibration of the at24
(o.aondB)

(O.OIdB)

(0,03dB)|(0.05dB) (0.02dB)i_|_ 1(0, idB)

Figure 36. Angular error, 9^, in degrees from nominal (theory) versus the dial setting, 6, in degrees, determinedfrom measurements by

the power ratio, modulated subcarrier, and i-f substitution methods.

tenuator over a large range. Each measurement

system was used to cover a different range of about

30° of angular rotation of the center vane.

7.1.1. Measurements of Precision Gear Driven RotaryVane Attenuator

The measured results were obtained as foUows:

the power ratio method, 0 to 30°; the modulated

subcarrier method, 30 to 60°; and the i-f substitution method, 60 to 87.5°. The interval of measure- ment taken was every 2.5° within the 30° section.

The measured attenuation at each dial setting was

compared with the theoretical value [19] to determine the average vane-angle error in degrees. In

figure 36, the curve shows the angular error,

d[,, in degrees from nominal (theory) versus the dial

setting, d, in degrees. Each measured value is shown by an X at the 2.5° dial settings of d. The

cyclic indexing error is caused by eccentricity

(eq (10)) and shows a variation from 0.050 to — 0.010°.

The dashed straight line is drawn as the axis of

the ± 0.030° cyclic indexing error, and represents an average vane-angle error of about 0.020°. In

addition to a dial setting scale in degrees, the corre- sponding values of attenuation in decibels are in- dicated on the lower part of the horizontal axis

of the graph. In other words the range of attenuation difference measurements that were taken by

the three different methods were as follows:

0.02 to 2.5 dB, 2.5 to 12 dB, and 12 to 55 dB, by

the power ratio, modulated subcarrier, and if

substitution methods, respectively.

7.1.2. Angular Resettability of Attenuator

The two dashed lines drawn ±0.010° about the

cyclic indexing error curve (fig. 36) approximate the

angular resettability of the attenuator. The basic

part of the error of resettability is caused by gearing

in the commercial attenuator. In addition to the error of resettability the relation of center distances

between these gears is the principal cause of the

eccentricity or indexing error. The drive gear should

be replaced if the runout error is large and the spring

loading converted to positive loading of the gear.

The arrows shown on the upper part of the graph

give the value of resolution which is indicated within

the parenthesis. The resolution in decibels corre- sponds to the resettability of 0.020° at the various

values of 6. All values of angular deviation fell within the range of 0.020°, but the deviation in

attenuation vary greatly. For example, the deviations in attenuation vary from 10 /xbels at 0.02-dB

dial setting, to about 1 dB at 100-dB dial setting.

When the measured angular deviations were

converted to decibels, all the deviations in attenuation were within the systematic and random errors

of the corresponding measurement system. This

close agreement in following the indexing error of

the attenuator shows that any one of the measure- ment systems could be used to calibrate the

attenuator over an assigned part of its range.

Therefore extrapolation of the cyclic error over any other part of the range could be used to set limits of error for the entire attenuator.

7.2. Mounting the Gear Drive

We recommend that the drive gear be selected

with care and spring loading be removed, before

applying a precision gear mechanism to the at- tenuator. Figure 37 illustrates the angular error of

the attenuator when a gear box was mounted on the

rotary-vane attenuator without modifying the drive

gear. The curve illustrates the angular error over

573-735 OL - 75 - 3
a range of about 70° rotation of the center vane

(about two and one-third revolutions of the drive

gear for a 12 to 1 ratio). The large half-cycle error was caused by a binding effect between the drive

gear and the driven gear (concentric to the rotor

section). When more precise machining techniques were applied to the mounting of the precision

readout, the cyclic indexing error became a cyclic

pattern as shown in figure 38. Note that the average

angular displacement error was reduced from about

0.450 to 0.040°.

.700

.600

.500

; .400 —

.300

.200

.100

0 10 20 30 40 5 0 60 70 80 9 0 & (Dial Setting in Degrees)

Figure 37. Angular error caused by binding effect between the drive gear and the driver gear (concentric to the

rotor section)

.

7.3.1. Measurements on Optical Rotary-Vane

Attenuator

In order to evaluate the attenuator over a wide

dynamic range, it was calibrated by three different

methods in the same manner as was the precision

gear driven attenuator. The attenuation deviations

in decibels and the angular deviations in degrees

are plotted versus dial setting in degrees (refer to

fig. 39). The portion of the curves corresponding to the first 30° of dial setting shows the deviations in

attenuation and angular displacement as determined

by the power ratio measurement system. This

portion of the curve shows deviations in attentuation

from —0.0025 to 0.0045 dB or in angular displacement from —0.046 to 0.024°. Neither the power

measurement system nor a precision attenuator cause such large mechanical or electrical deviations.

The calibration data for 30 to 60° and 60 to 87.5°

portions of the dial settings were obtained by the

modulated subcarrier, and i-f substitution methods,

respectively. Again the electrical deviations were

large for each specific method: 0.004 dB in the subcarrier system and 0.026 dB in the i-f system. In

addition to large electrical and mechanical equivalent angular deviations, the apparent average vaneangle error falls off from a +0.010° to a -0.005°.

This error falls off more rapidly at the higher values

of attenuation. All of these deviations in measure- ment of attenuation and decrease in the angular

errors show that the center vane has insufficient

maximum attenuation (below the required amount

for a precision rotary-vane attenuator). The evidence

of 0.015° decrease in the average vane-angle error indicates that the maximum attenuation is less than

90 dB.

S

.100

to

0) O

1 '

1

I I

1 1 -\ Average Vone Angle Error

1 1 'a> 0 10 20 30 40 50 6 0 70 80 90

9 (Dial Setting in Degrees)

Figure 38. Angular error, 6', in degrees versus dial setting in degrees, 6, after precise machining was applied.

7.3. Optical Rotary-Vane Attenuator

The optical rotary-vane attenuator designed at NBS virtually eUminates gear eccentricity errors. The readout scale of the attenuator gives an optical

display of the angular rotation of the rotor section

in degrees, minutes, and seconds of arc from 0 to 360°. However, the attenuator is used in its normal

function from 0 to 90°. The final version of the optical

rotary-vane attenuator followed the cos squared law

more closely than any attenuator previously calibrated at NBS. Notwithstanding, earlier fabrications

of the attenuator had problems other than gearing

to solve.

Jc 024

.019 lIB I

.026 dB

Figure 39. Deviation in decibels and degrees versus dial

setting in degrees.

26
.005

• Decibels X Degrees

Figure 40. Deviation in decibels and degrees versus dial setting in degrees, after repair of the rotor section.

7.3.2. Measurements after Rotor Repair

The center vane was replaced and care taken to properly cement it to the rotor section. After repairing the rotor section, the attenuator was recalibrated using the same systems as before. In figure

40 the plot of these measured deviations shows that

the average vane-angle error is now 0.033°. The

deviation in attenuation difference is about ±0.001

dB with reference to the average vane-angle error

line from 0 to 60° of 6, about ±0.002 dB from 60 to 80°, and ±0.005 dB at 87.5° of 6. The curve with the

mark X shows the attenuation deviations converted

to angular deviations. These deviations have decreased greatly from those shown in figure 39.

More important is that the fall off at the higher

values of d decreased to about 0.003°; this cor- responds to about 105-dB maximum attenuation in

the center vane. The attenuation deviations from a curve cor- responding to a vane-angle misalignment of — 0.033°

and to angular deviation from the —0.033° fine were

plotted. Figure 41(a) shows the value for a dial

setting of 0 to 45° while figure 41(b) shows the values

for a setting of 45 to 87.5°. The deviations of atten- uation from the curve corresponding to the —0.033°

vane misahgnment were quite small and indicate

that such would be a very good compensation for

transmission error over the dial range of 0 to 87.5°.

8. Resolution and Resettability

There are two possible readouts that can be used

for rotary-vane attenuators: (1) direct reading of

attenuation in decibels; and (2) angular reading of

rotor vane rotation in degrees. The use of a readout

with angular notation offers the advantage in that

the scale is linear, while a direct reading decibel

5 10

Dial Setting in Degrees

9

15 20 25 30 35 40 45

1 1 1 1 1 1 1 1 1 1 1

Vone Angle

1 1 1

X » •

Angular

Error

in

Degrees

(Q)

• Measured Decibels

X Degrees

Dial Setting in Degrees 9

,45 50 55 60 65 70 75 80 85 90

Figure 41. (a) Deviation of measured attenuation and equivalent angular deviation from theoretical values for a vane angle correction of —0.033° versus dial

setting of 0 to 45°.

(b) Deviation of measured attenuation and equivalent angular deviation from theoretical values for

a vane angle correction of —0.033° versus dial

setting of45 to 87.5°.

27
scale decreases rapidly in resolution at the high

values. In addition, interpolation becomes more

difficult to estimate as the attenuation rate increases on the decibel scale.

There are occasions when it is important to know

to what accuracy a rotary-vane attenuator can be

set over its usable range. In order to demonstrate

the accuracy of resettabihty we have elected to use

angular notation. Figure 42 shows the resolution

error, eR, in attenuation in decibels versus the dial

setting, /4(iB, in decibels for several values of O'k, the angular resettabihty of the rotor vane in degrees. The curves show the magnitude of the resolution error, €«, for values from 0.1 /jihel to 100

decibels at dial settings of 0.001 to 200 dB for

angular resettabihty of 1 second and 0.001 to 1.0°

of arc. The curves (A to H) provide a quick and con- venient means of determining the accuracy in

decibels one can expect for a known angular resolution. Also, if the deviation in attenuation from

nominal is known, the required angular correction can be determined from the graph. For example,

for a rotary-vane attenuator with a deviation of

about 0.013 dB at a 10-dB dial setting, curve (E)

shows that a correction of 0.03° would be required

to give the nominal value of attenuation.

9. Resolution of Rotary-Vane

Attenuator in Percent of Dial

Setting

The question may arise as to the optimum value

of attenuation to measure for intercomparison of

laboratory standards, or to determine the characteristics of a variable attenuator standard. In figure

43, the resolution of the dial in percent of dial setting

is plotted versus dial setting in decibels for a rotary- vane attenuator with an angular resolution of 0.01°.

At each end of the curve the resolution of dial in

percent of attenuation value rises very rapidly.

For example, at the dial settings of 0.01 and 100 dB,

the resolution of dial is about 1 percent and appears

to have the lower percent values from 6 to 20-dB

dial settings, with the lowest occurring at about 12

dB. If an attenuator has finer resolution, such as 0.001° or 1 second of arc, then the resolution of

dial in percent of attenuation will be correspondingly

lower. From figure 42 it can be determined that for

attenuation values of 1, 12, and 40 dB, the resolution

of dial in percent are 0.011, 0.0045, and 0.0075

percent, respectively, for 0.001° dial resolution, and

the corresponding values are about 0.003, 0.0013,

and 0.002 percent for one second dial resolution.

Again in both cases, the 12-dB dial setting has the

lower resolution of dial in percent of attenuation.

2 0.05

3,0 6.0 12

Dial Setting in Decibels

20 30 50 100

Figure 42. Resolution error in decibels versus dial setting

decibels.

Figure 43. Resolution of the dial in percent of attenuation

versus dial setting in decibels for an attenuator

with angular resolution of0.01 °.

10. Frequency Sensitivity of the

Rotary-Vane Attenuator

Although the rotary-vane attenuator has some

excellent properties, such as stability, resolution

and low reflection at the input and output ports,

all of which are necessary criteria for good transfer

standards, it also exhibits an undesirable characteristic, frequency sensitivity. The frequency sensitivity

28
becomes more pronounced at high values of at- tenuation; thus calibration of the attenuator at the operating frequency is essential for precise

measurement with this device over large ranges

of attenuation.

10.1. Spectrum of Microwave Attenuation

Calibration Systems 2.6 to 40 GHz

For a period of more than 15 years, the microwave

attenuation calibration system [16] has been used at NBS to calibrate rotary-vane attenuators over the

microwave spectrum of 2.6 to 40 GHz. This included

the following waveguide sizes: WR284, WR187,

WR137, WR112, WR90, WR62, WR42, and WR28.

Three frequencies for microwave cahbrations were

suggested for each waveguide size. These three

frequencies were approximately as follows: the

lower frequency limit increased 10 percent, the

middle of the waveguide band, and the upper fre- quency limit decreased 10 percent. For example, the

frequency band for WR90 waveguide is 8.2 to 12.4

GHz, and the suggested frequencies for calibration were 9, 9.8, and 11.2 GHz.

3 Selected Frequencies Each in WR284, WR90, and

WR28 Waveguide Sizes

It is helpful to use the data of cahbrated rotary- vane attenuators in several waveguide sizes to evaluate their frequency sensitivity. For example,

the waveguide sizes WR284, WR90, and WR28

cover the lower, middle, and upper portion of the

microwave frequency range used in this sample of

rotary-vane attenuators. The deviations of attenuation from nominal in decibels versus dial settings

of 10 to 50 dB at three NBS selected frequencies in

each of the above waveguide sizes are shown in

figures 44 to 50. In each figure the points plotted for

each dial setting are coded as follows: the square,

, at the lower frequency; the triangle. A, at the

middle frequency; and the circle, O, at the higher

frequency. The smooth curves indicate the average

deviation in attenuation and the corresponding vaneangle error is shown in degrees [17]. The spread

between the curves indicates the magnitude of the

error caused by frequency sensitivity. Corrections can be applied to minimize the frequency sensitivity.

Figures 44 and 45 show the deviations of attenuation for two attenuators in WR90 waveguide. In

figure 44 the average vane-angle error is positive

and yields values of attenuation greater than

nominal, while in figure 45 the average vane-angle

error is negative and gives values of attenuation less

than nominal. The random variation of the calibrated

points at each dial setting are due to gearing runout,

resettability, mismatch, and system drift. An example will now be given to show how the

deviation in frequency sensitivity across a given

waveguide size can be minimized. If a vane angle

correction of —0.067° is appUed to the data plotted

in figure 44, then the average vane-angle error at

9.0, 9.8, and 11.2 GHz will be +0.031, +0.013, and — 0.031° respectively.

29
-0.400L

20 30

DIAL SETTING IN dB

Figure 45. Deviation of attenuation for average vane-angle errors of —0.032, — 0.042, and — 0.054° versus dial setting in decibels at 9.0, 9.8, and 11.2 GHz.

Figures 46 and 47 show the deviations in atten- uation for two rotary-vane attenuators in WR28.

The random scatter of the point-by-point values

are larger in the smaller waveguide size because

gearing runout can produce greater angular displacement error [6]. which correspondingly induces

larger deviations in attenuation. The deviations in

attenuation from nominal are illustrated for three

WR284 rotary-vane attenuators in figures 48, 49,

and 50. These curves show that two attenuators

have a neeative average vane-angle error while the

third has a positive angular error. In addition, in

figures 48 and 49, the curve showing the higher

frequency error falls between the middle and lower

frequency errors. This could be caused by the

warping or curling of the tapered vanes in the end

sections, which is characteristic of this model of

rotary-vane attenuator. However, the curve for the

higher frequency did not fall between the other two

and the spread of the deviation in attenuation

appears to be less for the data obtained with another

model of WR 284 attenuator, shown in figure 48.

0 .800r

0.600

0.400

0.200

0.000

WR 28 R.V. ATTEN.

O 37 GHz A 33 GHz

29 GHz

_1_ _1_

1 0 2 0 30

DIAL SETTING IN d

B

Figure 46. Deviation of attenuation for average vane-angle errors of 0.024, 0.035,

and 0.049° versus dial setting in decibels at 29, 33, and 37 GHz.

30
WR 28 R.V. ATTEN. O 37 GHz a 33 GHz

29 GHz

-0.014°

10 20 30

DIAL SETTING IN dB

40 50

Figure 47. Deviation of attenuation for average vane-angle errors of 0.008, —0.014,

and — 0.042 ° versus dial setting in decibels at 29, 33, and 37 GHz.

0.020

0 .000

-0.020

-0.040

-0.060

-0.080

-0.100

-0.120

-0.140

-0.160

-0.180

-0.200

WR 284

R.V. ATTEN

O 3 . 55 GHz

3 .25 GHz

2.85 GHz

I 20 3 0

DIAL SETTING IN dB

40 50

Figure 48. Deviation of attenuation for average vane-angle errors of —0.031, — 0.010, and 0.013° versus dial setting in decibels at 2.85, 3.25 and3.55

GHz.

31
0 10 20 30 40 50

DIAL SETTING IN dB

Figure 49. Deviation of attenuation for agerage vane-angle errors of 0.128, 0.105,

and 0.120° versus dial setting in decibels at 2.85, 3.25, and 3.55 GHz.

MR 234

R.V. ATTEN.

O 3 .55 GHz

a 3.25 GHz O 2 .85 GHz

20 30

DIAL SETTING IN dB

Figure 50. Deviation of attenuation for average vane-angle errors of —0.070, — 0.067, and —0.032° versus dial setting in decibels at 2.85, 3.25, and

3.55 GHz.

32
10.2. Statistical Analysis of the Frequency

Sensitivity from Calibration Data at 30, 40,

and 50 dB

In order to obtain a statistical analysis of the

frequency sensitivity, data were selected from

calibrations performed on 154 attenuators at the

established frequency limits. The analysis utilized

the calibration data of the higher dial settings of

30, 40, and 50 dB of each rotary-vane attenuator.

Since these dial settings were common to all calibrations, these values were used in computing the

standard deviation for each waveguide size. In

figures 51 to 58 each graph shows the limits of

one-sigma error in attenuation in decibels versus frequency in GHz for the rotary-vane attenuator in

Figure 51. Limits of magnitude of one-sigma error in attenuation versus frequency in GHz for twenty WR284

rotary-vane attenuators at W, 40, and 50-dB dial

settings.

each specific waveguide size at 30, 40, and 50-dB

dial settings. In each figure the vertical lines /i and

f-z are the hmits of the selected frequencies. However, the frequency of each graph was extended to include the total frequency range of that specific

waveguide size. The greatest change in attenuation

in decibels occurs at the dial setting of 50 dB in

WR62 waveguide and is about 0.75 dB for a frequency range of 12.4 to 18.0 GHz, as shown in

figure 56. The least change in attenuation for the

50-dB dial setting was about 0.3 dB in WR284 and

WR42 waveguide sizes (figs. 51 and 57).

Figure 53. Limits of magnitude of one-sigma error in attenu- ation versus frequency in GHz for eighteen WR137

rotary-vane attenuators at 30, 40, and 50-dB dial

settings.

0.35p

Figure 52. Limits of magnitude of one-sigma error in attenua- FIGURE 54. Limits of magnitude of one-sigma error in attenuation versus frequency in GHz for tiventy-one WR187 tion versus frequency in GHzfor twenty-three WR112

rotary-vane attenuators at 30, 40, and 50-dB rotary-vane attenuators at 30, 40, and 50-dB dial

dial settings. settings.

33
0.80,-

FlGURE 55. Limits of magnitude of one-sigma error in attenua- Figure 56. Limits of magnitude of one-sigma error in attenuation versus frequency in GHz for fifty-one WR90 tion versus frequency in GHz for seven WR62 rotary- rotary-vane attenuators at 30, 40, and 50-dB dial vane attenuators at 30, 40, and 50-dB dial settings,

settings.

Figure 57. Limits of magnitude of one-sigma error in attenuation versus frequency in GHz for seven WR42 rotary- vane attenuators at 30, 40, and 50-dB dial settings.

34
o.70r

0.60

0.40

1 0.20

0.10-

26.0 26.5 30 . 0 35.0 40.0

FREQUENCY IN GHz

Figure 58. Limits of magnitude of one-sigma error in attenuation versus frequency in . GHz for seven WR28 rotary-vane attenuators at 30, 40, and 50-dB dial

settings.

10.3. Frequency Sensitivity of Rotary-Vane

Attenuators for Eight Waveguide Frequency

Ranges

Table 14 summarizes the frequency sensitivity

of the rotary-vane attenuators for eight waveguide

designations. The term dB/GHz indicates the

deviation from nominal attenuation adjusted so that

the deviation is zero at e bottom frequencies of

the waveguide range. The values of dB/GHz were

determined from (j/2 minus cr/i divided by ^ minus

/i (upper and lower selected frequencies, respectively) where cr/2 and ct/i are the standard deviations

of the respective frequencies. These values of

dB/GHz are listed in columns four, five, and six

for the dial settings of 30, 40, and 50 dB, respecTable 14. Limits of magnitude of one-sigma error in attenuation

in dB per GHz for rotary-vane attenuators in WR28, WR42,

WR62, WR90, WR112, WR137, WR187, and WR284 waveguide

at 30, 40, and 50-dB dial settings

WR

Frequency

range in GHz

Band

width

in GHz

dB/GHz

30 dB 40 dB 50 dB

28 26.5 -40.0 13.5 0.014 0.034 0.050

42 18.0 -26.5 8.5 .002 .013 .035 62 12.4 -18.0 5.6 .054 .086 .137 90 8.2 -12.4 4.2 .089 .132 .158 112 7.0 -10.0 3.0 .023 .044 .106 137 5.85- 8.20 2.35 .068 .081 .212 187 3.95- 5.85 1.9 .072 .129 .176 284 2.6 - 3.95 1.35 .043 .099 .227

tively. Note that the frequency sensitivity in

dB/GHz shows the smallest limits of magnitude of

one-sigma in attenuation at each dial setting for the

WR42 waveguide rotary-vane attenuator, and yields

the largest hmits of magnitude of one-sigma in

attenuation at 30 and 40, and 50-dB dial settings for

WR90, and WR284 waveguide rotary-vane at- tenuators, respectively.

11. Evaluation of the Rotary-Vane

Attenuator by "Bootstrapping" and

Check Standards

Bootstrapping (often erroneously referred to as

self-calibrating) as used here is a technique of

calibrating or evaluating a device by utihzing its own characteristics instead of absolute standards.

Only dimensionless quantities, of which attenuation

is one, can be determined. For example, a stable

repeatable attenuation step whose absolute value

in decibels is unknown can be measured by the

rotary-vane attenuator at several different values of

dial settings. In this case the increment of attenuation difference is the same for each measurement,

but the location of the increment will be at different

positions on the dial. To best utilize this technique,

certain characteristics of the attenuator, such as

rotor misalignment and resettability must be known

or determined. In any case rotary-vane attenuators

having optical [2] or digital [4] readouts are the

most desirable to use, as gear-driven readouts are subject to runout and backlash errors [6].

35
11.1. Errors in Attenuation for the Initial

and the Final Setting of the Rotary-Vane

Attenuator for an Attenuation Difference

Measurement

The initial setting of an attenuation difference

measurement of a rotary-vane attenuator can be

written as

A'i =Ai±eio+ eu.

11.2. Graphical Presentation

In order to illustrate the deviation in attenuation

due to rotor-vane alignment error, graphs are used

to display these deviations from nominal attenuations. This deviation from nominal in a determination of attenuation difference occurs at both the

initial and final dial settings of the rotary-vane

attenuator.

where Ai is the theoretical value of attenuation at the initial setting; €,0 and e,/ are the errors due to the operator and inherent error, respectively, at the

initial setting.

The error in attenuation at the initial setting may

be expressed as

e!0+e,7 = — 40 logio cos iei±eio+eu)

cos di

where the angular values at the initial setting are:

di, the vane angle to obtain the theoretical attenuation; 6io, the vane-angle error due to the operator;

and Oil, the inherent vane-angle error. In a like manner, the final setting of an attenuation difference measurement may be expressed as

A'f = Af ±eyu + e//

11.2.1. Deviations in Attenuation Due to Rotor-Vane

Alignment Error

Figure 59(a) is a graph of error, e', in decibels for

attenuation in 10-dB increments with assumed

rotor-vane alignment error, d\, equal to 0.100, 0.200,

and 0.300°. The value of e', the error from nominal,

is determined from minus e^, when

40 logio" cos {e„+e'i)

cos da

and

€^ = — 40 logio cos {Ob+e'i)

cos 9b

da is the initial rotor vane angle, Ob is the final rotor vane angle, and 9'^ is defined above.

where Aj is the theoretical value of attenuation at the final setting, e/o and e// are the errors due to the

operator and the inherent error, respectively, at the

final setting.

The error in attenuation at the final setting may

be expressed as

cos {9f±dj^,^-dfi)

6/0 + €// = — 40 logio 7

COS 9f

where the angular values at the final setting are:

Of, the vane angle to obtain the theoretical attenuation; 9fo, the vane-angie error due to the operator;

and 9fi, the inherent vane-angle error [18].

Any deviation from ideal alignment of the rotor vane with reference to the scale readout causes a systematic error in the attenuation rate of the entire

range of the rotary-vane attenuator. Though this

mechanical error can be constant angular displacement, it produces an increasingly greater error in

attenuation as the value of 9 increases. Also, the

error in attenuation caused by angular limits of

resettability becomes greater with increases of 0. Since bootstrapping action usually results in higher

value of attenuation, the smallest errors of alignment and resettability are essential to keep the limits

of uncertainty minimal.

The magnitude variations of e' are illustrated by

three different straight lines: the solid line for

O'l = 0.300°, the dot hne for 0', = 0.200°, and the dashdot-dash hne for 0^ = 0.100° (This legend also

applies to the figs. 61, 63, 65, and 67.) Five different

increments of 10 dB each were measured as

follows: 0 to 10 dB, 3 to 13 dB, 6 to 16 dB, 10 to 20 dB, 15 to 25 dB. The values of e' at the same

10-dB increments are smaller when O'j is equal to 0.200 and 0.100° as indicated by the dot, and the

dash-dot lines. For a given O'l, the value of e' is the

least at the dial settings of 3 to 13 dB.

11.2.2. Attenuation Versus 6 in Degrees

Figure 59(b) is the curve of attenuation versus

0 in degrees of rotor angular displacement. The

segments of the curve, numbered (1), (2), (3), (4), and (5), are equal to 10-dB increments of attenuation.

The chart shows three positions of the rotor vane in

degrees; the initial, Oc, the final. Of-, and their

difference, AO.

Although the increments of attenuation are equal,

the angular increments, AO, become less at higher

values of 0. For example, the angular displacement

for the 15 to 25-dB increment is approximately

one-fifth of the value for the 0 to 10-dB increment.

36
ATTENUATION IN 10 dB INCREMENTS

20 - e: = 0.300°(R0T0R VANE MISALIGNMENT) —

_

ej = 0.100°

(15 TO 25dB)

D d

1 5 (10 TO 20dB) 1 , -40 log cos(e^+ej)

1 1 la

-40 log cos(ej^+ej)

(0 TO lOdB) ''al ,

,

TO 16dB) 1

1 1 1 ( 6 ^3 1

1

1 1 (3 TO 13 dB)

J. 1 t' COS,

D

10 1 1

'

1

1 1 —1 1

]

05 ^1

1 1

1 1 1

1 1 'iL-

' 1 1

1 11

1

1 1

. —-1 1 1 1

1

^' ' ] i

i 1

1 1 1 III '1 II

(a)

0 5 10 15 20 25

DIAL SETTING IN dB

e IN DEGREES

59. (a) e' error from nominal (10 dB) increments versus dial setting in decibels for rotor misalignment, dj equal to 0.100, 0.200, and 0.300°.

ib) Attenuation in decibel versus 6 in degrees, and angular limits in degrees for attenuation difference of 10 dB.

37
Figure 60. e' error in decibels versus 0, from 0 to ±0.300° for 10-dB increments as follows: 0 to 10 dB, 3 to 13 dS, 6 to 16 dB, 10 to 20 dB, and 15 to 25 dB.

The change in the e' error in decibels versus

d'l is plotted for both the positive and negative values

of vane misalignment in figure 60. The lower portion

of the graph shows the limits of the 10-dB increments

which are numbered to correspond with the specific curve. The error e' in this sample of 10-dB increments is a minimum for 3 to 13 dB and a maximum

for 15 to 25-dB dial settings.

In figures 61(a, b), 63(a, b), 65(a, b), and 67(a, b) are plots of the error, e', in decibels for 6, 3, 1, and

0. 1-dB increments with assumed rotor vane misalignment, d',, of 0.100, 0.200 and 0.300°. The plots

of each of the different decibel increments illustrate

that the minimum value of the error, e', occurs when the angular displacement limits of the rotor vane are centered near 45°.

The change in the e' error versus d'j is plotted

for the positive values 6' only in figures 62, 64, 66,

and 68. The negative values of 9'^ would plot as a near mirror image with a slight decrease in error

(see fig. 60).

The difference in the error, e'. does increase at higher values of attenuation. For example, the differ- ence between the positive and negative value of e' for e; equals 0.300° is about 0.0015 dB at the 10-dB

dial setting, and about 0.152 dB at the 50-dB dial

setting.

11.2.3. and e' Versus Dial Setting (in Degrees

and decibels)

In order to illustrate the relationship of the

inherent misalignment error, e^, to the resettability

error, e'^, we have plotted their deviations in

attenuation from nominal in figure 69. The values of

e;,, e;^, and d',^ are shown as 0.100, 0.200, and

0.300°, respectively, and d'^ equal to ±0.010°. The

three curves are a plot of the deviations in attenuation from nominal versus dial setting (degrees and

decibels) from 1 to 10 dB. The center lines are the

deviations in attenuation caused by 9'^, and the

fines on each side of the center lines are the Hmits

of deviation caused by 9'^. The curves show that

each subsequent 1-dB increment requires less

angular rotation of the rotor as 9 increases. However,

the errors in attenuation caused by 9'^ and 9'^ are greater as 9 increases.

1 1.2.4. Minimal Value of e'

Since the error, e', is minimal at the mid-region of

the angular displacement of the rotor, the attenuation increment of 1 dB between the 5 and 6-dB dial

settings of the rotary-vane attenuator was selected for

further investigation. Let us examine in detail this

1-dB nominal value of attenuation with limits of

equal ±0.010°, and 9] equal ±0.100, ±0.200,

and ±0.300°. Figure 70 shows the deviations in

attenuation versus dial setting (degrees and decibels)

for the above conditions, where 9 are the rotor angles

corresponding to 5 and 6-dB dial settings. The

nominal values of 5 and 6 dB are given at the end

segment of each curve, and the vertical segments

indicate the limits of resettability.

38
ATTENUATION IN 6 dB INCREMENTS

0.10

0.05

-ej = 0.300° (ROTOR VANE MISALIGNMENT)

18 TO 24dB

e| = 0.200°

= 0.100° 1 5 TO

0 TO 6dB

3 TO

12 TO 18dB

9 TO

6 TO 12dB

9dB

1 5dB

21 dB

10 15

DIAL SETTING IN dB

20

-40 log cos( + e ;

)

a i

-40 log cos ( e^^ + e j

)

25

(a)

25

20

15

1

0

f Ae

(1

)

0 44 93° 44 .93°

(2) 32.71° 53 44° 20 . 73°

(3) 44.93° 59 92° 1 4 . 99°

(4) 53.44° 65 06° 11 .62°

(5) 59 . 92° 69 22° 9 . 30°

(6) 65.06° 72 63° 7.57°

(7) 59 . 22° 75 45° 6.23°

16 24 32 40 48

9 IN DEGREES

80

Figure 61. (a) e' error from nominal (6 dB) increments versus dial setting in decibels for rotor mis- alignment, e[, equal to 0.100, 0.200, and 0.300°.

(b) Attenuation in decibels versus 6 in degrees, and angular limits in degrees for attenu- ation difference of 6 dB.

39
0 0.100 0.200 0.300°

e; IN DEGREES

Figure 62. e' error in decibels versus d{ from 0 to +0.300° for 6-dB increments as follows: 0 to 6 dB, 3 to 9 dB, 6

to 12 dB, 9 to 15 dB, 12 to 18 dB, 15 to 21 dB, and

18 to 24 dB.

12. Evaluation of Precision RotaryVane Attenuator With Waveguide

Fixed-Step Attenuator

Evaluation of a precision rotary-vane attenuator

by using a repeatable step attenuator requires a

stable high-resolution measurement system. A

nominal 7-dB waveguide step attenuator and the

microwave attenuation measurement system (series

substitution) were used with the optical rotary- vane attenuator as the standard to obtain determinations of attenuation difference.

A summary of these measurements is shown in

table 16. The attenuation difference of the step

attenuator was measured by using several different

initial dial settings from 0 to 60 dB on the rotary- vane attenuator. Column one lists the initial dial

settings of the standard rotary-vane attenuator for

each determination. The measured values of the

waveguide-step attenuator are recorded in column

two, with the average value of 7.6544 dB listed at the bottom of the column. These results were obtained by applying a negative rotor vane angle

correction, d'l , of 1'18" or 0.0217° (previously

determined) to all readings. In column three is given the deviation from the average attenuation

difference. The random deviation from the average

is about ±0.005 dB for initial dial settings of 0 to 45 dB, and increases to about 0.02 dB for settings

of 50 to 60 dB. Column four gives the deviations

from average before applying the rotor vane angle

correction to the readings. It will be noted that

these are all positive and increase as the initial dial

setting increases.

Note that the deviations were minimal at the midangular regions of the rotary-vane attenuator. This

was true regardless of the correction of d'l ; however,

for the most accurate results, the correction must

be applied.

13. Attenuation Measurement With

the Rotary-Vane Attenuator as the

Standard

13.1. Introduction

In order to fully utihze the attenuation properties

of the precision optical-rotary-vane attenuator as the standard, a dual detection microwave bridge

system was incorporated in a series substitution

system, providing an ingenious technique for

microwave attenuation measurements [22]. The

stability and resolution of this microwave attenuation measurement system is consistent with the

rotary-vane attenuator standard's resolution of

0.00005 dB at 1-dB dial setting. The system maintains this stability and resolution up to a 30-dB

measurement of attenuation difference or insertion

loss.

The frequency band covered with this WR90

waveguide system is 8.2 to 12.4 GHz, and the atten- uation measurement of fixed and/or variable devices

ranges from 0 to 70 dB. The following discussion of

the measurement system is adapted from NBS

Tech. Note 647.

13.2. The Measurement System

A simplified block diagram of the microwave

attenuation calibration system is shown in figure

71. The attenuator under test is located in the same

waveguide section as the standard attenuator,

between the standard and the waveguide detector.

A change in the attenuator under test is equal to the change required in the standard attenuator to rebalance the bridge. An attenuation measurement

is made in the following manner: (1) at the start set standard and attenuator under test to their re- spective initial setting and balance the bridge for a null using the level-set attenuator, (2) make the

desired change in the attenuator under test, and

(3) rebalance the bridge with the final setting of the

standard attenuator.

Figure 72 shows a more detailed block diagram

of the system and illustrates the interconnection of

the waveguide components, standard attenuator,

and associated electronic equipment. The basic

waveguide components and instrumentation equipment of the system were developed with commer40
0.06

0.05

0.04 -

0.03

0.02

0.01

0 TO 3

21 TO 24

TO 5

0.00

ATTENUATION IN 3 dB INCREMENTS

ej = 0.300° (ROTOR VANE MISALIGNMENT)

6J

= 0.200=

eJ = 0.100°

18 TO 21

15 TO 181

12 TO 15

9 TO 12

6 TO 9

3 TO 6

I

I

I

I 1

I 1

0 10 15

DIAL SETTING IN dB

20 25

-40 log cos(e^ + e;)

a _i_ cos 9,

-40 log cos( + 9

j

cos e.

(a)

AS

(1) 0 32 71 ° 32.71°

(2) 26.97° 41 42° 14.45°

(3) 32.71° 44 93° 12.22°

(4) 44 .93° 53 44° 8.51 °

(5) 53.44° 59 92° 6.48°

(6) 59.92° 65 06° 5.14°

(7) 65.06° 69 22° 4.16°

(8) 69.22° 72 63° 3.41 °

(9) 72.63° 75 45° 2.82°

(1) 2dB

6dB

5dB

(2)

24dB

(9)y

21 dB^

15dB

1 8dB

(b)

_L- 16 24 32 40 48

9 IN DEGREES

56 64 72 80

Figure 63. (a) e' error from nominal (3 dB) increments versus dial setting in decibels for rotor misalignment, d[ , equal to 0.100, 0.200, and 0.300°.

(b) Attenuation in decibels versus 6 in degrees, and angular limits in degrees for attenuation difference of 3 dB.

41

573-735 OL - 75 - 4
0.06

(1)

(2)

(3) (4)

(5)

(6)

(7)

(8) (9)

0 TO 3 dB

2 TO 5 dB

3 TO 6 dS

6 TO 9 dB

9 TO 12 dB

12 TO 15 dB

15 TO 18 dB 18 TO 21 dB

21 TO 24 dB

(6)

(1)

(8L.

(2)-.

(5);

-(4) ~(3)

0.100 0.200

Figure 64. e' error in decibels versus 9[ from 0 to +0.300° for 3-dB increments as follows: 0 to 3 dB, 2 to 5 dB, 3

to 6 dB, 6 to 9 dB, 9 to 12 dB, 15 to 18 dB, 18 to 21 dB, and 21 to 24 dB.

e; IN DEGREES

cially available componenls. In addition, this

measurement system has the favorable feature that

attenuation measurements are obtained to a high

degree of precision without power stabilization of

the RF signal source, and employs a single RF

source. The null amplifier was designed at NBS and

a detailed schematic diagram is given in NBS

Tech Note 647.

In figure 73, a recording chart of the stability of

measurement indicates that for a 30-dB value of

attenuation maximum variations are in the order

of ± 10 at the output detection system.

13.3. Errors of the Microwave Measurement

System

13.3.1. Systematic and Random Errors

With the application of the correction required

for rotor-vane misalignment of the rotary-vane

attenuator standard, and precise matching technique, the estimated systematic error, at the two

insertion points of the waveguide system, is re- duced to about ±0.002 dB for values of attenuation

measurement from 0 to 30 dB.

The measurement of attenuation difference and

insertion loss of five precision interlaboratory

transfer standards gave a prehminary estimate of

the standard deviation, sigma (cr), equal to 0.0010

dB for over one hundred determinations.

13.3.2. Insertion Point of the Device Under Test

Two tuned insertion points are required in the

microwave attenuation measurement system (series

substitution), one for the working standard (precision rotary-vane attenuator), the other for the

device under test. Refer to the block diagram in

figure 72.

Only the insertion point for the device under test

is opened during an insertion loss measurement.

Also, this point is located in the system in such a way that the least possible movement of waveguide

components is required. An opened insertion point

of rectangular waveguide and an inserted fixed

rectangular waveguide attenuator under test are shown in figures 74 and 75, respectively. This

insertion point can be adapted very easily for use

as a coaxial insertion point. In figure 76 the photo

shows the insertion point converted to admit coaxial devices by using waveguide £'-plane bends, coax to waveguide adapters, and a double (male)

coaxial adapter as added components to the waveguide line. The addition of these components

does not increase greatly the length of the movable

section or hinder the ease of inserting coaxial

devices into the Une of the system (fig. 77).

The waveguide multistub tuners adjacent to each side of the insertion point are used to match

the line to either rectangular waveguide or coaxial

insertion point. The waveguide insertion point can

be tuned by using a portable reflectometer [23], or the built-in reflectometer that is located in the

waveguide section of the system. Tuning the coaxial insertion point requires the use of a coaxial

slotted section.

13.3.3. Mismatch Error in Attenuation Measurement

Mismatch is a significant source of error that

should be considered in the calibration of microwave fixed or variable attenuators. In the measure- ment process of any attenuation device, a large

amount of degrading of the accuracy will depend

upon the matching of the insertion point of the

calibration system. The match of the insertion point

becomes more critical for low values of attenuation

[24, 25, 26].

42
.050 -

.040 -

.030 -

.020 -

.010

ATTENUATION IN 1 dB INCREMENTS

9| = 0.300° (ROTOR VANE MISALIGNMENT)

ej = 0.200°

e; = 0.100°

D a -40 log (cos + ei)

a 1

(39 TO 40dB)

(0 TO IdB) cos 6

.

(29 TO 30dB)

(5 TO 6dB)

9 10

DIAL SETTING IN dB

30 39

42 -

36 -

30

24

18

12

(1) 0 19 25° 1 9 25°

(2) 41 .42° 44 92° 3 50°

(3) 3.44° 55 78° 2 34°

(4) 79.14° 79 76° 62°

(5) 83.92° 84 26° 34°

40 48

e (DEGREES)

(a)

40

Figure 65. (a) e' error from nominal (1 dB) increments versus dial setting in decibels for rotor mis- alignment, ei, equal to 0.100, 0.200, and 0.300".

(b) Attenuation in decibels versus 6 in degrees, and angular limits in degrees for attenuation difference of 1 dB.

43
In a microwave measurement system, attenuation

difference of a variable or rotary-vane attenuator can be measured by using the zero setting as a reference angular position, then moving to the

attenuation or the vane angle desired to establish

the value of attenuation difference to be measured.

For an attenuation difference measurement of a variable attenuator the mismatch error can be

expressed as

e.(dB)=20 logio

(i-'/'r,r,)(i-'/'s,2r,)|

(-<''r,r,) (i-'^'S22r,j|

where the frontscripts (i) and (/) pertain to the initial and final values, respectively, and F, is the input

voltage reflection coefficient of the variable attenuator that is terminated with a load of reflection

coefficient, F/,. The reflection coefficient of the

generator is Fg, and 522 is the reflection coefficient

at the output port when the input port is terminated

with a nonreflecting load. Engen and Beatty show

that the mismatch error becomes very low when

small incremental attenuation measurements are made on a rotary-vane attenuator [12].

The mismatch error for insertion loss measure- ment of a fixed attenuator can be expressed as

e/(dB)=20 logio

( 1 - 5 n F, ) (1 - S22 F, ) - S ,2521 F/J, I |i-r,F.|

where Su is the attenuator input reflection coefficient when the output is terminated in a nonreflecting load, and S12 and S21 are the attenuator

transmission coefficients.

In addition to the mismatch error caused by the

reflections at the input and output ports of the

attenuator, internal reflections can occur between

the stator and rotor which must be added to the total

reflection error. Mariner [5] indicates that there are

eight main places where reflections can occur,

namely, each end of the three vanes, and the two

waveguide transitions. Mariner concludes that usually these internal reflections wiU not contribute

significantly to the total error.

13.4. External Leakage

The effects of RF leakage from microwave components upon the performance of a microwave

measurement system are often subtle and difficult to identify. Thus leakage from a good standard must

be kept to an absolute minimum. In the NBS

optical A^-band rotary-vane attenuator [3], the leakage was reduced more than 120 dB below the

incident power. This was achieved by the use of

chokes and liberal amounts of microwave absorbing material around the rotary-joints of the attenuator, as shown in figure 78 and figure 86.

Figure 88 shows how microwave absorbing material was used to reduce external leakage from the

modified WR15 rotary-vane attenuator.

44
.01 00

.0050

.0000

ATTENUATION IN 0.1 dB INCREMENTS

= 0.300° (ROTOR VANE MISALIGNMENT) 50 TO 50.1

0 TO 0.1

I

= 0.200'

0. 1 00°

0

50

40

COo

S 30 o

I—

<:5 20

h-I—

<c

10

(1) 0.1

-40 log cos (

I

COS 6

a -40 log cos ( +

cos

6 1 TO 6.0 10.0 TO 10.1 r

:

(

1

1

1

1 1

1 1

1

1

1

1

6 .0 6.1 10.0 10.1 30.

DIAL SETTING IN dB

AS

(1) 0 6.14° 6 14°

(2) 44.93° 45.26° 0 33°

(3) 55 . 78° 56.01° 0 23°

(4) 79 . 76° 79.82° 0 06°

(5) 86.78° 86.80° 0 02°

50.0 50."

50 . 0

(5) 50.1

30.0

(4)/ 30.1

10.1

10.0^

6.0

6 . (3) (b)

(2)

1 0 20 30 40 50 60

e IN DEGREES

70 80

Figure 67. (a) e' error from nominal (O.I dB) increments versus dial setting in decibels for rotor misalignment, 0',, equal to 0.100, 0.200, and 0.300°.

(b) Attenuation in decibels versus 6 in degrees, and angular limits in degrees for attenuation difference of 0.1 dB.

45
Figure 68. e' error in decibels versus d[ from 0 to -\- 0.300° for

0.1-dB increments as follows: 0 to O.I dB, 6.0 to 6.1 dS, 10 to 10.1 dB, 30 to 30.1 dB, and .50 to 50.1 dB.

0 I 1 1 I I I U I L_l I I I I b

0 8 16 24 32 40 48 56°

1 2 3456789 lOdB

DIAL SETTING (DEGREES 8 dB)

Figure 69. Deviations in attenuation from nominal in decibels versus dial setting

in degrees and decibels for 6[ equal 0.100, 0.200, and 0.300°, and do equal

±0.010.

46
5dB(e')

6dB(c^)

e', = 0.010°

(t) 0.0030

(-) 0.0030

Figure 70. Deviations in attenuation from nominal in decibels versus dial setting in degrees and decibels (for 5 to 6 dB) when e\ equal ±0.100, ±0.200, and ±0.300°,

and do equal ±0.010°.

41 I 42 43 44 I

I I 5dB 6d

DIAL SETTING (UEGREES 8 dB)

Table 15 Deviations from nominal 1-dB increment of attenuation (dial setting changed from 5 to 6 dB) for So = ±0.010° and

e, =0,± 0.100, ±0.200, and ±0.300°.

6l'o=± 0.010° 0',

6/5

Actual attenuation

increment

6 dB 5 dB + + + 0.300° 1.0108 + + .300° 1.0162 + + .300° 1.0048 + .300° 1.0102 + + + .200° 1.0073 + + .200° 1.0127 + + .200° 1.0013 + .200° 1.0067 + + + .100° 1.0039 + + .100° 1.0093 + + .100° 0.9979

+ .100° 1.0033 + + .000 1.0003 + .000 1.0057 + .000 0.9943

.000 .9997 + + - .100 .9968 + - .100 1.0022 + - .100 0.9908 - .100 .9962 + + - .200 .9933 + - .200 .9987 + - .200 .9873 - .200 .9927 + + - .300 .9898 + - .300 .9952 + - .300 .9838 - .300 .9892

T.-VBLE 16. Attenuation difference measurements of a waveguide

step attenuator at 10 GHz with initial dial settings of the standard RVA from 0 to 60 dB.

T 1 initial IVieasureci Deviation troin setting of attenuation Deviation average without

standard ditterence in

rirom average d'l correction

in decibels decibels with

d'l correction

(all positive)

0 7.6590 + 0.0046 0.0139

1 7.6548 + .0004 .0075

2 7.6536 - .0008 .0052

3 7.6533 - .0011 .0050 4 7.6549 + .0005 .0065

5 7.6549 + .0005 .0066

6 7.6558 + .0014 .0076

7 7.6553 + .0009 .0073 8 7.6559 + .0015 .0083 9 7.6562 + .0018 .0087 10 7.6522 - .0022 .0051

11 7.6530 - .0014 .0062

12 7.6550 + .0006 .0085

13 7.6552 + .0008 .0092

14 7.6538 - .0006 .0082

15 7.6540 - .0004 .0087 16 7.6533 - .0011 .0085

17 7.6536 - .0008 .0079

18 7.6548 + .0004 .0102

19 7.6539 - .0005 .0108 20 7.6545 + .0001 .0120 22 7.6522 - .0022 .0110 24 7.6540 - .0004 .0144 26 7.6545 + .0001 .0176 28 7.6549 + .0005 .0190 30 7.6515 - .0029 .0173 32 7.6546 + .0002 .0236 34 7.6490 - .0054 .0211 36 7.6586 + .0042 .0342 38 7.6500 + .0044 .0356 40 7.6590 + .0046 .0396 45 7.6539 - .0005 .0412 50 7.6374 - .0170 .0426 55 7.6360 - .0180 .0650 60 7.6352 - .0192 .0854

7.6544

Average d', = -ri8' = -0.0217°
LEVEL-SET ATTENUATOR

CRYSTAL

DETECTOR

MICROWAVE

SIGNAL

MODULATOR

1 kHz

REF.

STANDARD ATTENUATOR INSERTION

POINT"

ATTENUATOR

UNDER TEST

NULL DETECTOR

CRYSTAL

DETECTOR

Figure 71. Block diagram of microwave attenuation measure- ment system.

Figure 72. Detailed block diagram of microwave attenuation measurement system.

48
12 MINUTES

Figure 73. A recording showing the system stability at a 30-dB measurement level.

I
Figure 76. Photo of the rectangular waveguide with adapter:

to admit coaxial devices at the insertion point.

Figure 77. Photo of a fixed coaxial attenuator under test being

inserted into the line at the coaxial insertion point.

14. Conciiision

The departure of a rotary-vane attenuator from

the ideal behavior is caused by the following:

insufficient attenuation in the center vane; angular

displacement errors when eccentricity is present in

the gear drive; the inherent error related to rotor vane aUgnment; and the Type A and Type B errors caused by rotationally misaligned stators. Each of

the above causes the attenuation to deviate from the

nominal (theoretical) value and the deviations will

become larger as the rotor angle, 6, increases.

A precision rotary-vane attenuator with an optical

angular readout attached to its rotor has excellent

properties as a primary standard, and provides a readout that eliminates the eccentricity error of

angular displacement common to the gear driven

readout. The error misalignment of the rotary-vane

attenuator can be improved an order of magnitude

by applying correction of vane alignment equal to the average vane-angle error. The Type A error is the larger error caused by misahgned stators. To

reduce the Type A error, the zero or index can be

corrected by one-half the angle between the misaligned stators. The deviations from nominal setting

then become the Type B error provided gear

eccentricity is not present. However, if the zero or index is not exactly coincident with the average

position of the stators, the Type A error can be the

predominant factor in the deviations from nominal.

The compact rotary-vane attenuator is a useful

device where large dynamic attenuation range is not required or where length of the device is at a premium. The modified law for rotary-vane attenuators gives an accurate result of the attenuation

difference that is obtainable with the device.

The precision optical rotary-vane attenuator is a very excellent working standard for attenuation

difference employed with the microwave attenuation

measurement system (series substitution). The use

of the precision optical attenuator with the above

RF system yielded the resolution and stability that

provided a very accurate international intercomparison of attenuation difference; the spread between the mean values of five different interlaboratory standards was about 0.001 dB.

The work of this paper is not the work of one per- son but the coordinated effort of many coworkers in

the Electromagnetics Division. The author is indebted especially to Eugene Campbell and Ron

Hunter for their contributions over a period of

several years in fabrication of waveguide components, and instrumentation design used in the

measurement systems; Edward Holland for suggestions in design and precise fabrication of the optical

rotary-vane attenuator standard; C. C. Cook and

F. L. Warner for the thorough review of the paper,

helpful suggestions and corrections; and Janet R.

Jasa for the excellent job of typing.

15. References

[1] Southworth, G. C, Principles and Applications of Waveguide Transmission (Van Nostrand, New York, 1950),

p. 374.

[2] Hand, B. P., Broadband rotary waveguide attenuator. Electronics 27, 184-185 (Jan. 1954).

[3] Little, W. E., Larson, W., and Kinder, B. J. A rotary-vane

attenuator with an optical readout, J. Res. Nat. Bur. Stand.

(U.S.), 75C (Eng. and Instr.). No. 1. 1-67 (Jan.-Mar.

1971).

[4] Warner, F. L., Watton, D. O., and Herman, P., A very accurate X-band rotary attenuator with an absolute digital

angular measuring system, IEEE, Trans, on Instr. and

Meas. IM-21,No. 4 (Nov. 1972).

[5] Mariner, P. F., An absolute microwave attenuator, Proc. IEEE (London), 415-419) (Sept. 1962).

[6] Larson, Wilbur, Gearing errors as related to alignment

techniques of the rotary-vane attenuator, IEEE Trans.

Instr. and Meas. IM-14, No. 3 (Sept. 1965).

50
[7] Larson, Wilbur, Analysis of rotationally misaligned stators

in the rotary-vane attenuator, IEEE Trans. Instr. and

Meas. IM-16, No. 3 (Sept. 1967).

[8] James, Allan V., A high-accuracy microwave attenuation

standard for use in primary calibration laboratories, IRE

Trans, on Instrumentation I-l 1, 285-290 (Dec. 1962).

[9] Otoshi, Tom Y., and Stelzried, Charles T., A precision

compact rotary-vane attenuator, IEEE Trans, on Micro- wave Theory and Tech. MTT-19, No. 11, 843-854

(Nov. 1971).

[10] Foote, W. J., and Hunter, R. D., Improved gearing for rotary- vane attenuators. Rev. Sci. Inst. 43, 1042-1043 (July

1972).

[11] Beatty, R. W., Microwave attenuation measurements and

standards, Nat. Bur. Stand. (U.S.), Monogr. 97, 49 pages

(Apr. 1967).

[12] Engen, G. F., and Beatty, R. W., Microwave attenuation

measurements with accuracies from 0.0001 to 0.06 decibel over a range of 0.01 to 50 decibels, J. Res. Nat. Bur. Stand. (U.S.), 64C (Eng. and Instr.), No. 3, 139-145

(Apr. -June 1960)

[13] Schafer, G. E., and Bowman, R. R. , A modulated subcarrier

technique of measuring microwave attenuation, Proc. lEE (London) 109, Pt. B, Suppl. No. 23, 783-786 (May

1962).

[14] Nemoto, T., Beatty, R. W., and Fentress, G. H., A two

channel off-null technique for measuring small changes in attenuation, IEEE Trans. Microwave Theory and Tech.

(correspondence), MTT-17, 396-397 (July 1969).

[15] Grantham, R. E., and Freeman, J. J., A standard of attenuation for microwave measurements. Trans. AIEE 67,

329-335 (June 1948).

[16] Larson, R. E., Microwave measurements in the NBS

electronic calibration center, Proc. lEE (London), 109,

Pt. B. Suppl. 23, 644-650 (May 1962).

[17] Larson, W., Table of attenuation error as a function of vaneangle error for rotary-vane attenuators, Nat. Bur. Stand.

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

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

rotary-vane attenuator, IRE International Convention

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

[19] Larson, W., Table of attenuation as a fimction of vane angle

for rotary-vane attenuators (^ = — 40 logio cos 0), Nat. Bur. Stand. (U.S.), Tech. Note 229, 186 pages (Jan. 1965).

[20] Nielsen, T. C, Angular errors in gears. Product Engineering,

pp. 56-61 (Aug. 15, 1960).

[21] Michales, G. W., Gear position error control (American

Society of Mechanical Engineers, New York, N.Y.),

Paper No. 59A-21 (Dec. 19.59). [22] Larson, W., and Campbell, Eugene, Microwave attenuation

measurement system (series substitution), Nat. Bur. Stand. (U.S.), Tech Note. 647, 24 pages (Feb. 1974).

[23] Anson, W. J., A guide to the use of the modified reflectometer technique of VSWR measurement, J. Res. NBS,

65C, No. 4, 217-223 (Oct.-Dec. 1961).

[24] Beatty, R. W., Mismatch errors in the measurement of ultrahigh-frequency and microwave variable attenuators,

J. Res. Nat. Bur. Stand. (U.S.), 52, No. 1, 7-9 (Jan. 1954)

RP 2465.

[25] Rahman, M. H., and Gunn, M. W., Waveguide reflections from rotary-vane attenuator (correspondence), IEEE

Trans, on Microwave Theory and Tech., pp. 402-403

(July 1969).

[26] Holm, J. D., Johnson, D. L., and Champlin, K. S., Reflections

from rotary-vane precision attenuator, (correspondence)

IEEE Trans, on Microwave Theory and Tech., pp. 123-124

(Feb. 1967).

16. Appendix A. DeHnitions and

Terms

rC£' = Total composite error.

t' = Total angular displacement {/S' + y') in

degrees.

6 = Angle of drive gear rotation in radians.

8' = Angle of drive gear rotation in degrees.

0 = Angular rotation of center section vane

(rotor) relative to the stationary end section vane stator in degrees.

6' = Misalignment angle of center vane (differ- ence between the indicated vane angle and

the true vane angle) in degrees.

e = Error in attenuation caused by incorrect vane rotation in decibels. = Estimated average vane-angle error in

degrees.

^^' = Angular displacement of the vane caused

by backlash error in degrees.

0y = Angular displacement of the vane caused by

indexing error in degrees.

d'r' = Angular displacement of the vane caused by

total angular error in degrees.

/? = Pitch radius in inches.

Z) = Pitch diameter in inches. = Basic pressure angle in degrees,

a = Angular difference between the zero point

of the drive gear eccentricity and the zero

point of the scale on the dial in degrees.

ey= Error in attenuation caused by the indexing

error in decibels.

eo = The error, in decibels, for Type A misaUgnment.

€6 = The error, in decibels, for Type B misalignment.

e' = The error from nominal in decibels, minus

_<

er= Transmission error due to insufficient at- tenuation in the rotor.

(})t = The phase shift of the transmitted signal as a function of 6.

/4,' = Initial setting of an attenuation difference

measurement of a rotary-vane attenuator. — Final setting of an attenuation difference

measurement of a rotary-vane attenuator. = Theoretical value of attenuation at the initial

setting.

/i/= Theoretical value of attenuation at the final

setting.

€0 = Error due to operator at initial setting.

e,7 = Inherent error at the initial setting.

e/D= Error due to operator at final setting.

€// — Inherent error at the final setting.

eF = Mismatch error in decibels for a variable

attenuator.

€/= Mismatch error in decibels for a fixed

attenuator.

Appendix B. Machine Drawings for

Optical Rotary-Vane Attenuators

51
52
TT"

1 7 - J

L

1 t— -ffas?^

0^

/

i"

to

1

(K'ttvJ /roc:^f —

I— as^se —

1

— dsM- —

jji a 0000 '

I

53
54
55
56
57
58
59
60
61
Figure 88. Exploded view of a rotary-vane attenuator utilizing a Spiroid gear set in WR15 waveguide.

62

U.S. GOVERNMENT PRINTING OFFICE ; 1975 OL-573-735
NBS-n4A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBS-MN 144

\ 1 rw r /\ f i~ <z c: 1 t~\r\ No.K/^fii'vifnt c /K F' G c ^ t^n IM r\

4. TITLE AND SUBTITLE

The Rotary-Vane Attenuator as an Interlaboratory Standard

5. Publication Date October 1975

6. Performing Organization Code

7. AUTHOR(S)

Wilbur Larson

8. Performing Organ. Report No.

g PKRFDRMlMr, DR r, AN 17 A TIDN NAMF AND AnnRF';'^

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2764460

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same as Item 9.

13. Type of Report & Period

Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Library of Congress Catalogue Card Number: 75-619099

16. ABSTRACT (A 200-word or less factual summary of most si^ificant information. If document includes a significant

bibliography or literature survey, mention it here.)

This paper presents a comprehensive report on the measurement and the use of the

rotary-vane attenuator as an interlaboratory standard.

Methods of attenuation measurement developed at NBS are used to supply data for the

evaluation of the deviations from theoretical cos^ law due to rotor misalignment, gear

eccentricity, resettability , resolution, and insufficient maximum attenuation.

A precision rotary-vane attenuator with an optical readout capable of 1 second of arc

angular resolution has an effective attenuation resolution of 0.00005 dB at a 3-dB dial

setting, and 0.0005 dB at a 30-dB dial setting. This type of precision attenuator is

an effective standard for use in the dual detection microwave bridge measurement system.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

Attenuation; interlaboratory standard; measurement; rotary-vane attenuator.

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