Relative Voltmeter for VHFUHF Signal Generator Attenuator Calibration-J8e

22 IRE TRANSACTIONS ON INSTRUMENTATION March

0.4 where y, and 'Y2 are the values of y needed to give quasi-

0.2- 2Lexp(-X) X(4-erfX) peak voltages equal to 0.74o and o- respectively. Thus0.2- ffi1r 2 / with such direct relations, the variable resistance might

be calibrated to indicate the values of these coefficientso- J 1L directly and individually.

Q 30.2 3CONCLUSIONS

References in the past to the quasi-peak detector have

04 viewed the device as a weighted circuit chosen for itsability to reflect the subjective effect of certain kinds of

f (X) interference on specific communication systems. Un-0°2- certainty as to what electrical quantities are being- N measured has led to differing views on the merit of the

o 1 1 1.2device.._0.3 This work was aimed at establishing more firmly the

connection between the reading of such a device withthe probability density function being measured; thatis, showing its objective side. On the assumption that ahalf-wave linear diode can be realized, it was shown that,

0.8- > f141X) by some variation in the circuit used in the past, the pdfcan be determined from its readings.

ACKNOWLEDGMENT

The author wishes to thank Professor F. Haber forfruitful discussions and advice, and Dr. R. M. Showers

Fig. 3-Components of -jx vs normalized voltage, x. who suggested the work.

Relative Voltmeter for VHF/UHF Signal GeneratorAttenuator Calibration *

B. 0. WEINSCHELt, G. U. SORGORt, AND A. L. HEDRICHt

INTRODUCTION other than the calibration of signal generators. It is

flF! HE standard signal generator has become one of basically an insertion loss test set and, as such, can bethe most useful tools in the modern electronics used to measure insertion loss over a very large rangelaboratory. These generators usually consist of a with high accuracies.

stable generator, a level monitoring device and an at- A frequency range of from 100 to 1000 mc is coveredtenuator. The level into the attenuator is set, and then by the instrument as it now exists but its upper fre-the attenuator is relied on to reduce this to the required quency limit is restricted only by the availability of thelevel for the measurement being made. proper local oscillators and mixer assemblies. The volt-The need for a means of checking and calibrating the age range (in a 50 ohm system) of from 20 my to 20 pv

output level of such generators has long been felt, and (-20 dbm to -82 dbm) is covered with an accuracy ofthe equipmenlt described in this paper was developed to 0.02 db/1O db. This range can be extended by 6 db onfill this need. The instrument has, of course, many uses both the upper and lower ends with an accuracy of 0.1

db/10 db in the extended portions. It should be pointedout here that this instrument is not an absolute volt-

* Manuscript received by the PGI, June 18, 1958. Presented at meter, but rather is a relative voltmeter and indicatesthe IRE-URSI Spring Meeting, Washington, D.C.; April 24-26,'1958. This work was supported by the Air Force under Contract No. voltage ratios-thus, the expression of accuracies inAF .33(600)-25238 with Wright Air Development Center, W\right- terms of decibels. The reproducibility of a measurementPatterson Air Force Base, Dayton, Ohio.

t XVeinschel Engineering, Kensington, Md. iS in the order of 0.01 db over the entire range.

Authorized licensed use limited to: Imperial College London. Downloaded on June 07,2010 at 19:39:53 UTC from IEEE Xplore. Restrictions apply.

1959 Weinschel, et al.: VHF/UHF Signal Generator Attenuator Calibration 25

PHASE S01JSiTIVE - iP00 CP5 MULL^ s IQDlCA'TOP FOP FIRQUEAECY C0MPARPlM

l~~~~~PHASE \ / i 1EMSITIVITY : 10 (-c/ I DlVSlONI. ~~~~~~~~~~~~DISCPUMISJATOR _y-

EQUIPMEMT } . ~~~~~~~~~~TUS)ED.\,00 CPSUNDE.R TEST 'COMPAWA50t LNlTER AMPLIFIER, *flJ spO CPS

l C00HF-AD AMI PLIFIF-T 0E.TOCT0Il l~~~~~~~~~~~~M) |c Mr|3 AGEScu |v PmSTIIY

$IC-JSAL 0._.l BDAIFFEREN CE/ao

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mm IOTG-I I ICTOq

MAETER 4100oDBL -A XG} . . 2 DIRECT IMDEXO1i (A V0 DB STEPS 1

ISTUBL 0E.B 0FFE0I CALIBRATLO N .01 OB DFVV5I0TQETIEAPLFETOaS=1

PAD TO CEADE)TEST EQUIPMWtT OCT EPQDEJUTAX 1TO ON RE. TEST FREK,

MIEXER AN LOCAL OSCALLATO ATO BEDOUBLE DlC lI D' LECTMD FOR PROER R.F. FRQ.

Fig. 1-Blocki diagram.

The basic idea of the instrument was encountered in of this modulation, the sense of the inequality can beEngland during the survey phase of the development determined-hence, the use of phase sensitive detectors.

[1], [2]. The frequency discriminator and its phase sensitivedetector are provided to insure that the mixer output

DESCRIPTION OF THE SYSTEM is adjusted to exactly the frequency of the standard 30-A block diagramn of the system is shown in Fig. 1. mc source so that no 1000-c modulation can be intro-

The signal from the generator being calibrated is con- duced due to a slope in the IF amplifier characteristic.verted to 30 mc in a linear mixer. By a linear mixer, we A photograph of the complete equipment is shown inmean one in which the amplitude of the output voltage Fig. 2.at the intermediate frequency is linearly related to the It will be noted that the IF amplifier and everythingamplitude of the input signal. The output of the piston following it are not critical as regards linearity and sta-attenuator, which is fed from a standard 30 mc source, bility; they serve the purpose of a null detector. Theis equated to the muixer oultput. The amount of change mixer and piston attenuator, however, have very rigidin attenuation of the piston attenuator required to requirements if high accuracies are to be obtained. Be-maintain this equality gives the change in signal gener- cause of their critical nature, these two elements are toator output. The IF amplifier, detector, 1000-c tuned be considered in detail.amplifier, discriminator, and synchronous detectors areprovided to indicate equality of the voltages. RF MIXER

This is accomplished by modulating both the local It is necessary that the mixer be used only over thatoscillator and the standard 30-inc source at a 1000-cps portion of its characteristic where the intermediate-rate. The modulation is done with square waves in such frequency output amplitude is linearly related to thea manner that the oscillators are switched completely signal input amplitude.on and off in counterphase so that they are on during The maximum input signal that can be handled byalternate half cycles of the modulating signal. Thus the the mnixer without going outside the linear range is de-IF amplifier and the following circuits see first one and termined by the local oscillator level, which in turn isthen the other of the signals being compared. If they determined by crystal characteristics, noise, etc. Theare unequal, the signal in the IF amplifier appears to be circuit was first analyzed theoretically, and then themodulated at a 1000-c rate and by observing the phase theory was verified experimentally.



A( W5-o)t - ore

From this point on only a1, the coefficient of the funda

-r~~ ~ ~~~~w

Fig. 2-IF substitultionl attenFuatiogrtest set. j-O

If two high-frequency signlals are comllbinledaby simpl-eal =- o +C.2 -r2 Eos coswot2cw,tdaddition, the resultant will be another high-frequenlcy aiF Jis ±oon - a, the cos td( fud)signal that will, on first inspection, appear to be ampli- Es(1 i t2)s/2 rl t

tude modulated at a frequency equal to the difference al = -____b- Jo[1 ± A coswrti2 cosiretd(.rt) (2)in frequency between the two original signals. On closer hinspection, however, it is seen that the modulation en- 2rvelope contains harmonics of this difference frequency, .1 =-

and that these harmoniics become an appreciable part of 1 + r2the envelope as the ratio of the amplitudes of the two Expand (1 +-i COS Crt)112 in a binomial series.signals approaches unity. T.et:A constant large-amplitude signal is mixed with a

smaller-amplitude variable signal and the resultant sig- A cos sort = x2 and Wrt = 6

nal is rectified in a linear detector. It is desired to deter- X2 .4 1 . 3x6 1 3 .5x8mine the variation of the fundamental component of the (1 + x2)1/2 1 ±- - - +- - --- *difference frequency as a function of the ratio of the 2 2.4 2 4 6 2 4 6 8amplitudes of the two mixed signals. A A 2 A 3

Fig. 3 shows the vector diagram of the three voltages: (1+ A cos0)= 1 + - cos 0 - cos2 0 + cos32 86the local oscillator signal Eo, with an angular frequency, Eo(1 + 1!2wc0o; the signal voltage E., with an angular frequency, a, = -f (I + A cos 0)1/2 cos OdOco,; and the resultant e,, with an angular frequency, wr. T OThe instantaneous amplitude of the envelope is equal Eo(t + r9)1/2 { * r 1 27tto the magnitude of the vector E, and has a fundamental a, = --- sin 0 +- +-sin 20anigular frequency: 7r 2 L2 4 jo

W, W. wo- = - sin O(cos2- + 2)From the law of cosines, the instantaneous envelope 8 3 o

amplitude can be written as: Al3 3f 3 1112.

+30

+ sin 0 + cs' 0 sin 0] ..e, = [Eo02 + E2 - 2E0E8 cos Wrt]l2. (1) 16 8 16 4 los

Expanding (1) in a Fourier series: It is obvious, at this point, that terms containing evene, = ao + al cos w,t + a2 cos 2w,t + * powers of A go to zero wlheni the limits are put in.


1959 Weinschel, et al.: VHFIUHF Signal Generator Attenuator Calibration 25

2Es 1 3A2 7 15A4 33- 105AIa, = __ + ~~ + + +p AUD/t

(1 + r2) / 2 64 265 24 1024-384 GENERATfA i IN 2152E,

L

a, = l (0.5 + .04687A2 + .0171A4 + .0088A6 ._ GP

r(1+ r) TT E,','UA TO A.T gTEMATOR ct e ,* t2 e2+ .0054AI + .0036A 0 + ). I * AT-E_/URTOR

al is computed as a function of r with constant Eo inTable I. AN 7L 47 -ALAT/A/ '

TABLE I_ EXCO 1 s~~~~~~~~~~~~~~~~~~~~~~~~~~A-5 |

r Yl (5so0 cns5)

0.05 0.04998 Fig. 4-Block diagram of the setup used for mixer0.1 0.09987 linearity measurements.0.15 0.149570.2 0.198890.25 0.24801 coupling of 20:1. The intermediate-frequency load im-0.3 0.29656

pedance is 2000 ohms, as represented by the input to the0.35 0.343940.4 0.39171 Weinschel Engineering Model BA-5 Attenuation Cali-

brator, which is used as an intermediate-frequency

If the system were perfectly linear the amplitude of amplifier. The mixer input of about 1000 ohms, inI parallel with the local oscillator impedance of 5000 ohms

the fundamental would be directly proportional to r. and the 2000 ohms across the output of the signal at-The ratio of r to a1, therefore, gives a measure of the

' . g . . . . ~~tenuators, presents a load of approximately 600 ohms todeparture from linearity. These ratios, given in decibels these attenuators. Since the impedance of differentand indicated as AX db, are shown in Table II. crystals varies quite a bit, at least 20 db of attenuation

is always left in the signal attenuators to mask theTABLE II effects of any mismatch that niight exist.

r A db =20 log r/al The local oscillator and signal frequencies were 5500

0.05 0--035 and 4500 cps respectively with a resultant intermediate0.1 0.0113 frequency of 1000 c. The intermediate-frequency ampli-0.15 0.0252 fier and indicator is a Weinschel Engineering Co. BA-5

0.25 0.0442 Attenuation Calibrator which consists of a precision0.3 0.1002 audio attenuator followed by a high-gain-tuned 1000-0.35 0. 15150.43 0.1822 cps amplifier and indicator. The local oscillator voltage

was adjusted to 1 volt across the crystal with the signallevel reduced to a negligible value. The signal attenuator

The above data are plotted in Fig. 5. was adjusted to apply a signal voltage of about 3 Av toThe relationship between the intermediate-frequency the mixer which is well within its linear range. The gain

output voltage and signal input voltage is independent and attenuator setting of the BA-5 is adjusted to pro-of frequency (local oscillator frequency, signal frequency duce a full scale indication on the BA-5 output meter.and intermediate frequency), as long as the crystal char- The signal level is increased a known amount by re-acteristics do not change with frequency [4]. This al- moving attenuation from the signal source, and the at-lows the experimental verification of the foregoing tenuation in the BA-5 is increased to return the indi-theory to be made at audio frequencies where more ac- cator to full scale. The difference between the two at-curate measurements are possible. tenuator settings is the nonlinearity. The theoretical

and experimental data are compared in Fig. 5. TheExperimental Veritfication of Miixer Linearity at Audio agreement is quite close.FrequenciesThe crystal should be provided with a low resistance Lev2el of Mixer

return circuit to prevent a large back bias being built In view of the above results the local oscillator levelup. This resistance should be kept below 200 ohms, and was adjusted to about 0.2 volts rms across the crystal,at the same time a high-input impedance at the local which is equivalent to 1.2 milliwatts into the crystal.Oscillator and signal frequencies should be maintained. This level was monitored by measuring the rectifiedThe output filter should pass only the intermediate fre- crystal current. 1.2 milliwatts corresponds to about 0.6quency on to the circuits following the mixer. The ar- ma dc.rangement used to make these measurements is shown Using this local oscillator level, one can estimate thein Fig. 4. The oscillator is decoupled from the mixer by deviation from linearity as a function of RF signal level.mneans of the 5000)-ohm resistor which results in a de- A SO-mv signal should produce a deviation of .07



-26 ia t~~~-~- -~-A -rEA5URED VALIE-ACTUAL VALU

1N34 j ____________ ~~~~PlEAS.UREDE1 I_Vl.v3 (I500 /ps)

.18 _ /.MAX E, -46 Vr" (500cp5)

.161F /000 Cps / V-rEORETICAL

.12

.08 .7-

.06

~~~~~7IP ~~~~~~~~~~~~~~~ELECTRICAI-D_ ------/ -1AGNET1C

o.d a. 0.3 0.- 0 Fig. 6-Magnetic and electric field lines of the TE11 modein a circular waveguide.

Fig. 5 Measured deviation from the mixer linearityvs the ratio Esig/Elo.

db. Fig. 17, which shows the overall performance of thevoltmeter, indicates that at this level the measurementerror due to all causes is 0.1 db. Clearly this is prin-cipally due to mixer nonlinearity.

THE PISTON ATTENUATOR

If an electromagnetic wave of frequency lower thanthe lowest cutoff-frequency of a waveguide is launchedin such a guide, it is attenuated exponentially along thelength of the guide. A cylindrical tubing of the properdimensions can thus be used as an attenuator by launch-ing a wave at one end and receiving it at a point downthe tube depending on the amount of attenuation de-sired. The major advantage of this type of attenuatoris the fact that the attenuation can be accurately cal-culated from the frequency and physical dimensions ofthe waveguide.

If the foregoing advantages are to be realized to their Fig. 7-Arrangement of sending (and receiving) coil infullest extent, it is very important that only one mode circular waveguide.be propagated in the waveguide. If more than one modeis propagated, the exponential law of attenuation along Capacitive Antennasthe guide will no longer hold because, although all A piston attenuator using this type of antenna is de-modes may be attenuated exponentially, they are at- scribed by Meinke [8], and employs the TMo1 mode.tenuated at different rates. Under these conditions, one There is a major disadvantage in using this mode, sincemode may be important at one point and another im- it has a larger attenuation constant than the TE11 mode.portant at another point in the guide. If only one mode If there is any TE11 mode present, it will be attenuatedis propagated and the physical dimensions and electrical less than will the TMo1 mode, causing an appreciableproperties of the waveguide are alike at all points, the error at high attenuations. Any asymmetry will pro-attenuation law will be exponential. duce this undesired mode and it is not advisable to use

It is a common misconception that the exponential this type of antenna if large accurate attenuations arelaw of attenuation in such an attenuator does not hold required.for very small separations of the sending and receiving IdcieAnenantennas. The problem here is entirely one of mode ngtvAteapurity. If only one mode is propagated, the exponential In this case, two coils are used-one as the transmit-attenuation law holds down to the smallest measurable ting antenna and the other as the receiving antenna. Ifseparation of the antennas. It is, therefore, very im- the attenuation constants of all possible modes in a cir-portant to provide the proper types of antennas and cular waveguide are compared, it will be seen that themode filters to insure that this condition will be met. TE11 mode has the smallest. It is, therefore, the bestThe antennas can be either one of two types: capacitive mode to be used if large, accurate attenuations are re-or inductive, and they are usually made similar. quired. A cross section of a circular waveguide showing



Fig. 8-Simplified representation of a piston attenuatorusing the TEI, ! lode.

Fig. 10-Piston attenuator and indicator assembly of L.F.substitution attenuation test set.

probable error of the calculation and( not a machiniingtolerance.

IS STRIP3 1 DEEP From (8) in the Appendix, it can be seen that thea attenuationi varies approximately as 1/r from which can

Fig. 9-Faraday screen for suppressing the TMo1 mode. be calculated the allowable machininig tolerance. If themaximum error is not to exceed 0.02 db for a range of

the an Hlnesof aTE1 moe isshon inFig 6.100 db or 0.0002 db for 10 db, the diameter must be heldThis mode can be excited with a coil having its axis to wh ±0.00016 ice thefial adjust of hole

to within + 0.00016 inches. The finial adjustment of holealong a diameter of the guide and having circular sym- d

etry. This is shown in Fig. 7. To gain a physical pc- the diameter were made usinlg an air pressure bridgeture of the way in which this mode can be excited, it isnecessary only to picture the magiietic field around the type gauge and a standard with ai accuracy of 0.00001

.. . . l~~~~~~~~~nch.The average deviation from the nominal valuecoil in free space and then place a circular guide around . .

the coil, chaIgingthemanover the critical five-inch portion of the hole wasthe coil, changing the magnetiC lines so that the elec- 0.000017 inch. The deviation from the expected attenua-trical field lines terminate perpendicularly on the guide 0.02 dbove thee d i-

surface and are orthogonal to the magnetic field lines. tio is, therefore,Fig. 8 shows schematically a sending and receiving

coil as used in such an arrangement. The most trouble- The Associated Circuitssome of the undesired modes is the TMo1 mode which The critical problem in the constructioni of a precisioncorresponds to a capacitive coupling between the two piston attenuator is encountered in the design of thecoils. A Faraday Screen acts as an effective suppressor sending and receiving circuits. Close physical tolerancesfor this irmode and is shown in Fig. 9. It is effective in anid the use of a good mode filter solve most of the otherattenuating the TMol mode by 60 db while at the same problems.time it attenuates the desired TE,, by only 0.06 db The design of these circuits can be approached in two[10 ]. ways, viz., through the use of waveguide theory or

Circttlar Waveguide Dimensions through the use of low-frequency coupled circuit analv-

To facilitate the design of the indicatinig mechanism, sis. It is assumed throughout the following that the

the attenuator is designed to have ani attenuation of piston attenuator is to be tused at only one frequency,

exactly 20 db per inch. With such a design, it is possible ' *mc.

Resonant sending and receiving circuits are used toto use readily available dial gauges and gauge blocks as achieve a minimum loss in voltage between input andattenuation indicators. This mechanism can be seen in r

o

Fig. ~10 Prcso.ag lcs r sdt ne h output of the attenuator. Barlow and Cullen [12]j*F*g..0. Precision gauge blocks are used to index thetreated the problem of the linearity of a piston attenu-10-db steps and a dial indicator interpolates between ator in an excellent iner, using waveguide theory10-db steps to a precision of 0.01 db.10-dbstepsto

.a precisionof,.0.01 dand assuming untuned circuits operating at high fre-

To obtain a high degree of structural stability adomnresistance to corrosion, stainless steel #316 was selected quencs to minimize nonli uecondi-as the waveguide material. A thin wall tubing of this generator and load which have impedaced twee amaterial was pressed into a heavy brass block producing generatoan ad wihavim pedance tha area thermal coefficient of expansion equal to that of the purelyresistve andeu in magniudtot hbrass. The Appendix covers the details of the calcula- teritiwaeimpdancenof the attenuator.tion of the physical dimensions of the waveguide. The Undethee coitis te andiameter of the attenuator cylinder is calculated to be1.59561±0.00002 inches. The 20 micro-inches is the A = al - ln 2 + In [1 + e-al]nepers (3)



EI~~~~~~~ #~~~~C2 ~

(a) _i _

(W#Ij7

Fig. 12-Equivalent circuit of piston attenuator withassociated circuits.

7

} coils. To determine the decay of the magnetic field(b) strength, waveguide theory is used. The attenuation of

Fig. 1- Equivalenit circuit of piston attenuator. the TE1, mode merely expresses the decay of the fieldstrength along the tube and, therefore, the decrease in

where the coupling factor, k, as the coils are moved apart. Thecoupling factor k, is, therefore, proportional to e51

A = total attenuation in nepers where a is the attenuation constant for the TE11 mode.

a = attenuation constant appropriate for the guide Input Circuitand mode under consideration

*=distance between coils. Fig. 12 shows the equivalent circuit of the piston at-tenuator with the associated input and output circuits.

If the maximum allowed nonlinearity is 0.02 db, the The primary circuit is a series resonant circuit with aminimum attenuation must be 24.4 db. large L/C ratio. This arrangement results in a highThe matched conditions required would be very dif- magnetic field strength. The inductance was made as

ficult to achieve in this application, since the character- large as practical and still have sufficient capacity foristic wave impedance for the TE11 mode in this wave- good stability. The values are L1= 1.35 4h and C1= 21guide is approximately 2.61 ohms, which is much too ,uf. The Q of the circuit is approximately 100, giving asmall to be conveniently handled. resonant impedance at 30 mc of about 2.5 ohms. TheA much more fertile approach in this case is that of effective Q, of course, must be considered with the gen-

considering the entire piston attenuator as a tuned erator connected. The generator impedance will deter-bandfilter with mutual inductive coupling. The equiva- mine the primary current and bandwidth. If it is toolent circuit is shown in Fig. 11. The equivalent circuit low, the bandwidth will be narrow and stability require-of Fig. lib is developed from lla in a straightforward ments become severe and if it is too large, no advantagemanner, if it is assumed that both coils are identical and is gained by series tuning. There are other considerationsthat no nonlinearity exists. to be discussed later. The optimum value is approxi-A simple analysis of the circuit of Fig. 11 shows that mately 25 ohms resulting in an effective Q of 10 and a

the ratio of voltage across the receiving coil to the volt- bandwidth of 3 mc.age across the sending coil is proportional to thecoupling, k, for small values of k, which corresponds to Output Circutloose coupling. The coupling factor, k, can be expressed The minimum insertion loss for a given nonlinearityas the ratio of the magnetic field strength at the receiv- is determined for parallel resonance and for series res-ing coil to the magnetic field strength at the sending onance of the output circuit.coil. This ratio depends on a number of factors amongwhich are the spacing between coils and the environ-ment. Included in the latter factor is the presence of the This is shown in Fig. 12. Calculating the magnitudetube making up the waveguide which surrounds both of E2/E0 as a function of the coupling factor, k, yields:

Rk

lE2 47Ri2 ± (wL)2 - ' (2wL --1)

-1E= R,2R-(w,L)2 +-L12+(,)/1+ k22 ( +k



Fs/o-~~v'3H IIIII I I 11 SW 4F R1 'r -- -- e'- i-- C

I

O aas co2 cto s i C'ejo" cv OACR C L-b C

Co,A{N0S JO L

IA~~~~~~" -

Fig. 13-Deviatwion from linearity vs coupling factor r - -- 93 '5OJK with Cl as parameter. --- /v-

or I5L S c >< 0t

RI c

Eo Vl1+a$3,2k2 +b/32k4 II'2Stt>where: _ Il'_C l__

1~~ ~~~ /'1

13 [R,2 + (tL)9-- - 1)] Fig.15 ,/LTreLz5Cl \ c5C1/ J Fig. 15-~~~~~~Complete schematic diagram of pisto

attenuator circuit.L

a =R%R - (tL)2-__

C~~~~~~~~~~C m

resonance of the output circuit.b = R2 + (teL)2. It is interesting to rewrite (6) as follows. First take the

It is clear that for very small values of k, the ratio logarithm of both sides:|E2/E0I is very nearly proportional to k and the de- Io w\ / (o)nominator of (4) and (5) contain] the deviation from this In - - - lnk-ln(l +l+In(l1+ -- kO)|.linear relationship. Fig. 13 shows the deviation from lnai \Rsc\R RRi /lInearity with Ci as a parameter. The factor a in (5) can Letbe made positive, zero or negative by proper selectionof R, Ri, L and C1. R, Ri and L have already been deter- k = e-atrined and C is, therefore, chosen as the parameter. IEoIn Fig. 13, Co is the capacity required to tune the in- A = in_

put circuit to 30 n-ic with k =0. As can be seen from thefigure, an imnprovement in linearity is obtained by / woL\ 7 (teL)2 ~\makinlg Cl slightly greater than Co. If a mlaximum devia- A =te- In t R)J + ln t1 + RR-e-2 (7)tion of 0.02 db is to be allowed, C should be made about1.119G0. The coupling, k, can then be increased to which bears a striking resemblance to (3).greater than 0.1 without exceeding the maximum al-lowed deviation. Complete Piston Attenuator Circuit

Case Il-Series Resonance This is shown in Fig. 15. The parallel resonlant circuit

Fi.1* hw h icit h ai 2E~aa func described in Case I above is used in the output circuit

Flg.~~~ ~ ~ ~ ~~~~~~514-shwhLc'.Th ai2E a uc

t roof k* because of the increase in linearity for large values of k.C2 is adjusted to resonate L2 to 30 mc with k=0. R1 is

k-L the IF amplifier input impedance and is 800 ohms re-

I E2 | R, (6) ~~~sistive. R2 is the mixer output impedance and is aboutlEol- (teL)2 ()100 ohms with the proper local oscillator level. R3 and

1 R4 are selected to fulfill two conditions: 1) to furnish aRR, 400-ohm load for the mixer for only then is the IF signal

For small values of k, |E2/E0| is still approximately fairly independent of the local oscillator level and 2) toproportional to k, but it is not possible to minimize the obtain maximum voltage at the amplifier input as adeviation from linearity as it was in the case of parallel function of k. The optimum solution would be R3=0



so II l1MMUENCY 480 MWAWCACY?C r.1

o&bmn V1,W

0V 0W4E'b -4 d

O4D 90~~~~~~-o4h-

30-o

xK 7 - twa7 to mit- .Itput with Fig. 17-Deviation of measured attenuation of 10 db attenuator20 20 -Lampling betwan from nominal value vs signal level at input of attenuator.

A bt Cl twad to mxlu output with

_~~~~~~~~~~~57t deopvso txwn/ ~~~~~~bothGonga.

tlzU o t -egbetvm d Ibvoltage with the coils one inch apart and represents the- 0 - - - - - -optimum condition. Curve b represents results obtained

- X- - t- - t t 1 with the sending circuit tuned with the coils as far apart10--F W T l l l l l las possible, and curve c with the coils as close together

as possible.7_ EASURED CURVES OF ATTENIUATION

V5. DI3PLACMENT OF EXPERIMENTALPI/TON ATTENUATOR WITH C,CS ACCURACYPARAMIETER

0 --L_ILJLLLL.L Overall accuracy of the instrument was evaluatedo .I 6 1 , 2/ 2+ 27 30

I -L I

using a well calibrated attenuator with a VSWR of 1.011.5PLACEMENr and an attenuation of 10.02 db in a 50-ohm system at

Fig. 16-Measured curves of attenuation vs displacement of 480 mc. A large number of measurements were madeexperimental piston attenuator with C1 as parameter. at different power levels fronm which the accuracy of the

instrument can be evaluated. The results are shown in

and R4=800 ohms. Variations in mixer output imped- Fig. 17. They can be summarized as follows:ance, however, make it necessary to maintain a resist- 40 mV to 20 mV (-14 dbm to -20 dbm) 0.1 db/10 dbance between th.e piston attenuator and the mixer of at 20 mV to 20 AV (-20 dbm to -82 dbm) 0.02 db/10 dbleast 350 ohms. With the resistance values given, the 20 AV to 10 AV (-82 dbm to -88 dbm) 0.1 db/10 dbload resistance into which the piston attenuator worksis 220 ohms. The reproducibility of the measurement is in the orderThe maximum nonlinearity must not exceed 0.2 per of 0.01 db over the entire range.

cent or 0.02 db. Fig. 13 shows that the optimum value APPENDIXfor C1 is 1.119 C0 and that this allows a maximum cou-pling factor of 0.105 with an output lE2/Eo0 of 0.90.This assumes a perfectly stable capacity which of course The circular cross section for the piston attenuator isis nonexistent. If a change in capacity of + 1.5 per cent selected as the easiest to fabricate with the required pre-is allowed and a mean value of 1.110 C0 is used, the two cision, and the TE11 mode (H11) is selected for propaga-curves in Fig. 13 mnarked C1= 1.096 Co and C1= 1.124 CD tion because a high degree of mode purity is most easilyrepresent the extremes. Under these conditions, a maxi- obtained with this mode. For convenience, the attenua-mum coupling of 0.05 may be used and the maximum tor is designed to give exactly 20 db per inch of travel.output is |E2/E0I =0.30. For structural stability and resistance to corrosion,A spacing between coils of only 0.01 inch is required stainless steel #316 was selected as the tube material. It

to achieve this coupling but the mode filter and its is used as a thin walled tubing inside a heavy wall brassholder limit the minimum- spacing to about 0.5 inch block. This produces a thermal coefficient of expansionwhich corresponds to a coupling factor of 0.017 and a equal to that of brass. Its resistivity (p) is 74 X 10-6 ohm-minimum insertion loss of |E2/E0 _ 0.1. cm and its permeability (,u) 1.003. The frequency ofMeasurements were made to verify these calculations operation of the piston attenuator is the IF frequency

and the results are shown in Fig. 16. Curve a was taken 30 mc.with the sending circuit tuned for mlaximum output From [11] the attenuation constant is


1959 Weinschel, et al.: VHFIUHF Signal Generator Attenuator Calibration 51

2,x / /Ac\2 1 This gives the diameter of the attenuator tubea = (8)

D = 1.59561 inches + 0.00002 inch.where the cut off wavelength

(0.00002 is the probable error of the calculation and not2rr/e (9) a machining tolerance.)

Sr,9

Note that the constant term which Nas neglected inthe first approximation arises from the finite conduc-

X= 1/p conductivity tivity of the tube material. If this conductivity were

Xe = the wavelengthi atn30am of t/3 Xnterior10 f theinfinite, the first approximation (ro) would be the correct

e= the dielectric constant of t iri result. The correction made by the conductivity is thus

guide e-1.000 585+.000005 [14] (Air) the difference between r and ro or 16/8,000=0.2 perc = the velocity of light in free space 299 790.2 ± .9 cent.

km/sec. [15] Note in (10) that the radical is approximately 1. SoSmn = a numerical constant characteristic of the wave- that the attenuation a varies approximately as l/r. The

guide mode. In the present case, Smn =Sl is the 0.2 per cent error in r would therefore represent a 0.2first root of the first derivative of the first order

Besselfuntion 1.84184 [13 1.per cent error in ae or 0.02 db per 10 db. Thus to obtainBesselfadiunton 1.841184 [13].ntimeter the design accuracy of 0.02 db over the entire 100-db

rubstheutionradiusofthetubein centimeterange of the piston attenuator, the conductivity correc-Substitution in (8) gives tion and hence the conductivity must be known to 10

____~//2irrfx \ 2 1 per cent. We expect that the conductivity of the honedsi= 2'/-I -7r\I - __ db/cm (10) surface does not vary from that of the bulk metal moreAr V/f. \ slic / rV\irMfk than 10 per cent.

where A is inserted to convert from nepers per cm to dbper cm A =0.11512925

If we square both sides of (10) and attempt to solve ACKNOWLEDGMENTfor r in terms of a we have a cubic equation The authors are indebted to R. B. Stolzenbach of

r[A 2 4Ir2f2 Wright Air Development Center for his support and en-

r31 (- 2 + - r + = 0 (11) couragement. Dr. Samuel J. Raff of the Naval Ordnance]V/Sll2w2J\/ruf Laboratory is responsible for many of the calculations

The required value of a is 20 db per inch, and offered many helpful suggestions.

20 BIBLIOGRAPHY__- = 787.400005 db/meter

.02540005 [1] R. A. Bailey, H. A. French and T. A. Lane, "The comparisonand calibration of power measuring equipment at wavelengths of

Substitutinlg the indicated values, (11) becomes 3 cm and 10 cm," Proc. IEE, vol. 101, Part 3, pp. 325-329; Sep-Substituting ~~~~~~~~~~~~tember,1954.

2425.728r3 - r + 7.8926 X 10- = 0 (12) G. F. Gainsborough, "A method of calibrating standard signalgenerators and radio frequency attenuators," J. IEE, vol. 94,Part 3, pp. 203-210; May, 1947.

where r is in meters. [3] C. M. Allred, "Precision Piston Attenuator,"' Natl. Bur. ofStandards, Boulder, Colo., Report 3557; November 1, 1955.

Because of the smallness of the constant term, the [4] T. 0. Strutt, "Diode frequency changers," Wireless Eng., vol. 13,equation is most readily solved by successive approxi- pp. 76-80; February, 1936.

[5] F. M. Colebrook and G. H. Aston, "Diode as frequencymations. Neglecting the constant term, the equation is changer," Wireless Eng., vol. 20, pp. 5-14; January, 1943.quadratic, the soltution being [61 G. F. Gainsborough, "Diode as frequency changer for measure-

ments at UHF," Nature, vol. 44, pp. 548-549; September, 1939.

ro = .020303875 inches [7 ]M. Wind and H. Rapaport, "Handbook of Microwave Measure-ments," Microwave Res. Inst., Polytechnic Inst. of Brooklyn,

= .7993635 inches. Brooklyn, N.Y., pp. 3-20; 1954.[81 H. H. Meinke, "Felder und Wellen in Holelleitern," ("Fields and

Waves in Wave Guides"), Ch. 1, p. 24; Oldenbourg, Munich,This is correct for infinite conductivity. Germany; 1949.

To~~~~~~~ ~ ~obaith,etapoiainotiigtecr [9] 5. Ramo and T. R. Whinnery, "Fields and WVaves in ModernTo obaln tenex apprx1maton cota1n1g tnecor- Radio,"' J. Wiley and Sons, New York, N.Y., 2nd ed., p. 376;rection for finite conductivity, rewrite (12) approxi- 1953.

[10] R. E. Grantham and T. T. Freeman, "A standard of attenuationmately as ~~~~~~~~~~~~~formicrowave measurements,"r Tralns. A IEE, vol. 67, pp. 535-

7.8926x10-s [11] ~~537, June, 1948.7.8926X10-5 [11] ~C. M. Allred, "Chart for the TE11 mode piston attenuator," J.

2425.728r2 - 1 + - = 0 Res. NBS, vol. 48, no. 2, pp. 109-1 10; February, 1952.r0 1121 H. M. Barlow and A. L. Cullen, "Microwave Measurements,"

2 1- .03872 Constable and Co., Ltd., London, Eng., pp. 384-388; 1950.1 -.0388= 4.106448 X 10-i [131 Ramo and Whinnery, op. cit., Section 9.05.

2425 728 *114] International Critical Tables.DJ I ° ~~~~~~~~~[15]J. W. Dumond and E. R. Cohen, "Least squares adjusted valvesof the atomic constants," Phys. Rev., vol. 82, p. 555; May 15,

r = .02026437 meters = .797808 inches. 1951.'


Documents

Relative Voltmeter for VHFUHF Signal Generator Attenuator Calibration-J8e