AD-Ai3l 060 A FORTRAN COMPUTER.PROGRAM TO COMPUTE THE RADIATION IPATTERN OF AN ARRAY-FED PARAROLO00 REFLECTORIU) NAVALRESEARCH LAR WASHINGON ONC J K HSIAD 21 JUL 83

UCASFED NRL-8740 FG 9/2

00-E 111

V ____

liii 1.01812.0

II

MICROCOPY RESOLUTION TEST CHARTNATOVNAL BUREAU 01 S TANI)ARDS ] A

4

NRL Report 8740

A FORTRAN Computer Program to Compute theRadiation Pattern of an Array-Fed

Paraboloid ReflectorJ. K. HSIAO

rElectromagnetics Branch

Radar Division

July 21, 1983

@ DTIO

- NAVAL RESEARCI! LABORATORY 'cLa... W 7shington, D.C.

~Approved for public release, distribution unlimited.83 08 04 J08

CL ELECT

.. . . . . . . . .. . . . . . . ... . .. .. . .. . . . . . . . . .. . . . .. ...Z. . . .. ..)l i I . . . ... r t ll a

SECURITY CLASSIFICATION OF THIS PAGE (Wh.n Del. En(red)

PNPAGE rAD INSTRUCTIONSREPORT DOCUMENTATION BEFORE COMPLETING FORM

I REPORT NUMBER 2. GOVT ACCESSION NO. I RECIPIENT'S CATALOG NUMBER

NRL Report 8740

4. TITLE (end S.blirl.) S. TYPE OF REPORT 6 PERIOD COVERED

Interim report on a continuingA FORTRAN COMPUTER PROGRAM TO COMPUTE NRL problemTHE RADIATION PATTERN OF AN ARRAY-FED S PERFORMING ORG. REPORT NUMBER

PARABOLOID REFLECTOR7. AUTHOR(a) S. CONTRACT OR GRANT NUM9ER(,)

James K. Hsiao

9. PERFORMING ORGINIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT TASKAREA 6 WORK UNIT NUMBERS

Naval Research Laboratory 62712N; XF 12-141 -100Washington, DC 20375 53-1854-0

I. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

Naval Electronic Systems Command July 21, 1983W-shington, DC 20360 13.5UMUER OF PAGES

14. MONITORING AGENCY NAME & AODRE$S.'i d)lJf'enl Iran, CoeroD)lInE 01 r l c *) 15. SECURITY CLASS. (of thle report)

ISO. DEC.ASSIFICATION/DOWNGRAOINGSCNEDULE

I6. ODISTRIUTION STATEMENT lot thli Report)

Approved for public release; distribution unlimited.

17. DISTRIBUTION STATEMENT (at it betract entered in Block 20, If different from Report)

IS. SUPPLEMENTARY NOTES

IS. KEY WORDS (Continue n revere elide It neceesry and Identify by block number)

AntennaReflector antenna n-Antenna pattern

20. ABSTRACT (Cenlinue en reverse sIe It neceeary and Identify by block nutlbor)

- This report describes a computer program to compute the radiation pattern of a paraboloidreflector fed by an array The program is formulated without simplification and approximationassumptions. Its results should represent an exact solution. The program is designed so that itis efficient for multiple sources. Judging from the examples computed, the increase in computertime is modest when the number of source elements increases.

DD 1473 EDITION OFI NoV . S IS OBSOLETES/N 0102-014- 6601

SECURITY CLASSIIlCATION OF THiS PAGE (mn bet.e Eneroed)

CONTENTS

INTRODUCTION......................................................................................... I

MATHEMATICAL FORMULATION ...................................................................... 1

COMPUTER PROGRAM ................................................................................... 5

EXAMPLES .............................................................................................. 6

CONCLUSIONS........................................................................................... 8

REFERENCES............................................................................................. 8

APPEN4DIX A-Derivation of Equation (11) ........ ............. I....................................... 9

APPENDIX B-Computer Program List.................................................................. 10

tc~-c T'o

YT' ~~ d1 '

Availability Codes

AwaIl and/orDit Special

-Ai

A FORTRAN COMPUTER PROGRAM TO COMPUTETHE RADIATION PATTERN OF AN ARRAY-FED

PARABOLOID REFLECTOR

INTRODUCTION

Computing the radiation pattern of a paraboloid reflector has been treated widely in literature I1-4]; however, most of this treatment concerns only the problem of single-feed source whether thesource is at the focal point or offset. In all these treatments, when the source is offset, it is alwaysassumed that the offset is very small and that the distance from the source to a point on the reflectorsurface can be approximated by adding a few linear terms to the case of the feed at the focal point.This approximation may be acceptable in a single-source case when the feed point usually is locatedclose to the focal point to avoid high sidelobes. However, in the case of an array-fed system, thisassumption may not be valid.

To facilitate fast computation, the longitudinal current component is ignored in this computation[11 The error introduced by this omission, in general, is small in the region close to the main beam.However, when fields far from the main beam are of interest, the amount of phase error can not beignored. Galindo-Israel and Mittra [31 introduced a method to correct this error; however, this correc-tion depends on the location of the offset feed. It probabily would not be efficient for a multiple-feedcase.

In this report a computer program to compute the radiation pattern of an array-fed paraboloidreflector is presented. This program is written so that it is efficient for multiple-feed sources and thesolution will be exact. No simplification or other approximating assumption is made.

The purpose of developing this computer program is threefold.

* It will be used as a reference to check the validity and efficiency of other programs whichmay be developed using a more simplified approach.

* It is an interim step to develop a computer program to compute the radiation pattern of adual-reflector system which is currently under a feasibility study at NRL.

* This program may be used to investigate the pattern-synthesis method for an array-fedreflector antenna system.

MATHEMATICAL FORMULATION

Figure 1 shows an array-fed paraboloidal reflector antenna system. The radiation field at a point 4band 9 has the form

o0 ) C c , (0, 46) exp-

Manuscript approved May 9. 193.

1. .,

JAMES H. HSIAO

x

Rz

I/

ydp

Fig. I - Configuration of an array-fedparabaloid reflector

NRL REPORT 8740

where Jj.(9, ,) is the current density induced on the surface of the reflector and pi s the distance forthe nth array feed element to a point on the surface, and

f.- , (2)

where e. is a position vector from the reference point to the location of the nth array element. Forconvenience, the reference point is assumed to be at the focal point of the parabola. Unit vector Rpoints the direction from the current source to a field point which is a function of 4) and 0.

Assume that only part of the paraboloid is used. This used part is known to be a circle at theupper half of the reflector (see Fig. 1). The center of this circle is at a distance d, above the z-axis.Any point on this circle can be represented by

x-psin0cos 6- rcos4o (3a)

y -p sin 0 sin 0 - r sin . (3b)

In terms of the coordinates of the ' and r, of this circle,

x - d, + r, coso'

and (4)

y - r, sin €'.

The position vector from a feed element in the array to a point (x, y, z) on the reflector surfaceis

(x - C.) (Y-f (z - f')

-p' + P + P' i (5)

The paraboloid surface can be described by the following equation:

x1 + y2 - 4f(f + z) (6)where f is the focal length of the parabola.

The surface currents 7. are related to the feed element exciting field by the following relation:

7. - A x A,, (7)where , is a unit vector in the direction of the tangential field on the surface of the paraboloid which isexcited by the nth array element and

where D. is a unit vector in the direction of the field in the nth array element. Assume that the arrayelements and paraboloid have the same coordinates, and that

i. - uij + U.; + uM (9)

where l - 1.

The normal vector A in Eq. (7) for a paraboloid surface has the following form:

Tn - & + 13. i

- + ni + . + n,. (10)

3L-

JAMES H. HSIAO

Anpendix A shows that

J{ u.(nyp + n;p ) + un + upnjnz

+ [u,,p n - u,(nxpa + nzp ) + unp.njyy

+ [u,.pn + Unynp' - Un(nxP , + nyp(I)I, 011)

where a = pL = yp .p '+ + .

The u,,, uy and u,,2 are the normalized excitation field at the nth element in the feed array. Usu-ally, the elements are linear polarized either in the x or in the y direction. In this case only one com-ponent will be equal to unity.

The A.' components are

p, - (d, + r, cos e'- e,,)/Ip,,I, (12a)

puy - (r I sin 0'- ey)/jpI, (12b)' { J - W4f -(d 2d, r, cos 0' + r')l-' 1P, 1, 012c)

,and components of h vector are

n.-- (dl + r, cos 0')/InI. (13a)

ny - - r, sin -0'/Inf, (13b)

n. - 2f/lInI, (13c)where Inl - (d + 2dlrl coso' + r + 41 2) 1/ 2.

When inserting these relations into Eq. (1), on finds that the current J. is a function of r, and 0'which will be used as the integration variables. The vector A has the following form:

-(d, + r, cos 4') + r, sin 4.1 - _ 4j2 - (d - 2dr, cos 0' + r2)J IpI (14)

and

-sin 0cos 4.i + sin 0sin O, + cos O (15)

Therefore,

4 - {(d, + r, cos 0') sin O cos 4) + r, sin 0' sin O sin 4)

- T [4f 2 - (d? - 2dr, cos 0' + r?)cos @}/Ipl. (16)

Insert this relation into Eq. (1) and perform the integration. The electric field has the following form:

(0, 1) - Cf f Z (r )') -L exp [-jk(p. - A)JI rdrid6'. (17)

The 0 and 0 components are

EO - cos O(cos OE, + sin OEy) - sin O)E, (18a)

4

NRL REPORT 8740

and

E4, - - sin OE, + cos OE. (18b)

where Ex, E, and E, are the x, y, and z components of (0, 4)) in Eq. (17).

COMPUTER PROGRAM

The preceding formulation is coded into a FORTRAN computer program which has been tried onthe Texas Instruments ASC computer. Appendix B lists that program. The FORTRAN program cancompute the ratiation pattern of a reflector which is only a portion of paraboloid. This portion is a cir-cle, has a radius r, and center at d, as shown in Fig. 1. The integration is then computed by integratingthe 0 angle from 0 to 21r and the radius r, from 0 to a desired value. The first data card has a 15 fixedpoint format which specifies the following parameters:

I lEND is the number of points to be integrated in the radius r, direction

* JEND is the number of points to be integrated in the ,' direction (from 0 to 2v radians).

* NEL is the number of feed array elements.

* NPT is the number of feed point to be computed at a given 4) angle.

* NPOL specifies the feed element polarization, if NPOL - 1, the excitation field is polarizedat y-direction. If NPOL = 0, the polarization is at x-direction.

The second data card has an 8F10.6 floating point format.

* FO is the focal length.

* RSO is the radius of the complete paraboloid.

* DI is the center of the circle of the portion of the paraboloid to be used.

* Al is the radius of the circle of the portion of the paraboloid to be used.

* FIC is the 4) angle in degrees.

* ARAG is the range of 0 angel to be plotted in degrees.

All of the preceding data, except angles, are in terms of wavelength.

The next few data cards specify the location of the array elements in x, y, and z directions. Thesecards are all in F10.6 form; each contains 8 data. Therefore, the number of cards required depends onthe number of array elements. For example, if the array has 24 elements, three cards are required tospecify the locations of each coordinate. Nine cards are then needed. The sequence is that first read inthe x-component locations, then the y, finally the z-locations. The output of this program is a plottedantenna pattern for E@ and E0 components at a cut of 4) angle specified by FIC and plotted a rangefrom 0 degrees to ARAG degrees. However, if ARAG is negative, then it will plot from -ARAG to+ARAG.

A function subroutine PATF is included in this program. This function specifies the array ele-ment pattern in its own coordinates sin 0', and cos 46'. At the presented time, the subroutine functionis set at an isotropic element pattern. The user may change it to fit his requirement.

5

JAMES H. HSIAO

EXAMPLES

Figures 2a and 2b show the radiation pattern of a paraboloid dish with a 13.88-wavelength radiusand a 25.9-wavelength focal length. A single source located at the focal point is used in both plots.Figure 2a is plotted by use of the method developed by Galindo-Israel [2]. This method uses a Jaco-bian series to expand the integral of Eq. (1) into a series of functions in terms of 4 and 0. Thisapproach should be efficient in computation time. However, when the series is expanded for betterconvergence, the transformation must be performed at the vicinity of the center of the main beam.Since the main beam position is a function of the sources' location, this program is not necessarilyefficient when multiple sources are used. Figure 2b is plotted by use of the method described in theMathematical Formulation section of this report. The patterns on both figures are exactly the same.The central processing time for Fig. 2a is 41.6 s and that for Fig. 2b is 52.46 s. Galindo-Israel's methodis about 30% more efficient.

-I0

-20-

-60 I , I

0

-- 50

0 5

I0

ANGLEW(EGREES)

Fi, 2a - Radiation pattern of a paraboloid reflector computed

by the series expans~ion method

0

-40

-50

I

-6 0 1I ,I

I to

ANGLE (DEGREES)

Fig. 2b - Radiation pattern of a paraboloid reflector computed

by the exact solution

06

NRL REPORT 8740

Next, we tried an offset case. The results are shown in Fig. 3. The required central process timesfor our program and the Galindo-Israel program are about the same as that in Figs. 2a and 2b. Twocases of a two-source and a five-source are tried. Their patterns are shown in Fig. 4. The central pro-cess time is 54.73 s for the two-source case and 57.68 s for the five-source case. There is no way tocompare with Galindo-Israel's method because that program is not designed for multiple-feed sources.

From these examples, the increase of computer time for multiple sources is reasonable. This pro-gram probably is efficient in this sense.

o --

-10

--0-

w -40 -

-50'-

_601

0 5 I0ANGLE (DEGREES)

Fig. 3 - Radiation pattern of a paraboloidreflector -off-set feed

0

-IO0 _

-20

9 -30

-40

-50--50 O I I I I I

-6005 10

ANGLE (DEGREES)

Fig. 4a - Radiation pattern of a paraboloidreflector-two multiple-source off-set feed

.7

JAMES H. HSIAO

-10 t-

2 0

z

-40

-50 -

-60 L I 1 i l -_ - I 1 K0 5 10

ANGLE (DEGREES)

Fig. 4b - Radiation pattern of a paraboloidreflector-five multiple-source offset feed

CONCLUSIONS

A computer program which computes the radiation pattern of a paraboloid reflector with multiplefeed sources is presented. From some computer exampes, the program is efficient for a large numberof feed sources.

REFERENCES

1. S. Silver, ed., "Microwave Antenna Theory and Design," in Radiation Laboratory Series (McGraw-Hill, 1949), Vol. 12.

2. J. Ruze, "Lateral-Feed Displacement in a Paraboloid," IEEE Trans. Antennas Propag.. Sept. 1965.

3. V. Galindo-lsrael and R. Mittra, "A New Series Representation for the Radiation Integral withApplication to Reflector Antennas," IEEE Trans. Antennas Propag., Sept. 1977.

4. R. Mittra, Y. Rahmat-Samii, V. Galindo-Israel, and R. Norman, "An Efficient Technique for theComputation of Vector Secondary Pattern of Offset Paraboloid Reflectors," IEEE Trans. AntennasPropag., May 1979.

- k__

Appendix A

DERIVATION OF EQUATION (11)

pn, = p k + P" + P 2,

= n= j + uny5 + Ui,

hn n.,i + n,5 + ni

where

Im + p12 + p'2.U"2 + U"2 + a4"21

n~+~ + n,2 -1

and vectors p,3,, 4n,, and h are defined in Eq. (5), Eq. (9), and Eq. (10) respectively.

- a~n a. -.(~Let

A'a- (u.P . + Unypn' + unzp 2)

Fn- (u, - Ap )i + (u. - aP,)$V + (u"Z ap- i

e,

7~ -nr- a 2 C,2,fj7

- 1 -u,.,(n~P,, + nzp.) + ui,,p .ny + ump nj~i

+ lupn - u.~(np + nzp,.) + u,~p~nz]5

" tu,,p~n, + uyp - uz(nxg + nyp~)Ji.

9y

Appendix B

COMPUTER PROGRAM LIST

40JRgt LISTING AS., FAST FORTRAN COMPILEK .(ELEASk FT;E05VAT

LSN STArEALNF LP OPTIONS =(dv09fvK*MtV) UATC = 061/e18,2 LSN

0001 PROGRAM4 REFPAT 01320002 0oMM3N/Dd/..O.(s9l00) 01330003 COMPLEX PFIPPP.PSUMPP 0 1. 40004 DIMENSION PFI(39500),PSUM(s,500)sPi'T(3,500),PP(3).JSP(500) 01350005 DIMENSION ERAS(500), AX(5 00), 11(500) 013600fl6 JIME.MS LO sliAC( 0),COTAC(200).SIFI(200).COFT(2D0) 01j70007 DIMENSION EPL-N( 100)sFJX(100),FJY(100).FJZ(100) 0138

L THIS5 PROGRAM COMPUTES THE RADIATION PATTERN OF OFF-SET REFLECTOR 0139WITH cXACT SOLUTIONP NE:LtCrOK (,AN BE PORTION 0; rNL REFLECTOR 0140OF A PRABOLOID AND 0I CAN HAVE MORk THEN ONE RADIATION SOURCE 014#1

oooB CALL RsSTOP 01420009 KEAD I00PILND9JEN0,NLg NPT#NPOL 01430010 IOC FORMAT(1615) 014

L IEND, NUMBER( OF POINTS INTEGRATED IN R DIRECTION 0 14 5tC jEND, NUMBER OF POINTS INTEGRATED IN Fl DIRECTION 0146

IEND AND JLND MUST Bc ODD 0147VPT, NJMB$ER OF FIELD POINTS IN THETA DIRECTON 0148

6 MEL, NUMdEA OF ARRAY ELEMENTS 0149C NPOL~I, Y -POLARI1ATIONvX=0v X-POLARIZATION 0150

0011 RLAD l01.FOvRSO9D1,A1,* IL*ARAG 01510012 101 FORMATOFIO.6) 015 a

&. FOP REFLiCTOR FOCAL LLNGTHCINUAVkLkNGTH) 0153C RSOP REFLECTOR RADIUS IN WAVELENGTH 0154

3 19 CENTER OIF THL LIRCLE OF PORTION OF THE RL"LE6TOR USED 0155L. Al, RALJIJS OF THE USED REFLECTOR CIRCLE 0156C FIC# FIELD PONT AT FIC PLANE 0157C ARAG ANGLE RANGE 015b

IF AKAG.LT.0. PLOT -ARAG TO ARAG 01590013 PRINT 102, IENDoJENDNPTtNE L9NPOL 01600014 102 FORMAT(1OX91615)0015 PRINT l03tFORSOt0I9AlFIC9 ARA60016 103 OCRMAT(1OX,9=10.4)0011 Pl=3.14159265360018 ATRaPI/180.0019 P12wPI*2.009.0 !IC=2IC.RTA0021 COFIC=COS(FIC)0022 SIFlC=SIN(FIL)0023 ASL=8.0024 VSL=5.0025 XFCARAG.5t.0.)GO TO .

0026 ARAGk=-ARAG*co002? TA=ARAG*ATR00ts Asr=ARtAG0029 ASF=-ARA5O0iO GO TO 40031 3 ARAG2cARAG0032 TA-0.00.,3 AST=O.0034. ASFzARAG

10

NRL REPORT 8740

AT SOJRCk L1St1I4G ASL. FAST FORFRA4i rLPILER RELEASE FTFX05

CSN STA7TI4ENT L.P OPTIONS (8#09Ev~vM9V) OAlk 06/24fb2

0035 4 rAC1NM.AKAGf(NPf-1)0036 rAl4N=tAC14C*ArR00j? TAC.=D.0038 XSCL=XL/ARAG200$9 ad I t4Z1,NPI0040 PSUAC1,N)=CNPLX(O.,O.)0041 PSU%(2,F)MPLX(o.90.)0042 PSUR(3tI)=L.MPLJ(0.p0.)0043 X()TLXL0044 LOYACCN)=CO5(7A)0045 SITAL(N)=SINCTA)0046 tA=TA#TAINC004? 1 TAC=TAC*TA:IN0048 TA=0.0049 TA1Nr.P1S/JtNlD0050 DO 2 J=1IJEND0051 CQF[(J)=COGS(rA)0052 S1FI(J)=S1N(TA)0053 jxOD=NOD(jvi)0054 JSP(J)zJNOD*2+(I-JROD)*4Do5s 1P(J.EJ.1.Oek.J.tJ.JEND)J,'P (.1)=I0056 z tA=TATAIt4C0057 F02=FO*O0058 SINC=A1I/END0059 RA1S1NC

G, ENTER OFF-SET ARRAY ELERENT LOLAT1OM40060 READ l01.(ELOCC1.1I)I1NEL)0081 READ 101w(ELOCCZ,[)t,11,NEL)0062 READ I0Im(tLOC(3*I)o[=1,NLL)0063 PRINT 103,((ELOC(KI),K=193)1=gt4EL)0064 Do 10 11,lolNo0065 ROSQ=Rl**2+01.*20066 R01%Rlsol0067 )0 11 N4=19%PT0068 PFI(1.N)aC.WPLX(0.,0.)0069 PFX(2oM)=CNPLX(0.90.)0010 11 PFI(~,N)xCAPLX(0.s0.)0011 )0 20 J=1,JEMD0072 RSR(DOt*D*,~()0073 RCOF1:(01.RI.CQF1(J))0074 ASIFIRsalsIPI(J)0015 R2=R*R0076 FOR2%FO-R2f(4.*FO)0071 12 UNmSUjRT(R2+4.*FOZ)0078 PIsRPX.$&0019 PP(Z)gLNPLXCO..0.)0060 PP(3)*fMPLX(0.#0.)0081 00 22 Lz.NEL0082 P*CF-LL1L0083 PTaRSIF1-ELO,(29L)0084 Pt=-FORZ-ELOL(3sL)0085s lX2zpE**z0086 Prz=PY*.20087 p123P1**4008b EPLEN2aPKZPY2P.20089 OLLU(L):4RT(LPLENZ)0090 IF(NPOL.6PT*0)O TO 210091 U~xSIRTCPY2*Pt2)0092 :JNOR=UN*U4*tPa ,N(L)0093 FJX(L)=(RSIF[*PV-2.*FO.PZ)/FJNOR0094 FJV(L)--RCOFLeP1IFJNORk0095 FJS(Ij=-RC0PI.P4/FJNORk0096 GO TO Z30097 21 JN*SQRTCPXZ2PZ2)0098 FJNORsUN*UN*EPLkNCL)

JAMES Ii. HSIAO

3A) SOURCE LISTING A. FAST FORTRAN :3MPILEK kLLEASt FTXKO5

LSN .TATEL44 LP OPTIONS =(~,,Kmv DATE 06/24/82

0099 ~ FJtL(L)=-&SII-I*PX/FJNOR0100 :JY(L)=(KLOF I*PX-2..0.Pl)/-JNM0101 .JL(L)=-RS1F 1*PZ /FJN0R0102 4.) AUG=EPLtNL)*PI&0103 PC=CNPLA(L*5(AUG)#SIN(AUG))

01fl5 PP(2)=PP(2)+FJY(L)P.0106 PP(3)=PP(3),I:JZCL)*PL0107 22 C.ONTINUE

.OMPUTt 01HA~t DUL TO DIFFE~ENt FIELD POINT0108 RCCzRCOFF. OFIc.RS1FI.SIFXL0109 JJ 0 N=1.NPTCl10 PI$ASE=FOR2.LOTAL(N)-RCC..SITAC(N)0111 AUG z4HASAe0112 P~zC4PiX ((0S(AUG)vSINCAUG))0113 PFI( 1.N)=PFI(1,N).PP(1).JSP(J)*PL0114 PF 1(2,N) PFI(2tN).PP(2).JSP(J)*PC

0116 30 CONTINUE0117 2u LONTINUEoUls IF(1.EQJ. EN0)RS1NIP=R0119 KSIHP=JSP(j).RClio JO 15 L=1,NPF01~c1 PSU(1.L)=PSuN(1,L)4PF1( 1.L)*RSLNP012Z PSUN(2,L)=PSUN4(2. L)*PFX(2. L)*RSINP01t.3 15 PSU(3.L)=P5tP(3,L).PF I(3aL.)*Rb1NP

L. FIND PATTERN FUNLTION0125, PNOR=0.O0e.6 )a 40 1=11NPI(1127 PC= COTAL()*(PSJN(1,1)*COFICPSJN(2. 1)*SIF14)'-PSJN(3. 1)*SITAC(I)01.8 PAr(1.i)=P*GNJG(PL.)012s'I(*(.1.,.PO)NRPT11

0131 PAT(es1)=PL*LONj(()

12

.. .....NRL REPORT 8740

DAT $OURCE LISTING AS; FA!ST FORTRAN C04PILER RELEASE FTFXOS

LSM STATEMENT GP OPTIONS z (BDvkA#Pl#V) DATE 06/24/82

0132 IF(PAT(2.I).Gr.PNOk)PNoR=PAT(2,x)0133 PRINT 105q(PSU"(K9I),K=I,3)0134 105 FORMAT(10X96k1Z.4)0135 40 CONTINUE0136 PRINT 1049(PAT (1I)o.I*NPT)0137 PRINT 104,(PAT (,)I1Nr0138 104 FORMAT(f/,(10Xo8E12.4))0139 CALL PLOTS(ERAS#500,2.)0140 CALL ORIGIN(4.s0.)0141 CALL SQJARE(0.,XSL#0.tYSL)0142 LALL NXAXIS(O.90.PAST a 5.9ASF 9XSL9-.I@.Iv-1)0143 CALL NTAXISCO.,0..-60. l.10. YSL,-.1,..1,-1)0144 CALL CENTER(XSLj'2.,-.8..3,14NANGLEDEGREf.S),0.,1,)0145 CALL. CENTER(-.5.VSL/2. ,.3.Ilh4RADAATlDN(Db),90..13)0146 DO 50 K ,#20147 DO 60 Iz1,NPT0148 IF(PAr(KI).LE.0.)GO TO 610149 08mI0.*ALOG10(PAT(KoI)fPNOR)0150 VW(I)z(l..DB/60.)*VSL0151 GO TO 620152 61 TV(I)=-60.0153 6,d IFCII(1).GT.YSL)YYCI)zVSL0154 60 IF(?T(1).Lr.O.aVY(I)=0.0155 JJ=00156 IF(E.Gr.1)jj=100157 CALL LINE(XXYVNPTsIsJJs4)015b 50 CONTINUE0159 CALL ENDPLF0160 ENO

j 13

Ij