(PDF) Mismatch Errors in Microwave Power Measurements - DOKUMEN.TIPS (2024)

PROCEEDINGS OF THE I.R.E.

from the simple diagram reveal the presence of addi-tional parameters, such as holder losses or interferingmodes which may otherwise be overlooked and may thuscause false results for the fundamental crystal param-eters. The requirement stated at the beginning of thissection can be met by using bridges or the Q-meter. How-ever, null methods usually yield the higher accuracy,therefore, bridges are to be preferred which use ca-pacitors only for balancing both the resistive and reac-tive (or the conductive and susceptive) components ofthe vibrator. Therefore Schering bridges like the gen-eral radio rf bridge and the twin-T impedance measuringcircuit are recommended for precise laboratory measur-ing methods.

VI. DEPENDENCE OF EQUIVALENT PARAMETERSON AMPLITUDE OF VIBRATION

It has been assumed in the foregoing chapters thatthe equivalent parameters are independent of the ampli-tude of vibration. But this is an approximation usuallyvalid only for small amplitudes. The variation of theparameters with amplitude varies greatly with thetype of vibrator. The amplitude is a function of the cur-rent through the vibrator or a function of the voltageacross it, and affects both the resistance and frequencyof the vibrator and is in addition to changes due tointernal heating. Therefore, the current or the voltagelevel used at the measurement must be specified. Addi-tionally, the difference between the measuring fre-

quency and fs must be known, because the ratiosamplitude/current and amplitude/voltage depend verymuch upon this difference. As has been pointed out byGerber,27 it is advisable to use current measurements forspecifying the amplitude if frequencies in the neighbor-hood of fr are involved, and voltage measurements, ifmeasurements are made close to fa. If these precautionsare taken, the change of the mentioned voltage andcurrent to amplitude relations with frequency aremoderate and the influence of different values of R,upon amplitude is small.

It is advisable, however, to use the power dissipationin the vibrator as a measure of amplitude, if measure-ments are made at several different frequencies, becausethe ratio amplitude-power dissipation is independent offrequency.

VII. ACKNOWLEDGMENT

The author wishes to express his gratitude to A. C.Prichard and M. Bernstein for interesting discussionsconcerning the series resonance oscillator circuits, andto M. F. Timm for his aid in preparing the manuscript.Furthermore, the author is indebted to colleagues ofthe IRE Committee on Piezoelectric Crystals for manyhelpful suggestions.

27 E. A. Gerber, 'Amplitude of vibration in piezoelectric crystals,"Electronics, vol. 24, no. 4, pp. 142, 204-218; April, 1951, and no. 9,p. 326; September, 1951.

Mismatch Errors in Microwave Power Measurements*R. W. BEATTYt, MEMBER, IRE, AND A. C. MACPHERSONt

The following paper is published with the approval of the Tutorial Papers Subcommitteeof the IRE Committee on Education.-The Editor

Summary-Expressions are derived for error due to mismatchwhen a UHF or microwave power meter is calibrated by comparisonwith a standard power meter. Three different methods are con-

sidered: (a) alternate connection to a stable power source, (b) the useof a microwave junction which simultaqeously supplies power to theuncalibrated power meter and the standard power meter in a knownratio, (c) alternate connection to a microwave junction. The relativemerits of the methods are discussed.

Expressions are derived for error due to mismatch when using a

calibrated power meter in the following situations: (a) direct con-

nection of power meter to power source, (b) reduction of powerinto the power meter by means of an attenuator, (c) reduction ofpower into the power meter by means of a directional coupler.

* Decimal classification: R245. Original manuscript received bythe Institute, July 9, 1952; revised manuscript received April 20,1953.

f National Bureau of Standards, Washinigton, D. C.

I. INTRODUCTION7ff HE EFFECTS of mismatch' have been recog-

nized2 but are often neglected in the calibrationand use of ultra-high frequency (UHF) and micro-

wave power meters. Experience has shown that neglectof mismatch is not always justified and serious errorsmay occur. The magnitude of the error depends not

1 A uniform section of UHF or microwave transmission line orwaveguide is said to be matched when it is terminated in such a waythat no net reflection of energy occurs. A termination which causes anet reflection of energy in the uniform section is termed a mismatch.

2 C. G. Montgomery, "Technique of Microwave Measurements,"McGraw-Hill Book Company, New York, N. Y., p. 130, 1944.

3B. P. Hand and N. B. Schrock, "Power measurements from 10to 12,400 megacycles," Hewlett-Packard Journal V. 2, no. 7 8;March-April, 1951.

1112 Sepbtemb)er

Beatty and AMacPherson: AMismatch Errors in Microwave Power Measurements

only upon the degree of mismatch but also upon theproperties of any power dividing or attenuating devicewhich may be used.

For this reason, various circuit arrangements em-ployed in the calibration and use of UHF and micro-wave power meters have been analyzed with regard tomismatch errors. Equations are given for the evalua-tion of these errors.

II. CALIBRATION OF POWER METERSA. General DiscussionA power meter is calibrated by comparing its indi-

cated power with the power it actually absorbs. Best ac-curacy of calibration is obtained by avoiding the use ofsecondary standards, attenuators or directional couplersand comparing the meter directly with a reference stand-ard which may be a bolometric or calorimetric device.This may be done by alternate connection of the meterand the standard to a stable source or by the use of cer-tain power splitting devices enabling simultaneous com-parison, or by a combination of methods. Power splittingdevices having a power ratio of unity have the ad-vantage that geometric symmetry is possible, permittingprecise mechanical construction which leads to a cor-responding excellence of electrical symmetry.The end result of a power meter calibration is often

a correction factor f which is used to convert the meterreading Rm to the power PM absorbed by the meter(PM =fRM). The correction factor f may be obtained interms of observed quantities:

f PM P PS () Ps

RM Ps/Rm Rm(1)

where Ps represents the power absorbed by the standardpower measuring device. In the following methods ofcalibration, the power division ratio K is normally unityexcept as affected by mismatches and by deviationsfrom ideal properties of the power dividers.

ZG PS ZG P

e L z Zs ZML r-

Fig. 1-Alternate connection to stable source.

B. Method 1-Alternate Connection to a Stable PowerSourceThe power meter and the standard are alternately

connected to a stable generator as shown in Fig. 1. Thegenerator output is padded to prevent the change inloading from affecting its amplitude or frequency. Theratio of the powers absorbed by the meter and thestandard iS4-5

4The derivation is straightforward, remembering that Z/Zo=1i+r/1-r.

6 It is evident that K1 equals unity if rM= Ps, a condition whichmay be recognized by a method described in "Accuracy with whichtwo loads can be matched on a magic T,"' A. C. Macpherson and D. M.Kerns, Electronics, vol. 23, no. 9, p. 190; September 1950.

PM 1 - rGPS 2 1-PrM12K1 = - =Ps 1 - rGrm i - rs 1 2 (2)

where rP, rs, and rM are the voltage reflection coeffi-cients respectively of the generator, the standard, andthe power meter, measured at the place of connection.

It is convenient to measure the voltage standing-wave ratio6 (VSWR or r) corresponding to the magni-tude of P. Assuming that the worst phase combinationscan exist in (2).

rM /Grs + 1\2I / rG + rS 2>K=1.-

rs rG + rM/r \rGrM + 1,(3)

In a specific example, if rG=4.0, rs=1.05, andrM=1.25, K1 lies between 0.84 and 1.17, a mismatcherror between - 16 and +17 per cent if K1 is errone-ously taken to be unity.The range of error can be reduced by "matching

back" toward the generator, making rP vanish. In thiscase, (2) becomes:

1-I rPM2 - (rs + 1\2

1-|I rs2 rArM+ l/ (4)

With rs= 1.05 and rM=1.25 as before, K1'=0.99, andthe mismatch error is -1 per cent.

Caution must be used in attempts to further reduce themismatch error by matching the power meter input. Ifan adjustable transformer is used for this purpose, theloss in the transformer itself will cause an error whichcannot be readily evaluated. Only transformers withknown loss can be safely used for this purpose.

C. Method 2-Comparison Using T-Junctions1. Simultaneous Comparison: The generator is con-

nected to the center arm (No. 3) of a symmetricalT-junction as shown in Fig. 2. The standard and thepower meter are connected to the other two arms (arms1 and 2, respectively).

Fig. 2-T-junction comparison.

It can be shown that equal power will be deliveredto the standard and the meter by a symmetrical T pro-viding that their impedances are identical. A high de-gree of symmetry can be achieved by precise mechanicaldesign and construction and by special techniques, suchas electroforming. The degree of symmetry achievedmay in some cases exceed the accuracy with which itcan be measured. In the general case, however, in whichasymmetry must be taken into account, the ratio of

6 | rl =r-1/r+1.

11131953

PROCEEDINGS OF TIIE I.R.E.

powers absorbed by the meter and the standard is:'

PMK2 = -=

Ps

S13 ) 2

21 - 1rM - 122S23 22

S131 IIM 12

1 I]S 12

The coefficients of the form Sm,n are the scattering co-

efficients8 of the T. These scattering coefficients are

either voltage reflection coefficients (m = n), or voltagetransmission coefficients (m Hn), and can be measured9with a standing-wave machine.

It is possible to obtain the magnitudes of the coeffi-cients in (5) from VSWR measurements and calculatethe limits of K2 as the phases are permitted to vary.

Assuming that the T is symmetrical and lossless, K2 liesbetween the limits:

rMrs K21

(6)rmrs

Specifically; if rs= 1.05, and rm= 1.25, K2 lies between0.76 and 1.31, an error between -24 and +31 per cent.

2. Alternate Connection to T-Junction: The generatoris connected to the center arm (No. 3) of a T-junctionas shown in Fig. 3. An uncalibrated power monitor is con-nected to one arm (No. 1) and the generator output isadjusted to maintain a constant indication of themonitor. The meter and the standard are alternatelyconnected to the other arm (No. 2).

method. In the case of a symmetrical lossless T, thelimits of K3 as determined from measurements of themagnitudes of the coefficients are the same as the limitsof K2, as expressed in (6),

(5)

M

L rL

Fig. 4 Magic T comparison.

D. Method 3 Comparison Using Magic T

1. Simultaneous Comparison: The standard and thepower meter are connected to the symmetrical arms

(numbers 1 and 2, respectively) of a magic T"O as shownin Fig. 4. A generator and a matched load are connectedto the other arms (numbers 3 and 4, respectively). Itcan be shown that equal power will be delivered to thestandard and the meter by a symmetrical magic T pro-

vided that their impedances are identical. But in thegeneral case in which the asymmetry and mismatch are

taken into account the ratio of powers absorbed by themeter and the standard is,1"

Fig. 3-Alternate connection to a 1 junction.

The ratio of powers absorbed by the meter and thestandard from these conditions, applying (5), is

PM

Ps

PM PMO

PMO Ps

1 - (s22~_S23 2)

1 - 22-_ 23S12) r

-jI rs52

Comparison of this equation with (5) shows that theeffect of asymmetry of the T has been reduced by this

7 This equation follows from the scattering equations of a three-arm junction.

8 C. G. Montgomery, R. H. Dicke, and E. M. Purcell, "Principlesof Microwave Circuits," McGraw-Hill Book Company, New York,N. Y., pp. 146-151; 1948.

9 See Appendix.

PM ab-cd FL 2 1- I'2PS bg - dfFLrM 1 - F 12

where:

a = S23(1 - Sllfs) + S12S13Fsb = S13(1 - S44FL) + Sl4S34FL

c = S34(1 - SIl,s) + S13S14FS

d =S14S23 -S13S24

f = S12S34 - S13S24

g = S13(1 - S22PAI) + S12S23FJ.

(9)

The scattering coefficients of the magic T can be meas-

ured9 with a standing-wave machine or the ideal'2values can be used if the losses in the T are sufficientlysmall, the internal matching is sufficiently good, andthe mechanical construction is sufficiently precise.

10 A conventional waveguide magic T may be defined as a four-arm junction having the form shown in Fig. 4 which is symmetrical,lossless and matched looking in each arm.

l1 This equation follows from the scatteriing equationis of a four-arm Junction.

12 See pp. 448-449 of referenice of footnote 8.

rAirs > K3 >1

rmirs (8)

1114 September

Beatty and MacPherson: Mismatch Errors in Microwave Power AMeasurements

If the four-arm junction is an ideal magic T havingproperly chosen reference planes, S11 = S22 = S33 =S44=S12 = S34 = 0, and S14 =-S24 = S13= S23.

It is possible to simplify (9) in several ways. For ex-ample, if it is assumed that the load is perfectly matched(FL=O) (9) reduces to (5). If in addition some of theproperties of an ideal magic T are substituted in thisequation (Sll = S22 = S12 = 0, and S13 = S23 ), it reducesto (4). A nomogram representing (4) is shown in Fig. 5.

K- . rm

1.0 -

1.2 -

1.3 -,

1.4

w

E 5 -: .

w0a. 1.6 -

U)w

U.o 1.7crv)

E 1.8 -

1.9 -

2.0

Fig. 5-

IEl 0CL a.

0I-4cr:

crw00

1.12 -

1.10 -

1.08 -

I.06 -

1.04 -

1.02 -

I.00-

0.98 -

0.96 -

0.94 -

0.92 -

2.0 -

1.9 -

x 1.8 -1--

cr

¢ 1.7 -0a.

O 1.6 -z

cn

U.0 1.5 -

cn1.4 -

1.3 -

1.2

0 90 p1.0 -~

-Mismatch effect in the calibration of power meters.

2. Alternate Connection to Magic T: The generatorand a load are connected to the symmetrical arms (num-bers 3 and 4, respectively) of a magic T as shown in

l

Fig. 6 Alternate connection to a magic T.

Fig. 6. An uncalibrated power monitor is connected toarm No. 1 and the meter and standard are alternatelyconnected to arm No. 2. The generator output is ad-justed to maintain a constant indication of the monitor.The ratio of powers absorbed by the meter and thestandard is:

where:

PM PM PMOK5 = = *-

PS PMO PS

K bg' - dfPLFS 2 1 -] rM IK5 =

bg - dflrLrM 1 - rS 12(10)

b = S13(1 - S441L) + S14S341L

g' = S13(1 - S22rS) + S125231S

d = S14S23 -S13S24

f = S12S34 -S13S24

g = S13(1 - S22FM) + S12S23]PM.

If the load is matched (FL =0), (10) reduces to (7). It isevident that the asymmetry effect is generally less inthe alternate connection method than in the simul-taneous comparison method. If the magic T is verynearly ideal, substitution of some of its properties(S12=S22=0) into (7) reduces it to (4). For a perfectmagic T,

PM 1- IJM 12 rMrs +l 12

Ps 1- rI rskrMsImlJ(4)

III. DISCUSSION OF CALIBRATION METHODSA general discussion of all power meter calibration

methods is beyond the scope of this paper. The methodsdescribed in the previous section have their advantagesand limitations with regard to accuracy, flexibility,equipment requirements and speed and ease of meas-urement.The alternate connection of the meter and the stand-

ard to the same generator is a simple and flexible methodwhich can be employed with waveguide or coaxial line.No auxiliary power dividing equipment is requiredand the mismatch error is relatively small and can beeasily evaluated from VSWR measurements if the gen-erator is matched. The generator must remain stable inpower output and frequency during the calibration andmust be padded to prevent oscillator pulling caused bychanges in loading.The use of a power divider permits simultaneous

comparison of the meter and the standard. This re-duces the necessity for padding the oscillator and thestability requirements are not as great.

If the degree of symmetry is low, the mismatch andasymmetry error may be reduced by using the alternateconnection method with a power monitor. The generatorpadding and stability requirements are increased and itis necessary to provide a smoothly adjustable generatoroutput.

Symmetrical three-arm T's are commercially avail-able in waveguide and coaxial line. Because of the centerconductor, the coaxial T involves additional difficultiesof construction not encountered in the waveguide T.The mismatch error can be evaluated from measure-

1953 1115

PROCEEDINGS OF THE I.R.E.

ments of the parameters of the T. The range of mis-match error, even with a perfect T, is greater than thatobtained by alternate connection of the meter and thestandard to a matched generator.

Symmetrical waveguide magic T's are commerciallyavailable but magic T's or hybrid circuits in coaxial lineare not readily obtainable. Carefully constructed wave-guide magic T's make excellent power dividers for powermeter calibration, permitting simultaneous comparisonwith no more mismatch error than is encountered withalternate connection to a matched generator. If asym-metry is appreciable, it can be determined from meas-urements of the T parameters.The effect of asymmetry can be reduced by using the

alternate connection method with a power monitor.A magic T can also be used to accurately compare

two impedances.5 If one impedance is adjustable, thetwo can be made equal. Applying this principle to powermeter calibration, the impedances of the meter and thestandard can sometimes be made nearly equal, per-mitting a reduction in the mismatch error.

IV. USE OF POWER METERS

A. General Remarks

If the power to be measured is within the range of thepower meter, a direct measurement can be made. If thepower is greater, a calibrated device such as an attenu-ator or directional coupler is used in such a way that aknown fraction of the power is measured by the powermeter.

B. Direct Measurement

In the direct measurement of the power that a givengenerator will deliver to a given load, the power meter issimply substituted for the load. This is the same situa-tion encountered in the alternate connection of twopower meters to a stable source. If the meter and theload are nearly matched, it is often erroneously assumedthat the power measured by the meter is the same asthat delivered to the load. Assuming that the generatoris well padded, the ratio of powers absorbed by the loadand the power meter is given by (2) with an appropriatechange in subscripts

PL l- FG FM 2 1j-J IL I'K6 =-, =-_ (11)PM l-T'PGFPL 1 - IFM 12 (1

In this expression the reflection coefficients of the gen-erator, meter, and load are designated as IFs, 1M, and FL,respectively. If the power meter reading is assumed tobe correct, it is multiplied by the factor K6 to obtain thepower that the generator will deliver to the load. It isapparent that (11) and (2) are of the same form andthat the limits of K6 are:

rL rG +rM 2 rL (rGrM+1 2

= K6 = -r12rrm \rGrL + I rm rG7+ rL/ (2

In a specific example, taking rG=4.0, rM=1.05, andrL=1.25, K6 lies between 0.84 and 1.17, a mismatcherror of between -16 and +17 per cent.

If the generator is matched, the mismatch error in theprevious example is approximately -1 per cent.

C. Use of Calibrated AttenuatorIf a calibrated attenuator is used to extend the range

of power meter as shown in Fig. 7, the measured power isnormally multiplied by the attenuator ratio to obtainthe power available to the load. If the error of iismatch

PiG - -2 PM~~~ CA LIB6R A TE D r X1Ze r CATTENUATOR M M

rG

ZG PL

e F ZL

Fig. 7-Use of calibrated attenuator.

is taken into account, the previous result is multipliedby a correction factor K7 to obtain the power deliveredto the load when it is connected directly to the gen-erator. The factor K7 is given by:13

PL 1-11GFl (l 2r FL 121-(rG -S22PM 1- |2

PM,,RA 1 FGFLI-IrM1(13)

In (13) the reflection coefficients of the generator, load,and meter are denoted by FG, FL, and FM, respectively.The scattering coefficients of the attenuator are denotedby Sm,n and Fi represent the input voltage reflectioncoefficient of the attenuator with its output connectedto the power meter. From the scattering equations for atwo terminal-pair network,

S122rMFi = Sii + '2F

1 - S22PM

and the attenuation in decibels is:

1 2AT = 10 log1o RA = 10 logio

S12

(14)

(15)

If only the VSWR's are measured corresponding tothe reflection coefficients of (13), the limits of K7 are:

rL [(rGr1 + 1) (r22rM + 1)02rM [(rG+ rL)(r22 + (r +21)

. K7 24 rL r (rG + ri)(r22 + rM) ]2rML(rGrL+ 1) (r22+ 1) (r- + 1)1

In a specific example, taking rG= 2.0, rM = 1.20, rL = 1.1,r22=1.20 and r1= 1.25, K7 lies between 0.89 and 1.14,a mismatch error between -11 and +14 per cent.

13 This equation follows from (11) and the scattering equations ofa two terminal-pair network.

September1116

Beatty and MacPherson: Mismatch Errors in Microwave Power Measurements

If desired, the error may be evaluated by measuringthe reflection coefficients appearing in (13). The meas-ured value of Pi may be checked by measuring the scat-tering coefficients of the attenuator and substituting in(14). Inspection of (14) and (15) shows that P1 ap-proximately equals S,1 if the attenuation is large.

If the attenuator is reflection-free (S11= S22=0) (13)reduces to:

K7t I Gi 2 1 -ILI1 - rGrL 1 - IMI2

and (14) reduces to:

Prl = S122r.p.

(16)

(17)

In a specific example, taking rG= 2.0, rM = 1.20, rL= 1.1,and r1 = 1.019 (10 db attenuator), K7' lies between 0.970and 1.046, a mismatch error between -3 and +5 percent.

If the generator is matched (PG =0), (16) reduces to:

connected as shown in Fig. 8 is ri. The scattering coeffi-cients of the coupler are designated by Sm,n. The cou-pling C, and directivity D, are defined in the usualmanner:

1 2

C = 10 logio Rco = 10 logioS1o

8132D = 10 logio82

(20)

It can be shown by a solution of the scattering equationsfor a three-arm junction that the reflection coefficient P,is:

+H

S122IPLrl=sll+ S2L

S13(l-S22FL) +S12S23rLL-S 2L

in )2r(1-S221PL)

S12(1-S33rM) +Sl3S23rMS23PM

S132rM(21)

(18)

Assuming that rL= 1.1 and rM= 1.20, K7" equals 1.007,representing a mismatch error of less than 1 per cent.

D. Use of Directional Couplers1. A directional coupler is often used to extend the

range of power meters as shown in Figs. 8 and 9. In Fig.8, the coupler is temporarily inserted between the gen-

erator and load and the power is measured with a power

ZG P2Ie'-' rj-o D. C. rL*

3

ZG PLe

Fig. 8-Temporary insertion of directional coupler.

meter. The measured power is normally multiplied bythe coupler ratio to obtain the power available to theload. If the effect of mismatch is taken into account, theprevious result is multiplied by a correction factor Ksto obtain the power delivered to the load when it is con-

nected directly to the generator. The factor K8 is givenby: 4

PL 1- FGI?lK8 =- - S 12

PmRco I _rGrL

s12(l -S33rM) + Sl&S23PM 2 1 - L 2_S23(Pl - Sll) + S12S13 1 - FM 12

In (19) the reflection coefficients of the generator, meter,and load are denoted by FG, PM, and FL, respectively.The input reflection coefficient of the directional coupler

14 The derivation of this equation is straightforward, starting fromthe scattering equations of a three-arm junction.

S12(1 -533PM) +Sl3S23FM(1-s33rM) S(1-522FL+S12S23FL

If the directional coupler can be considered to be per-fect, having infinite directivity (S23= 0) and being re-

flection-free (Sll=S22 = S33 = 0), the above equationssimplify, (21) reducing to:

rl' = Sll + S122rL + S132rM (22)

and (19) reducing to (16). If in addition the generator ismatched (PG = 0) (18) applies.

ZG 2 PLe r; D C. rL ZL

--rG -3+XPM

Fig. 9-Permanent installation of directional coupler.

2. A directional coupler is often permanently in-stalled between the generator and the load as shown inFig. 9. The power delivered to the load is normally ob-tained by multiplying the power meter reading by thecoupler ratio. If mismatch is present, it is necessary tomultiply this result by a correction factor K. This factoris given by:"5

PLKg =

PMRCO

S1I2(I-S33FM) +S13S23PM 2 1 IL

S13(1(-S22]PL)+S12S23rL rM (

Note that Kg= 1 when FLI= rMI =0, and IS12= 1. Ifthe directional coupler can be considered to be perfect(Sll = S22 = S33 = S23=0) and the coupling is loose (S12=1),(23) reduces to (18).

15 The derivation is similar to that for (19).

Ir1- IrL 12 rLI, rm + I I

K7" =I-

- r(+rAl krL + l

1953 1117

PROCEEDINGS OF THE I.R.E.

In a specific example let rL=1.5 and rM=1.25. Adirectional coupler is used having a directivity of 25decibels, a coupling of 20 decibels and reflections in eacharm producing a VSWR less than 1.1. Assuming theworst phase conditions the limits of error calculatedfrom (23) are approximately -8 and +2 per cent.

If the directional coupler is assumed to be perfect inthe same example, the error calculated from (18) is ap-proximately -3 per cent.

If these examples can be considered typical, it is evi-dent that the simplified equation cannot be used toevaluate the mismatch error unless the directionalcoupler is very nearly perfect and the degree of mis-match is small.

ACKNOWLEDGMENT

The authors wish to thank Dr. David M. Kerns andthe other readers who gave valuable criticism and sug-gestions.

APPENDIX

Measurement of Scattering CoefficientsA network having n-terminal pairs and a scattering

matrix S is shown in Fig. 10. The scattering coefficients

A,-

Bi .6

sI=1

S 12

Lsn

12 In

S2n Snn

Fig. 10 Network having n-terminal pairs.

are of the general form Sp,q where p and q are integers,each denoting a given terminal pair.

If p = q = K, the voltage reflection coefficient SKK ismeasured at the Kth terminal pair with all other ter-minal pairs connected to reflection-free loads.

/~~~~RS C rp

pp~~~~~P

Fig. 11 Reflection coefficient circle.

If p z q, the voltage transmission coefficient Spq ismeasured in the following way. The qth terminal pair isconnected to a variable reactance. All other terminalpairs with the exception of the pth pair are connectedto reflection-free loads. The input reflection coefficientrp, is measured for various reactances at q. The locus ofthe measured points is a circle as shown in Fig. 11. Themagnitude and phase of Spq are:

Spq 12=RI 1 - Sqj I2}Ypq = 2(4 + Yqq).

(24)

A short derivation follows:If A and B denote the incident and reflected voltage

waves at a pair of terminals p and q,

Bp ppAp + SpqAqBq = SpqAp + SqqAq.

(25)

Let

Bq= 6.Bq

Then

Aq Spq

lip e-j6-Ss(26)

and:

-BPAp

Aq= Spp + Spq -=Spp +

ASpq2

E'o- Scqq(27)

A variation of 0 represents a change in the reactanceconnected to terminal pair q. As shown in Fig. 12, themagnitude of the vector quantity (FPp-Spp) goesthrough maximum and minimum values as 0 changes.

Fiz. 12 Translated reflection coefficient circle.

At these points M and m,

(rP - SPP)M = ei(2pqYS(rP~-Spp>1 - Sqq Yqq)

(Fp SPP)m = pq 2 ei 2YpYqq±+lr)I1+ ISqq

(28)

(29)

The radius of the circle is:

1 r 1SPq7 I2 Sqq30R=2 -1 - IS, l+1+ ISq I-

Spq I2I - IS 12

1 1 1 8 September

(30)

Baker, Lebow, Rediker and Reed: The Phase-Bistable Transistor Circuit

The distance to the center of the circle is:

I IS" 12 _ tSpql 12

2 1- Sqq 1+ SqqlI__SpqSp'

Spq~_ SqI =RRSqq (31)

Denoting the phase angle (2Ypq -yqq) by 0, the diagramof Fig. 11 can be drawn.An alternate method of measuring the scattering co-

efficients of an n-terminal pair network is as follows.Referring to Fig. 10, the scattering coefficients Spp, Sp,,and Sqq are determined by terminating terminal pair q

in three different loads having voltage reflection coeffi-cients FL1, FL2, and lL3, and measuring the correspond-ing input voltage reflection coefficients F,, F2, and r3 atterminal pair p with all other terminal pairs terminatedin matched loads.

Solving the three equations for input voltage reflec-tion coefficient of the form

2

F = SPP -pSqFLC1 - SqqFL

(32)

the following expressions are obtained for the scatteringcoefficients.

s FPLlrL2r3(rl T'2) + rL2FL3Fl(r2 - F,) + rL3rLlr2(r3 - rl) (33)

rLlrL2(rl - 2) + FL2FL3(r2 - F,) + FL3FL(F3 - F

SFLI(F2 - J3) + FLF(r3 -rF) + rLi(Fl - r2)S q = ---(34)rL1FL2(rl - r2) + rL2rL3(r2 - r3) + FL3Fpl(r3 -Fr)

2 I(F - F9)(r2 - r3)(r3 - rl)(FL1 - FL2)(rL2 - FL3)(F3L- rFL)Sp = 35)Spq 2=.. [FL.rFL2(F - F2) + rL2rL,(I2 - F3) + IL3FLl(r3 - rF)]2

The Phase-Bistable Transistor Circuit*R. H. BAKER, MEMBER, IRE, IRWIN L. LEBOW, ROBERT H. REDIKER, AND I. S. REEDt

Summary-A synchronized transistor switching circuit has beendesigned for use in computer applications. The circuit is phase bi-stable rather than amplitude bistable. The basic unit of the circuitis a commutating ring which is operated by clock pulses and whichis sampled at one-half the repetition rate of the clock. An input pulsechanges the phase of the ring with respect to the sample pulses. Thisis analogous to a change in the output amplitude of a conventionalamplitude bistable device caused by introduction of an input pulse.The basic transistor circuit used is the one-shot multivibrator. Thelatter device has proved to be more reliable than any amplitude-bistable transistor circuit.

In section I are presented some features of a transistor switchingcircuit. Section II contains a simplified description of the phase-bistable circuit and its mode of operation. In section III is describedthe transistor circuitry, while in section IV some general applicationsto digital computers are discussed.

I. INTRODUCTION

N THE DESIGN of transistor switching circuits oneencounters certain difficulties which severely limitthe apparent versatility of the point-contact tran-

sistor. If we connect the transistor in the circuit of Fig.1(a), we obtain the familiar bilateral characteristic of

* Decimal classification: R282.12. Original manuscript receivedby the Institute, February 13, 1953. (The research reported hereinwas supported jointly by the Army, Navy and Air Force undercontract with the Massachusetts Institute of Technology.)

t Massachusetts Institute of Technology, Cambridge, Mass.

Fig. 1 (b). Such a circuit may be made astable, mono-stable, or bistable by proper selection of the input load-line parameters, Re and V66. Using the astable connec-tion, we may design free-running multivibrators; with

Re

vee+ F_

(a ) (b)

Fig. 1-Point contact transistor circuit and bilateralcharacteristic.

the monostable connection we may design regenerativepulse amplifiers and one-shot multivibrators; and withthe bistable circuit it is possible to design flip-flops. Be-cause of the "hole-storage" phenomenon,1 the triggerpulse necessary to switch the circuit from its conductingstate (point "a" of Fig. lb) to its non-conducting state(point "b") must be relatively wide. For most available

1 R. H. Baker, I. L. Lebow, and R- H. Rediker, to be published.

1953 1119