The Rotary-Vane Attenuator as an Intel-laboratory Standard

ScienceDocs.U.S. DEPARTMENT OF COMMERCE/Nationai Bureau of StandardsThe Rotary-Vane Attenuator asan Intel-laboratory Standard

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The Rotary-Vane Attenuator asan Interlaboratory StandardWilbur LarsonInstitute for Basic StandardsNational Bureau of StandardsBoulder, Colorado 80302U.S. DEPARTMENT OF COMMERCE, Rogers C B. Morton, SecretaryJames A. Baker, III, Under SecretaryDr. Betsy Ancker-Johnson, Ass/sfanf Secrefary for Science and Techno/ogyNATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting DirectorIssued November 1975

Library of Congress Cataloging in Publication DataLarson, 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*37175-619099National Bureau of Standards Monograph 144Nat. Bur. Stand. (U.S.), Monogr. 144, 70 pages (Nov. 1975)CODEN: NBSMA6U.S. GOVERNMENT PRINTING OFFICEWASHINGTON: 1975For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402(Order by SD Catalog No. C13.44:149). Price $5.05. (Add 25 percent additional for other than U.S. mailing)Stock Number 003-003-01416-8

ContentsPage1. Introduction..................................... 12. Theory of operation............................ 12.1. Zero setting............................. 22.2. Stator alignment....................... 22.3. Transmission error or insufficientattenuation in the rotor............... 43. Dial readout of rotary-vane attenuator..... 54. The measurement of the rotary-vane attenuator by different methods ............... 84.1. NBS developed attenuationsystems.................................. 84.2. Comparison of modulated subcarrierand dc substitutionmethods................................. 104.3. Comparison of modulated subcarrierand i-f substitutionmethods................................. 104.4. Simultaneous measurement bymodulated sub-carrier and dc substitution methods...................... 114.5. Measurement of precision opticalrotary-vane attenuator by dc andi-/substitution methods.............. 114.6. Power ratio (dc) versus off-nullmeasurements......................... 115. Procedures for evaluating the rotary-vaneattenuator........................................5.1. Determination of average vane14angle error and eccentricity fromcalibration data........................ 155.1.1. Analysis of calibrationdata........................... 155.1.2. Cyclic pattern of angulardisplacement............... 155.2. Gearing errors related to rotaryvaneattenuator........................5.2.1. Effects of a on ey .........16175.2.2. Effects of pitch diameteron error of attenuation... 196. Compensation for transmission error ofrotary-vane attenuator......................... 216.1. Transmission error versus dialsetting in decibels .................... 216.2. Stator realignment.................... 216.3. Illustration of transmission errorand compensation for 110-dBmaximum............................... 226.4. Mechanical compensation andmeasured results...................... 247. Measurement of precision rotary-vaneattenuators with high resolution readouts. 247.1. Measurement of rotary-vane attenuator with a gear drivenreadout.................................. 247.1.1. Measurements of precision gear driven rotaryvaneattenuator............. 25in7.1.2. Angular resettability ofattenuator...................7.2. Mounting the gear drive..............7.3. Optical rotary-vane attenuator .....7.3.1. Measurements on optical rotary-vane attenuator............................7.3.2. Measurement after rotorrepair.........................8. Resolution and resettability..................9. Resolution of rotary-vane attenuator inpercent of dial setting.........................10. Frequency sensitivity of the rotary-vaneattenuator........................................10.1. Spectrum of microwave attenuation calibration systems 2.6 to40 GHz.................................10.2. Statistical analysis of the frequency sensitivity from calibration data at 30,40, and 50 dB......10.3. Frequency sensitivity of rotaryvaneattenuators for eight waveguide frequency ranges.............11. Evaluation of the rotary-vane attenuatorby "bootstrapping" and check standards ................................:...............11.1. Errors in attenuation for theinitial and the final setting of therotary-vane attenuator for an attenuation difference measurement ....................................11.2. Graphical presentation.............11.2.1. Deviations in attenuation due to rotor-vanealignment error..........11.2.2. Attenuation versus 0in degrees.................11.2.3. (j and e/ versus dialsetting (in degrees anddecibels)...................11.2.4. Minimal value of ©.....12. Evaluation of precision rotary-vane attenuator with waveguide fixed-stepattenuator........................................13. Attenuation measurement with therotary-vane attenuator as the standard .................................................13.1. Introduction...........................13.2. The Measurement system.........13.3. Errors of microwave measurement system..........................13.3.1. Systematic and random errors................13.3.2. Insertion point of thedevice under test........Page25252626272728282933353536363636383840404040424242

13.3.3. Mismatch error m attenuationmeasurement.......13.4. External leakage.....14. Conclusion.......................Page15. References.......................................16. Appendices42 A. Definitions and Terms.................44 B. Machine Drawings for Optical50 Rotary-Vane Attenuators..............rage505151List of FiguresFigure 1. Pictorial diagram of the rotaryvaneattenuator __________ ___Figure 2. Illustration of the determinationof b© with measured distances 61and & 2 from the reference planeas viewed from the rectangularwaveguide input flange _______Figure 3. Rotor index or zero coincidentwith first (or second) stator ___._Figure 4. Rotor index or zero coincidentwith average position of stators _ _Figure 5. Type B alignment: first attenuation maximum, MI, at 9© /2 priorto 90 ; saddle minimum, M s , at90 ; and second maximum, M%,at 19/2 beyond 90 ______________Figure 6. Type A alignment, rotor advanced to 9©72: first attenuationmaximum, MI, at 90 0©; saddleminimum, Ms , at 90 -072; andthe second maximum, M2 , at90 _.________________________Figure 7. Type A alignment, rotor retarded:first attenuation maximum, MI,at 90 ; saddle minimum, Ms , at90 -f 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 6cycle ________________________Figure 10. Rotary-vane attenuator dial readout in decibels cylindrical 9cycle ________________________Figure 11. Graph of the deviation in attenuation from nominal versus dialsetting in degrees which corresponds to a linear deviation of0.020" for three rotary-vaneattentuators __________________Figure 12. Dial readout in units, tenths,hundredths and thousandthsof degrees for rotary-vaneattenuator _________________Figure 13. Pictorial view of drive unit forrotary-vane attenuator________Figure 14. Machine drawing of driveunit gearing for rotary-vaneattenuator __________________333Figure 15. Illustrated deviation of therotor vane of an attenuator calibrated by different methods:power ratio (1960), off-null, andpower ratio (1968) ____________Figure 16. Apparent deviation of rotor vanein degrees from nominal at eachdial setting in degrees. Theindicated vane angle correctionhas been applied to each resultFigure 17. Graphs of deviations in attenuation from nominal versus dialsetting 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 -_-___-___-_______4 Figure 18. Graphs of the cyclic pattern ofangular displacement curve,Or, with average vane-angle errorof +0.064 and O©r with -0.064correction ____________________4 Figure 19. Variations ingear eccentricityerror ________________________5 Figure 20. Attenuation as a function of vaneangle, variation in the indexingerror for the three cycles, and the6error in attenuation from nominalfor the dial settings of 0 to 9(f _Figure 21. Errors in attenuation at the dial6setting of 10 dB versus the anglea. for different pitch diameters _ _Figure 22. Errors in attenuation at the dialsetting of 20 dB versus the anglea for different pitch diameters _ _Figure 23. Errors in attenuation at the dial6setting of 30 dB versus the anglea for different pitch diameters _ _Figure 24. Errors in attenuation at the dialsetting of 40 dB versus the angle7a for different pitch diameters _ _Figure 25. Errors in attenuation at the dial8setting of 50 dB versus the anglea for different pitch diameters _ _Figure 26. Errors in attenuation at the dialsetting of 10 dB versus pitch131316161617171818181819IV

Page Pagediameter for the angular displacement error ____________________Figure 27. Errors in attenuation at the dialsetting of 20 dB versus pitchdiameter for the angular displacement error __________________Figure 28. Errors in attenuation at the dialsetting of 30 dB versus pitchdiameter for the angular displacement error_ __________________Figure 29. Errors in attenuation at the dialsetting of 40 dB versus pitchdiameter for the angular displacement error ____________________Figure 30. Errors in attenuation at the dialsetting of 50 dB versus pitchdiameter for the angular displacement error ____________________Figure 31. Estimate of the transmission errorversus dial setting in decibels formaximum attenuation values of60 to 160 dB _________________Figure 32. Illustration of stator rotation androtor alignment to induce the typeB error ______________________Figure 33. Estimated angular displacementof stators in degrees versus themaximum attenuation value ofrotor vane in decibels for thecompensation required to approach theoretical cos 2 #law____Figure 34. Deviation in attenuation causedby misalignment of the stators,O f equals 0.2 , and insufficientmaximum attenuation of 110 dBfor the dial setting of 20 to 70dB __________________________Figure 35. Deviation of attenuation fromnominal versus dial setting indecibels for rotary-vane attenuator with 72-dB maximum: (a)Curve of calibration points, (b)Curve of correction induced bymisaligning the stator 0.87 , and(c) Plot of calibrated values afterstator misalignment ____________Figure 36. Angular error, O©r , in degrees fromnominal (theory) versus the dialsetting, 0, in degrees, determinedfrom measurements by the powerratio, modulated subcarrier, andi-f substitution methods ________Figure 37. Angular error caused by bindingeffect between the drive gear andthe driven gear (concentric to therotor section) __________________Figure 38. Angular error, #©, in degreesversus dial setting in degrees, 0,after precise machining was19 applied ______________________ 26Figure 39. Deviation in decibels and degreesversus dial setting in degrees _ _ _ _ 26Figure 40. Deviation in decibels and degrees20 versus dial setting in degrees,after repair of the rotor section __ 27Figure 41. (a) Deviation of measured attenuation and equivalent angular20 deviation from theoretical valuesfor a vane angle correction of-0.033 versus dial setting of 0to 45 ________________________ 2720 (b) Deviation of measured attenuation and equivalent angulardeviation from theoretical valuesfor a vane angle correction of20 0.033 versus dial setting of45 to 87.5 0__________ 27Figure 42. Resolution error in decibels versus dial setting in decibels______ 2821 Figure 43. Resolution of the dial in percentof attenuation versus dial settingin decibels for an attenuator with21 angular resolution of 0.01 ______ 28Figure 44. Deviation of attenuation for average vane-angle errors of 0.098,0.080, and 0.036 versus dial setting in decibels at 9.0, 9.8, and11.2 GHz___________________ 2922 Figure 45. Deviation of attenuation for average vane-angle errors of 0.032,-0.042 and -0.054 versus dialsetting in decibels at 9.0, 9.8,and 11.2 GHz__ ______________ 30Figure 46. Deviation of attenuation for aver-23 age vane-angle errors of 0.024,0.035 and 0.049 versus dial setting in decibels at 29, 33, and 37GHz ______ _________________ 30Figure 47. Deviation of attenuation for average vane-angle errors of 0.008,-0.014, and -0.042 versus dialsetting in decibels at 29, 33, and37 GHz_________________ 3124 Figure 48. Deviation of attenuation for average vane-angle errors of 0.031,-0.010, and 0.013 versus dialsetting in decibels at 2.85, 3.25,3.55 GHz ___________________ 3125Figure 49. Deviation of attenuation for average vane-angle errors of 0.128,0.105, and 0.120 versus dial setting in decibels at 2.85, 3.25, and263.55 GHz_______ ________ Figure 50. Deviation of attenuation for average vane-angle errors of 0.070,32

Page Page0.067, and -0.032 versus dialsetting in decibels at 2.85, 3.25,and 3.55 GHz_ _________Figure 51. Limits of magnitude of onesigmaerror in attenuation versusfrequency in GHz for twentyWR284 rotary-vane attenuatorsat 30, 40, and 50-dB dial settings _________________Figure 52. Limits of magnitude of onesigmaerror in attenuation versusfrequency in GHz for twenty-oneWR187 rotary-vane attenuatorsat 30, 40, and 50-dB dial settings ________________Figure 53. Limits of magnitude of onesigmaerror in attenuation versusfrequency in GHz for eighteenWR137 rotary-vane attenuators at30, 40, and 50-dB dial settings _Figure 54. Limits of magnitude of onesigmaerror in attenuation versusfrequency in GHz for twentythreeWR112 rotary-vane attenuators at 30, 40, and 50-dB dialsettings ______________________Figure 55. Limits of magnitude of onesigmaerror in attenuation versusfrequency in GHz for fifty-oneWR90 rotary-vane attenuators at30, 40, and 50-dB dial settings _Figure 56. Limits of magnitude of onesigmaerror in attenuation versusfrequency in GHz for seven WR62rotary-vane attenuators at 30, 40,and 50-dB dial settings ________Figure 57. Limits of magnitude of onesigmaerror in attenuation versusfrequency in GHz for seven WR42rotarv-vane attenuators at 30, 40,and >0-dB dial settings ________Figure 58. Limits of magnitude of onesigmaerror in attenuation versusfrequency in GHz for seven WR28rotary-vane attenuators at 30, 40,and 50-dB dial settings ________Figure 59. (a) e© error from nominal (10 dB)increments versus dial setting indecibels for rotor misalignment,0; equal to 0.100, 0.200, and0.300 _ ______________________(b) Attenuation in decibels versus0 in degrees, and angular limitsin degrees for attenuation difference of 10 dB ________________Figure 60. e f error in decibels versus 0/from 0 to 0.300 for 10-dBincrements as follows: 0 to 10dB, 3 to 13 dB, 6 to 16 dB, 10 to20 dB, andl5to25dB______32 Figure 61. (a) e© error from nominal (6 dB)increments versus dial setting indecibels for rotor misalignment,0;, equal to 0.100, 0.200, and0.300 _ _______________________(b) Attenuation in decibels versus336 in degrees, and angular limitsin degrees for attenuation difference of 6 dB______________ __Figure 62. €* error in decibels versus Ojfrom 0 to +0.300 for 6-dB increments as follows: 0 to 6 dB, 3 to339 dB, 6 to 12 dB, 9 to 15 dB, 12 to18 dB, 15 to 21 dB, and 18 to24 dB ______________________Figure 63. (a) e© error from nominal (3 dB)increments versus dial setting in33decibels for rotor misalignment,0;, equal to 0.100, 0.200, and0.300 _____________(b) Attenuation in decibels versus6 in degrees, and angular limitsin degrees for attenuation differ-33erence of 3 dB _______________Figure 64. e© error in decibels versus 0/from 0 to + 0.300 for 3-dB increments as follows: 0 to 3 dB, 2 to5 dB, 3 to 6 dB, 6 to 9 dB, 9 to 1234dB, 15 to 18 dB, 18 to 21 dB, and21 to 24 dB _________________Figure 65. (a) e© error from nominal (1 dB)increments versus dial setting indecibels for rotor misalignment3407, equal to 0.100, 0.200, and34353737(b) Attenuation in decibels versus0 in degrees, and angular limitsin degrees for attenuation difference of IdB __________________Figure 66. e© error in decibels versus 0/from 0 to + 0.300 for 1-dB increments as follows: 0 to 1 dB, 5 to6 dB, 9 to 10 dB, 29 to 30 dB, and39 to 40 dB _________________Figure 67. e© error from nominal (0.1 dB)increments versus dial setting indecibels for rotor misalignment,0/, equal to 0.100, 0.200, and0.300 _______ __________(b) Attenuation in decibels versus0 in degrees, and angular limitsin degrees for attenuation difference of 0.1 dB ______________Figure 68. e© error in decibels versus 0/from 0 to +0.300 for 0.1-dBincrements as follows: 0 to 0.1383939404141424343444545VI

The Rotary-Vane Attenuator as anInterlaboratory StandardWilbur LarsonThis paper presents a comprehensive report on the measurement and the use of the rotary-vaneattenuator 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 2 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 angularresolution has an effective attenuation resolution of 0.00005 dB at a 3-dB dial setting, and 0.0005 dB at a30-dB dial setting. This type of precision attenuator is an effective standard for use in the dual detectionmicrowave bridge measurement system.Key words: Attenuation; interlaboratory standard; measurement; rotary-vane attenuator.1. IntroductionIn the past decade a considerable amount ofmaterial has been published on use of the rotaryvaneattenuator for attenuation measurements inthe microwave region. During this period an efforthas been made to establish an improved standard forattenuation that would be useful and adaptable tocalibration of commercial attenuators over the entiremicrowave frequency range.The dial readout of the rotary-vane attenuatorindicates either the angular displacement in degreesor the corresponding value of attenuation in decibels.The purpose of this report is to discuss the workand experiments employed in the development andevaluation of the rotary-vane attenuator as an interlaboratory standard.2. Theory of OperationThe rotary-vane attenuator has the propertiesessential for a standard attenuator. This type ofattenuator is a device that has a dissipative resistivevane which can be rotated in a circular section ofwaveguide. The attenuation produced follows verynearly the cosine squared 0 law where 6 is the angular displacement of the vane from the polarizationof the TEi t i mode of the waveguide.Intrinsically, the rotary-vane attenuator consistsof three sections of waveguide, two ends which arerectangular/circular transitions and the circularcenter section. These three sections are placed intandem on the longitudinal axis as shown in figure 1.A resistive vane is mounted across the center ofeach circular section of waveguide. In the minimumROTARY VANE ATTENUATORESIN0ECOS0 ©ECOS0ECOS0S!N0JECOS2 0ATTENUATION = »20 LOG(0COS 20 =-40 LOG(0COS0FIGURE 1. Pictorial diagram of the rotary-vane attenuator.i

attenuation position, the vanes in the three sectionsare parallel to each other and the wide side of therectangular waveguide (i.e., perpendicular to theelectric E field). The entire center section, the rotor,can be rotated about the longitudinal axis of thewaveguide, thus putting the vane parallel to a portion (E sin 6) of the E field. The resistive filmabsorbs the component E sin 6, while the componentE cos 0, normal to the center vane, passes throughunattenuated to the vane in the second stator. TheE cos 6 component upon entering the second statorsplits into two components. The resistive filmabsorbs the E cos 6 component, and the E cos 02component emerges in a plane normal to the original.Thus, the attenuation, A, stipulated from thisrelationship can be written as^=-201og 10 cos 2 0 + C (1)where 0 is the angle of the rotating vane relative tothe stator vane of the input section, C is the residualattenuation, and A is the corresponding attenuationin decibels [I]. 1The center section is mounted concentricallywith either a driven gear mechanism, an opticaldevice [3], or an electrical transducer [4] for translation of angular rotation to a suitable display.Each of the above methods of displaying the angularrotation will be discussed later in detail, which willinclude their respective desirable features ordisadvantages.2.1. Zero SettingThe variable attenuator can be used for attenuation difference with a known reference level.Usually, this reference is zero dial setting, corresponding to minimum insertion loss. The value ofminimum insertion loss appears to be the mostlogical position to align the rotor and the statorvanes to correspond to zero dial setting. However,if achieved electrically, the angular displacementof the rotor section from 0 requires more than 0.6to correspond to a 0.001 dB in attenuation. But,when the rotor vane approaches a right angle withthe stator vane, the same 0.6 of angular rotationcorresponds theoretically to a change greater than100 dB. Although the maximum attenuation is muchless than the theoretical value (approaches a limitof 110 to 120 dB) the loss of sensitivity in measuringsuch large values of attenuation more than offsetsthe advantage of high angular resettability for agiven value of attenuation. Therefore, an equal angletechnique of approximately 10 either side of 90appears 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 output1 Figures in brackets indicate the literature references on pageat 80 . The midpoint of these two angles representsthe true electrical plane of the attenuation vane.This technique is only valid for direct driven dialmechanisms, where the angular displacement dueto gear eccentric or run out is not present [5], Themisalignment encountered by eccentric gearinghas been evaluated at NBS [6].Some commercially available attenuators havestops to prevent angular rotation beyond zero,and/or 90 the theoretical maximum for attenuation. This type of mechanical stop makes it impossible to align the rotor vane by the equal angletechnique. In addition, striking the stop a severeblow during rotation at either end could reorientthe center rotor vane due to gear or shaft slippageand cause undesirable deviation from the cos 2 lawat the high angle setting.2.2. Stator AlignmentIn the fabrication of a precision rotary-vaneattenuator it is not only essential that the zero ofthe dial readout be oriented with the referenceplane of the vane in the rotor section, but the vanesof the end sections or stators should lie in the sameplane. If the end vanes are not parallel the insertionloss will increase slightly, but more important, therotor to stator alignment will be impaired, and causean angular misalignment about the longitudinal axis,as shown in figure 2. Here, the distances to the statorvanes from the reference plane are indicated asbi and 62, and the difference as 6©.Figures 3 and 4 illustrate two methods of initiallyaligning the rotor vane with reference to the statorvanes. Two types (Type A and Type B) of errors arepossible for rotary-vane attenuator with rotationallymisaligned stators [6]. The Type A occurs when therotating section index or zero is coincident to thefirst (or second) stator vane, and the Type B occurswhen the rotating section index or zero is coincidentto the average position (or bisection) of the statorvanes.The error, in decibels, for Type A misalignment iscos (0+0©)SlO©cos 0and the error, in decibels, for the Type B misalignment is(2)cos(0+|-)cos(0-|-)e 6 = -201oglo £-rr . (3)cos 2 0With the use of trigonometric identities the TypeB error can be written [7] as6 = -20 log cos2 -- tan 2 6> sin 2 - dB (4)

RECTANGULARWAVEGUIDEFLANGEAVERAGE POSITION(or BISECTOR) fcOF STATORSFIGURE 2. Illustration of the determination ofb' with measured distancesfrom the reference plane as viewed from the rectangular waveguide inputflange.TYPE "A" ERRORROTOR-TYPE "B" ERRORSTATORROTORSTATORZERO OF ROTOR (INDEX)-ZERO OF ROTOR (INDEX)FIGURE 3. Rotor index or zero coincident with first (or second)sector.FIGURE 4. Rotor index or zero coincident with average positionof stators.Regardless of the type of alignment with referenceto the dial zero, the entire range of attenuation isaffected by any misalignment of the stators. Forexample, in a Type B alignment, a 90° rotation of therotor vane will coincide with the saddle portion of adouble hump maximum attenuation, figure 5. Figure5 shows that the first maximum attenuation will bereached to coincide with 8'12 prior to 90° on the dial,while the second maximum will occur at 0*12 beyond90° on the dial.-However, the Type A alignment givesrise to two possible situations, an advanced rotorvane or a retarded rotor vane with reference to eitherstator vane. In figure 6, the rotor vane is assumed tobe advanced 0'/2. The first maximum attenuationoccurs at 90°- 0', the saddle minimum at 90° — 072,and the second maximum attenuation at 90° of the

7T/2DIAL 9, (DEGREES)ZERO OF ROTOR J(INDEX)STATOR#2FIGURE 5. Type B alignment: first attenuation maximum, MI,at 0' 12 prior to 90°; saddle minimum, M s , at 90°;and second maximum, MZ, at 6/2 beyond 90°.FIGURE 7.rSTATOR#2Type A alignment, rotor retarded: first attenuationmaximum, MI, at 90°; saddle minimum, Ms, at90°+0'/2; and the second maximum at 90° + 8'.dial setting. To observe the conditions for a retardedrotor vane of 6'/2 refer to figure 7. In this case thefirst maximum attenuation occurs at 90°, the saddleminimum at 90° + 0'/2, and the second maximumattenuation at 90°+ 6' of the dial setting.The double-humped attenuation curves shown infigure 5, 6, and 7 only occur when end vane misalignment and insufficient attenuation are simultaneously present. With perfect vanes, attenuationwould tend to infinity at two angles.DIAL 0, (DEGREES)STATOR#2FIGURE 6. Type A alignment, rotor advanced to 6 f /2: firstattenuation maximum, MI, at 90° —0'; saddleminimum, Mg, at 90° — 0'/2; and the second maximum,M2 , at 90°.2.3. Transmission Error or InsufficientAttenuation in the RotorThe ideal characteristics of the cos 2 law is notobtainable with the rotary-vane attenuator at thehigh setting of 6 due to the transmission error. Although one may argue that any error occurring during transmission of a wave through a rotary-vaneattenuator could be called transmission error, theauthor here follows the common practice of manywriters on the subject and assigns the transmissionerror entirely to the error resulting from insufficientmaximum attenuation in the center vane. Of course,the theoretical cos 2 6 law assumes infinite attenuation in the center vane. In addition to large transmission error, the lack of sufficient maximum attenuation shows increased phase shift and frequencysensitivity at the higher setting of 9.

The error related to the transmission error andphase shift of the rotary-vane attenuator has beentreated by James [8], Otoshi [7], and Mariner [5].The transmission error is given by, = -20 log -*'tan 2 0)dB (5)where the term e~al can be determined experimentally by setting 6 to 9(F and then measuring A(maximum attenuation)1A' (6)Where / is the distance the wave travels in therotor section of the attenuator and a is equal to thedifference between the attenuation constants ofthe tangential and normal electric field componentsin the rotor.The calculated error from eq (5) and a measuredvalue of 90 dB for 0=7r/2, shows that e, = 0.086dB at a dial setting of 50 dB.The phase shift of the transmitted signal as afunction of 6 is given bycos 2 0 + e-« l sin 2 0 cos piwhere j8 = /3o —)8i. The quantity pi can be foundexperimentally. Where /3 is equal to the differencebetween the phase shift constants of the tangentialand normal electric field components in the rotor.If pi equals 90°, the phase shift will be less than0.2° between 0 to 40 dB.For use in the deep space project a compactrotary-vane attenuator was developed. Any compactness, especially in the rotor section of theattenuator would affect its cos 2 response in relationto maximum attenuation, phase shift and frequencysensitivity. However, at a fixed frequency and lowvalues of attenuation, this device can be a standard.A shorter rotor section provides less maximumattenuation, thus increasing transmission error.A modified law derived by Otoshi [9] corrects forthis effect of transmission error. His treatment ofthe transmission error is similar to James [8] butdoes not assume that the transmission error signaleffect is of a known magnitude or phase.The attenuator's physical length need not be longas the modified law does not require a zero transmission error. This permits a marked decrease inphysical length where this is a physical factor.In addition, the modified law can be used forcorrections, that are necessary to extend thedynamic attenuation range of the present precisionrotary-vane attenuator. A mechanical technique forcompensating for insufficient attenuation will bediscussed in a later section of the text.(7)3. Dial Readout of Rotary-VaneAttenuatorThe readout scale indicates the value of attenuation in decibels for most rotary-vane attenuators.Let us consider several of the methods that can beused for presenting a decibel scale of the attenuation, such as the 3 cycle spiral, and 6 and 9 cyclecylindrical readouts as illustrated in figures 8,9, and10 respectively.X-band (WR90) rotary-vane attenuators wereused in the evaluation of 3 and 6 cycle readouts andan S-band (WR284) attenuator was used to evaluatea 9 cycle readout. It is estimated that setting theindicator line of the readout on either edge of a givenmark on the scale corresponds to a linear deviationof about 0.020". The angular displacement of therotor section, that is equivalent to 0.020" linear displacement on the dial, was calculated for each ofthree types of scales. The results of these calculations are summarized in table 1. Column five in thetable shows the calculated angular displacement ofthe rotor in degrees which corresponds to a lineardeviation of 0.020" (the nominal width of a scaleline) on the scale readout. Note that the value ofangular displacement of the rotor changes with eachspiral in the 3 cycle readout for a given linear deviation, but remains constant for all parts of the cylindrical readouts. Graphs of the deviation of attenuation from nominal in decibles versus the dial settingin degrees, 0 to 86.5 (0 to 50 dB), are shown for eachof the three types of readouts in figure 11. The devia-MAXFIGURE 8. Rotary-vane attenuator dial readout in decibelsspiral—3 cycle.

Fu;i : HE 9. Kotary-i>ane attenuator dial readout in decibels —Cylindrical — 6 cycle.Fn.l RE 10. Rotary-vane attenuator dial readout in decibelscylindrical—9 cycle.tion of attenuation from nominal in decibels is verynearly the same for the 3 cycle spiral, and the 6cycle cylindrical readout, in WR90 waveguide. However, the deviations are considerable less for the9 cycle cylindrical readout in WR284 waveguide.NBS has designed a drive unit for a commercialrotary-vane attenuators that have a gear mechanismratio of 12. The use of the drive unit modifies theattenuator to give the angular rotation of the rotorsection in decimal parts of a degree. Figure 12 showsTABLE 1. Angular displacement of rotor corresponding to a linear displacement of0.020 inches on the readout scale for .{, 6, and V cycle readoutsType of scale3 cycle(spiral)6 cycle(cylindrical)9 cycle(cylindrical)(rearrat in12:124:136:1Diameter ofscale readout1,75" {0-2. 5 dB)2.75" (2.5-12 dB)3.80"(12-max)1.27"2.25"Diameterof drivenrotor gear1.59"1.59"1.59"2.17"4.5"Rotor angulardisplacementdejjree0.021°.014°.009°.010°.002°1TYPE OF READOUT__ 2 —— 6 CrCLE SPIRAL3WAVEGUIDESIZEMR 90the three dial readout of the rotor in units, tenths,hundredths and thousandths of a degree. The useof a three dial readout is an appropriate method toincrease the resolution of the angular displacementdial to thousandths of a degree. In order to convertan angular displacement to decibels for incrementsof 0.001° refer to NBS Technical Note 229. Figure13 and 14 show the machine drawings of the drivemechanism and scale used to display the angulardisplacement of the gear driven rotor (ratio of 12)6FIGURE 11. Graph of the deviation in attenuation from nominal versus dial setting in degrees which correspondsto a linear deviation of 0.020" for three rotaryvaneattenuators.

in 0.001° increments from 0 to 90°. A simplifiedgear drive for rotary-vane attenuators was developedrecently at NBS in WR15 waveguide size [10]. Thisone-step drive consists of a 180:1 precision spiroidgear set which provides an accurate and repeatablereadout an order of magnitude better than commercial attenuators. This drive mechanism permitsreadout of 0.01° increments of vane angle displacement. To convert this readout to decibels, refer toNBS Technical Note 229.A rotary-vane attenuator with an optical readout[3] was designed at NBS, Boulder, that provides anangular displacement and readout with a resolutionof ± 1 second of arc. A table is very useful fordetermining the attenuation in decibels for angulardisplacements in degrees, minutes, and seconds aswould be obtained from the above attenuatorreadout. Three computer tapes have been run offfor the function (A = — 40 logio cos 6) versus degrees,minutes, seconds as follows:Tape(1)(2)(3)Attenuation(0.000000-2.498726 dB)(2.498775-12.041054 dB)(12.041200-212.577005 dB)e(0°0'Q"to29°59'59")(30°0'0"to59°59'59")(60°0'0"to89°59'59")The computer tapes provide 324,000 values ofattenuation to six decimal -places from 0 to212.577005 dB for every second of arc from 0 to89°59'59".HUNDREDTHSANDTHOUSANDTHSTENTHSFIGURE 12. Dial readout in units, tenths, hundredth^ andthousandths of degrees for rotary-vane attenuator.

FIGURE 13. Pictorial view of drive unit for rotary-vane attenuator.4. The Measurement of the Rotary-Vane Attenuator by DifferentMethodsIn most of the microwave standards laboratoriesseveral methods are available for the measurementof waveguide attenuation devices. At NBS severalexcellent methods were developed to calibraterotary-vane attenuators. The inherent propertiesof the rotary-vane attenuator make this device anexcellent standard for intercomparison of calibration systems. In order to obtain the best results fromany measurement data, it is essential that the interlaboratorystandard used meets the criteria of adesirable standard [11].The purpose of this section of the report will showthat the calibration data of the rotary-vane attenuatorused in several systems enables one to evaluate boththe systems and the interlaboratory standard,simultaneously.4.1. NBS Developed Attenuation SystemsThe power ratio method was developed in 1959 atNBS/Boulder for microwave attenuation measurements and the error affiliated with this techniquehas been carefully evaluated [12]. The application ofthis method resulted in a significant improvement inthe resolution and stability of attenuation differencemeasurements, especially for small attenuationvalues, over a broad frequency range. Other systemswere developed at NBS in the microwave attenuation measurement area, namely, the modulated subcarrier[13] and off-null [14] methods. In addition tothese highly accurate and precise measurementsystems, the i-f substitution method for attenuationmeasurement has been developed to a high degree ofexcellence [15, 16]. The i-f substitution method isthe most commonly used in both waveguide andcoaxial systems at NBS. At present the i-f substitution waveguide systems are used over the frequency8

sneer f orFIGURE 14. Machine drawing of drive unit gearing for rotaryvaneattenuator.range from 1.7 to 65 GHz in the waveguide sizesfrom WR430 to WR15. The other systems mentionedabove were developed predominantly in the X-bandregion.During the past 15 years NBS/Boulder has calibrated many rotary-vane attenuators in ninedifferent waveguide sizes. Most of these attenuatorshave been commercially purchased for use as interlaboratorystandards in public, military, and government agencies.A commercially available X-band rotary-vaneattenuator 2 was calibrated by the NBS powerratio method [12], This work revealed the limitations of commercial rotary-vane attenuators forvalues greater than 1 dB; it was shown that the resolution and repeatability deteriorate rapidly at thehigher values of attenuation. In other words, thepower ratio calibration system challenged the pre-2 Certain commercial equipment and materials are identified in this paper in orderto adequately specify the experimental procedure. In no case does such identificationimply recommendation or endorsement by the National Bureau of Standards, nordoes it simply that the material or equipment identified is necessarily the best availalbefor the purpose.9cision and resolution that could be obtained with thepresent available rotary-vane attenuator.A short time later another method of measuringmicrowave attenuation was developed at NBS.This new method known as the modulated subcarriertechnique [13] utilized commercially available components to provide resolution and accuracycomparable to the power ratio method.In the evaluation of this new method, attenuationmeasurements were compared with those obtainedby the power ratio or (de-substitution) and thei-f substitution (30 MHz standard) techniques. Thesame commercial rotary-vane attenuator of WR90waveguide size was calibrated at specific dialsettings by each of the above methods at about 9.4GHz. Although the measurement data was takensome years ago, recent additional evaluations havebeen made regarding the properties of the rotaryvaneattenuator. Also, a recently discovered defectin the fabrication of the interlaboratory standardused in the above measurements sheds new lighton this calibration data.573-735 OL - 75 - 2

4.2* Comparison of Modulated Subcarrierand dc Substitution MethodsTable 2 shows a comparison of the modulatedsubcarrier with those of the dc substitution method(power ratio). The dial setting of the attenuatorin decibels is given in column one. In columns twoand three the measured values for each dial settingby the modulated subcarrier and dc methods arelisted, respectively. Column four gives the discrepancy between the dc and subcarrier methods.This discrepancy between the two methods is shownto be less than 0.0020 dB from 0.01 to 1-dB values,while the discrepancy increases to 0.03 dB at the30-dB value. A large portion of these discrepanciesare due to attenuation resettability and operatorperformance.caused a deviation of about 0.5 dB between the twodifferent subcarrier measurements at the 50 dBdial setting.The discrepancy between the subcarrier and i-fmethods 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-dBdial setting (less than for the dc and subcarriermethods). In addition, table 2 shows the measuredvalues of attenuation to be less than in table 3 fordial settings of 40 and 50 dB. This change could becaused by the vertical and/or the horizontal positionsof the attenuator under calibration [13], as indicatedin table 2 and table 3.TABLE 3. Comparison of measurements obtained by modulatedsubcarrier and i-f substitution methodsTABLE 2. Comparison of measurements obtained by modulatedsubcarrier and dc substitution methodsAttenuatordial readingdB0.01.02.03.04.05.06.07.08.09.10.12.14.16.18.20.25.50123510152025304050Measured attenuation (with attenuator vertical)ModulatedsubcarriermethoddB0.0111.0218.0308.0413.0532.0626.0718.0814.0918.1037.1206.1388.1590.1796.2023.2482.49941.0041.9993.0004.9919.97115.0119.9725.0030.1040.4452.39dc methoddB0.0107.0214.0303.0407.0521.0609.0700.0802.0909.1021.1191.1375.1573.1783.2007.2471.49791.0041.9962.9984.9909.96514.9919.9525.0130.0740.3352.24Discrepancybetween dcand subcarriermethodsdB+ 0.0004+ .0004+ .0005+ .0006+ .0011+ .0017+ .0018+ .0012+ .0009+ .0016+ .0015+ .0013+ .0017+ .0013+ .0016+ .0011+ .0015.0000+ .003+ .002+ .001+ .006+ .02+ .02-.01+ .03+ .11+ .154.3. Comparison of Modulated Subcarrierand {-/Substitution MethodsTable 3 shows the similar comparison betweenthe modulated subcarrier and i-f methods with thesame rotary-vane attenuator as the interlaboratorystandard. A change of position of the attenuator10Attenuatordial readingdB0.1.2.5123510152025304050Measured attenuation (with attenuatorhorizontal)ModulatedsubcarriermethoddB0.1026.2010.49781.0021.9972.9984.9899.95814.9819.9424.9530.0240.2451.70i-f methoddB0.101.199.498.9981.9992.9974.9809.96514.9919.9524.9530.0040.1551.66Discrepancybetween i-fand subcarriermethodsdB+ 0.0016+ .002-.0002-K004-.002+ .001+ .009-.007-.01-.01.00+ .02+ .09+ .04The data from each comparison shows that thedial of the attenuator agrees rather closely with themeasured values for the range from 0.01 to 30 dB.However, this is not true for the dial settings of 40and 50 dB. At 50dB the deviation is greater than2 dB as shown in table 2. An increase in attenuationof this magnitude is not a normal characteristic of arotary-vane attenuator, especially since it has goodagreement to 30 dB. The usual indication is adecrease in attenuation from nominal at the highervalues. This older type rotary-vane attenuator has alow maximum attenuation value of about 80 dB. Thedeviation in attenuation below nominal caused bythis low value of maximum attenuation is about0.3 dB at 50 dB.Concentric Rotor Gear SectorAt a later date, the drive mechanism of thisattenuator was disassembled. This revealed that thegear concentric to the rotor was a sector of about120°. This gear sector was welded to the outer case

of the rotor section. A slight tilt of the gear sectorduring the welding process would cause an angulardisplacement. It has been shown that an error in thedriven gear of 0.36° will produce a deviation inattenuation of more than 2 dB at the 50-dB dialsetting [17].The physical orientation of the attenuator undertest can cause deviations in measurements as shownin tables 2 and 3. The measured values at the 50-dBsetting deviate by about 0.7 dB between vertical andhorizontal positions of the attenuator. End play inthe bearings of the rotor section, and backlash in thegearing can cause angular displacement in thecylindrical dial readout. A change of angular displacement equal to 0.13° causes a change of 0.7 dBatSOdB [17].4.4. Simultaneous Measurement by Modulated Subcarrier and dc SubstitutionMethodsIn order to more truly compare the subcarrier anddc substitution methods, the rotary-vane attenuatorwas measured in a special situation. A three channel [13] system was devised so that simultaneousmeasurements could be made by the dc and subcarriermethods for a given dial setting. The resultsof these measurements are shown in table 4. Thedeviations between the two methods are 0.0005 dBup to 0.5-dB measurements, and slightly over0.001 dB up to 10 dB. While the deviation increasedto 0.006 dB at 20 dB, this confirms that the largerdeviations shown in tables 2 and 3 are due to mismatch error, resettability, and operator performance.TABLE 4. Differences between measurements made simultaneouslyby modulated subcarrier and dc substitution methodsAttenuatordial readingdB0.01.02.05.10.501.02.05.010.020.0Difference(with attenuator vertical)dB+0.0002-.0002-.0001+.0005+.0001-.0012-.0003-.0011+.0012+.00664.5. Measurement of Precision OpticalRotary-Vane Attenuator by dc and i-fSubstitution MethodsThe X-band optical rotary-vane attenuator [3]developed at NBS/Boulder increased the resolutionand resettability of the RVA to 2 seconds of arc. Inaddition, the optical readout feature eliminatesangular displacement errors due to gear eccentricity. This precision attenuator was measured over adial range of 0 to 87.5° in 2,5° increments. Themeasurements were made using the power ratiomethod for attenuator dial readings of 0 to 60° andusing the ^/substitution method for dial settings of62.5 to 87.5°. In table 5, the calibration of theoptical attenuator is shown for the frequency of 9.0GHz. Column one lists the dial setting in degrees(0). Column two gives the theoretical value ofattenuation in decibels corresponding to the anglesof column one. Column three shows the calibratedvalue of attenuation at each dial setting. From thisdata the average apparent vane angle deviation wasdetermined [18] to correspond to a retardment ofthe rotor vane of 2 minutes of arc or 0.033°.The attenuator was recalibrated with a correctionof 2' applied to each dial setting. The results arerecorded in column four. The application of thecorrection to the dial reading enabled the measuredattenuation values to follow the cos 2 law moreclosely. The deviation of these measurements fromthe corresponding theoretical values of attenuationin decibels are listed in column five. The deviationsfrom the theoretical value are shown to be less than0.001 dB for measurements up to 60° (12 dB), andvary from 0.001 to 0.012 dB; from 62.5 to 87.5°(13 to 54 dB). The values of the discrepancy of themeasurements that were made simultaneouslybetween the subcarrier and the dc methods are inclose agreement with those made with the highresolution optical attenuator (see tables 4 and 5).This illustrates the excellent^agreement of attenuation measurements between systems and that a highresolution attenuator eliminates the need forsimultaneous measurement to obtain precise datafor intercomparison of systems.4.6. Power Ratio (dc) Versus Off-NullMeasurementsA two-channel off-null technique for measuringsmall values of attenuation was developed at NBS[14]. The interlaboratory standard chosen forintercomparisons of this measurement system wasthe X-band rotary-vane attenuator that was calibrated by the power ratio (dc) method eight yearspreviously [12].The rotary-vane attenuator exhibits very littlephase shift and provides high resolution at smallvalues of attenuation; thus these inherent characteristics make the attenuator an excellent device forthis intercomparison. The attenuation range for theintercomparison was 0.01 to 0.1 at 0.01-dB intervals.It is estimated that the resettability of this type ofrotary-vane attenuator corresponds to an angulardisplacement of the rotor of about 0.006°. Then thelimits of error of resettability for the attenuationfrom 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-f substitutionsystems at 9.0 GHzDial settingin degreesTheoreticalvalue ofattenuationin decibelsCalibratedvalueof attenuationin decibelsCalibratedvalueof attenuationwith 2'correctionDeviationfromtheoreticalvaluein decibels2.55.07.510.012.515.017.520.022.525.027.530.032.535.037.540.042.545.047.550.052.555.057.560.062.565.067.570.072.575.077.580.082.585.087.50.0165.0662.1493.2659.4167.6022.82321.08051.37541.70892.08282.49872.95883.46544.02134.63005.294S6.02066.81277.67738.62219.656310.791312.041213.42414.96216.68618.63820.87423.48026.58630.41335.37242.38854.4130.0161.0653.1478.2640.4145.5996.82031.07721.37151.70462.07792.49312.95263.45864.01364.62185.28586.01086.80187.66538.60949.641910.775012.022613.40614.94216.66218.61120.84323.44326.54330.35735.29642.26654.1780.0166.0662.1491.2658.4166.6022.82331.08061.37551.70912.08302.49892.95873.46574.02144.63035.29576.02036.81357.67718.62319.656910.790812.041413.42514.96716.69218.64020.87623.47926.58730.41335.36742.37954,401+0.0001+.0000-.0002-.0001-.0001-.0000+.0001+.0001+.0001+.0002+.0002+.0002-.0001+.0003+.0001+.0003+.0009-.0003+.0008-.0002+.0010+.0006-.0005+.0002+.001+.005+.006+.002+.002-.001+.001.000-.005-.009-.012TABLE 6. Comparison of calibration data for the same attenuator at 9.39 GHz using two independent methods (powerratio 1960 versus off-null)TABLE 7. Comparison of calibration for the same attenuator at9.39 GHz using two independent methods (power ratio 1968versus off-null)Dialsetting(dB)0.01.02.03.04.05.06.07.08.09.10Measured attenuationdifference (dB)1968Off-nullmethod [1]0.0103.0208.0294.0397.0513.0598.0695.0792.08%.10081960Power ratiomethod [2]0.0107.0214.0303.0407.0521.0609.0700.0802.0909.1021Discrepancy between1960 power ratioand 1968 off-nullmethods (percent)-3.7-2.9-3.0-2.2-1.5-1.8-.7-1.2-1.4-1.3Dialsetting(dB)0.01.02.03.04.05.06.07.08.09.10Measured attenuationdifference (dB)1968off-nullmethod [1]0.0103.0208.0294.0397.0513.0598.0695.0792.08%.10081968power ratiomethod0.0101.0205.0290.0394.0507.0595.0687.0786.0890.1003Discrepancy between1%8 power ratioand off-nullmethods (percent)Average. 2.0 Average. 1.0+ 2.0+ 1.5+ 1.3+ .8+ 1.2+ .5+ 1.2+ .8+ .7+ .512

The results of the measurements made by thepower ratio methods in 1960 and the off-null methodin 1960 are compared in table 6. Column four showsthe discrepancy between the two methods in percent of the measured value. The greatest percentdiscrepancy, 3.7, occurs at the 0.01 dB-dial setting;however the largest deviation in attenuation is0.0013 dB and occurs at the dial setting of 0.10 dB.But more significant is the negative sign common toall values in column four. Two factors suggest asystematic error, the common minus sign in thediscrepancy column, and the 0.0013-dB differenceat the 0.10-dB measurement. Table 4 shows that thegreatest deviation in measurement for the range of0.01 to 0.10 dB between the subcarrier and dc substitution method was 0.0005 dB at a dial setting of0.10 dB. These above factors led us to furthermeasurement and evaluation.The rotary-vane attenuator was calibrated laterin 1968 by the power ratio method. The results ofthese measurements were compared with thosetaken with the off-null method, and are shown intable 7. The discrepancy between the 1968 powerratios and off-null methods are listed in columnfour. The greatest percent discrepancy, 2, occurs atthe 0.01 dB-dial setting, as was the case in table 6,but the value of the percent of discrepancy wasreduced almost one half. Also, the average valueof the percent of discrepancy for all measurementsof the latter measurements was decreased by onehalf.The measured values of attenuation difference forboth the power ratio and the off-null methods wereanalyzed for apparent angular deviations [18, 19].The dial setting of the attenuator was assumed to bethe true value for this analysis. Figure 15 illustratesthe apparent deviation of the rotor from nominal dialsetting in degrees, which correspond to attenuationvalues of 0.01 to 0.10 dB. The average vane angleerror representative of each measurement is shownas a straight line with the angular deviation indegrees indicated as follows: the power ratio methodof 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 lineshows a decease from +0.044° in 1960 to a -0.012°in 1968 for the power ratio method. This shift in theaverage vane angle error line indicates that the rotorvanechanged 0.056° during the eight year period.Angular slippage is very possible when the zeroreference of the dial readout is on the shaft of thedrive mechanism geared to the rotor section. Thisis not uncommon if either end stop is struck sharply.When a correction equal to the slippage for eachmethod is applied, the average vane angle error lieson the zero deviation line, as shown in figure 16. Thisfigure more clearly illustrates the random point topoint deviation which indicates the random error inthe measurement process. Table 8 shows the deviation in decibels from nominal after the correctionwas applied to the angular deviation. In addition,Dial Setting in DegreesPowtr Rotio i960— Off Null 1968— Power Rotto I968FIGURE 15. Illustrated deviation of the rotor vane of an attenuator calibrated by different methods: powerratio (I960), off-null, and power ratio (1968),2345DIAL SETTING IN DEGREES-POWER RATIO 1960— OFF NULL 1968_ POWER RATIO 19680.044 POWER RATIO 19600.008 OFF NULL 19680.012 POWER RATIO 1968FIGURE 16. Apparent deviation of rotor vane in degrees fromnominal 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 averagediscrepancy is improved from 2 to 0.17 percent andfrom 1 to 0.08 percent, respectively, as shown intable 9, columns five and six.In figure 16 the large apparent angular deviationsare caused by internal reflections and irregularitieswithin the rotary-vane attenuator. The phenomenawill be noted in evaluating the low values of attenuation in the optical rotary-vane attenuator. There is aslight indication of a half cycle of eccentricity present, but the 2 degree cycling shown is not caused byeccentricity.13

TABLE 8. Comparison of deviation from the average values with vane-angle correction appliedDialsetting(dB)0.01.02.03.04,05Average deviation fromnominal after correctionfor rotor slippage0.00024.00073.00066.00020.00011Spread ofmeasured valuesafter correction0.00003.00007.00021.00008.000101960Power ratio+0.00001+.00001-00012-.00001.00000Deviation from average value1968Off-null-0.00002-.00004+.00011-.00006+.000011968Power ratio+0.00001+.00003+.00008+.00007-.000040.06.07.08.09.100.00025.000%.00104.00054.000660.00020.00047.00009.00021.00022-0.00001-K00025+.00004-.00008-00001+0.00015-.00022+.00001.00011-00010-0.00010-.00004-.00005+.00005+.00012TABLE 9. Comparison of calibration data with average vane-angle error correction appliedDialsetting(dB)I960Power ratioDeviation (in decibels) from nominal aftercorrection for rotor slippage1968Off-null1968Power ratioDiscrepancy betweenoff-null and each powerratio method (in percent) withcorrection applied1960Power ratio1968Power ratio0.01.02.03.04.05.06.07.08.09.10-0.00024-.00074+.00048+.00019-.00109+.00020+.00121+.00108+.00046-00065-0.00022-.00069+.00077+.00014-.00114+.00040+.00074+.00105+.00065-.00056-0.00025-.00076+.00074+.00027-.00104+.00015+.00092+.00099+.00059-00078-0.2-.25+ 1.0-.1+.1+.3+.7-03+.2_ i-0.3-.35+.1-.3+.2+.4-3+.07-.07-.2Average 0.17 0.085. Procedures for Evaluating theRotary-Vane AttenuatorOne of the factors affecting the closeness withwhich the rotary-vane attenuator follows the cos 2law 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 withthe alignment of these vanes. (The limit of idealismis also affected by the maximum attenuation of therotor section, which will be discussed later.)Several methods are available for the adjustmentof the vanes in the rotary-vane attenuator. Opticalequipment may be used for a mechanical alignment of the vanes. The electrical method utilizesa waveguide measurement system, where the sameenergy level is maintained at the detector duringthe positioning of scale at equal angular markseither side of the 90° position of the rotor vane [5].Any incorrect alignment of the rotor vane withreference to the scale readout (degrees or decibals)causes a systematic error that is inherent[6] to the rotary-vane attenuator. During the cali14bration of an attenuator, the operator induces arandom error in setting the dial readout on a mark.In making an attenuation difference measurementof a rotary-vane attenuator, the errors at thefinal setting may be written as€/o + e// = — 40 log10coscos Ofwhere 6f is the vane angle at the final setting toobtain the calculated attenuation, 0/o is the vaneangleerror made by the operator at the final setting,and Ofj the inherent vane-angle error caused bymisalignment.A table of attenuation error as a function of vaneangleerror for rotary-vane attenuators is given inNBS Technical Note 177. The table gives the error,e, for a given value of attenuation (^= — 40 logiccos 0) according to the relationship= -40 log 10cos (0+0')cos 0(8)(9)

where 6 is the true vane angle and 6 f is the angle ofvane misalignment. Thus, the angle 6' is the difference between the indicated vane angle and the correct 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 dBin 0.1-dB increments; 1 to 20 dB in 1-dB increments; and 20 to 70 dB in 5-dB increments. Theattenuation errors corresponding to vane-angleerror ranging from 0 to ±0.499°, in increments of0.001°, are presented for each value of attenuation given above.5.1. Determination of Average Vane-AngleError and Eccentricity from CalibrationDataWith the aid of the table of Technical Note 177,the calibration data of the rotary-vane attenuator canbe analyzed for numerous characteristics, such asmisalignment of the scale readout with referenceto the rotor and stator vanes, gear-eccentricityrelated runout and backlash, realignment techniques, and resettability.The equal angle technique of rotor vane alignmentwas assumed to be without error, but NBS hasreported that eccentricity in the gear mechanisminduces an error of alignment when the above technique is analyzed [6],5.1.1. Analysis of Calibration DataLet us evaluate the calibration data at specificdial settings of the rotary-vane attenuator for thepresence of an alignment error and eccentricity.A range of attenuation from 10 to 50 dB requires alittle more than one cycle of the 3-cycle gear driveand scale readout. Table 10, columns one and two,show the dial settings and measured values ofattenuation in decibels. The dial error or the deviation of the measured values in decibels fromnominal are shown in column three. The estimatedvane angle for each dial setting is determined byuse of NBS Technical Note 177 and is recorded incolumn four. (An example of the use of Note 177:on page 90, for a nominal setting of 10 decibels, themeasured dial error of 0.038 dB is found in rownine, column six, to correspond to a vane-angleerror of 0.085°.) Column five shows the attenuationerror corresponding to the average vane-angleerror of 0.064° for each dial setting. The estimatedvane-angle error (column four) minus the averagevane-angle error (0.064°) yields the values in columnsix. Column seven shows the error in decibels aftercorrecting for the average vane-angle error. Infigure 17a the circles are a plot of column three andthe solid curve represents the values from columnfive. In figure 17b, the circles are a plot of columnseven. The deviations around the zero reference lineindicate the appropriateness of applying an averagevane-angle correction to all the readings.5.1*2. Cyclic Pattern of Angular DisplacementIn order to illustrate the magnitude of the apparentangular displacement in degrees, the values ofcolumn four and six (table 10) are plotted in figure 18.The curve Q'c is a plot of column four with the average vane-angle error value, 0.064°, as a reference.The cyclic pattern of the angular displacementindicates the presence of an indexing error [6], Thecurve Qy is a plot of column six, and indicates thereference line shift when the 0.064° correction isapplied to the rotor alignment.TABLE 10. Summary of data for determining average vane-angle error of a rotary-vane attenuatorDial settingin decibelsMeasuredvalue indecibelsDial errorin decibelsEstimatedvane-angleerrorAttenuationerror indecibels forthe average ofthe estimatedvane-angleerror indegreesDeviationfrom averageestimatedvane-angleerrors indegreesError indecibels withcorrectionfor averageestimatedvane-angleapplied101214172025303550Average.....10.03812.05014.04817.04620.02625.03430.07235.16050.4750.038.050.048.046.026.034.072.160.475+ 0.085+ .096+ .079+ .061+ .029+ .027+ .043+ .071+ .087+ 0.0640.028.034.039.048.058.080.107.145.348+ 0.021+ .032+ .015-.003-.035-.037-.021+ .007+ .023+ 0.009+ .017+ .009-.002-.032-.046-.035+ .016+ .12715

- (o)attenuator [6]. The angular rotation of the drivengear concentric about the rotor section of the attenuator is represented as the angle 6. With a gearratio of 12 to 1, the angle of the drive gear 8' equals126. Let a be the angular difference between thezero point of the drive gear eccentricity and thezero point of the scale on the dial in degrees.The angular displacement of the rotor vane indegrees caused by the indexing error is written as0.10VANE ANGLE6 ' = + 0.064°180 TCE sin(120+a) (10)£ 0.0060°25 30 35I I, Iwhere D is the pitch diameter and TCE is the totalcomposite error.The angular displacement of the rotor vane indegrees caused by backlash error is written as360 TCE [l-cos(120+a)] tan

DRIVE GEAR ROTATIONIN DEGREESFIGURE 19. Variations in gear eccentricity error.cos(0+0y)r' cosTCE = 0.00!"D{ PITCH DIAMETER} =1.5912 0=8'( DEGREES)(b) is a plot of eq (10) displaying the indexing errorfrom maximum to minimum for the 3 cycles ofthe drive gear (8'), or as 6 increases from 0 to 90°.The curve (c) is a plot of eq (9) representing the errorin attenuation in decibels for the values of 6 from 0to about 90°. The curve of the error in attenuationshows the cyclic pattern similar to the indexingerror but the magnitude of the attenuation errorincreases at the larger values of 0. For example, theattenuation error is less than 0.005 dB during thefirst cycle of the gear drive, 0 = 0 to 30°; increases toabout 0.015 dB in the second cycle, 0=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 thatthe maximum error occurs at about 88° for the vaneangle 0, which is about 5| degrees from the maximumindexing error during the third cycle.5.2.1. Effects of a on crThe zero point on the scale of the readout doesnot usually coincide with the zero point of drivegear eccentricity. Nor does the manufacture attemptto control this phenomenon. Therefore the value ofthe angle a may vary from 0 to ±180°. Table 11shows the values of the angle a where the maximumand minimum deviations in attenuation, €y , occursfor the dial settings of 10, 20, 30, 40, and 50 dB. Itcan be seen that the difference between the twovalues of a at any setting of 0 is always 90°.TABLE 11. Angular values of a for maximum and minimum€y at 10,20,30, 40, and 50 dB dial settingsDialsettingin decibelsVmax€yamin €y30 45 60 75VANE ANGLE IN DEGREES, 9FIGURE 20. Attenuation as a function of vane angle, variation in the indexing error for the three cycles, andthe error in attenuation from nominal for the dialsettings ofO to 90°.The curve of angular displacement for G'y (fig. 18)shows the maximum value to be ± 0.040° betweendial setting of 10 to 50 dB (55° to about 85°). Let usassume 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 indexingerror relative to the error in attenuation by plottingthe values obtained in eqs (1), (10), and (9) versus thevane angle rotation, 6, in degrees, as shown in figure20. The curve (a) is a plot of eq (1) showing theincrease of attenuation from 0 to greater than80 dB as 0 increases from 0 to about 90°. The curve102030405055.7821°71.5650°79.7567°84.2608°86.7763°-39.3852°-48.7800°+ 32.9196°-21.12%°-51.3156°+ 50.6148°+ 41.2200°-57.0804°4-68.8704°+ 38.6844°The graphs in figures 21, 22, 23, 24, and 25 showthe error in attenuation for different pitch diametersof the driven gear for dial settings 10, 20, 30,40, and50 dB, respectively. These errors were determinedby calculating 0'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 line indicatesthe values of the error in attenuation when a equalszero, and 8' indicates the number of degrees rotationof the drive gear to obtain a dial setting of 10 dB.In order to change the value of attenuation from10 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 cyclesrange of the attenuator. The driven gear has aangular rotation (55.7821 to 86.7763°) of about 31° or17

a IN DEGREES+50.6148° -57.0804*032.91960.0125 -ODOo^_< D20.025 —0.03T5 —DIAL SETTING0:55.7821°= O.OOt"PRESSURE ANGLE = 20°. 5852° to+50.6148*).eg§0.050 -o:oo:DC0.050 —PITCH DIAMETER^ 0.6386B = 0.9583C = 1.2777D= i-5972E = 2.2222F = 3.1805FIGURE 21. Errors in attenuation at the dial setting of 10 dBversus the angle a for different pitch diameters.o:occtrUJ0.100 —0.150 —DIAL SETTING 30 db9 -- 79.7567°TCE =0.001"PRESSURE ANGLE - 20°a f-57.0804 0 to+32.9196)PITCH DIAMETERA = 0.638B = 0.956C = 1.276D - 1.590E =2.228F =3.180FIGURE 23.Errors in attenuation at the dial setting of 30 dBversus the angle a for different pitch diameters.a IN DEGREES•68.8704°PITCH DIAMETERA - 0.6388B - 0.9583C = 1.2777D = i.5972E ~- 2,2222F = 3.18050.050 -QD(JLJOZzro0.100 —0.150 —-48.78 -41.22°cro(TCC0,200 —0.250 —0.300 —DIAL SETTING 40 db9 - 84.2608°TCE^O.OOl"PRESSURE ANGLE = 20°af2l.l296° to+68.8704°)PITCH DIAMETERA = 0,6388 = 0,956C = 1.2760 = 1.590E ^ 2.228F = 3.180a IN DEGREESFIGURE 22. Errors in attenuation at the dial setting of 20 dBversus the angle a for different pitch diameters.18FIGURE 24. Errors in attenuation at the dial setting of 40 dBversus the angle a for different pitch diameters.

-51.3156'OjOSO —0.1000.150 —0.200 —0.250 —0,300 —0.350 —+38.S844*5.2.2. Effects of Pitch Diameter on Error of AttenuationThe pitch diameter of the driven gear affects theangular displacement errors as indicated by eqs (10),(11), and (12). The waveguide size usually is thedetermining factor for the value of the pitch diameter used as the driven gear. The rotary-vane attenuators in the millimeter range require smallerwaveguide components and normally a driven gearhaving a smaller pitch diameter is mounted on therotor section. The graphs of figures 26, 27, 28, 29,and 30 indicate the maximum error in attenuationfor the displacement angles Qy, 8p and 9'T forchanges in pitch diameter at 10, 20, 30, 40, and 50-dB dial settings, respectively. The pressure angle (f>appears in eqs (11) and (12) and curves are plottedfor 20° and 14.5° pressure angles to illustrate thechange in attenuation error for d'T > and Op . Theindexing error is not changed by the pressure angleof the gears; thus, only one curve is needed to showthis error at each dial setting. All graphs show thatan increase in pitch diameter of the driven geardecreases the error in attenuation caused by anyone of the displacement errors.0.400 —DIAL SETTING 50 db= 86.7763°TCE-O.OOl"PRESSURE ANGLE= 20Of (-51.3156° to+38.68440.6000.450 —0.500FIGURE 25. Errors in attenuation at the dial setting of 50 dBversus the angle a for different pitch diameters.DIAL SETTING 10 db0TA = TOTAL ANGULAR ERRORB{ =• INDEX ERROR9'B = BACKLASH ERRORTCE= 0,001"one third of the 0 to 90° possible displacement ofthe rotor section. As shown in figure 20, the indexingerror goes through three positive and three negativemaximums from 0 to 1080° rotation, 8', of the drivegear. The maximum positive and negative indexingerrors occur at fixed angular displacements of 6.Table 12 shows the angular values of 6 where thesemaximums occur and their respective theoreticalvalues of attenuation in decibels.TABLE 12. Angular values of 6 where maximum (+ or —) deviations of attenuation occur due to indexing error in 3-cycledrive and the corresponding theoretical attenuation valuese7.5°22.5°37.5°52.5°67.5°82.5°Max+ —+ —+ —Decibels0.1492571.3753864.0213348.62211516.68641435.3720930,2 0.4 ae 0.8 1,0 1.2 1.4 i,e 1.8 2.0 2.2PITCH DIAMETER IN INCHESFIGURE 26. Errors in attenuation at the dial setting of 10 dBversus pitch diameter for the angular displacementerror.19

0.7000.900ID2LU0.6000,5000.4000.300DIAL SETTING 20 db£ TA = TOTAL ANGULAR ERROR0f - INDEX ERROR8'B = BACKLASH ERRORTCE= O.OOl"PRESSURE ANGLES(1) =20°(2) - 14.5°0.8000.700 -0.600DIAL SETTING 40 db#TA = TOTAL ANGULAR ERROR&i = INDEX ERROR&Q = BACKLASH ERRORTCE= 0.001"PRESSURE ANGLES111 =20°(2) = 14.5°(TaCLCL0.2000.400I 0,300O.!000.2000 0,2 0,4 0,6 0.8 1,0 1,2 1.4 1,6 1,6 2,0 2.20,100PITCH DIAMETER IN INCHES0 0.2 0,4 0.6 0.8 1,0 1.2 1,4 1.6 1.8 2,0 2.2FIGURE 27. Errors in attenuation at the dial setting of 20 dBversus pitch diameter for the angular displacement error.PITCH DIAMETER IN INCHESFIGURE 29. Errors in attenuation at the dial setting of 40 dBversus pitch diameter for the angular displacement error.0.9000.800 -C.9000,8000,700DiA! SETTING 50 d b, = TOTAL ANGULAR ERROR= INDEXING ERROR•- BACKLASH ERRORTCE- O.OOl"PRESSURE ANGLES(! ) =20°(2) -- 14,5°0.700 -0.6000.500 -DIAL SETTING 30 d D= TOTAL ANGULAR ERROR= INDEX ERROR= BACKLASH ERRORTCE- 0.001"gC.600§ 0,5000.400 -0,300 -trocrLUcc0,4000,3000,200 -0,2000100 -0,1000 0.2 0.4 0.6 0.8 1,0 1.2 1.4 1.6 1.8 2.0 2.2PITCH DIAMETER IN INCHESFIGURE 28, Errors in attenuation at the dial setting of 30 dBversus pitch diameter for the angular displacement error.200,2 0,4 0.6 0,8 1.0 1,2 1.4 1,6 2,0 2,2PITCH DIAMETER IN INCHESFIGURE 30. Errors in attenuation at the dial setting of 50 dBversus pitch diameter for the angular displacement error.

6. Compensation for TransmissionError of Rotary-Vane AttenuatorThe transmission error becomes less as the magnitude of the maximum attenuation is increased inthe rotor section of the attenuator. Otoshi [9] haspresented a modified law that provides a tool forextending the useful dynamic range of the rotaryvaneattenuator with low values of maximum attenuation. A mechanical technique of increasingthe dynamic range may be achieved by adjusting theinput stators of the attenuator.6.1. Transmission Error versus Dial Settingin DecibelsWith a known maximum attenuation value at 0equals 90°, the transmission error can be determinedfrom eq (5). In order to make quick estimates of thetransmission error, eq (5) was used to obtain figure31. The graphs show that the transmission error isabout 0.03 dB at the dial setting of 50 dB for an attenuator with a 100-dB maximum. The error increases 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-dBmaximum attenuation can be achieved in the centersection of the attenuator.i .06.2. Stator RealignmentThe mounting holes of each stator are enlarged toenable angular rotation around the longitudinalaxis of the waveguide sections of the rotary-vaneattenuator. The stators may be rotated either direction writh 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° clockwiseand stator S2 was rotated 1/2° counterclockwise;and in part (B) indicates that the stators were rotatedconversely. From eq (3) the calculated deviationwas determined to be 0.066 dB for the dial setting of40 dB. The measured attenuation differencedeviated from calculated attenuation by 0.009 and0,015 dB for the conditions A and B, respectively,at the dial setting of 40 dB. However, the 1/2° rotation of the stators induced an increase in the attenuation difference of about 0.08 dB in both cases atthe 40-dB setting. In other words the Type B errorof misalignment increases the value of attenuationfor nominal dial settings. As will be shown later,intentional misalignment of the stators can effectively compensate for insufficient maximumattenuation.-TYPE "B" ERROR -ROTOR ZERO POSITION ALIGNED TO AVERAGE POSITION OF STATORSc.c.w.-ROTORROT° RDIAL SETTING40.075 db - - - - — — 40 db - - - —— - - -40.081 dbMEASURED VALUEMEASURED VALUEFIGURE 32.Illustration of stator rotation and rotor alignment to induce the Type B error.0.00010.00001FIGURE 31.10 20 30 40 50DIAL SETTING IN dBEstimate of the transmission error versus dialsetting in decibels for maximum attenuation valuesof 60 to 160 dB.60Angular Displacements versus Maximum AttenuationIn figure 33 the smooth curve provides an estimate of the angular displacement, 0'/2, which thestators require to compensate for the values ofmaximum attenuation. The angular displacementequals about 1.05° for 70 dB and decreases to anangle of 0.018° for 140-dB maximum attenuation.For example, the graph shows that the stators mustbe rotated about 0.18° to compensate for the transmission error when maximum attenuation equals100 dB. In order to determine the value of compensation in decibels, refer to NBS Technical Note 177.Page 139 gives the attenuation deviation versus21

angular deviation for the nominal value of 50 dB,0 = 86.7763°. For example, column 1 and line 2 givevalues of +0.997123 dB and -0.942820 dB corresponding to the angular deviation of 0.18°. The valueof compensation, e'h , equals 0.027515 dB, which isone-half of the algebraic sum of the attenuationdeviation in decibels. This result can be computedfrom eq (3). Figure 31 shows that the deviation fromi .00nominal attenuation in decibels equals about 0.027dB for a dial setting of 50 dB and the maximumattenuation line of 100 dB.Realignment of the stators causes the end ports ofthe rotary-vane attenuator to be out of alignmentwith the ports at the insertion point of the measurement system. Therefore, a waveguide adapter withan angular twist equal to d'/2 should be placed at theends of each stator. The twists becomes a part of theattenuator after the angular displacement is determined by the maximum attenuation of each attenuator. Table 13 shows the angular correction, 072,required for maximum attenuation values of 90 to160 dB in 10-dB intervals. The distance b f necessaryto produce the angular correction is given for elevenwaveguide sizes from WR15 to WR650. The angulardisplacement has been converted to length in inchesor distance b' from a reference plane, as shown infigure 2.6.3. Illustration of Transmission Error andCompensation for 110-dB Maximum70 80 90 TOO 110 120 130 140MAXIMUM VALUE OF ROTOR VANE ATTENUATION IN dBFIGURE 33. Estimated angular displacement of stators indegrees versus the maximum attenuation valueof rotor vane in decibels for the compensation required to approach theoretical cos 2 6 law.Figure 34 illustrates the deviations in attenuationfrom nominal by giving both the increase in attenuation caused by misaligning the stators and the decrease caused by insufficient maximum attenuation,respectively. The deviations are plotted for dial settings from 20 to 70 dB. The solid curve indicates thecalculated (eq (5)) deviations in attenuation for anattenuator of 110-dB maximum. (Fig. 31 can be usedfor rapid estimates.) The dashed curve indicatesthe calculated (eq (3)) deviation in attenuation for anattenuator with 0.1° (0'/2) stator misalignment. Inother words the misalignment of the stator by 0.1°induces an increase in the attenuation which closelycompensates for the decrease in the attenuationcaused by an insufficient maximum value of 110 dB.TABLE 13. The angular correction required for different values of maximum attenuation and the distance b' necessary to producethe angular correction for various waveguide sizesWReka90 dB0.320°100 dB0.180°HOdB0.100°120dB0.057°b'130 dB0.032°140 dB0.018°150 dB0.010°160 dB0.008°1528426290112137187284430650(0.148)(.280)(-42)(.622)(.900)(1.122)(1.372)(1.872)(2.840)(4.300)(6.500)0.000800.001500.002270.003370.004880.006080.007450.010150.015410.02330.035270.000460.000880.001320.001950.002830.003520.004310.005880.008920.013510.020420.000260.000490.000730.001090.001570.001%0.002390.003270.004%0.007500.011340.000170.000310.000470.000700.001010.001260.001540.002110.003190.004840.007310.000080.000160.000230.000350.000500.000630.000760.001040.001580.002400.003620.000040.000090.000130.000200.000280.000350.000430.000590.000890.001350.002950.000030.000050.000070.000110.000160.000190.000240.000330.000500.000750.001130.0000200.0000380.0000570.0000840.000120.000150.000190.000250.000380.000580.00088b' = a tan 07222

.080--MAX * 110 dBo*2 ~~ - 100 *0' * .2-.084T.050-- MISALIGNEDSTATORCD•o.020--o

6,4. Mechanical Compensation andMeasured ResultsIn order to experimentally evaluate the compensation technique of stator realignment, a commerciallyavailable rotary-vane attenuator was modified.The stator flange bolt holes were enlarged to permitrotation of the stators and the vane in the rotor section was decreased in length. The measured maximum attenuation (at 0 equals 90°) dropped from aprevious 90 to 72 dB after the rotor section modification. In figure 35, the calibrated values of themodified attenuator are plotted as X points on thesolid line curve at dial settings of 20,30,40,50,60, at70 dB. The solid line curve indicates the calculateddeviation in attenuation for an attenuator with 72-dBmaximum attenuation. Referring to figure 33, theangular displacement required for 72-dB maximumis 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 line.The calibration points plotted as indicate thatthe compensation caused the values of 10 to 40dB to fall in a random manner about the zero deviation line. However, the larger deviation shown at 50dB is within the limits of the system error and theresettability of the commercial attenuator.0.700.600.500,400.300.200.100(c)1 - CALIBRATED VALUESAFTER STATORSMISALIGNMENT(0)- DEVIATION OFCALIBRATED VALUESWITHOUT REALIGNINGTHE STATORS(b) /- CORRECTION /INDUCED BY /MISALIGNING /THE STATORS 0,87° / (b)7. Measurements of Precision Rotary-Vane Attenuators With HighResolution ReadoutsA calibrated high precision rotary-vane attenuatorcan be regarded as an ideal working or transferstandard for making precise measurements in amicrowave standards laboratory. Regardless of thegreat care taken in the fabrication of the attenuator,or the high resolution of the dial readout, the deviceshould be evaluated before it is used as a standard.Though several attenuators may be built of identicaldesign and precise fabrication each has distinctinherent characteristics [3,18].At present the commercially available rotary-vaneattenuators have a dynanic maximum range of 90 to100 dB. This value of maximum attenuation providesonly one-half of the theoretical value attainable at 1arc second less than 90° rotation of the rotor. Theusable scale of these attenuators are marked from0 to 50 dB. Thus, about one-fourth of the total rangeof attenuation is at present being used for calibratedinterlaboratory standards. Usually this type ofrotary-vane attenuator utilizes a spiral scale for thedial readout of attenuation in decibels. The attenuator must be calibrated at nominal values, but eventhen the resolution and scale readout usually aretoo coarse for precise interpolation between pointsof calibration.At present several angular displacement readouts have been designed for use with precisionrotary-vane attenuators. A gear mechanism designed by NBS can be installed onto commercialrotary-vane attenuators to give dial readings ofangular displacement of 0.001° from 0 to 90°. TheNBS optical rotary-vane attenuator provides anangular displacement with a resolution of ± 1 second of arc. The Royal Radar Establishment of England has developed a digital angular readout forrotary-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-0.60 --0.70!0 20 30 40DIAL SETTING IN DECIBELSFIGURE 35. Deviation of attenuation from nominal versus dialsetting in decibels for rotary-vane attenuator with72-dB maximum:(a) Curve of calibration points,(b) Curve of correction induced by misaligningthe stator 0.87°, and (c) Plot of calibrated valuesafter stator misalignment.50The gear mechanism illustrated by the drawingsin figures 13 and 14 has been used successfullywith commercial rotary-vane attenuators in WR62,WR90, and WR112 waveguide sizes, and adaptsto rotary-vane attenuators in waveguide sizesWR137 and WR187 with minor modifications.The modified attenuator, which now reads inangular displacement of the rotor section, mustbe calibrated in an attenuation measurement system for use as an attenuation device. The vaneangleerror and gear eccentricity can be determinedfrom the calibration data as shown in 5.2. Inorder to obtain the best possible evaluation of themodified gear driven readout, three measurementsystems were used in the calibration of the at-24

:.060.050.040.030.020(O.WdB)(Q ( Q3dB>|(0.05dB).010.000-.010-.020O.OldB l.OdB- POWER-6.0dB lOdB 12dBDIAL SETTING IN DEGREES AMD DECIBELS———————— SUB-CARRIER—————————————4-~T30dB 40dB5GdB lOOdB60dB ,I,F,-SUBSTITUTIONFIGURE 36. Angular error, 0'T , in degrees from nominal (theory) versus the dial setting, 0, in degrees, determined from measurements bythe power ratio, modulated subcarrier, and i-f substitution methods.tenuator over a large range. Each measurementsystem was used to cover a different range of about30° of angular rotation of the center vane.7.1.1. Measurements of Precision Gear Driven Rotary-Vane AttenuatorThe measured results were obtained as follows:the power ratio method, 0 to 30°; the modulatedsubcarrier method, 30 to 60°; and the i-f substitution method, 60 to 87.5°. The interval of measurement taken was every 2.5° within the 30° section.The measured attenuation at each dial setting wascompared with the theoretical value [19] to determine the average vane-angle error in degrees. Infigure 36, the curve shows the angular error,6'r,, in degrees from nominal (theory) versus the dialsetting, 6, in degrees. Each measured value isshown by an X at the 2.5° dial settings of 0. Thecyclic 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 ofthe ±0.030° cyclic indexing error, and representsan average vane-angle error of about 0.020°. Inaddition to a dial setting scale in degrees, the corresponding values of attenuation in decibels are indicated on the lower part of the horizontal axisof the graph. In other words the range of attenuation difference measurements that were taken bythe three different methods were as follows:0.02 to 2.5 dB, 2.5 to 12 dB, and 12 to 55 dB, bythe power ratio, modulated subcarrier, and i-fsubstitution methods, respectively.7.1.2. Angular Resettability of AttenuatorThe two dashed lines drawn ±0.010° about thecyclic indexing error curve (fig. 36) approximate the25angular resettability of the attenuator. The basicpart of the error of resettability is caused by gearingin the commercial attenuator. In addition to the errorof resettability the relation of center distancesbetween these gears is the principal cause of theeccentricity or indexing error. The drive gear shouldbe replaced if the runout error is large and the springloading converted to positive loading of the gear.The arrows shown on the upper part of the graphgive the value of resolution which is indicated withinthe parenthesis. The resolution in decibels corresponds to the resettability of 0.020° at the variousvalues of 6. All values of angular deviation fellwithin the range of 0.020°, but the deviation inattenuation vary greatly. For example, the deviations in attenuation vary from 10 /xbels at 0.02-dBdial setting, to about 1 dB at 100-dB dial setting.When the measured angular deviations wereconverted to decibels, all the deviations in attenuation were within the systematic and random errorsof the corresponding measurement system. Thisclose agreement in following the indexing error ofthe attenuator shows that any one of the measurement systems could be used to calibrate theattenuator over an assigned part of its range.Therefore extrapolation of the cyclic error overany other part of the range could be used to setlimits of error for the entire attenuator.7.2. Mounting the Gear DriveWe recommend that the drive gear be selectedwith care and spring loading be removed, beforeapplying a precision gear mechanism to the attenuator. Figure 37 illustrates the angular error ofthe attenuator when a gear box was mounted on therotary-vane attenuator without modifying the drivegear. The curve illustrates the angular error over573-735 OL - 75 - 3

a range of about 70° rotation of the center vane(about two and one-third revolutions of the drivegear for a 12 to 1 ratio). The large half-cycle errorwas caused by a binding effect between the drivegear and the driven gear (concentric to the rotorsection). When more precise machining techniqueswere applied to the mounting of the precisionreadout, the cyclic indexing error became a cyclicpattern as shown in figure 38. Note that the averageangular displacement error was reduced from about0.450 to 0.040°.30 40 50 60 70 80 900(Dial Setting in Degrees)FIGURE 37. Angular error caused by binding effect between thedrive gear and the driver gear (concentric to therotor section).7.3.1. Measurements on Optical Rotary-VaneAttenuatorIn order to evaluate the attenuator over a widedynamic range, it was calibrated by three differentmethods in the same manner as was the precisiongear driven attenuator. The attenuation deviationsin decibels and the angular deviations in degreesare plotted versus dial setting in degrees (refer tofig. 39). The portion of the curves corresponding tothe first 30° of dial setting shows the deviations inattenuation and angular displacement as determinedby the power ratio measurement system. Thisportion of the curve shows deviations in attentuationfrom —0.0025 to 0.0045 dB or in angular displacement from —0.046 to 0.024°. Neither the powermeasurement system nor a precision attenuatorcause 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 themodulated subcarrier, and i-f substitution methods,respectively. Again the electrical deviations werelarge for each specific method: 0.004 dB in the subcarriersystem and 0.026 dB in the i-f system. Inaddition to large electrical and mechanical equivalent angular deviations, the apparent average vaneangleerror falls off from a +0.010° to a -0.005°.This error falls off more rapidly at the higher valuesof attenuation. All of these deviations in measurement of attenuation and decrease in the angularerrors show that the center vane has insufficientmaximum attenuation (below the required amountfor a precision rotary-vane attenuator). The evidenceof 0.015° decrease in the average vane-angle errorindicates that the maximum attenuation is less than90 dB..100^Average Vane Angle Error — 0 10 20 30 40 50 60 70 80 909 (Dial Setting in Degrees).015 r*/ MODIFIED OPTICAL REA88UT/ ROTARY VANE ATTENUATOR7.0045 it.005 IBFIGURE 38. Angular error, 6', in degrees versus dial setting indegrees, 6, after precise machining was applied.*.003 riB001 dB zis~ £7.3. Optical Rotary-Vane AttenuatorThe optical rotary-vane attenuator designed atNBS virtually eliminates gear eccentricity errors.The readout scale of the attenuator gives an opticaldisplay of the angular rotation of the rotor sectionin degrees, minutes, and seconds of arc from 0 to360°. However, the attenuator is used in its normalfunction from 0 to 90°. The final version of the opticalrotary-vane attenuator followed the cos squared lawmore closely than any attenuator previously calibrated at NBS. Notwithstanding, earlier fabricationsof the attenuator had problems other than gearingto solve..82(11.803 IB £1.805 dB

.005 r.003-.0012 -.001-.003-.005 LFIGURE 40. Deviation in decibels and degrees versus dial setting in degrees, afterrepair of the rotor section.7.3.2. Measurements after Rotor RepairThe center vane was replaced and care taken toproperly cement it to the rotor section. After repairing the rotor section, the attenuator was recalibrated using the same systems as before. In figure40 the plot of these measured deviations shows thatthe average vane-angle error is now 0.033°. Thedeviation in attenuation difference is about ±0.001dB with reference to the average vane-angle errorline from 0 to 60° of 0, about ±0.002 dB from 60 to80°, and ±0.005 dB at 87.5° of 6. The curve with themark X shows the attenuation deviations convertedto angular deviations. These deviations have decreased greatly from those shown in figure 39.More important is that the fall off at the highervalues of 6 decreased to about 0.003°; this corresponds to about 105-dB maximum attenuation inthe center vane.The attenuation deviations from a curve corresponding to a vane-angle misalignment of— 0.033°and to angular deviation from the —0.033° line wereplotted. Figure 41(a) shows the value for a dialsetting of 0 to 45° while figure 41(b) shows the valuesfor a setting of 45 to 87.5°. The deviations of attenuation from the curve corresponding to the —0.033°vane misalignment were quite small and indicatethat such would be a very good compensation fortransmission error over the dial range of 0 to 87.5°.10 15 20 25 30 35 40 45Dial Setting in Degrees 845 50 5510 65 70 758. Resolution and ResettabilityThere are two possible readouts that can be usedfor rotary-vane attenuators: (1) direct reading ofattenuation in decibels; and (2) angular reading ofrotor vane rotation in degrees. The use of a readoutwith angular notation offers the advantage in thatthe scale is linear, while a direct reading decibel27FIGURE 41. (a) Deviation of measured attenuation and equivalent angular deviation from theoretical values fora vane angle correction of —0.033° versus dialsetting of 0 to 45°.(b) Deviation of measured attenuation and equivalent angular deviation from theoretical values fora vane angle correction of —0.033° versus dialsetting of 45 to 87.5°.

scale decreases rapidly in resolution at the highvalues. In addition, interpolation becomes moredifficult to estimate as the attenuation rate increaseson the decibel scale.There are occasions when it is important to knowto what accuracy a rotary-vane attenuator can beset over its usable range. In order to demonstratethe accuracy of resettability we have elected to useangular notation. Figure 42 shows the resolutionerror, €#, in attenuation in decibels versus the dialsetting, A dB, in decibels for several values of Q'R ,the angular resettability of the rotor vane in degrees. The curves show the magnitude of the resolution error, e#, for values from 0.1 /ubel to 100decibels at dial settings of 0.001 to 200 dB forangular resettability of 1 second and 0.001 to 1.0°of arc.The curves (A to H) provide a quick and convenient means of determining the accuracy indecibels one can expect for a known angular resolution. Also, if the deviation in attenuation fromnominal is known, the required angular correctioncan be determined from the graph. For example,for a rotary-vane attenuator with a deviation ofabout 0.013 dB at a 10-dB dial setting, curve (E)shows that a correction of 0.03° would be requiredto give the nominal value of attenuation.9. Resolution of Rotary-VaneAttenuator in Percent of DialSettingThe question may arise as to the optimum valueof attenuation to measure for intercomparison oflaboratory standards, or to determine the characteristics of a variable attenuator standard. In figure43, the resolution of the dial in percent of dial settingis plotted versus dial setting in decibels for a rotaryvaneattenuator with an angular resolution of 0.01°.At each end of the curve the resolution of dial inpercent 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 appearsto have the lower percent values from 6 to 20-dBdial settings, with the lowest occurring at about 12dB. If an attenuator has finer resolution, such as0.001° or 1 second of arc, then the resolution ofdial in percent of attenuation will be correspondinglylower. From figure 42 it can be determined that forattenuation values of 1, 12, and 40 dB, the resolutionof dial in percent are 0.011, 0.0045, and 0.0075percent, respectively, for 0.001° dial resolution, andthe 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 thelower resolution of dial in percent of attenuation.10'0.01 3.0 6.0 12Dial Setting in Decibels20 30 50 10010"FIGURE 43. Resolution of the dial in percent of attenuationversus dial setting in decibels for an attenuatorwith angular resolution of 0.01 °.10"10. Frequency Sensitivity of theRotary-Vane Attenuator10" 10©(A dB ) DIAL SETTING IN DECIBELSFIGURE 42. Resolution error in decibels versus dial setting indecibels.28Although the rotary-vane attenuator has someexcellent properties, such as stability, resolutionand low reflection at the input and output ports,all of which are necessary criteria for good transferstandards, it also exhibits an undesirable characteristic, frequency sensitivity. The frequency sensitivity

ecomes more pronounced at high values of attenuation; thus calibration of the attenuator atthe operating frequency is essential for precisemeasurement with this device over large rangesof attenuation.10.1. Spectrum of Microwave AttenuationCalibration Systems 2.6 to 40 GHzFor a period of more than 15 years, the microwaveattenuation calibration system [16] has been used atNBS to calibrate rotary-vane attenuators over themicrowave spectrum of 2.6 to 40 GHz. This includedthe following waveguide sizes: WR284, WR187,WR137, WR112, WR90, WR62, WR42, and WR28.Three frequencies for microwave calibrations weresuggested for each waveguide size. These threefrequencies were approximately as follows: thelower frequency limit increased 10 percent, themiddle of the waveguide band, and the upper frequency limit decreased 10 percent. For example, thefrequency band for WR90 waveguide is 8.2 to 12.4GHz, and the suggested frequencies for calibrationwere 9, 9.8, and 11.2 GHz.3 Selected Frequencies Each in WR284, WR90, andWR28 Waveguide SizesIt is helpful to use the data of calibrated rotaryvaneattenuators in several waveguide sizes toevaluate their frequency sensitivity. For example,the waveguide sizes WR284, WR90, and WR28cover the lower, middle, and upper portion of themicrowave frequency range used in this sample ofrotary-vane attenuators. The deviations of attenuation from nominal in decibels versus dial settingsof 10 to 50 dB at three NBS selected frequencies ineach of the above waveguide sizes are shown infigures 44 to 50. In each figure the points plotted foreach dial setting are coded as follows: the square,D, at the lower frequency; the triangle. A, at themiddle frequency; and the circle, O, at the higherfrequency. The smooth curves indicate the averagedeviation in attenuation and the corresponding vaneangleerror is shown in degrees [17]. The spreadbetween the curves indicates the magnitude of theerror caused by frequency sensitivity. Correctionscan be applied to minimize the frequency sensitivity.Figures 44 and 45 show the deviations of attenuation for two attenuators in WR90 waveguide. Infigure 44 the average vane-angle error is positiveand yields values of attenuation greater thannominal, while in figure 45 the average vane-angleerror is negative and gives values of attenuation lessthan nominal. The random variation of the calibratedpoints at each dial setting are due to gearing runout,resettability, mismatch, and system drift.An example will now be given to show how thedeviation in frequency sensitivity across a givenwaveguide size can be minimized. If a vane anglecorrection of —0.067° is applied to the data plottedin figure 44, then the average vane-angle error at9.0, 9.8, and 11.2 GHz will be +0.031, +0.013, and— 0.031° respectively.DIAL SETTING IN dBFIGURE 44. Deviation of attenuation for average vane-angleerrors of 0.098, 0.080, and 0.036° versus dial settingin decibels at 9.0, 9.8 and 11.2 GHz.29

20 30IAL SETTING IN dEFIGURE 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 11.2GHz.Figures 46 and 47 show the deviations in attenuation for two rotary-vane attenuators in WR28.The random scatter of the point-by-point valuesare larger in the smaller waveguide size becausegearing runout can produce greater angular displacement error [6], which correspondingly induceslarger deviations in attenuation. The deviations inattenuation from nominal are illustrated for threeWR284 rotary-vane attenuators in figures 48, 49,and 50. These curves show that two attenuatorshave a negative average vane-angle error while thethird has a positive angular error. In addition, infigures 48 and 49, the curve showing the higherfrequency error falls between the middle and lowerfrequency errors. This could be caused by thewarping or curling of the tapered vanes in the endsections, which is characteristic of this model ofrotary-vane attenuator. However, the curve for thehigher frequency did not fall between the other twoand the spread of the deviation in attenuationappears to be less for the data obtained with anothermodel of WR 284 attenuator, shown in figure 48.0.80 Or0.600WR 28R . V . A T T E N .0.400O 37 GHZA 33 GHzD 29 GHz0. 2000.000,-0.20020 3050DIAL SETTING IN dBFIGURE 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

0.6002 0.400WR 28R.V. ATTEN.O 37 GHzA 33 GHzD 29 GHz~ 0.2000.008°0.00010 20 30DIAL SUITING IN dB4050FIGURE 47. Deviation of attenuation for average vane-angle errors of 0.008,and — 0.042 ° versus dial setting in decibels at 29, 33, and 37 GHz.-0.014,0.0200.000-0.020-0.040-0.060-0.080-0.100-0.120-0.140-0.160-0.180-0.20020 30DIAL SETTING IN d&40FIGURE 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 and3.55GHz.31

WR 284R.V. ATTEN.20 30DIAL SETTING IN dBFIGURE 49. Deviation of attenuation for agerage vane-angle errors of 0.128, 0.-705,and 0.120° versus dial setting in decibels at 2.85, 3.25, and 3.55 GHz.o. 100,00-0.10-0.20-0.30-0.40-0.50-0.60WR 234R.Y. ATTEN.O 3.55 GHzA 3.25 GHzO 2.85 GHz-0.70-0.80-0.9020 30DIAL SETTING IN dBFIGURE 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, and3.55 GHz.32

10.2. Statistical Analysis of the FrequencySensitivity from Calibration Data at 30, 40,and 50 dBIn order to obtain a statistical analysis of thefrequency sensitivity, data were selected fromcalibrations performed on 154 attenuators at theestablished frequency limits. The analysis utilizedthe calibration data of the higher dial settings of30, 40, and 50 dB of each rotary-vane attenuator.Since these dial settings were common to all calibrations, these values were used in computing thestandard deviation for each waveguide size. Infigures 51 to 58 each graph shows the limits ofone-sigma error in attenuation in decibels versusfrequency in GHz for the rotary-vane attenuator ineach specific waveguide size at 30, 40, and 50-dBdial settings. In each figure the vertical lines f\ and/2 are the limits of the selected frequencies. However, the frequency of each graph was extended toinclude the total frequency range of that specificwaveguide size. The greatest change in attenuationin decibels occurs at the dial setting of 50 dB inWR62 waveguide and is about 0.75 dB for a frequency range of 12.4 to 18.0 GHz, as shown infigure 56. The least change in attenuation for the50-dB dial setting was about 0.3 dB in WR284 andWR42 waveguide sizes (figs. 51 and 57).7.01 FREQUENCY IN GHzFIGURE 51. Limits of magnitude of one-sigma error in attenuation versus frequency in GHz for twenty WR284rotary-vane attenuators at 30, 40, and 50-dB dialsettings.FIGURE 53. Limits of magnitude of one-sigma error in attenuation versus frequency in GHz for eighteen WR137rotary-vane attenuators at 30, 40, and 50-dB dialsettings.~ 0.30-0.20 -0.20 -0.15 -0.10 -1 FREQUENCY IN GHz 2FREQUENT IN GHzFIGURE 52. Limits of magnitude of one-sigma error in attenuation versus frequency in GHz for twenty-one VFR187rotary-vane attenuators at 30, 40, and 50-dBdial settings.33FIGURE 54. Limits of magnitude of one-sigma error in attenuation versus frequency in GHz for twenty-three WR112rotary-vane attenuators at 30, 40, and 50-dB dialsettings.

WR62WAVEGUIDE12.4 - IS.OGHzFREQUENCY IN GHz12.416.0FREQUENCY IN GHz18.0FIGURE 55. Limits of magnitude of one-sigma error in attenuation versus frequency in GHz for fifty-one WR90rotary-vane attenuators at 30, 40, and 50-dB dialsettings.FIGURE 56. Limits of magnitude of one-sigma error in attenuation versus frequency in GHz for seven WR62 rotaryvaneattenuators at 30, 40, and 50-dB dial settings.0 .30,-0.25WR42WAVEGUIDE13.0 - 26.5 GHz0.200.1520.0 22.0 24.CFREQUENCY IN GHz26.0 | 28.026.5FIGURE 57. Limits of magnitude of one-sigma error in attenuation versus frequency in GHz for seven WR42 rotaryvaneattenuators at 30, 40, and 50-dB dial settings.34

0.70 r0.50HR28WAVEGUIDE26.5 - 40GHz0.400.1026,0 26.5FREQUENCY IN GHzFIGURE 58. Limits of magnitude ofone-sigma error in attenuation versus frequency inCHz for seven WR28 rotary-vane attenuators at 30, 40, and 50-dB dialsettings.10.3. Frequency Sensitivity of Rotary-VaneAttenuators for Eight Waveguide FrequencyRangesTable 14 summarizes the frequency sensitivityof the rotary-vane attenuators for eight waveguidedesignations. The term dB/GHz indicates thedeviation from nominal attenuation adjusted so thatthe deviation is zero at .! e bottom frequencies ofthe waveguide range. The values of dB/GHz weredetermined from 072 minus cr/i divided by f% minus/i (upper and lower selected frequencies, respectively) where

11.1. Errors in Attenuation for the Initialand the Final Setting of the Rotary-VaneAttenuator for an Attenuation DifferenceMeasurementThe initial setting of an attenuation differencemeasurement of a rotary-vane attenuator can bewritten aswhere A\, is the theoretical value of attenuation atthe initial setting; e^o and €,-/ are the errors due tothe operator and inherent error, respectively, at theinitial setting.The error in attenuation at the initial setting maybe expressed as,•/ = —40 logiCOS ( ft ± ftpCOS ftwhere the angular values at the initial setting are:ft, the vane angle to obtain the theoretical attenuation; 0,0, the vane-angle error due to the operator;and ft/, the inherent vane-angle error.In a like manner, the final setting of an attenuation difference measurement may be expressed aswhere Af is the theoretical value of attenuation atthe final setting, €/o and e// are the errors due to theoperator and the inherent error, respectively, at thefinal setting.The error in attenuation at the final setting maybe expressed as€/o + €// = — 40 log 10COS (6f±Bjy+8fl)cos 6fwhere the angular values at the final setting are:0/, the vane angle to obtain the theoretical attenuation; 0/o, the vane-angle error due to the operator;and 0//, the inherent vane-angle error [18].Any deviation from ideal alignment of the rotorvane with reference to the scale readout causes asystematic error in the attenuation rate of the entirerange of the rotary-vane attenuator. Though thismechanical error can be constant angular displacement, it produces an increasingly greater error inattenuation as the value of 0 increases. Also, theerror in attenuation caused by angular limits ofresettability becomes greater with increases of 0.Since bootstrapping action usually results in highervalue of attenuation, the smallest errors of alignment and resettability are essential to keep the limitsof uncertainty minimal.11.2. Graphical PresentationIn order to illustrate the deviation in attenuationdue to rotor-vane alignment error, graphs are usedto display these deviations from nominal attenuations. This deviation from nominal in a determination of attenuation difference occurs at both theinitial and final dial settings of the rotary-vaneattenuator.11.2.1. Deviations in Attenuation Due to Rotor-VaneAlignment ErrorFigure 59(a) is a graph of error, e', in decibels forattenuation in 10-dB increments with assumedrotor-vane alignment error, 0,, equal to 0.100, 0.200,and 0.300°. The value of e', the error from nominal,is determined from e b minus e o whenand;—4oiogl5lO~COS (flq+fl/)COSCOS O aCOS6 a is the initial rotor vane angle, 0& is the final rotorvane angle, and 0^ is defined above.The magnitude variations of e' are illustrated bythree different straight lines: the solid line for0;-0.300°, the dot line for 0)-0.200°, and the dashdot-dashline for 0) = 0.100°. (This legend alsoapplies to the figs. 61, 63, 65, and 67.) Five differentincrements of 10 dB each were measured asfollows: 0 to 10 dB, 3 to 13 dB, 6 to 16 dB, 10 to20 dB, 15 to 25 dB. The values of e' at the same10-dB increments are smaller when 0/ is equal to0.200 and 0.100° as indicated by the dot, and thedash-dot lines. For a given 0), the value of e' is theleast at the dial settings of 3 to 13 dB.11.2.2. Attenuation Versus 9 in DegreesFigure 59(b) is the curve of attenuation versus0 in degrees of rotor angular displacement. Thesegments 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 indegrees; the initial, 0{; the final, 0/; and theirdifference, A0.Although the increments of attenuation are equal,the angular increments, A0, become less at highervalues of 0. For example, the angular displacementfor the 15 to 25-dB increment is approximatelyone-fifth of the value for the 0 to 10-dB increment.36

.20 -.15 -.10 -.05 -ATTENUA' [ION IN 10 dB INCREMENT300°(ROTOR VANE MISALIG NMENT)?00°(15 TO 25dB)00°- —— ej = o.:——. ej = o.;———— 9j = 0.1a 31f. __ 1 __a 2 ,(10 TO1(0 TO It2^ ——— 4(6 TO 16dB)!3 TO 13 dB)-.;-!—11r- —111 1b 2 L ____ L-- __ ___ -EL-1-——* ' —1- b]J—i-—-;—-" "i " ii i10 15s20dB)F—— -DIAL SETTING IN dB. —————————20 25••E< = e b - e a-40 log cos(6 a +6j)-40 log cos(e.+e')^ ' cos,(a)25A925dB20(1)(2)(3)(4)(5)032.71°44.93°55.78°65.06°55.78°61 .76°66.54°71 .57°76.28°55.7829.0521 .611 5.7911 .22~ 151032 40 486 IN DEGREES56 64 72 80FIGURE 59. (a] e' error from nominal (10 dB} increments versus dial setting in decibels for rotormisalignment, 0[ equal to 0.100,0.200, and 0.300°.(b) Attenuation in decibel versus 8 in degrees, and angular limits in degrees for attenuation difference of 10 dB.37

a.150o, 100-0.100-0.150(1) 0 TO lOdB(2) 3 TO 13dB(3) 6 TO 16dB(4) 10 TO 20dB(5) 15 TO 25dBFIGURE 60. e' error in decibels versus 6j from 0 to ±0.300° for10-dB increments as follows: 0 to 10 dB, 3 to 13dB, 6 to 16 dB, 10 to 20 dB, and 15 to 25 dB.The change in the e' error in decibels versusO'i is plotted for both the positive and negative valuesof vane misalignment in figure 60. The lower portionof the graph shows the limits of the 10-dB incrementswhich are numbered to correspond with the specificcurve. The error e' in this sample of 10-dB increments is a minimum for 3 to 13 dB and a maximumfor 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, and0.1-dB increments with assumed rotor vane misalignment, 0'/, of 0.100, 0.200 and 0.300°. The plotsof each of the different decibel increments illustratethat the minimum value of the error, e', occurswhen the angular displacement limits of the rotorvane are centered near 45°.The change in the e' error versus 0, is plottedfor the positive values 0' only in figures 62, 64, 66,and 68. The negative values of B'{ would plot as anear mirror image with a slight decrease in error(see fig. 60).The difference in the error, e', does increase athigher values of attenuation. For example, the difference between the positive and negative value of e'for 0; equals 0.300° is about 0.0015 dB at the 10-dBdial setting, and about 0.152 dB at the 50-dB dialsetting.11.2.3. €Q and c' Versus Dial Setting (in Degreesand decibels)In order to illustrate the relationship of theinherent misalignment error, e'r to the resettabilityerror, e'Q , we have plotted their deviations inattenuation from nominal in figure 69. The values of0'n , 0;2 , and 0;3 are shown as 0.100, 0.200, and0.300°, respectively, and 0; equal to ±0.010°. Thethree curves are a plot of the deviations in attenuation from nominal versus dial setting (degrees anddecibels) from 1 to 10 dB. The center lines are thedeviations in attenuation caused by d'r and thelines on each side of the center lines are the limitsof deviation caused by 0^. The curves show thateach subsequent 1-dB increment requires lessangular rotation of the rotor as 0 increases. However,the errors in attenuation caused by 0^ and 0^ aregreater as 0 increases.11.2.4. Minimal Value of e'Since the error, e', is minimal at the mid-region ofthe angular displacement of the rotor, the attenuation increment of 1 dB between the 5 and 6-dB dialsettings of the rotary-vane attenuator was selected forfurther investigation. Let us examine in detail this1-dB nominal value of attenuation with limits of0; equal ±0.010°, and 0'7 equal ±0.100, ±0.200,and ±0.300°. Figure 70 shows the deviations inattenuation versus dial setting (degrees and decibels)for the above conditions, where 0 are the rotor anglescorresponding to 5 and 6-dB dial settings. Thenominal values of 5 and 6 dB are given at the endsegment of each curve, and the vertical segmentsindicate the limits of resettability.38

ATTENUATION IN 6 dB INCREMENTS0.05—— ej = 0.200°0.10 -,—— .ftj = o.inn 0 15 TO 21dB0 TO 6dB~ 3 3 b 3| 12 TCti, 9 TO 15dB| 6 TO 12dB3 TO! 9dB ja 2 b 2'1 I1 ii. ____'__ —— ^I 1I 1____ _ i j ||a ! b ! i i"-" "1•—!8dBr~""^"^~ "e ' =G' =£ b =-40 log cos(e a + ej)cos 0-40 log cos(6 b + ej)l ii if ii ii io ——————————————————————————————————i it iii t j i i ti0 5 10 15 20 25(a)DIAL SETTING IN dB250320= 1 5(1) 0 44.93° 44.93°(2) 32.71° 53.44° 20.73°(3) 44.93° 59.92° 14.99°(4) 53.44° 65.06° 11.62°(5) 59.92° 69.22° 9.30°(6) 65.06° 72.63° 7.57°(7) 69.22° 75.45° 6.23° ^18dB>r !5dBf 21dB9dB(1]3dB24 32 40 486 IN DEGREES56 64FIGURE 61. (a) e' error from nominal (6 dB) increments versus dial setting in decibels for rotor misalignment, 0;, equal to 0.100, 0200, and 0.300°.(b) Attenuation in decibels versus 0 in degrees, and angular limits in degrees for attenuation difference of 6 dB.39

.100(1) 0 TO 6 dB(2) 3 TO 9 dB(3) 6 TO 12 dB(4) 9 TO 15 dB(5) 12 TO 18 dB(6) 15 TO 21 dB(7) 18 TO 24 dBof 50 to 60 dB. Column four gives the deviationsfrom average before applying the rotor vane anglecorrection to the readings. It will be noted thatthese are all positive and increase as the initial dialsetting increases.Note that the deviations were minimal at the midangularregions of the rotary-vane attenuator. Thiswas true regardless of the correction of #/; however,for the most accurate results, the correction mustbe applied.(2)(3)13. Attenuation Measurement Withthe Rotary-Vane Attenuator as theStandard.0250.100 0.200 0.300°IN DEGREESFIGURE 62. € error in decibels versus B{ from 0 to +0.300° for6-dB increments as follows: 0 to 6 dB, 3 to 9 dB, 6to 12 dB, 9 to 15 dB, 12 to 18 dB, 15 to 21 dB, and18 to 24 dB.12. Evaluation of Precision Rotary-Vane Attenuator With WaveguideFixed-Step AttenuatorEvaluation of a precision rotary-vane attenuatorby using a repeatable step attenuator requires astable high-resolution measurement system. Anominal 7-dB waveguide step attenuator and themicrowave attenuation measurement system (seriessubstitution) were used with the optical rotaryvaneattenuator as the standard to obtain determinations of attenuation difference.A summary of these measurements is shown intable 16. The attenuation difference of the stepattenuator was measured by using several differentinitial dial settings from 0 to 60 dB on the rotaryvaneattenuator. Column one lists the initial dialsettings of the standard rotary-vane attenuator foreach determination. The measured values of thewaveguide-step attenuator are recorded in columntwo, with the average value of 7.6544 dB listed atthe bottom of the column. These results were obtained by applying a negative rotor vane anglecorrection, 0}, of 1'18" or 0.0217° (previouslydetermined) to all readings. In column three isgiven the deviation from the average attenuationdifference. The random deviation from the averageis about ±0.005 dB for initial dial settings of 0 to45 dB, and increases to about 0.02 dB for settings13.1. IntroductionIn order to fully utilize the attenuation propertiesof the precision optical-rotary-vane attenuator asthe standard, a dual detection microwave bridgesystem was incorporated in a series substitutionsystem, providing an ingenious technique formicrowave attenuation measurements [22]. Thestability and resolution of this microwave attenuation measurement system is consistent with therotary-vane attenuator standard's resolution of0.00005 dB at 1-dB dial setting. The system maintains this stability and resolution up to a 30-dBmeasurement of attenuation difference or insertionloss.The frequency band covered with this WR90waveguide system is 8.2 to 12.4 GHz, and the attenuation measurement of fixed and/or variable devicesranges from 0 to 70 dB. The following discussion ofthe measurement system is adapted from NBSTech. Note 647.13.2. The Measurement SystemA simplified block diagram of the microwaveattenuation calibration system is shown in figure71. The attenuator under test is located in the samewaveguide section as the standard attenuator,between the standard and the waveguide detector.A change in the attenuator under test is equal tothe change required in the standard attenuator torebalance the bridge. An attenuation measurementis made in the following manner: (1) at the start setstandard and attenuator under test to their respective initial setting and balance the bridge fora null using the level-set attenuator, (2) make thedesired change in the attenuator under test, and(3) rebalance the bridge with the final setting of thestandard attenuator.Figure 72 shows a more detailed block diagramof the system and illustrates the interconnection ofthe waveguide components, standard attenuator,and associated electronic equipment. The basicwaveguide components and instrumentation equipment of the system were developed with commer-40

.CQz-,0.060.05£T 0.04-oCO-Jacac 0.03o2s:0QC

0,04( 1 ) 0 TO 3 dB(2) 2 TC 5 dB(3) 3 TO 6 dB(4) 6 TO 9 d8(5) 9 TO 12 db(6) 12 TO 15 dB{7} 15 TO 18 dB(8) IB TO 21 dB(9) 21 TO 24 dB0.02(3)0.100 0.2000.300°FIGURE 64.e' error in decibels versus 0J from 0 to +0.300° for3-dB increments as follows: 0 to 3 dB, 2 to 5 dB, 3to 6 dB, 6 to 9 dB, 9 to 12 dB, 15 to 18 dB, 18 to 21dB, and 21 to 24 dB.0: IN DEGREEScially available components. In addition, thismeasurement system has the favorable feature thatattenuation measurements are obtained to a highdegree of precision without power stabilization ofthe RF signal source, and employs a single RFsource. The null amplifier was designed at NBS anda detailed schematic diagram is given in NBSTech Note 647.In figure 73, a recording chart of the stability ofmeasurement indicates that for a 30-dB value ofattenuation maximum variations are in the orderof ± 10 /x/3 at the output detection system.13.3. Errors of the Microwave MeasurementSystem13.3.1. Systematic and Random ErrorsWith the application of the correction requiredfor rotor-vane misalignment of the rotary-vaneattenuator standard, and precise matching technique, the estimated systematic error, at the twoinsertion points of the waveguide system, is reduced to about ±0.002 dB for values of attenuationmeasurement from 0 to 30 dB.The measurement of attenuation difference andinsertion loss of five precision interlaboratorytransfer standards gave a preliminary estimate ofthe standard deviation, sigma (cr), equal to 0.0010dB for over one hundred determinations.13.3.2. Insertion Point of the Device Under TestTwo tuned insertion points are required in themicrowave attenuation measurement system (seriessubstitution), one for the working standard (precision rotary-vane attenuator), the other for thedevice under test. Refer to the block diagram infigure 72.42Only the insertion point for the device under testis opened during an insertion loss measurement.Also, this point is located in the system in such away that the least possible movement of waveguidecomponents is required. An opened insertion pointof rectangular waveguide and an inserted fixedrectangular waveguide attenuator under test areshown in figures 74 and 75, respectively. Thisinsertion point can be adapted very easily for useas a coaxial insertion point. In figure 76 the photoshows the insertion point converted to admit coaxial devices by using waveguide J?-plane bends,coax to waveguide adapters, and a double (male)coaxial adapter as added components to the waveguide line. The addition of these componentsdoes not increase greatly the length of the movablesection or hinder the ease of inserting coaxialdevices into the line of the system (fig. 77).The waveguide multistub tuners adjacent toeach side of the insertion point are used to matchthe line to either rectangular waveguide or coaxialinsertion point. The waveguide insertion point canbe tuned by using a portable reflectometer [23], orthe built-in reflectometer that is located in thewaveguide section of the system. Tuning the coaxial insertion point requires the use of a coaxialslotted section.13.3.3. Mismatch Error in Attenuation MeasurementMismatch is a significant source of error thatshould be considered in the calibration of microwave fixed or variable attenuators. In the measurement process of any attenuation device, a largeamount of degrading of the accuracy will dependupon the matching of the insertion point of thecalibration system. The match of the insertion pointbecomes more critical for low values of attenuation[24, 25, 26].

.050 -ATTENUATION IN 1 dB INCREMENTS———— 6J = 0.300° (ROTOR VANE MISALIGNMENT)———— 6J = 0.200°——— ej = 0.100°(39 TO 40dB)x:o.040 -(0 TO.030 -a b.020 -z E b " e a-40 log (cos 6 3 + 0})„. ^ a idB) ^ cos 9 a(2-40 log (cos 6. + 91}cos 6. b9 TO 30dB)_„-«—...010o— —(5 TO 6dB) (9 TO lOdB)I i 1 —————— 11 II 1f— . — 4 p-- — 1iii i— .15 69 10 29 30 39 4(a)DIAL SETTING IN dB18 -12 -6 -40 486 (DEGREES)FIGURE 65. (a) e' error from nominal (1 dB) increments versus dial setting in decibels for rotor misalignment, 6{, 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 I dB.43

.0500.0375(!) 0 TO 1 dB(2) 5 TO 6 dB{3} 9 TO 10 dB(4) 29 TO 30 dB(5) 39 TO 40 dBf .0250.0125 -0.100 0.2006 IN DEGREES0.300°FIGURE 66. e' error in decibels versus 0,' from 0 to +0.300° for1-dB increments as follows: 0 to 1 dB, 5 to 6 dB, 9to 10 dB, 29 to 30 dB, and 39 to 40 dB.In a microwave measurement system, attenuationdifference of a variable or rotary-vane attenuatorcan be measured by using the zero setting as areference angular position, then moving to theattenuation or the vane angle desired to establishthe value of attenuation difference to be measured.For an attenuation difference measurement of avariable attenuator the mismatch error can beexpressed ase r (dB) = 201og 10 -where the frontscripts (i) and (/) pertain to the initialand final values, respectively, and Ft is the inputvoltage reflection coefficient of the variable attenuator that is terminated with a load of reflectioncoefficient, FL. The reflection coefficient of thegenerator is F^, and £22 is the reflection coefficientat the output port when the input port is terminatedwith a nonreflecting load. Engen and Beatty showthat the mismatch error becomes very low whensmall incremental attenuation measurements aremade on a rotary-vane attenuator [12].The mismatch error for insertion loss measurement of a fixed attenuator can be expressed as€/(dB) = 201og 10(i -44where Sn is the attenuator input reflection coefficient when the output is terminated in a nonreflectingload, and Si 2 and £21 are the attenuatortransmission coefficients.In addition to the mismatch error caused by thereflections at the input and output ports of theattenuator, internal reflections can occur betweenthe stator and rotor which must be added to the totalreflection error. Mariner [5] indicates that there areeight main places where reflections can occur,namely, each end of the three vanes, and the twowaveguide transitions. Mariner concludes that usually these internal reflections will not contributesignificantly to the total error.13.4. External LeakageThe effects of RF leakage from microwave components upon the performance of a microwavemeasurement system are often subtle and difficultto identify. Thus leakage from a good standard mustbe kept to an absolute minimum. In the NBSoptical A^-band rotary-vane attenuator [3], the leakage was reduced more than 120 dB below theincident power. This was achieved by the use ofchokes 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 themodified WR15 rotary-vane attenuator.

ATTENUATION IN 0.1 dB INCREMENTS.01000 TO 0.1"3"— ej = 0.300° (ROTOR VANE MISALIGNMENT)— ej = 0.200°—- ej = 0.100°50 TO 50.1.0050,3 2-40 log cos(6 a + 61 )cos e-40 log cos(e b + 6jicos(a)fi i TO * n 10 ° T030 TO 30.1, ,.00000.16.0 6.1 10.0 10.1 30.030.150.0 50.1DIAL SETTING IN dB5040- 302OI—5 201020 30 40 506 IN DEGREES60 70 80 90FIGURE 67. (a) €' error from nominal (0.1 dB) increments versus dial setting in decibels for rotormisalignment, 0;, equal to 0.100, 0.200, and 0.300°.(b) Attenuation in decibels versus 0 in degrees, and angular limits in degrees for attenuation difference of 0.1 dB.45

,010(1 ) 0 TO 0.1 dB(2) 6.0 TO 6.1 dB(3) 10.0 TO 10.1 dB(4) 30.0 TO 30.1 dB(5) 50.0 TO 50.1 dB.004,002FIGURE 68. €' error in decibels versus 0; from 0 to + 0.300° fo0.1-dB increments as follows: 0 to OJ dB, 6.0 to 6.dB, 10 to 10.1 dB, 30 to 30.1 dB, and 50 to 50.1 dl0.100 0.2000.130dB16 24 32 4048 56°1 2 3456789 3 4lOdBDIAL SETTING (DEGREES 8 dB}FIGURE 69. Deviations in attenuation from nominal in decibels versus dial settingin degrees and decibels for Q[ equal 0.100, 0.200, and 0.500°, and 0'0 equal±0.010.46

5dB( C M+) 0.0030-} I'. 00305.9097FIGURE 70. Deviations in attenuation from nominal in decibelsversus dial setting in degrees and decibels (for 5 to6 dB) when 0J equal ± 0.100, ± 0.200, and ± 0.300°,O'o equal ±0.010°.41 I424344145"I I5dB 6dBDIAL SETTING (DEGREES « dB)TABLE 16. Attenuation difference measurements of a waveguidestep attenuator at 10 GHz with initial dial settings of thestandard RVA from 0 to 60 dB.TABLE 15 Deviations from nominal 1-dB increment of attenuation (dial setting changed from 5 to 6 dB) for 0J> = ± 0.010° and0 7 = 0,± 0.100, ±0.200, and±0.300°.0'0= ±0.010°0/6dB 5dB6/5+ ++—— —+ —+ ++ —_— + —+ ++ _— +——+ ++—— —+ —+ ++—— —+ —+ ++—— —+ —+ ++—— —+ —+ 0.300°+ .300°+ .300°+ .300°+ .200°+ .200°+ .200°+ .200°+ .100°+ .100°+ .100°+ .100°.000.000.000.000- .100- .100- .100- .100- .200- .200- .200- .200- .300- .300- .300- .300Actual attenuationincrement1.01081.01621.00481.01021.00731.01271.00131.00671.00391.00930.99791.00331.00031.00570.9943.9997.99681.00220.9908.9962.9933.9987.9873.9927.9898.9952.9838.9892Initialsetting ofstandardin decibels012345678910111213141516171819202224262830323436384045505560Measuredattenuationdifference indecibels withO'i correction7.65907.654S7.65367.65337.65497.65497.65587.65537.65597.65627.65227.65307.65507.65527.65387.65407.65337.65367.65487.65397.65457.65227.65407.65457.65497.65157.65467.64907.65867.65007.65907.65397.63747.63607.63527.6544AverageDeviationfrom average+ 0.0046+ .0004- .0008- .0011+ .0005+ .0005+ .0014+ .0009+ .0015+ .0018- .0022- .0014+ .0006+ .0008- .0006- .0004- .0011- .0008+ .0004- .0005+ .0001- .0022- .0004+ .0001+ .0005- .0029+ .0002- .0054+ .0042+ .0044+ .0046- .0005- .0170- .0180- .0192Deviation fromaverage without6'i correction(all positive)0.0139.0075.0052.0050.0065.0066.0076.0073.0083.0087.0051.0062.0085.0092.0082.0087.0085.0079.0102.0108.0120.0110.0144.0176.0190.0173.0236.0211.0342.0356.0396.0412.0426.0650.08540; = -l f 18" =-0.0217°47

1'MICROWAVESIGNAL,.MODULATOR1 kHzLEVEL- SETSTANDARDATTENUATOR ' ATTENUATORiREF.,."INSERTIONPOINT" — Sl/jJ.ATTENUATORUNDER TESTCRYSTAL . NULL CRYSTALDETECTOR DETECTOR DETECTORFIGURE 71.Block diagram of microwave attenuation measurement system.ISOLCRYSTALDETECTORNULLAMPLIFIER *CRYSTftL ^ | ro .DETECTOR ^ | ljt)L ATORMICROWAVE 1 Fnurc I !SIGNAL -*—— Jn Y AUDIOSOURCE ' ' OSCILLATORVVLEVEL-SETATTENUATOR•MJLAIUK 'SQLATORMODULATOR DRIV£R ISOLATOR

12 MINUTESFIGURE 73. A recording showing the system stability at a .W-dB measurement lei>el.FlGl'RK 74. Photo of the open rectangular waveguide at theinsertion point for devices under test.FlGL'RE 75. Photo of a fixed waveguide attenuator under testbeing inserted into the rectangular waveguide atthe insertion point.49

Fl(.l KK 76. Photo of the rectangular waveguide with adapter:to admit coaxial devices at the insertion point.attenuator can be improved an order of magnitudeby applying correction of vane alignment equal tothe average vane-angle error. The Type A error isthe larger error caused by misaligned stators. Toreduce the Type A error, the zero or index can becorrected by one-half the angle between the misaligned stators. The deviations from nominal settingthen become the Type B error provided geareccentricity is not present. However, if the zero orindex is not exactly coincident with the averageposition of the stators, the Type A error can be thepredominant factor in the deviations from nominal.The compact rotary-vane attenuator is a usefuldevice where large dynamic attenuation range isnot required or where length of the device is at apremium. The modified law for rotary-vane attenuators gives an accurate result of the attenuationdifference that is obtainable with the device.The precision optical rotary-vane attenuator is avery excellent working standard for attenuationdifference employed with the microwave attenuationmeasurement system (series substitution). The useof the precision optical attenuator with the aboveRF system yielded the resolution and stability thatprovided a very accurate international intercomparisonof attenuation difference; the spread between the mean values of five different interlaboratorystandards was about 0.001 dB.Fl

[7] Larson, Wilbur, Analysis of rotationally misaligned statorsin the rotary-vane attenuator, IEEE Trans. Instr. andMeas. IM-16, No. 3 (Sept. 1967).[8] James, Allan V., A high-accuracy microwave attenuationstandard for use in primary calibration laboratories, IRETrans. on Instrumentation I-11,285-290 (Dec. 1962).[9] Otoshi, Tom Y., and Stelzried, Charles T., A precisioncompact rotary-vane attenuator, IEEE Trans. on Microwave Theory and Tech. MTT-19, No. 11, 843-854(Nov. 1971).[10] Foote, W. J., and Hunter, R. D., Improved gearing for rotaryvaneattenuators, Rev. Sci. Inst. 43, 1042-1043 (July1972).[11] Beatty, R. W., Microwave attenuation measurements andstandards, Nat. Bur. Stand. (U.S.), Monogr. 97, 49 pages(Apr. 1967).[12] Engen, G. F., and Beatty, R. W., Microwave attenuationmeasurements with accuracies from 0.0001 to 0.06 decibelover 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 subcarriertechnique of measuring microwave attenuation, Proc.IEE (London) 109, Pt. B, Suppl. No. 23, 783-786 (May1962).[14] Nemoto, T., Beatty, R. W., and Fentress, G. H., A twochannel off-null technique for measuring small changes inattenuation, 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 NBSelectronic calibration center, Proc. IEE (London), 109,Pt. B. Suppl. 23, 644-650 (May 1962).[17] Larson, W., Table of attenuation error as a function of vaneangleerror 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 waveguiderotary-vane attenuator, IRE International ConventionRecord, Pt. 3, pp. 213-219 (1962).[19] Larson, W., Table of attenuation as a function of vane anglefor rotary-vane attenuators (A^ — 40 logjo cos 9], 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 (AmericanSociety of Mechanical Engineers, New York, N.Y.),Paper No. 59A-21 (Dec. 1959).[22] Larson, W., and Campbell, Eugene, Microwave attenuationmeasurement' 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 reflectometertechnique of VSWR measurement, J. Res. NBS,65C, No. 4, 217-223 (Oct.-Dec. 1961).[24] Beatty, R. W., Mismatch errors in the measurement ofultrahigh-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 reflectionsfrom rotary-vane attenuator (correspondence), IEEETrans. on Microwave Theory and Tech., pp. 402—403(July 1969).[26] Holm, J. D., Johnson, D. L., and Champlin, K. S., Reflectionsfrom rotary-vane precision attenuator, (correspondence)IEEE Trans. on Microwave Theory and Tech., pp. 123-124(Feb. 1967).16. Appendix A. Definitions andTerms~ Total composite error.r' — Total angular displacement (/3' -h y f ) ndegrees.8 = Angle of drive gear rotation in radians.8' = Angle of drive gear rotation in degrees.6 = Angular rotation of center section vane(rotor) relative to the stationary end sectionvane stator in degrees.0'= Misalignment angle of center vane (difference between the indicated vane angle andthe true vane angle) in degrees.e = Error in attenuation caused by incorrectvane rotation in decibels.6'e = Estimated average vane-angle error indegrees.0p> — Angular displacement of the vane causedby backlash error in degrees.0y> = Angular displacement of the vane caused byindexing error in degrees.0'T ' = Angular displacement of the vane caused bytotal angular error in degrees.R = Pitch radius in inches.D = Pitch diameter in inches, = Basic pressure angle in degrees.a— Angular difference between the zero pointof the drive gear eccentricity and the zeropoint of the scale on the dial in degrees.ty= Error in attenuation caused by the indexingerror in decibels.€a = The error, in decibels, for Type A misalignment.e& = The error, in decibels, for Type B misalignment.€ —The error from nominal in decibels, € rb minus€r = Transmission error due to insufficient attenuation in the rotor.

CntoFIGURES 78-87. Machine drawings for optical rotary-vane attenuator.

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MICROWAVE ABSORBING MATERIAL-STATORSPIROID GEARFIGURE 88. Exploded view of a rotary-vane attenuator utilizing a Spiroid gear setin WRI5 waveguide.62U.S. GOVERNMENT PRINTING OFFICE : 1975 OL-573-735

NBS-114A (REV. 7-73)U.S. DEPT, OF COMM.BIBLIOGRAPHIC DATASHEET1. PUBLICATION OR REPORT NO.NBS-MN 1442. Gov't AccessionNo.4. TITLE AND SUBTITLEThe Rotary-Vane Attenuator as an Interlaboratory Standard3. Recipient's Accession No.5. Publication DateOctober 19756. Performing Organization Code7. AUTHOR(S)Wilbur Larson9. PERFORMING ORGANIZATION NAME AND ADDRESSNATIONAL BUREAU OF STANDARDSDEPARTMENT OF COMMERCEWASHINGTON, D.C. 2023412. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)Same as Item 9.8. Performing Organ. Report No.10. Project/Task/Work Unit No.276446011. Contract/Grant No.13. Type of Report & PeriodCoveredFinal14. Sponsoring Agency Code15. SUPPLEMENTARY NOTESLibrary of Congress Catalogue Card Number: 75-61909916. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significantbibliography or literature survey, mention it here.)This paper presents a comprehensive report on the measurement and the use of therotary-vane attenuator as an interlaboratory standard.Methods of attenuation measurement developed at NBS are used to supply data for theevaluation of the deviations from theoretical cos 2 law due to rotor misalignment, geareccentricity, resettability, resolution, and insufficient maximum attenuation.A precision rotary-vane attenuator with an optical readout capable of 1 second of arcangular resolution has an effective attenuation resolution of 0.00005 dB at a 3-dB dialsetting, and 0.0005 dB at a 30-dB dial setting. This type of precision attenuator isan 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 propername; separated by semicolons)Attenuation* interlaboratory standard; measurement; rotary-vane attenuator.18. AVAILABILITY [^ Unlimited| ' For Official Distribution. Do Not Release to NTIS| -XOrder From Sup. of Doc., U.S. Government Printing OfficeWashington, D.C. 20402, SD Cat. No. C13« 44:144| J Order From National Technical Information Service (NTIS)Springfield, Virginia 2215119. SECURITY CLASS(THIS REPORT)UNCLASSIFIED20. SECURITY CLASS(THIS PAGE)UNCLASSIFIED21. NO. OF PAGES7022, Price$5.05USCOMM-DC 29042-P74