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300oRESEARCH AND DEVELOPMENT REPORT2

REPORT 1144 DECEMBER ING2-

mo291 338Lu

Simultaneous Multibeam Phase Com pensation

XI. A RESISTIVE-ELEMENT PHASE COMPENSATOR

L. 0. Morgan and R. 0. Strait

U. S. NAVY ELECTRONICS LABORATORY SAN DIEGO. CALIFORNIA

A BUREAU Of SHIPS LADORAT Off

THE PROBLEMEvolve new techniques for sonars to improve low-

frequency beam formation, reduce or eliminate mechanicalbeam steering by the application of electrical delay or phasecompensation, and realize 100 per cent time utilization bysimultaneous observation in all directions.

Specifically, this report deals with the design, con-struction, and evaluation of a phase compensator which usesresistive, rather than transformer, circuit elements.,

RESULTS

1i A single-beam, resistive-element phase compensa-tor network was designed and constructed for the 48-elementarray of the AN/SQS-4 Mod 3 sonar with half-wavelengthspacing, Its performance was zIetermined in the laboratoryby use of Sonar Test Set TS-826/SQS-4 and Target SignalSimulator Control C-1458/SQS-4.

2. The phase compensator produced a single beamwhich, with its minor lobes, was essentially identical to thebeams produced by the 48-beam transformer phase com-pensator, which was designed for the AN/SQS-4 Mod 3sonar and was tested in the same way.

3. Satisfactory operation of the phase compensatorthroughout the frequency range within ±17 per cent of thedesign frequency was demonstrated, yielding beam patternswhich were very similar to the transformer phase com-pensator patterns obtained in the same way.

4. Compared to the multibeam transformer phasecompensator, the multibeam resistive phase compensatorwill be more reliable in operation. Further advantages arereductions in weight, size, and cost made possible byprinted circuit or microminiature techniques. Manufactur-

ing, especially in large quantities, will be expedited, andtesting and maintenance simplified. The equipment offersconsiderable flexibility for interchange in the event ofoperational or combat damage.

RECOMMENDATIONS

1. Make available the information in this report tointerested contractors along with the recommendation thatthey consider the use of the resistive element phase com-pensator for those sonar receiving systems in which thetransformer phase compensator had been considered orplanned.

2. Design and construct, at NEL, a multiple-beam,resistive-element phase compensator and conduct completetests to investigate the multiple network intercouplingeffects.

ADMINISTRATIVE INFORMATIONWork on the resistive phase compensator was carried

out by members of the Special Research Division underAS 02101, SF 001 03 04, Task 8051 (NEL L3-2) as a portionof the sonar techniques program

The report covers work from February 1958 to October

1958, and was approved for publication 4 December 1962.

The single-beam resistive phase compensator wasdesigned by the authors from information on the AN/SQS-4Mod 3 transformer phase compensator supplied byC, J. Krieger, and was constructed by J. A. Thomson.

ii

CONTENTS

PREFACE,..page V

INTRODUCTION-. 1

DEFINITION OF SYMBOLS.. 2

DISCUSSION OF1 BEAM FORMATION... 6

COMPARISON OF THE TRANSFORMER AND THE RESIS-TIVE PHASE COMPENSATORS... 9Transformer Phase Compensator,.. 10Resistive Phase Compensator,.. 12Other Design Parameters.., 15

DESIGN OF A RESISTIVE PHASE COMPENSATOR... 18

TEST RESULTS OF THE SINGLE-BEAM RESISTIVE PHASECOMPENSATOR... 19

CONCLUSIONS. .. 25

RECOMMENDATIONS... 25

REFERENCES... 27

APPENDIX A: CIRCUIT ANALYSIS.. 31

APPENDIX B: MULTIBEAM COUPLING EFFECTS... 41

APPENDIX C: OTHER USES OF THE PHASE COMPENSA-TOR... 45

111

TABLE

1 Design parameters and key equations for resistive phasecompensator... page 19

ILLUSTRATIONS1 F'ormation of receiving beams by use of transformer phase

compensator... page 11

2 Formation of receiving beams by use of resistive phasecompensator... 13

3 Formation of beam for AN/SQS-4 Mod 3 by use of resistivephase com pensator, relative to portion of hydrophonearray used... 14

4 Circuitry of single-beam, 16-element resistive phase com-pensator... 21

5 Linear plots of directivity patterns of resistive and trans-former phase compensators.. 23, 24

A-i - A-6 Equivalent circuits Nos. 1 through 6... 31-37

B-1, B-2 Illustrations of cross talk.. 43, 44

C-i Typical one-to-three phase network using transformerelements... 47

C-2 Typical one-to-three phase network using resistorelements... 48

iv

PREFACE

this report is Part XtIin the terte* oftSiinultanteout Nultibeaft Phase Compenetattion. theother AUX reports in the oerteel-1 1 are Haotedbelow, with brief notation of the phase compeni-eating devicec and related etudiec with which theyare concerned*. Bibliographic descript ion of thecereport., and a list of other publication# on-ttaining related information, are given In* the listof reftrencet at the end of thit report.

NFIL Re~port 5829 (which preceded the numberedparts of the *eriec) describe. the first phasecompensat ion device built at NrIL, along with itstheory, called the iiScope Precenttat ion Array Co.-penteator."o It used synchros to provide sunt ofthe vector components of hydrophone electrical sig-nala for respect ive application to the x anddeflect ion plate& of an occilloodope.

Part. I and 11 (NIL Reportv 6.32) were thefirst discuss ion of the theory of multiple-beamphase compeneat ion.- They describe the Secondphase compensat ion device built at NIL, the9Tranaforner Coupled Potentiometer Compenator.9-Ohio device utilited recictive elements In a high-Impedance, sort"ec-unmat ion, multiplei-beam matrixwith xa--y ecope presentat ion.

Part 1 11 (NIL Report 6420) describes the pilotmodel which wao the third phase compensatingdevice built at NIL, and which wac the first toutilixe a transformer network with multiplesecondaries to achieve multiple-bea. format ion.Test results art given.

Part XY (NIL Report 670) gives more detailedlaboratory teat result* of the pilot model de."scribed in Pa-rt II-., Two append ix** present thegeneral theory of'phace oompeneat ion and It&application to linear arrays.

Part V (NJF4 Report 674) describes the fourthphase compensating device built at NILX, a labora-

V

tory breadboard for the circular array of theAN/SQS-4 Mod 1 gonar, with results of a labora-

tory evaluation.

Part VIr (NIL Report 75) describes the fifthphase comptneating deioce built at NZL, a phasecoMpnesator for use with the Lorad (linear array;40 elements; 100 feet long) sta-tion-keeping

Ve t CS.

Part VIi (NrIL Report 806) describe, thesixth phase compensating device built at NIL, aphase compensator for use with the AN/IVO-l1(*3.5 ko/0) sonar, with results of a laboratoryetuluatione In an appendix the theory of phasecompensation as applied to circular arrays isprea nt ed.

Part VILT (NIZL Report 951) describes thedesign and laboratory evaluation of the seventhphase compensating device built at NIL, a phasecompensator for the AN/SQS-4 Mod 3 sonar.

Part IX (NIL Report 985) describes the re-ceiving system for an AN/SQS-4 god 3 sonar de-signed for use with an NIL phase compenesator(Part ~zI). Thig 48-bean receiving system, withAGO bean amplifiers and video and audio displays,was installed on USS BRID.ET (DI 10*4) and seatested in April 1959. A complet* system descrip-tion and test results are given.

Part X (NIL Report 1009) describes a tech-nique which enables phase compensators to operateover a wide-band frequency range by adding extrasets of secondary windings to selected transformercores (hydrophone channels) to cover the add(-tional frequency bonds desired. Also brieflydescribed is a three-frequency band phase compen-

astor constructed for asinuthal beam formationfor the AN/5QO-83 sonar for either receiving or

low level (I kw) transmifasion. This is theeighth phase compensating device built at NIL.

Part Xjs, the present reportp describes arsstaftvewelement phase compensator.

Part XZn (NIL Report 110$) gives a very com-

prehenslie.oummory of phase oOmpeatfon and array

design.

INTRODUCTION

The transformer phase compensator has been providingpreformed receiving beams satisfactorily for several yearsin various experimental Sonar systems at NEL, and re-cently it has been adopted for use to provide a complete setof horizontal azimuth beams in the AN/SQS-26 sonar. itcan also be backfitted on AN/SQS-29 series sonars now inthe Fleet (replacing the scanning switch system) as part ofa program to improve performance. A prototype,AN/SQS-29 (XN-2), has been tested at sea on USSHANSON (DDR 832). Further tests are continuing on otherShips.

The phase compensator additionally lends itself to theformation of vertical beams for either transmission orreception.

Because of its demonstrated usefulness, and alsobecause of the increased interest in the phase compensatorfor use in Fleet sonar systems, the authors developed, in1958, an analogous phase compensator which is felt to bemore practical for Fleet use, in receiving systems, thanthe transformer type heretofore used. it is this analogous,

resistive-element phase compensator which this reportwill describe and discuss.

DEFINITION OF SYMBOLS

d Spacing of two adjacent array elements, in feet

E Equivalent cosine generator voltage

CE CVoltage on cosine bus proportional to

t N/2a. Cos 8

7 ott= -N/2

E- Voltage across RL produced by E

Et Signal amplitude at element t

E Beam output voltage, resistive phase compen-sator

E Equivalent sine generator voltage

S

s5 Voltage on sine bus proportional to

Cy t sin 8o.

E8,F Quadrature sum of X and Y

F Voltage across R produced by 2

E A voltage introduced at a beam output, wih

X zero input from the array preamplifiers, to

establish degree of beam-to-beam cross talk.E - E for any given conside ration.x 0

2

DEFINITION OF SYMBOLS (Continued)

eat, ect Voltages generated at tthelement of the resistive phase compensator. . = e = e

in amplitude, but e t and eCt may be of op-

posite polarity (1806 phase difference).

e- Cross-talk voltage from a given beam networkacross the resistance of a generator (preamp)contributing to that beam

.Element number

K Constant in resistive phase compensator

1

t= -NV/2

I2r/k (wave number)

N Number of elements in array

Nc Number of cosine winding turns

N Number of sine winding turns

R Quadrature sum of X and Y'. R = A -X JY

R Equivalent parallel resistance of the rC C

RL Load resistance of resistive phase compen-sator beam

R Value of characteristic resistance in resistive0 phase compensator. R *R = = W4 = I/wc

0 8 C

3

DEFINITION OF SYMBOLS (Continued)

flEquivalent parallel resistance of the rs

r Radius of circle of hydrophone elements,circular array

r- Generator (preamplifier) resistance

rCos attenuating resistor for tth element

r8C Sin attenuating resistor for tth element

S. Signal vector at element t. S = E. exp je

X Sum of cosine multiplied signals

1 Sum of sine multiplied signals

C 8Y k, Ykf Coupling correction factors

180 11V

0 Azimuthal direction of arrival of soundmeasured from array normal or axis ofsymmetry

a Phase at tth element, referred to a referencepoint, for any direction of arrival of sound

0 -r [cos[ T-( t1 81]

4

DEFINITION OF SYMBOLS (Continued)

or or Phase at tth e1erment, referred to a referencepoint, for sound arriving from direction ofcompensation (subscript c for linear array,and 6 for circular array)

6t kr [Cos (t T D sl

Ct C

at Shading factor of tth element

5

DISCUSSION OF BEAM FORMATION

To obtain a maximum response to signals from any onedirection by an acoustic array (or portion of an array) ofany configuration, the electrical signals generated by eachelement of that array must in some manner be causedeither to add together as though all elements had receivedthe acoustic signal at the same time or, in the event thatthe "signal" is a periodic wave train, to add the signalsfrom each element '"in-phase" with one another for thearrival of sound from the direction of compensation. Thefirst instance occurs naturally without co mpensation, forexample, in a linear array as a consequence of its shape.A plane-wave signal coming from anywhere in a plane per-pendicular to a straight line through the elements actuallyarrives at all of them at the same time. To "look" in anyother direction with a linear array, the electrical signalfrom each element can be delayed by the proper amount andthen electrically added to the last element's undelayed sig-nal at the time that it is generated. The first situationaio occurs naturally, without compensation, for circulararrays, if a plane wave acoustic signal arrives fromeither direction perpendicular to the plane of the array,since it arrives at all of the elements simultaneously.Again, to "look" in any other direction, each element'selectrical signal can be delayed by the proper amount oftime and added to the last element's undelayed electricalsignal at the time it is generated.

Electrical delay lines have been the primary means ofaccomplishing these necessary electrical delays in the past.With the requirements of new large sonar arrays and theuse of multiple preformed beams, the large number of de-lays and/or long delay periods necessitate almost prohibi-tively large, heavy, and costly delay line installationswhich, with their stringent requirements, approach thelimit of the state of the art. Another relatively new methodof accomplishing the necessary delays uses digital delay

6

(shift registers). 1 2 These are more compact than delaylines and somewhat less costly. There are several otherways in which the signals can be delayed, such as by mag-netic tape and drums, and by film and thermoplastic tech-niques. These offer promise, particularly for very largesophisticated systems.

However, if a single-frequency periodic wave train (asa "ping" from typical active sonars in the Fleet) is used, itmay not be necessary to delay a particular place in thewave train by the full time of travel of the acoustic wavefrom the first element in the array to the last. Instead,the individual elements can have their electrical signalsoperated on so that they electrically add "in-phase" (co-herently) for any particular direction of sound arrival,They will add in various phases for sound arriving from anyother direction, so the total response of the array to theperiodic signal arriving from the direction of compensationwill be greater than that for arrival from any other dire c-tion. This is what the phase compensator accomplishes.

Deay lines are basically broadband, passive deviceswhich pass both amplitude and phase (or time) information;shift registers are active broadband devices which passquantized phase (or time) information only; phase compen-sators are basically passive, single-frequency, or narrow-

band devices which pass both amplitude and phase informa-tion.

Delay lines for low frequencies and long delays arelarge, heavy, and expensive; they are, however, generallyreliable. Shift registers, for long delays, are much morecompact than delay lines and somewhat less costly theyhave a somewhat lower probability of reliability, usingconventional components, since the reliability factor of atleast one component, the transistor, is added relative tothe delay line. Phase compensators are very compact andinexpensive, compared to both delay lines and shift regis-

ters, with a higher probability of reliability since, for thetransformer phase compensator, the only circuit elementsare toroidal transformers plus one or two capacitors and

7

resistors (900 phase shifters) per beam. For the resistivephase compensator the only circuit elements are resistors,plus only one capacitor and one inductor (900 phase shifter)

per beam; their main limitation is, of course, that they areintended to operate only over a narrow frequency range.An earlier report" describes a technique to enable basicphase compensators for circular arrays to operate satisfactorily over a wide frequency range, with slight modifi-cation. The same method is also applicable to the resistivephase compensator.

8

COMPARISON OF THE TRANSFORMER AND THE RESISTIVEPHASE COMPENSATORS

Phase compensators perform four basic operations toaccomplish their "in-phase" addition of the hydrophone sig-nals in an array to form a beam:*

1. Multiplication of each hydrophone signal by a quan-tity proportional to cos 8., and summation of all "cos 8o

67, otmultiplied signals of the contributing hydr-ophones to give aresultant X component of the voltages.

2. Multiplication of each hydrophone signal by a quan-tity proportional to sin , and summation of all "sin T

multiplied signals of the contributing hydrophones to give aresultant Y component of the voltages.

3. Vector rotation of the result of operation (2)through "90 ° to make this resultant -JY, **

4. Summation of Xand *JY, where the new resultant,which is the beam response, is

RX -jY (1)

*See ref. 5, p. 7 and ref. 6, p. 14.

**The required vector rotation could be introduced before

summation, rather than after, as for example at the outputof each array element, or at the completion of the multi-plication of each hydrophone signal. Either of thesemethods, however, requires more phase shift networksthan vector rotation after summation,

9

Transformer Phase CompensatorThe four basic operations performed by the transformer

phase compensator are as follows (fig. 1):

1. To multiply._each hydrophone signal by a quantityproportional to cos e .,, the signal is applied to the primary

oz7,of a transformer whose secondary turns are proportional tocos e . To sum this with the other signals which have been

multiplied by their cos 8 -, the secondary is connected inseries with the secondar'es of the other hydrophone trans-formers. All primaries have an equal number of turns.

2. To multiply each hydrophone signal by sin ot

another secondary is placed on the transformer of step 1and its turns are proportional to the sin 7 .. To sum this

voltage with the other signals which have been multiplied bysin O , these secondary turns are connected in series withthe sne secondaries of the other hydrophone transformers.

3. Vector rotation (-jY) is performed with a phaseshift network. Either Y can be rotated 90°; or X can berotated +45" and Y, -45°; or any other desired combinationcan be used, as long as the relative phase shift is 906.

4. Summation of the two resultant vectors, X and .JY,is performed in a summation network. The phase shift andfinal summation can be suitably accomplished at one timein a single combined network.

It should be noted that the sin A and cos . will haveA 07,

either (+) or (H) values, or both. The (-) secondaries aretied in series with their winding ends reversed to obtainthe (-) terms, i.e., those 180* out of phase with the (+)secondaries.

10

BEAM I IOAONBEAM 2go.RE 9 PHASE 007.5' REL

0 Z SHIFTS

SIN COS, SIN -CO

®- ~37 ~UW ~3738 38 -- 1

39 - 39 6 **~

40-___ i~' 40 -4--

fl ,~ - 41 -

42 42

pg- - TO 46 OTHER PAIR OF45 46 SECONDARY 6STRINGSi

46 46 -b to FORM 46 OTHER? BEAMS. EACH CORE HAS

47 4* 24 PAIRS OIF SECONDARIES,

48? E jW r ~4 ONE PAIR FOR EACH BEAMWHICH IS FORMED USING

mum ~ - I 4THAT HYDROPHOE CHANNEL2 FOR ITS FORMATION.

4 4

-7 5

ii9

3-- 13 -0

14 -4

36

#OTE: EACH PRIMARY COUPLES INDUCTIVELY TO ITS SECONDARIESIN THE HORIZONTAL ROW TO ITS RIGH4T.(THE SHADED AREAS REPRESENT THE TOROIDAL TRANSFORMER CORES FOR THE WINDINGS SHOWN SUPERIMPOSEDON THEM.)THERE IS ONE PRIMARY FOR EACH HYDROPHONE CHANNEL,AND ONE PRIMARY FOR EACH CORE. ALL PRIMARIES HAVETHE SAME NUMBIER OF TURNS.

figure 1. format ion of two adjacent receivingbeams for the AN/SQS-4 Mod 3 sonar by use Of thetransformer phase compensator. Only 24 of the 48hydrophones in the array are used for each beam.This exemp2 i/lea transformer phase compensatorbeam formation for any circular array* Lineararrays use all the hydrophones to form each beam.

Resistive Phase CompensatorThe four basic methods by which the transformer

phase compensator operates on the signal (as described inthe preceding section) are performed by the resistive phasecompensator as follows (fig. 2 and 3):

1. To multiply each hydrophone signal by a quantityproportional to cos the signal is applied to a resistor

voltage divider and is attenuated to an amount proportionalto CoS 0. To sum this with the other signals which havebeen multiplied by their cos 0., all of the voltage dividersare designed to use a common load, which for any onedivider includes also the parallel load of the Other dividingresistors.

2. To multiply each hydrophone signal by a quantityproportional to sin O0, the signal is applied to a resistorvoltage divider and is attenuated to an amount proportionalto sin 8" As in step 1, the sine signals are summed intoa common load.

3. Vector rotation ( JY) is performed in a high-Q LCnetwork which is also simultaneously a part of all the sineand cosine voltage dividers' load. (Other types of 900phase shift networks could be used.)

4. Summation of the two resultant vectors X and -jYoccurs across a common resistive load. in a sonar systemthis would be the input resistance of the amplifier for thatbeam.

Figure 2. Formation of two adjacent receivingbeams for the AN/SQ$-4 Mod 3 sonar by use of theresistive phase compenseator. Only 24 of the 48hydrophones in the array are used for each beam.This exempifitea resistive phase compensator beamformation for any circular array. Linear arraysuse all of the hydrophones to form each beam.

!2

KANM IMEAN Emy000* mAL OOr?6 ftL

Sim - Sum" m. CS

OCIR

37 s~

4111 ------ TO 46 OTHER SETS OF

JIIL~. . _________ __________ RESISTORS TO FORM 46

Re' %.OtHER REAMS.

- ________2 4 HYDROPHORE CHANN4ELS42 lot M-~~ E EM ARE USED

- - ___ ___ ___________ EACH HYDROPHOHE CHANNEL*%, 6 ~ OREAMI OUTPUT TRANS-

FORMER I 'UECTS TO 2443,PA Or RESISTORiS ORE VIA

M POEACHEKAM INH

T;. ______ . ~ et _ FORID, 11664 THAT HY0110

4.,-- j FORMATION; ALL Or T E

- A.,e

E OA H E

-q__ _ r % u l;

_____

_ 48

A. I, to ______

. L No R

-08. R12 6 cl

e, t ,ec fs _q _ _ N

o-~~-e _ _ Re. % r~ _______

13

T fIA 14-34HYRPOEPREAIS

AND0 TRANSIFOWmERS

I4YDROPHONE STAVES

47 4812

SIGNAL ATEUTDT AUSPOORINLT, I o

149

Other Design ParametersBoth the transformer and the resistive phase compen-

sators must accommodate in their designs other parameterswhich will modify the basic response equations. In manypractical arrays, directional rather than omnidirectionalhydrophones are used. Each hydrophone in the array has adirectivity pattern of its own which, although broader,should be considered in the array design. A second factoris the use of amplitude shading, which is employed in manycurrent array designs and is accomplished by progressivelyattenuating the hydrophone channel outputs away from thecenter of the array (or the portion used for the beam beingconsidered) in a particular pattern. Its purpose is to re-duce the minor lobes of the directivity pattern relative tothe main lobe. This factor must be included in the phasecompensator design for each beam.

Only the transformer phase compensator has mutualcoupling errors which reduce its performance in smalldegree, unless corrected in the design. These factors aretabulated on page 6 of reference 8 for the phase compensa-tor design for a particular circular array. *

Also, in designing a phase compensator it is necessaryto be able to perform the four operations in terms of thespecific array cofiguration, namely, hydrophone spacingand arrangement in terms of the phase relations of thesound in water. ** The response to sound from any direction

of an unshaded circular array which has been compensatedfor the direction of the axis of symmetry is:

+iNI 2R F, expji, -90 )l (2

i. = -NI12

*See ref. 13, p. 43 ff.

**See ref. 7, Appendix; and ref. 8, p. 5 and 9.

15

The response to sound arriving from any direction, of acircular array with cosine-square law shading and allowingfor the response of a single element, is:

cos (t , cos E "-"T),I xje9 (3)tNIA

t -N/2

The number of secondary turns N and N, and theirC a

respective proportional voltages (for equal voltages intoeach primary), e . and e (fig. 1), and also the propor-tional attenuated voltages of the resistive compensator(fig. 2) are made proportional to the cosine and sine of A'

respectively, in both cases:

N ore osO (4)

N ore sine . (5)S 0 7,

The basic values above are now modified to include,for the transformer phase compensator: (1) the couplingcorrection factors y O and y-; (2) the shading factors,e.g., cos2- (t T 1) 7ND ; and"(3) the maximum number ofsecondary turns - - chosen for the AN/SQS-4 Mod 3 to be 112:

N C ' 112.cos2 [(tT1)7.5 °1 *coseot (6)

N - 112cos2 [(tF) 7.50] -sin (7)

The e t and e to be achieved for the resistive phasecompesa or do nok include the coupling correction or the

16

maximum number of turns and are:

e cos (j; )7. ° cos (8

e. ccos (t;t) 7e50 • sinO (9)

in general, for any array configuration, the e ande to be achieved for a resistive phase compensar aredirectly proportional to the basic number of correspondingsecondary turns, plus the shading factor, of a transformerphase compensator for the same array, The value of eachattenuating resistor will always be related to the number ofturns of each corresponding secondary winding in its trans-former compensator counterpart.

The cosine resistor network is designed as a minimumloss pad for summing the signals, The sine network intro-duces the additional loss relative to the cosine network re-quired by the shading factor.

17

DESIGN OF A RESISTIVE PHASE COMPENSATOR

Figure A-i in Appendix A shows a resistive phase com-pensator in schematic form. The quantities e , etc.,denote the voltage outputs of the tth hydrophone. T y havethe same amplitude, but may have opposite polarities.

The attenuating resistors r_. r. etc., are definedby equations A9 and Al0 of Appendix A:

at 77;7_e__

and

ct Ka -cot

where

R wL (eqn. A6, Appendix A)

and L and Care the phase-shift network elements.

K 1 - _ (eqn. A16, Appendix A)N

ja cos :0

and 0 . is the phase at the tth element (also see list of sym-bols, p. 2 ) This quantity is determined by the geometryof the array.

The shading factor of the tth element, at, is determinedby the desired minor lobe levels,

Thus all the r 's and r 's can be found. An exampleof the design of a single-beam resistive phase compensatoris given in the following section.

18

TEST RESULTS OF THE SINGLE-BEAM AN/SOS-4 MOD 3RESISTIVE PHASE COMPENSATOR

A singl-bearn, 16-elemnent, resistive phase comipen-sator Was designe d (s ee table 1) in February 1958 and testedin Ocoe 198o teA QS-4 Mod 3 Sonar, using SonarTest Set TS-826/SQS-4 and the Target Signal SimulatorControl C-1458/SQS-4.

TABLE 1, Design parameters and key equations for the design of e singlebeam, resistive phase ccmensal for the AMIS0S4-Mod 3 sonar.

cos _______ SIN _______

Caceaalcuz St. Value lo0,Cdw SOL Vilue

ohm si iate assedT lae Used6, Cons. cos-i * du~ hiehos' kit Sil k llifhs kllehffis

.pvZ L -522.43 _l10.31 -k95337 -02927 A3.3t8 17.1%6 16.9 -k.08 -0.931 -107342 54190 5Z.3

1 4018 0.43414 +0.761,16 +0.33091 t..814 -a25 1. -064856 w(028195 -1547 17.W-511.4___ 29L171 0 5a2 .0. 37002 .0.20916 +4 7816 2413? 23.7 -0. 9290 .0.52514 + 1906g .13 95

49-11. 11 1169134 -0. 95043 -0. 657W -1.5219 LW7.3 1.68 +0.31093 .0. 2149?+ .46518 231484 A.4 L -1123 _46030.19i52 -1479-2.376_ 3210 2. -0. 8A -0.617 -Wi 39 !A .3

3 -62.30 0.8906 .0.46355 .0.41%46 .Z.4028 12. 146 12. 1 -0.618W -a.79452 -128 6.3j54 6.3j42 §- It5 096194 40.9332 +0688818 .11259 5.68-4 5.76 0.(L384B -0.54 - 2.70 1646 117

1 -- 2.52 C0.L99572 +a.99914 .'6.976 .10063 S. 05 5.11 -0. 04393 -0.04372 -2.872 15.411 115.0-1 -2.52 0. 912' .0.5mw41 .0.9476 +.053 5.075 5.11 -. 49 007 2.78 1.1 1.

-2 - 22.58- It.96194 .0. 923321_+.88818 +L11259 5.684 5.76 -(1.3848 A -03694 - Z7 116666 13.1-3 -6238 (L89068 0.43551+0. 41566 .440511 12.14A 3t2.1I -0.8863 -0.702 IL 2W5 6 635-4 6.34--4 -121.23 It61438 -&.514521-. 41709 -Z.3976 12.104 12.1 -085584 -&G6779- 1039 1.W4 7.32

-5 -190.311 0. 69134 -0. 95043-0. 67 A. -15219 1.683 7.68 +0.31095 .0. 21497+ .6518 21484 2362

-6-97 056526 .0.37=2 f.0.2016 .47810. 24 137 2361 t09 0554*102 963 953

-W2? -8, -52243 10.3W 1 -05337 1-0.2W2 1-3.3982 117.156 116.9 -0.30182 1-.09316 -10.734 54190 52.3

I -NI2 i -N12I I6i cos i~iI - &4143 1 IoisinT15 I -6.0213

NoeThe values forg1i, o, cos!I, and sinli~ were otainedfromtale 1, pape6 st ueeecS -fyrthlessdorthe

design of the transformer phase compensator for the AWSQS-4 Nbd 3 sonar. Although 24 elements were used for the ANS QS -4 Alod 3only 16 elements were used here to form a beam.

-----------------------------------------

KEY EQUATIONS

L RU *d0i4chosen) 5. r, !o SW

2. K It I 4480II 2-- &.4143 6.r RIoI 60__ 004111 -I ~IoclnS 2U - 6.4r z-0 13 O

iXW jlI 1 -7142

Ci 1w%1 ~ 'ci2109.7 SK vlueZ Ilhos

19

Figure 4 shows the circuit tested. The transformersused were surplus, NEL No. 4646, with 1475 turns with anominal audio impedance of 1000, to 1,000i, Two of thesetransformers were connected to act as one for each of the,16 circuit transformers, with a 400-ohm, center-tappedload across each secondary. The resistors used were thenearest standard value of the RN 70 B encapsulated filmtype, ±1 per cent, watt. The inductor L was a small toroidwound at NEL with L 7.96 mh ±1 per cent and Q = 90. Thedesign value of the capacitor, C, was 0. 0221 f ±1 per centand was obtained by paralleling several glass capacitors ofnominal 5 per cent tolerance and bridging them. The inter-nal keyed oscillator of the test set was disabled for themeasurement and a steady external oscillator signal, moni-tored by a counter, was injected into the test set. Themanual target-bearing control was rotated at a slow, con-stant rate (approximately 1 revolution/35 seconds) by asmall motor gear box attached to the shaft. This simulated,as received by 16 of the 48 elements at a time, a plane-wave source circling around the AN/SQS-4 sonar at a con-stant rate.

The outputs of preamplifiers No. 41 through No. 8were then conmnected to the resistive phase compensatorinputs, thus forming a beam in the direction of relative

bearing 0000. Any other beam could have been chosen.The individual filters in each preamplifier could noteasily be removed for the tests, so it was necessary to

"brute force" the signals through them while measuringresponse of the phase compensator at other than the designfrequency. Of course this resulted in much lower signal/noise ratio at ±17 per cent from the design frequency, butthe most essential information remained above the noise.The output of the resistive phase compensator was amplifiedby a variable gain amplifier and recorded on a Briiel andKjaer Type 2304 logarithmic recorder as a linear plot ofthe directivity pattern,

Figure 4. Circuitry of the single-bam,16-eloment resistive phase compensator tested inOct ober 1958,

20

2.K- 16.9K

414

- 9.33K + 2.3 K

- 23.2K 64UK

440 JO ll _5 ?

45 2K +6.34k.. ,IZI

46- -n

- 13.7ik 6_.76K

~ 115 *5.IK - ~20 +

- 115k 5.1 IK I WS, 44 3-+ %- -- -- lI PE

+ I -- 0

.7K DETAIL OF-ACTUAI. TRANSORKIER USEDTWO NEL 4 646 TRANSFORMERS WIE CONNECTEDI

+ AS.7 SM AB OVE TO ACT AS ONE FOR ALL OF THE2 ~ -TEST UNIT TRANSFORMERS.

-- ~EACH TRANSFORMER HAD A NW&N MkDO SO2IiCfl OFLo 3000* TON3000*AND A TURNS *Aft3 OF 1675/1475

- 6.34K.. +12IKso +

II-- 7.32K.. - 12.1K-

232 .7.G6K

51--

1 7.4K WO.K

-- sm wis COS BUS

7.96H .0221 OF

r, RL6.1K 64* 1K OUT

-I 94A M

Figure 5A shows several strips of the resistive phasecompensator patterns recorded at frequencies above,below, and at the design frequency. Figure 5B gives threecomparative patterns for the transformer phase compen-sator, obtained in the same manner.

Figure 5. Phase compensator patterns at variousfrequencies. Per cent of design frequency isindicated at upper left of each pattern.

A. Linear Plot of directivity patterns of re-sistive phase compensator. Since these were ob-tained through the AN/VIS-4 preamp filters, theabsolute amplitudes cannot easily be correlated atdifferent frequencies; however, the beam shape,and amplitude relative to the minor lobes, arealmost identical to those of the transformer phasecompensator (and also the AN/SQS-4 scanning switchbeam) at the design frequency, and they appear toremain useful (at least 18 db minor lobe suppres-sion) at 83 to 117 per cent of the designfrequency -- is.e., over a bandwidth of approxt-mately fo +17 per cent.

22

D83

92%

-- AA-

100%

117%

mo 91f 1800 2700 00o

23

DB

DB

-woo 900 130 2700 0000

Figure 5 (Continued) B. 1 nea r plot of dirsctivity Patterns of transformer phase compensator,shown for comparison with those of the resistivephase compensator, figure 5A. The remarks on thatfigure also apply here.

24

CONCLUSIONS1. A single-beam, resistive-element phase compen-

sator network was designed and constructed for the48-element array of the AN/SQS-4 Mod 3 sonar with half-wavelength spacing. its performance was determined in thelaboratory by use of Sonar Test Set TS-826/SQS-4 and Tar-get Signal Simulator Control C-1458/SQS-4.

2. This phase compensator produ ced a single beamwhich, with its minor lobes, was essentially identical tothe beams produced by the 48-beam transformer phasecompensator, which was designed for the AN/SQS-4 Mod 3sonar and was tested in the same way.

3, Satisfactory operation of the phase compensatorthroughout the frequency range within ±17 per cent of thedesign frequency was demonstrated, yielding beam patternswhich were very similar to the transformer phase compen-sator patterns obtained in the same way.

4. Compared to the multibeam transformer phasecompensator, the multibeam resistive phase compensatorwill be more reliable in operation. Further advantages arereductions in weight, size, and cost made possible byprinted circuit or microminiature techniques. Manufactur-ing, especially in large quantities, will be expedited, andtesting and maintenance simplified. The equipment offersconsiderable flexibility for interchange in the event ofoperational or combat damage.

RECOMMENDATIONS1. Make available the information in this report to

interested contractors along with the recommendation thatthey consider the use of the resistive-element phase com-pensator for those sonar receiving systems in which thetransformer phase compensator had been considered orplanned,

25

2. Design and construct, at NEL, a multiple-beamresistive-element phase compensator and conduct completetests to investigate the multiple network intercoupilingeffects.

26

REFERENCESThe following references include those cited in the text

and others which present related information.

1. Navy Electronics Laboratory Report 582, Scope Pres-entation Array Compensator by F. R. Abbott 27 April

1955

2. Navy Electronics Laboratory Report 632, S imultaneousM-ultibeam Phase Compensation,i: Concept and Design ofTransformer Coupled _0Potentiometer-C ompenator;11: Uniform Linear Array Phase CoMpensation Analy is,by A. A. Hudimac, 30 November 1955

3. Navy Electronics Laboratory Report 642, SimultaneousMultibeam Phase Compensation, jII: Inductive ComprnsatorDesign and Operation, by F. R. Abbott, 2 De.ember 1955

4. Navy Electronics Laboratory Report 670, SimultaneousMultibeam Phase Compensation, IV: Linear Array Inductive Compensator Output Processing and Evaluation, byC. J, Kieger, 9 April 1956

5. Navy Electronics Laboratory Report 674, Simultane ousMultibeam Phase Compensation, V: Circular Array Induc--tive Compensator Evaluation, by C. J. Krieger,CONFIDENTIAL, 3 April 1956

6. Navy Electronics Laboratory Report 757, SimultaneousMultibeam Phase Compensation, VI: Phase Compensatorfor the Lorad Station-Keepng Receiver System, byC. J. Krieger and R. P. Kempff, CONFIDENTIAL,7 May 1957

7. Navy Electronics Laboratory Report 806, SimultaneousMultibeam Phase Compensation, VII: Circular ArrayPhase Compensator for the AN/SQS-11 Sonar, by-

C. J. Krieger and R. P. Kempff, 26 September 1957

27

8. Navy Electronics Laboratory Report 851, SimultaneousMultibeam Phase Compensation VIII: Des ig- and - Labratory Evaluation of a Phase Conpensator for the AN/SQS-4

Mod 3 Sonar, by C. J. Krieger and R. P. Kempff,CONFIDENTIAL, 18 July 1958

9. Navy Electronics Laboratory Report 985, SimultaneousMultibeam Phase CogipenXsation, X: A Multibeam Receiv-

ingSSytem for the AN/SQS-4 Mod 3 Sonar, by R. D. Straitand others, CONFIDENTIAL, 22 September 1960

10. Navy Electronics Laboratory Report 1009, Simultane-ous Multibeam Phase Cpmpensation X fBroadbAnd App~ication, by F. R. Abbott, 8 December 1960

11. Navy Electronics Laboratory Report 1108, Simul-taneouAMultibeam Phase Compensation,_ Xi.: Beam Forma.&tion with Line ar,_ Circular, and General Arrays bPhaseCompensation; Summary as of 1962, by R4 P. Kempff,7 May 1962

12. Anderson, V. C., "Digital Array Phasing,"Acoustical Society of America. Journal v. 32, p. 867-870,July 1960

13. Naval Postgraduate School. Phase Compensation ofSonar Arrays, by R. C. Olson, CONFIDENTIAL, 1957

14. Navy Electronics Laboratory Report 1085, A Scanning

Sonar Transmitter Employing the Matrix Phase Compensa-tor and Silicon Controlled Rectifier Switches, byJ. T. Redfern and F. R. Abbott, CONFIDENTIAL,18 December 1961

15. Navy Electronics Laboratory Technical Memorandum292, Proposal for the Design of a Phase Compensator forAN/SQS4 Mod4 1 Sonar, by R_-P. Kempff, CONFIDENTIAL,

24 June 1958*

28

16. Navy Electronics Laboratory Technical Memorandum337j AN/SQS-4 Mod 3 Sonar with Multibeam ReceivingSy stemTest Results, by C. J. Krieger, CONFIDENTIAL,19 June 1959*

17. Navy Electronics Laboratory Technical Memorandum351, Formation of Narrow Transmitted Sonar Beams E m-poying the Phase Compensator, by J. T. Redfern,30 July 1959*

18. Navy Electronics Laboratory Technical Mernoriandum388, Rotated Directional Sonar Transmission with Semi-counduct-orSwitching by F. R. Abbott and J. T. Redfern,10 February 1960*

*NEL Technical Memoranda are informal documents

intended primarily for use within the Laboratory.

29

APPENDIX A: CIRCUIT ANALYSISFigure A-I illustrates the circuitry for the formation

of one beam with the resistive phase compensator.

SINE COSINE

d

rsz

e N, - -I

I

:R

-L -_-

)'iqure A-i. Equivalent circuit No. 1.

It is desired to attenuate the signal e . from hydro-phone element t by means of resistance r* (which is a

physical resistor plus the generator resistance) to a valueat point B which is proportional to a1,. sin . . The same

result is desired for the e voltage. In addition we mustchoose the proper values -L and C so that the resultant

voltage from point A is phase-shifted -45 ° at point B, and

the resultant voltage from point C is phase-shifted +459

also at point B to give

ES = X- jY (Al)

To determine our relationships for this, we will putequivalent circuit No. 1 into the form of equivalent circuit

31

No. 2 (fig. A-2), letting R 1,and P respectively, be theequivalent resistances of tie rs in parallel, and of the rin parallel, so that StCt

N N

SR

Figure A-24 Equivalent circuit No. 2

Considerin g the effects of each equivalent generatorseparately (Es and Ec) by -superposition, we arrive atequivalent circuits 3a and 3b, for the sine and cosinesides, respectively (fig. A-3).

RL

__I _

Figure A-39 Equivalent circuits Noa. 3a and 3be

32

First, we will consider circuit 3a. Since we want toknow the ratio of the voltage out (E ) at B, to the voltagein (E) we will have so

8

L cf 1tC

11

R + Q :(R -j-)so - so L oC

aain and

F, 2 R (R--)(3

" L + -).RR++ -uj +

RL + c( C

Now if we specify the condition

R xRO Cy WL= (A4)5a Wu 0

at the design frequency, we realize considerable simplifi-cation, and

EE

9-3

60- 1 (l-j AAR RR

hL RL - L

The relative phase of the voltage is cps m 459, asilus trated below:

E

"s

33

Note that the phase shift is independent of RL. The ratio

AR IRL will determine the total attenuation from input to

output.

We can, in the same manner, evaluate equivalent cir-cuit 3b and find that

Ecc 1 (AO1 )(+ (E 1 2(1+) 2(1+

L RL RL

and that the relative phase of the voltage is p +456

¢ -+5

Ec

C

Thus the sum of the attenuated sine voltages will bephase-shifted 45*, and the sum of the attenuated cosinevoltages will be phase-shifted +45 - with respect to the inputreference. The sum of the attenuated sine voltages willthen be effectively phas-e-shifted "90 with respect to thesum of the attenuated cosine voltages. This will performthe rotation through -J, and R X - jY.

We can now establish conditions which will allow us to

find the values of each of the attenuating resistances, rand r

First we will consider the sine resistors by redrawingequivalent circuit 3a so that we may show a different im-pedance that will be useful.

34

As shown in equivalent circuit 4 (fig. A-4), we shouldnote that, at point A, we look to the right into impedance

and to the left into the resistive impedance PR, whicha 1 -swe have already specified as equal to uiL, -,and R

CEquivalent circuits 5a and 5b (fig. A-5) shobw how we canconsider each r in~ turn~ by allowing all of the i nparallel, except ihe one being considered, to berepre-sented by a new equivalent resistance R.

R

AA ___RL

F1igure A-4. Equivalent circuit No. 4.

8S A 010S

RS'

Oslo

31 A

Figure A-$. Equivalent circuits Nos. 5a and 5b.

35

Of, course, each P ' corresponding to each t .will bedifferent, but the impedance looking left at point A willalways be R, and looking right at point A will always be Zso the impelance at point A will be constant for considera-tion of each of the r 's.St

th .... , - -. .Since we wish the t attenuated voltage e. to be pro-

portional to a sin e,,, we write from equivalent circuit 5b

t

PtSi

r -- , -KI at Sin 0 (A7)

where K is a constant of proportionality.

We also see that 1 1 1R 1 1

or

1 r- ao(A8)R R r8 b St

Substituting into equation A7, we find

r o-- (A9)a K si

and similarly

R0

c os (A!O)

36

Using equation A2, we have

R ~ C U Csin60T., (All)

and

C' 0 cOt (A12)

Since our circuit design rests on the assumption thatR R~ (eq. A4) and since 1si9 is not neces-

sarily equal to io. ~ cos g~ principally because of

shading, 1 /P - and 1IR can be equalized by introducing aresistor r in parallel with the other r Is (fig. A-6). 'This

8 atresistor can be considered as an additional sine generator,

but with zero signal.

Figure A-6. Equivalent circuit No. 6.

37

1 1

if, for example, < , then - can be increaseda c a

to equal by means ofc a

N

1 K .-

-R-- R ,

s (A )

N1 K( '

R R L t Aocs o A

But from equation A6, 1 1 1

R R0 c

S o that

1 I COS I (A15)0O 0 -O

We can now solve for

1(A16)la teCos eo0 O

and substituting into equation A13 we find

r = - (A!7)

G t %sin @ OI

NtE IaoCS e0~ I

38

If., as a special case,

C, Isin eo aCose 0

then r and no shunt resistor is required.a

if < then can be increased to equalC S CS

39

APPENDIX B: MULTIBEAM COUPLING EFFECTSin 1957 a study of cross-talk suppression in an

inductive phase compensator was made by R. C. Olson, *

but these multiple coupling effects in a resistive phasecompensator have not been analyzed rigorously with ex-perimental verification. However, a qualitative approachwill be indicated here which should yield a workable solu-tion with a moderate amount of time and effort,

There are several different crosstalk-effect voltageswhich may be considered; these will be combined with thegenerator (preamplifier) signal voltages in a -mannerlargely determined by the nature of the sound received bythe hydrophone array. The nature of this sound can beconsidered to be in one or more of the following threecategories :

1. Essentially plane-wave coherent noise (listen-ing passively, received from other ships, torpedoes, etc.),or signal echo which may arrive either from (a) the com-pensated bearing of a given beam under consideration, or(b) from some other direction which, for purposes ofpractical significance, will be confined to bearings close tothe compensated bearing. Some types of reverberation aswell as multipath returns from other causes would be asource for these returns from other directions.

2. Semi-coherent self noise from all shipsources, including machinery noise, screw noise, turbulentwater and bubble noise, flow noise, and transducer fairing

excitation noise.

3. Ambient sea noise comprising marine lifenoise, surface noise, etc. Except for nearby fish noise,the ambient noise will probably be largely incoherent, de"pending on the local environment.

*Reference 13, p. 47, fig, 39, and Appendix III.

41

Additionally, electrical circuit noise will add itself, butits contribution to cross talk will probably be negligible,even under very quiet listening conditions.

The foregoing factors should be considered for a fullanalysis of multiple-beam cross-talk effects, However, itappears that category (1) will give the cross-talk effectwhich has the most practical significance, since the voltagesgenerated by categories (2) and (3), as well as circuit noise,will approach random phase sunimmation on the sine andcosine busses. This would tend to give only the same typeof beam-degrading effect as incoherent sound noise re-ceived directly by the hydrophones used to form any givenbeam.

Since the output voltages of the beams are of primeconcern, it appears that a useful criterion of cross talkcan be the amplitude relationship of the outputs of severalbeams adjacent to the one on which a compensated coherentsignal is being received. This may be visualized, as wellas simulated for practical measurement, by the injectionof a continuous signal voltage into a beam output at a knownlevel and calculating or measuring the adjacent beam outputvoltages, while at the same time insuring that there is noappreciable contribution by signal or noise voltages fromthe preamplifiers (such as zero input to all preamplifiers).

Figures B-1 and B-2 illustrate the fact that the multiplegenerators contributing to the network of each beam combinetheir multiple voltages into two single voltages which arethe summed "sine" and "cosine" voltages respectively, onthe "sine" and "cosine" busses. The current from thesesummed voltages will flow back through the parallel com-bination of any given generator resistance and the "other

beam" impedances to which it normally contributes.Therefore, the attenuation of the cross-talk voltage from agiven beam, via the path of one of its contributing genera-tors, is determined by the ratio of the particular "sine"and "cosine" resistors to the parallel generator resistanceand "other beam" impedances which it feeds. Obviously,the smaller the generator resistance, the smaller will be

42

SIGNAL. FROM: PREAMAP #I AND CROSSTALK FROMI SEAM I

to ONOE SEMwNETWORKS

J CROSSTALK CURENTSINTO rQi, AND ALSO

16L INTO THE OTHER SCAMreAMP NE MTWORKS TO WHICH

HYmOHNEI to TOtH f SAMS NOMLY TOM H

OTHER UNCU

HYOROHO# ~rca

OHAN P&LS Icowmi- TO OT RSEA MS

Ti M 9 -- AM. - rg ....

To OThER BEAMS

Ed. i N. r' L-

I. :/t KAM OUTPUT

Figure B-i. Tllust ration of cross talk, showingthe manner in which the summed beam quadrature

v~ltge$ , E) can be considered single gen-erators contributing cross-talk voltage to adja-cent beams by means of inducing current flow backthrough a given generator (preamp) resistance.

43

OUTPUTS OF KAMS TO WHICH GENERAO0 # I 4TitttUTj(ASITRARV KAM NUMBERS)

2 3 4 5 6 7 S 9 10 l 12 13 14 16 IS

e ri (PRtAUP 0,1I)

F igure B-2. An equivalent circuit, illustratingthat a voltage (0.) introduced at a beam output(with zero input into all preamplifiers) will feedan equivalent current back through a given genera-tofr resistance, creating a cross-talk voltage(e X ) which simulates the normal cross talk voltage(for sIingle-frequency considerations) from theother beam netw~or'ks (Z 1 .. Z 1 6 ) to which generatori normally contributes-a signal.

the cross-talk voltage across it to be imparted to the otherbeams to which it contributes. The preamplifier outputimpedance (design value), therefore can control the crosstalk between beams, since by going down to zero as thelimiting generator impedance, the cross-talk voltage wouldbe zero. However, it is desirable to design the preampli-

fier output impedance for maximum power transfer to themultiple beam circuits it feeds. If the generator design

impedance for maximum power transfer is not sufficientlylow to minimize the cross talk to an acceptable level, acompromise between the two factors will be necessary.

44

APPENDIX C: OTHER USES OF THE, PHASE COMPENSATORBasically, the phase compensator simply shifts the

phases of the signals from various elements of an array ofhydrophones (and the principle can also be applied to elec-tromagnetic antenna elements) so that they add in-phaseelectrically for acoustic (or electromagnetic) signals fromparticular directions. The first use of the principle was toprovide a simple, reliable, and compact package whichwould give multiple, preformed sonar beams. However, itmay be advantageous to utilize this concept in a variety ofother phase-shifting applications.

The technique can provide the formation of single ormultiple phased outputs from single or multiple phased in-puts anywhere that lumped (or determinable) constant cir-cuit elements can be used, and where circuit restrictionsare acceptable; and it is applicable with the use of trans-former, resistor, or capacitor circuit elements. This canbe done in one of two general ways:

1. in a phase compensator designed to provide re-ceiving beams from an array of elements by phasing andsumming the individual element voltages, the process isreversible; and by introducing a voltage signal into any beamoutput, a resulting group of voltages of various phases willappear at the (normal) inputs to the phase compensator. Itis in this manner that some transformer phase compensa-tors have been designed and constructed specifically toform transmitting beams for sonar arrays. 1 4 If, in the re-ceiving array above, two or more voltage signals of thesame or different phases were applied into the outputs oftwo or more beams having array elements in common, theresulting group of voltages appearing at the (normal) inputs

to the phase compensator would have phases and amplitudesdifferent from those with only one "beam" input. Of course,the specific values would depend on the design values of thephase compensator, as well as on the amplitude and relativephases of the voltages introduced into the "beam" outputs,Almost any combination and number of input/output voltagesfor a variety of circuit applications can be obtained in thisgeneral way.

45

2. One or more signal inputs may be consideredas analogous to the array elem ent inputs to the phase com-pensator when it is used to "form" receiving beams; and thedesired phased outputs may be considered as analogous tothe "beam" outputs. 'Thus an almost limitless number ofdifferent combinations of input/output voltages and phasesmay be obtained: two-phase to four-phase; two-phase tothree-phase; one-phase to six-phase, etc.

Figures C-i and C-2 indicate the general circuit con"figuration to obtain three-phase voltages from a singlephase input. This is analogous to a phase compensator fora one-element "array'-' forming three "beams" for pre-determined angles of compensation. There is unly onesignal input to "sum" its voltage on the sine and cosinebeam busses in the resistive phase compensator, so anadditional shunt resistor, to ground, is necessary to allowthe LOC 906 phase shift network to look "back" into the "R "

impedance that will not in general be the same as thatof each attenuating resistor used. By either using a differ-ent 900 phase network, or modifying the original circuitconstants, these shunt resistors might be eliminated. Thetransformer version does not generally impose this re-quirement with its RC 90* phase shift network.

46

PHASE ICl OUTPUT

Figure C-i. Typ~~ixa n-otre h. ewr

uaingtranforme eleent,

PHASE47

L __zi0: --SINGLE PHASE IPHASE 11 -R6 r' UTUINPUT m OPU

RC -OUTPUTTRLOU

Figure C-2.~~~t Typca on-otreephs ntwusig rsisor lemnts

48,,

-, 0

Zo -C Zo.

4. 0-0

z Ik

CC~CC(

--- --------

4 0 o

-' ''-0-

Z z- z wo 1.

wz w

000

.0 t

P4 0.0 a

I~ IL

'ao.

'~4~441.v

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