i~l~ll~ ~~E- E~ UNIVE R S ITY OF ENGINEERING RESEARCH 19 March 1956 M ICHIGAN A INSTITUTE Willow Run Laboratories Willow Run Airport Ypsilanti, Michigan Signal Property Officer Building No. 1150 Fort Monmouth Little Silver, New Jersey Subject: Contract DA-36-039-SC-64748, Phase I-A Notice is hereby given that all technical aspects of the subject phase, of the subject contract have been completed. This letter is incorporated as part of the final report of Phase I-A, of the contract. * ^ * l. -- I I~ Donald M. Brown Project Supervisor WRL Project 2411 DIB:em 111 111 U-I s UJKNIL/\SSFIIFII E

U LCL/A\S FEO UNIVERSITY i OF MICHIGAN COMPUTATION OF SPATIAL RADIATION PATTERNS OF RHOMBIC ANTENNAE Final, Report on Contract DA36-039-SC-64748-Phase I-A To Signal Corps Radio Propagation Agency Fort Monmouth, N. J. Period 15 July 1955 to 31 March 1956 James H. Borwn vLj"ye~* ERI Project 2411 Report 2411-1-F Donald M. Brown Project Supervisor - - UiL/A\SFfEEDO

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UiLCI/A\S FEEOJ UNI VERSITY OF MI C'H IGAN N 2411-1-F ABSTRACT A method of numerical analysis to compute the antenna gain for determination of the spatial radiation patterns for the various types of rhombic antennae is formulated. A program for solving the problem on the Michigan Digital Automatic Computer (MIDAC) is listed in external MIDAC language. Parameters for computing fourteen different types of antennae are listed (Table I), and an example of antenna gain for one type is given (App. B). _iiii. ft U1NCII/ASS 1FE1ED

yUHC~l/AE\S151FEOE,, _ _ UNI VE RS ITY OF 2411- l-F M I C H I GAN TABLE OF CON TENTS Letter of Transmittal Abstract List of Figures List of Tables 1. Statement of Problem 1.1. Equation for Antenna Gain 1.2. Parameter Variation 2. Solution 2.1. Ground Reflection Coefficients 2.2. Antenna Gain 3 * Mechanization 3.1. Part I, Parameter Variation 3.2. Part II, Ground Reflection Coefficients 3.3. Part III, Antenna Gain 3.4. Part IV, Print-Out 4. Organization 4.1l Operation 4.2. Error Halts 5. Subroutines 6. Results References i iii v 1 1 3 5 5 7 7 7 8 10 10 11 11 12 16 21 Appendix A Program For Calculation of Antenna Gain, Column Print-Out Appendix B Example of Edited Results ---- FEEEll~it --- —

_ _ __ __ Number 1.1 UWLCLL/A\ASF1 ED UNIVERS ITY OF MICHIGAN 24l11-1-F LIST OF FIGURES Title Geometry of Rhombic Antenna LIST OF TABLES Pag 2 Number I II III v IV Title Antenna Types Parameter Variation Ground Reflection Coefficients (equations for) Antenna Gain (equations for) Computational Flow Diagram Page 4 18 22 23 24 lil = C-I F F-I~

Ui ICL/A S IFII ED UNIVERSITY OF MICHIGAN 1. Statement of Problem,?lhase Ia of contract DAi-36-.39 3C-647t18 requires ther comprutation of~ the a.ntenna. ai n for 1i. different tyrpes of rhonbie antennas. This gain is to 1be calculated for thle parareter variations listed in section 1.2. 1.1 'quations for Antenna Gain. The antenna gain, A, in decibels, is givel by the equation t~12 2 (i. ) A = 10 log10 --—. (126.3) Tne horizontal and vertical polari.,ation co pronents, E,' and EV respecti. ely, are expressed in millivolts per reter at one mile by the equation Ev = r" GI ), wherc - K ecs 1IU2u(cos i( - sin C cos a), (1.3) F" = K cos T UIU2 sin. sin A, 1.1h) __2 __.). *The derivation of the following equations is given in reference 1.

UNVERSITY OF MICHI GA _ UNIVE RS I TY OF M I C H I GAN -2- K = constanrt ) U1 L 1 K _ K1 ) ) i ' I ) I A' (1.,5) Tr L K2 sin m't~ K K2 K. = - cos A sin (} + r) ),) ) (1.6) K = 1 -cos A sin (p - i, ture., d efines thle geometric quarntti -s of the above equations, I I I I rC1t Fig. 1.1 Geometry of -hombhic Antenna c oE

lUyiCL/A \55 F lED....UNIVERSITY OF MICHIGAN G = 1 + R e-jp' + (Tr4H/x)sir A] Gr 1 -.,i" e-J!P' + (itr'/X)s in L.8 G t - (1...8) 'h ere Rh e-j s - i A - c (12) sin A + (< C cos A)>.....R e-j P........_...... (1 10) S constant, ratio of arth-ai r di-lectric con. stan ts - = grounii conrl':ctivity, emu. The quantities C:, and Gf are thie round reflection factors for horizont.al and vertical polariz tinc, resc 'Ptivo-ely. o. 2 iarameter Variationi. 'Th,a::-:: t':e:s for' the calculation of the.ntenna gain are: L leg length, in feet. H = height above ground, in f:eet, = one-hall' the included angle, in de. A = vei-'tical aangle of wave arrival or departure, in d lerees = s l3azirmuthaal angle of wrave arrival or departure, in degrees. X - 300/f = wave len.ch in meters, wThere f = frequency in ec. UlCLL/AS5IFE E

__ UNI UNIVERSITY OF MICHIGAN T' e Li irst three parameters are funcsti'ons of- the antenna type. T'here are 1i of these types, i'iich are aited in Table I. The other t,-ree r..a:e-ters: iav the ranges 2 ic < 30 mec. = < 2 de.. A < A cleg. ) (12) / 0 deg, <I < l80 deg%. Tie calculation of the antenna gains is made for aech type of an'tennr. ma for: 29 firequencies, 2 through 30 mnc., inclsive 30 values of A, eaclh two degress from A = 2 to lh20, and each five deCrees from A = 4o to 8~5 )46 values oi p, each, two degrees fLrom = 0~ to 30, and each five deg-rees from,, 3G to 180~. Ti:s g:ives a total of 560,230 valules of the antelna gain r.u.re re TABtLE T uAntenna Tryes Typ:e L, ct.___ }[t.f _, ~,~e o A i375 6^- 70 B3 350 0O 70 C 31.;: 57 70 i 290 Q 67.5 E 270 53 65 F 245 51 62.5 G 225 50 60 (cont.) UINICL/ASSIIFIIHE

y Il ClLA\55.iFl EJ U N UNIVERSITY OF M I C H I GAN TABLE I (cont.) Tyve L, ft. H, ft. ___ deg. RD-1 C00. 130 67 PD-2 00 130 68 RD-3 100 130 69 R-1t 1oo 130 71 R-/D 1540 1 30 62 RD-6 L'50 13(0 61, sR:-7 h50 130 70 2. Solution. 2.1 Gou lnd reflection coefficients. Th;e.r&iurom reflection cocffi:ciernts, e 't and G" of c-quations (1.7);r2:d (1.8) are comp!lx quantities; therefore, the niagnitudes of the polarizatition coemponents used in equa tion (11) may be expressed as // " F' '(G' G'-) ) )]A~~ ~~(2.1) /zi/2 =,,"2(G" GI"-*) ) Let G0 G + G ) 1 2 ) (2.2) G" ' G" + I G ) e '. + j _j o "L ) (2.3)?J e p j + j Ri ) UJINICLL/ASIIFI I E

U NCL/AX55FFlEtD) - UNIVERSITY OF MICHIGAN -j iT H/X sin A n e <J. s = cos g + j sin~. (2.?.,,) TheRt, ftK~~ 1 d ) 2(2.:) t"' = - 1 - 'i j ) wsJhere = R c - s ) I 1 2 ) (2.6) t = jlg sin. + R2 cs C ) 2 ' R!t cos - R sirn g.) G') (2.7) '''t = A1t 'sin>l V + R cs g ) '-'? '. i p* s.;z.. ttex: r i I -," o~ Gs -- = (1 +,R)2 +;,2 ) 2 )A~~ ~~(2.3) R GC =1.,l ) + '24 1.~~~~~~~ 2. Equ.ations (1,) and (1.10) contain the term (i cos A).Since 't is a. ccipleorlex quanti ity i..s necessary t- determine the si r to be used upon t.aline the sIqare root, Let C1 - Co,. c - j n, B ej" (2.9) The factor n is aways:negat.; ve, ian t-he factor c is always:ojositve; t"-ierefore, the: ang.le & io.i il-n the fourth..quadrant. T.he s'uare root requires /2 Thi'e si5n: was c 'seon so tat the hal.f-anrle;uns also in the fourth 1uadrant; Ss, ) uent c ecks with ino, values proved that this was th:e correct assurm.tion, UINkCL/AS II'FED

1I ICL/A\S F lED UNIVERS ITY OF MICHIGAN I.., 2 2,2 a'nterna Gain, Te ftactors iFt and F" used in determinming the a.nt, nn a an involve straight —fo.rward algebraic and tri.onom.tric co._uutations.'. 'or pur.:poses of odii-.tal comrutation, equations (l.6) 'were ecpanded in terns contaninig the sines and' cosirne of 5 and,. 3 0 'h.echan iat ion. ThLe cor'ni. tation of tlhe antenna gain boy 'the KII-A1C involves not only the solution of0 th'e iei.en en qucati.rons, bu't also an orga-ni:. aton of the prograrl so th'.at als I;itt le timrre is srent in t;h com'mutaticn of eac'h val.uie of antengna gain -.as poss.ible, This is necessary bc aus3e of the large number of values to be computed. IThe complete prob1)le m was divided into four parts. Part I controls th'e;lrrmetter variation, and some s-nes ad c O,- nes a.re omcluted, in this part. Part 11 comrutes the gtrolud reflec.tion coe-fficients; Part III co::inpletes the cen-,:utation of the antenna gain Part IV is the printout piro:raml. 3.1 Part I, Parar,-weter -Variation. Trhe parnamter variation e;a3 chocsen so as to inir ise t'e amount of *calculation 'cquired. Lachr, of the 1)I antenna t ps req ui res te caclculation of.!.0,0 20 values of th-e asntenna.ain. T'-.s costitutes a run itthlin a run the an.-le is variedr the st;the requency,runM( hi~itzi~n a runl, th~e anvc-e toel Ir and th'e ang'le A follow, in decreasing order of vaia ti on Thus, the.vaeriation -is considered. to b in t, finnet r loc ith 'the Ii, INICI /E5II51FlEJ

U NI VE R S ITY OF MI C H I GAN vari-tion in. th Le;iddle loo00p; rn the l-va.ri.ati on h~l eimn the outer loop. Part I controls the A- and f-variation. -Associate(d with these t;wo pfarameters are two tallies i and j, respectively. By setting. these tallies to the proper integral value, as shown in Table II, any desired combination of the parameter variation for A and f for this problema may be obtained. Thre 3-variation is controlled by Part TII, Part I also complutes the quantities: sin, cos A, sin', and cos t, This is done at this point to 'help nirminJ.ze the amount of computation. These values are stored and used later on in the other parts 3.2 Part II, Ground lReflection Coefficients. The computation of the grround refl ction coefficients requires the square root of a compix quiant;ity (equation 2.9); thus (e - cos A)' = B (cos i- + j sin 2Q) (3.1) where B = [( -( cos2A)2 + (-6X 1012)22 -1 O6rX 10 12 -= tan 2 ---I- 2^ 6 - cos A In order to minimize coml. utationj sin; and cos.{ are found from the relations: sin (, - (V - cos )2 i) ~(3.1) cos = o (- + - cos &) )(

l I-I C L/A\S FI11 ) UNIUNIVERSITY OF MICHIGAN nTe real and iia"ginary.parts of equations (2.3) are obtai-ned from equations (1.9) and (1,10); thus, sin A - 3 (3.) J-2 3Bsin A sin </ ar _ — ' I I (3.6) There 2 1 Dt = sinA +3 B + 2 B2'sin A cos J (3.7) H2 in2 A - B _3.5) H - - (3.9) where::" H sin A +3 + 2(n B sin &s sin + s A cos:~) (3.10) = - e2 + n2 (3.11) Note that if the single underscored terms in equations (3.8) to (3.10) are replaced ly 1, and the double underscored terms are replaced by 0, th'ese eqations reduce to the corresnonding equations (3.5) to (3.7)..Th'is fact is used i.n.ro=rramriin: the equations. Table III lists the equations for the comrputation of the ground reflection coefficients which were actually progrmar.meda Equations (211) through iUINECLL/A SIIFIEEDO

Ui CL/A\551FII ED UNIVERSITY OF MICHIGAN -10 -(220) are corminon to both the h-orizont;al and vertical coefficients. Equiations (221) thrcugh (234) are repeated twice, with the modifications as indicated in equations (221) throug> (22W) for the horizontal and for the vertical coefficients. The final results are the magnitudes, squared, of th-e ground r-eflection coefficients. 3.3 Part III, Antenna Gain. Part III completes the calculation of the antenna gain. Table IV lists the equations used in the program for this calculation. The values of the sine and cosine of, are stored in a table, rather than comptuting the sine an cosine of each as its t used. Part III is the inner loop, and is computed 146 timles for each, time Parts I and( II are compu ted. The table look-up of the sines and cosines of 3 is faster than the computation of the function would be each time,,it is needed. The 4I6 values of the antenna gain are stored, to be used by the print-out routine In Part TV. 3.h Part IV, Print-out. TIhe print-out pro.ram for this problem was desi gned around the fact of the large anmotut of output required. The antenna gain is required to one decimral digit accuracy. The lim.it on the ima ra nitude of the gain is less than 100; therefore, only three numbers need be printed out for each value of antenna gain. 3y using- a fixed-point print-cut (always pritringi out three decimal digits, even though the first are zero), the decimal point need not be printed. This reduces U INIC'L/ASS IFBIEID

U INICI/A\55 II FIED UNIVERS ITY OF MICHIGAN -AN -11 -the nnmber of characters to be printed out. If the value of the antenna gain is negsative, the negative sign is printed after the number. Two print-out formats are available; single column and page, The running variable for the column is,. A page consists of 10 columns, with the column variable being A; three pages are used for one value of f. Before the gain is printed out, it is converted from binary (the internal language of the 1IDAC),to decimal. Also the number is rounded in the second decimal place, In cise the antenna gain becomes eaual or lar -ier t-han 100 in magnitude, the print-out progTram indicates this within the list of values. An id ent'ity w orc is printed out preceding the group of 4L6 values of gain for each A-f variation. 4.0 Organization...I Operation. The proFram for the calculaticn of the antenna gain on the IIDIAC is given in1 ippendix A. The program. was divisded into two sections to best lit into the high-speed storage, sptace of the,MIDLAC, The first section contains parts I and II, and the second section contains!irts III and IV, These two sections are a-tored on the (drtl, and.re cal.led into the Cacoustic memory when needed. The program starts by reading in the parameter tape specifying the antenna type. Tie first section (parts I'and II) is called in to:the acustice rerrory, and the ground reflection coefficients for a ~~~~~~~~~~~~~~~~~~~~~[S~jlt3i/ p:articular A-f colmbin ation are comn-uted and storedd The second. U I 1 C / $ 5 II F I E.

U CL/A\55 II1F ELD UNIVERSITY OF MICHIGAN -12 -section is then called in.. The antenna -ain for the 146 values of p are computed an:-E st;ored, the comluter cycling thrcoul-h Part IIi 416 timLres, The pri.nt-out routine is tlen enterec, and the A- and f-tallies an(d the lo values o_ thae antenna gain are printed out. Jection 1 is recalled, a new value of f is chlosen and. the process repeated,. -.. 'en t-he proeranr has cycled throlugah all the values of a ne'fw i 1i ch en. rhis continrues until,a run is co eted A run.-consists of L0,0i20 values of antenna gain. The pro.ra:3 is c.esirned so that it mayr e h-al.ted a' any point, and the co-alputation continued from t-,hat;poi nt at a later date. This ~i.. accotC.mplis ed by se.tting tlhe A- and f'-tallies to:the desired value (cf Ti'abl'e II) after read;in in the,anenna-type paraeters. Table V is th:e flo::ia, gramn for the computation of 'the antennra gain. ',The r program is written to be used 'ijth. the AGIC I syst-e of aut-:o1;iat ic pro rarlirng developed for the DL:AC.. (cf,.. re. 2), Du rin6g th-e. rerioe d of continuous operation of the.IDJ-.,,rand?'om m'Ch'ine alfun 'ti'.s ill oc Thi m ese occ' at- such a frequency, th-at.`or rumLs over an hour irn length, it is avsable. to provide recovery procedures, The recovery proee dues s-ould be as auto:(at'!ri22lac Las poss ible, and thlis4 may be done 'b progranrlra r ec ove' ries Tle mai;n miethod of' recovery after a mac'hine malfunct.ionr is tlhe LIs f.a.rolback *, At specfie Linterv-ls tdurin > l,?- co!l'u.tati on, UI1CNIL/A S flBF ED.~

- UNIVERSITY OF MICHIGAN -A N the, contents of the acoustic remnory is stored on the druor Then, if a recovery.P re quired ron a coPmpouiter malfunction, tV'-i:s stored contents is broul:.ht back into tahe '-coustic mreemory, and cr-t.aion lmay 'e 'rolled back' to the rpoint at which th-e coulstic emoryT was stored Thus, the entire comp.utation n ee not be repe.at l. Th''e. p'ro:ra;,mr:E'nin.a o.l a rollback routine e-quires the cornsid:era.tion of soie fact oa rs, The first factor is the assurance th',t thd con ten t of the.ac.ciustic mor is or orect be-fore it is stored, i., t he assurLanc- tt registers in the coustic memor y have not picked up or lost inforimation. A built-in checking circuit in the computer: autorLc ati l incates such an'e. rr error as each rerist:r. is ulsed, Ts, prior,o storing for rollback, a cycelin routj.ne is uscd i'.icl: reifers to evey r egister in the acoustic memory. If everything is correct, the acouistic ime mory is stored and the program continues. If there is an error, the, comiput(er halts autom,,at ically.1 The faulty component must be corrected,' and' thre p)rogram may be continued by calling in the previous ro llback. hleon t~h~e rollb:ack is used, the coml-puter must be started in the sanme state as at the time of storage for rollback., Th.is requires thfat the instruction counter and the b.ase counter be stored as part of the rollback. The first instructions of a rollb.ack use these stored values to reset t;he counters. uin~usss nl F F- I

yiNICLL/\554 S1FE U NIV E R SITY OF M I C H I GAN A rollback routine has been incorporated in the program f^or calculation cf the antenna gain. It consists of two parts: checking the acoustic imemory, storing the counters, anr storing the acoustic t-memory; and recalling the stored riemory, resetting the counters, and continuing the program. The checking of the acous tic memory is accomplished by adding, each register to a sum-register. This uses every register in the acoustic memory and will cause an error halt if inforimation has been altered by a malfunction. This suml is also stored, to be used by the second part. The values of the instruction and base counters are also stored. The second section performs the actual rollback. The stored mem-ory is recalled to the acoustic memory, sumr.ed and checked againstthe sum obtained in the first section. This checks the call-in from the drum. If there is a discrepency, the stored memory is called in again. This is repeated three times, after whi~ch the computer halts. Such a 1halt usually indicates major trouble, so the run is discontinued at thiis point. Sometimes the inlformation called in from the drum can be called in incorrectly. A drum read-in check program has been incorporated into the progra m from calculation of.the antenna gain. As each of the two sections are called in from the drum, each word of the section is automatically added to a suim register. Upoon completion of th2e call-in, this slum is compared with the known stum for that section. UICLL/ASI\55FEO

yiICl/A\551FO'11 ED - - _ UNIVERSITY OF MICHIGAN -15'If the sums agree, the program continues. If the sums do not agree, the call-in is rehemated as many as three times. If, after the third time, the sums still do not agree, the computer prints out the call-in order and the two.Sums being compared and halts. This 3:ives inform ation which helps locate the -malfunction. t;pon running again, the pror'rami automatlcally proceeds to t1he rollback routine and rolls back to the last previous meimory store, It was M:-entioned in describing the rollback routine, that the sum of the entire acoustic mremory was taken prior to rollback. The negative o01 this sumi is stored as the last word of the acoustic memory. Up.on calling in this stored memory for rollback, the complete sum should then be zero, The program rmay be halted at any point and the comrrutatiion resumled at a later time with very little loss in computation time. Th'is results from the use of tallies to cycle the parameters. The identity word which is printed out before each group of antenna gains, indi4cates -te i and j tallies, as listed in Table II. Before beginning comriutation again, these tallies are set t t their next value. By this ilmethod, the program will continue conmyutlation from where it left off. 5. Subroutines. Standard MiuDA suoroutines are used in the program for the calculation of antenna gain. Part I uses the sin-cos subroutine; F art II uses the square root subroutine. Part ITII uses the sine Ui NICLL/A\5IFIBED

LIINICLL/A\54 FIiEU UNIVERSITY OF MICHIGAN -16 -sUbnroLtinte, andi the lo, subroutine. ThA sines and cosines of the ~- values of r Swere cormuted separately, and Herc nincor-crated into the stain rpro- ranm as a table of valu es, 6. Results. The 560,280 values of the antenna gain were punched out on paper tape, via the high-speed teletype punch. Column format output was used with types D, E, F, G. Editing with this form of output was difficult because of the physical handling of the tapes and paper required. As a result, the program was revised so that the output was in page form. The output for the remaining types used this page format output. The following statistics resulted from this problem: Output -- lh runs. 87 pages/run 1218 pages. 3290 characters/page 4,007,220 characters. 10 char./in. of tape 400,722 in. tape 6.3 mi. tape. Production time on the lI4DAC. Computation of antenna gain 60.9 hours Print-out 18.5 hours Total 79.4 hours Editing time -- 10 minutes/page 203 hours UJlNCIL/A5 511F ED

U01 ~ CL/~\S F ED UNIVE RS ITY OF MICHIGAN -17 -Appendix B is an example of the edited output. The sample used is for Type C, with a frequency of 2 megacycles. The column variable is A; the row variable is, 'The first word of the column below the column heading is the identity word. One complete copy of the edited output (1218 pages) has been supplied to the contracting officer. LUJ CcLL/xl F 1 J I

yI1NICLL/A\55IFIIED UNIVERSITY OF MICHIGAN -18 -Table II PARAI-UYTEiR VA[IAI'IO5.N_ A =X i 0 O x 0 + i Al0 O + i A2X for 0 < i < 20 21 < i < 29 where: xo = 2 ceg. 60 deg Xo = -60 deg. Ax 0 a 2 deg. A2x = 5 deg. i hex dec 1, cveg; i hex dec i x0 deg. 00 01 02 03 04 05 06 rJ7, 08 09 Oa ()c Od 0o Of 10 11 12 13 ll 0 1 2!, 5 6 7 8 Q 10 11 12 13 lit 1t4 15 16 17 18 19 20 C. 2 It 6 8 1i7 12 14 16 18 2r' 22 24 26 28 3C 32 34 36 38 J4G 42 15 16 1.7 18 19 la lb lc ld 21 22 23 24 25 26 27. 28 29 45 50 55 60 65 70 75 80 85 -- U NIC L/ASSII[F ED

liJNfCL/L5A51 IFHEDJ -.. UNIVERSITY OF MICHIGAN -19-. f = X3 rm j ~ + j xi =X j a3 where: x' 2 me Ax = 1 mc 3 3 hex dec x3 me 3 j hex dec xj mc 3 00 01 02 03 04 05 06 07 08 09 Oa Ob Oc Od Oe Of 10 11 12 1? 13 15 16 17 18 I'a~.A./ I 0 1 2 3 4 5 '6 7 8!0 9 10 11 12 13 14 16 16 17 18 19 20 21 22 23 21 25 2 la 26 lb 27 lc 28 28 29 30 4 5./ 7 9 9 10 12 13 1^ 1 I: 17 18 19 20 2' 22 23 2h 25 2 (I 27 ~ LINlCL/\-gSAFEH E1E

OU INI CiLEA551YIIIE — UNIVERSITY OF MICHIGAN -20 - P3 x6 k O x6 k x6 + k A1x6 x6 = 16 for 0 < k < 15 0t where x6 = 0; Ax6 = 2 deg. oi + k = x6 + k.2x6 16 < k < 45...,. x6 = 0 5 deg; x6.= -45 deg; A2x6 = 5 deg. k hex dec k X6 deg k hex dec k x6 deg 6 00 01 02 03 0o 05 06 07 08 09 Oa Ob Oc Od Oe Of 10 11 12 13 15 16 17 18 0 2 3 4 6 7 8 9 10 11 12 13 15 16 17 18 19 20 21 22 23 24 0 2 4 6 8 14 16 18 2! 22 24 26 28 35 40. 45 50 60 65 70 75 19 la lb Ic ld le If 20 21 22 23 24 25 26 27 28 29 2a 2b 2c 2d 25 26 27 28 29 30 31 32 33 35 36 37 38 39 4. 41 42 43 44 45 80 85 90 95 100 105 110 115 120 125 130 135 140 1l45 150 155 160 165 170 175 180 m U 1i.IC[/ASS11F FED

U NI CUL/A551FiEiOD UNIVERSITY OF MICHIGAN -21 -T.. r,2-L. L., - '-, ki L 1,* iadio;rC aat aL on iTJin Technical Le2-ort 7: Linear Communi cation Antennast. as * 19;9 v 2. D'igiKtal ('omlui.,ers and _:ata Processors", Iotes for the Universityr of 'i — *an '.1tTer i ession, 19S., a Section T, 3,1: "t roeranm.nin, for t he 1 C I S r stemr UINI CI/ASS1IFI EE0

IUI N C IL/A \55 FI IE.UNIVERSITY OF MICH]. [ GAN Appendix Ai Progi;ram for Calcul-.at ion of Antenna Gain. — Column print-out. LU INICLL/A EIIFIEIJ I

Al 00l6ffoo1 2G4 M4 12-7-55 Antenna Gain IT Brown EXPLANATION adlO25m fdd39 acO08 cd faaOO faaOl faaO2 faa04 bOO 343 fOo eOO 2eOQ aO3 roo fOO fOO eO0 e00 0 *on.. 001 d37 -to @00 eOO 2eOO 2e00 cOO 001 510 511 2cOO 0 -O bO3 aOO a08 e00 leOO 2e00 511 la03 4ell 5ell a05 ao06 0 Ia ', fi ri cm 8u SU mr fi ad adcn on ri call in part III call in part III forced — > 101 O ->i s I 0 '> j xS(rad).2'3 file -> sin-cos sin x. 21 -1 co$ x5.2 Is i > 21? Is i > 30? halt 100 __v p ^ tta T I vv/ - fiVL UUI au cm **oe R I faaO5 eOO 5000 eOl ml 2 i 4x0. 2'8 3oO eOl elO ad- x - 2 fOO -O a07 cm forced... _. eOO 4c00 elO a03 6c00 eOl oOO 001 eO1 e10 511 la03 ml admr fl faa07 i A2 7. 2'~ % + ji X 0o > xo i -3 O * file -> sin-cos sin xi * 21 0. 28 fOO 510 2e10 ad

A2 faa08 faa09 fOO bl5 leOO 8o00 leOO fO0 lOcOO 12c00 eOl 3elO0 eOl 1300 a03 f00 fOO foo 511 001 7e00 eO.e00 e0 eOl llcOO 6e l 2el0 eOl 14co00 eOl 001 510 511 -*0 lelO lbl5 a09 eOO leO a04 eOl e01 3e10 3elO e01 eO1 eOl 511 la05 ell lell a24 fi cn ad su cm ml ad dvmr mr dv sn mrfi Su adcm cos X0. 2* 0~ store rollbabk 101 Is > 30? li ->i 0 -> j forced -> 10 J A ~ 2' 8 (fi 0 +j A3) 28 3 (X x x. -984.3/f). t2 ' 2 x.4 219 2 x4 X2. 22 (2x4x/x3 ). 2-8 (rev.) Q (rev. 12-) 2w@. 2'3 rad. file -> sin-cos 1/7 - sin (4x4x/x3). 2 1/6 cos ( " ) 2 forced... -- --------------- --— ~ ----* ---— ---- ---, --- —-- — Crr-LF -* —_ —lr-~-___ ---- -_ __ I__ _ --— ~~ —___ —~lt- _I~__- — ____. faa03 da06l 02902i 038038038e4 027028038e5 0261ff002ao 02dlff.lff85 lff0290066d IffO290036d lff02alff44 021022003ed 0271ffrlf84 olfo30030e4 OlelffO04ad lfelfelfe04 OlfOlclffo5 OlbOloO17ed lffOlfOO56d OlcO19feo5 lff0l81fe4l (sin-cos.iubroutine$

A3 lfflfflff04 01601'7feded Olal ff27ab 026026027e9 013011003e5 01201blffc5 0241fflff89 lffOlalff45 Ollffffffe5 ffeOOdffded OOeOldOlde5 Olelfflff89 OOcOlbOO ed OObOOa01cel 00O00dOlce5 00801aOlbel 00801a019e5 0061fflfe85 005006ffled 0150041ffcl 003004fdaed lff01alff45 lffO201ff45 -00000000000 00000000001 00000100000 80000000000 ffffffffff 3243f6a8886 96cbe3f9991 6487ed51lOb c9Ofdaa221 ( 00000074f6a -00001e28998 000541dad70 -00996964021 Oa335e3337c -52aef3988ae c90fdaa2211 0 0 0 0 (sin-cos subroutine continued) facOO daOO3 8efa351294f 00000000015 O00000l e def.2 ld -8b cOO /180. 25 IcO0 21. 2 -2c00 30.244 3c00 x0 o 28 init A' 0" -8 hcOO x0 * 2 init A" 5c00A 2 8 56c' A21xO 2-8 0 -8 6c00 x 2 2x0 -.60.2 2d -8b ld -8b Id -8b

da002 def daO03 000000000 d 00000000001.1.2.9843 04 ld ld 3d -8b -8b - 20b 7c00 8c00 9c00 10c00 lcOO 12c00 13c00 29. 244 1. 24 1 'o 2 A x. 2-8 x3. 2 2. 2-7 2vr. 2'3 c90fdaa2216 oooooooooo8 4ccOo. 2 44 eOl to faeOl cd faa24 faal8 2c10 3e37 3e37 le 10 lelO e38 lolO 8e37 e38 a22 fOO a22 fO0 8e37 e37 6o10 511 a22 fOO0 6c10 -.....s 3elO 17c10 3e37 lelO 4c10 e38 8e37 4e37 001 511 001 511 5o10 e38 e38 7c 10 001 511 e38 7 'I h 3e37 3e37 4e3'7.38 e38 8e37 e38 511 la22 e37 la22 5e37 e38 e38 511 511 la22 6e37 511 I - mr sn mr rar sn Su mr ad fi adfi ad sn dv ad sn fi ad su Sn (y * kgx3) ' 2. 12 -8 Y1 ' 2 2 -16 Y1 2 * 2 x2, 2" Xio 2 -8 (:2.1." k - %2) * 2.8 1 1. 2 -. 1r k 2 -8 2 -8 2.1.2 Y2 2 (P Y2.1 + 2) -;2t6 file sq. rto (y3 - yJ2). 2 1/2 Y2.1. 2 -1/2 2.1 / y2. 2 2 (y4 "~ + Y2./2y2). 2 -2 file -> sq. rt. (y 2 - Y2./2Y2) *2 r2, - 2

faa21 faa25 faa30 faa29 faa31 faa32 a22 fOO 5e37 e38 e38 fOO fOO fO0 10e37 5e37 fO0 fOO 12c10 fOO 3e37 3e37 2elO 7e37 9e37 5e37 5e37 e37 e38 6e37 e38 9e37 10e37 6e37 e37 9e37 001 511 2elO 6e357 7e37 8clo lOc10 llc10 10e37 5e37 -0 9clO 4e37 lolO le37 2e37 2elO e38 le37 e38 13c10 14clO 5e37 15c10 5e37 2e3 7 e38 13c10 16c10 e38 la22 7e37 e38 le357 2e37 a26 7e37 9e37 10e37 5e37 a29 a26 7e37 9e37 1e357 5e37 e38 6e37 e38 5e37 5e37 e38 5e37 e38 5e37 e38 10637 9e3 7 e38 9e37 fi 8Umr mr mr ad ad ad 8U su cm ad ad ad mr mr mr mrmr ad sn sn ad sn admr su sn sn Su y3.2 X ' Z -.*6 (Y8 y Y3 x2). 2 (y9 3 Yj 5 x2). 2 2a -> 2 1 216 -> Yl I -8!. 2 -> Yll -> Y12 O -> Y13 forced 2B -> 2 (y1 k2 +2 2-16 (Y11 = kl). 2 (Y12 1 y8) * 2 (Y13 1 y9) * 2 2 -2 X2. 2 (Y4 o X2) 218 Yl1. Y8. 2 2(y13 + Yl ' Y8) ' 2 1t ( ). 2 2 12 Y2 + 2(y1 + Y (y11.Y y).215 [y16=20(Y12-yllY9) 2-15 y. 2-" Y2' 2-15 (Y17 YA ' Y2) 2-15 1A file -> sq. rt. Y5 ' 2-1 1B 2 2 0 201 y18 Y)2-1

A6 faa33 faa26 faa27 faa28 10e37 lOe37 9e37 10e37 9e37 '(e37 5e37 9e37 5e37 '7e37 f00 3c10 2ell 2ell fOO 3c10 3ell 3ell fOO ell lell lell ell 6e37 e38 10e37. e38 7e37 -0 6e37 2ell 7e37 -0 6e37 3ell 7e37 -0 6e37 7e37 10e37 9e37 e38 6e37 e38 7e37 7e37 a27 2ell 2ell 2ell a30 3ell 3ell 3ell aOO mr mr mr mr su dv ad dv mr cm -16 1(Yl-' Y16 Y) 216 ).l -16 (Y9 " Y17 6) 2~ 2 (Y21 - 16 6) * 2-16 (Y22 - Y17 Y7). 2 [Y20 (19- l8)/Y15] 2-16 (22 + Y21) 26 [Y23 (Y22 +21)/Yl5] (Y23 ). 2 - 2 ad 1 + y, 2 mr + Y2)2 ad- [y25 - (1y20)2+ Y2 * cm Forced -> 1B su (1 -Y20) 24 2B mr (1 y2) 2 ad- [Y26 - (1-20)2* 23 2 2 nm forced EV,oI def faclO cd def.0.10 -.36756.1 -.6 -.2.5 -.1 fOO fO0.1 Od 2d -ld Id ld ld Od ld -0 -0 ld Ob -8b Ob -4b -44b - b -44b a27 a28 -16b cl -0 IclO kl. 2 12) 20 2c10 (k2 -6. 1012). 2 3c10 1. 24 '4cl0 -6. 2'4 5c10 1. 24 6c10. 5. 2 7c10 -1. 244 cm 8c10 2A cm 9c10 2B clO 1.2-16 10clO 1.2

A7.1 Id -8b.100.3 3d -16b id -44b.6 -.7 Id -44b d -44b ld -44b 12c10 1. 2 l-2clO k 2. 2 13c10 3. 2 14c10 4. 244 15clO 6. 2" 16c10 -7. 24 17c10 1. 244 ld -44b faa22 da027 sq. rt. 013014000cd 0121ffOO2ad 011012ffeed O10lffO02ac -OOllffOOOOf lff00001426 01300fO14e7 013013012e5 lff01101l67 OlOOc010e7 O0900aOOde5 o080oolffc5 lff00900b67 lff00c00b6b 00900a009e5 OOOOOOOOcad 00300a00ae4 lffo91off47 001002feeed -00000000000 fffffffffff -00000000001 0 0 0 0 0 fae38 fae37 ac429 cd e38 to e37 10e37 0 cm exit lb12 ad xfer 2I fabOO fabOl f00' fOO -0 bll 1 fOo -0 b05 cm forced

A8 fab02 fab0) fab04 fab05 fab13 fab06 fab07 fOO fOO fOO f00 fO0 bO 7 bOO bOO 4b ll 4bll fOO 0 fOO b12 lb12 0 fOO -001 001 002 fOO lbll -0 2bll -0 3bll -001 5bll bll1 6bll 7bll 0 0 f37 lb12 b12 4095m -0 003 bO6 b12 -0 lb12 b05 lb12 b05 lb12 -001 4bll bOO 4bll b13 b06 0 b12 blO blO -001 bOO b06 0 0 bl4 ad cm ad cm ad -fi ex ad <-4 sn ex ad ri ad cn on ba cm ba ro room xfer II forced xfer ZIII forced xfer IV file cb and clear y of exit -> tO modify exit shift t0'+12 bite - to set up xfer order xfer r o i order roi order xfer 2 is > L.? - 1 Is L L>?L reset cb forced -> emit repeat ri 3 times print ri order print Z S 2 i and halt forced -> rollback fablO -- - -- -- -- -- I — fabll daO08 0 000000001 0 0 0 00000fff OOOOOOOOOOc OOOfff bll Ibll 2bll 3bll 4bll 5bll 6bll T7b I 1. 2-36 III Iv to' y exit 12. 24 b exit fab 12 bl2 f

A9 ae2b12 od fab15 fabl6 lb12 ~ 0 bl5 f00 f37 fO0.oo f57 -001 f00 512 fO f00 fOO 0 -002 -001 512 fO f00 ftO -001 -006 003 fO0 fab14 fab09 4095m -001 0 f37 7b17 -0 511 f37 0 6bl7 -0 0 bl7 5bl7 d35 f37 6bl7 -o 005 b17 eO0 -0 0 -001 6bl7 f37 0 f37 b16 511 d35 0 0 0 0 0 bl8 0 b15 b09 0 0 b14 ba -fi ad su ad -ad ba BU ro ad cxa ba ro ro ri am ad cm ba ro rocm } 2 ->Z n store mem. reset overflow forced -> exit clear % print rb print rb call in rollbadk r a - 0? reset overfl forced * exit try 3 times print "rb ngw print i, J, k tallies and stop forced set ci and c file eb and clear save overflow o-> Z normal overflow fab18 fabl7 da008 o8 2c 40 4o 88 b17 lbl7 2b17 3b17 4b17 r b sp n g

AIO 0 00000000001 5b17 c.r. 6b17 store overflow 7b17 normal overflow d35 r.b. store adl408m fdd35 ac8bl 7 faeOO ac3eOO faelO ac8elO faell ac08 adlO88m fdd37 cd faa34 fab33 faa35 - ' ---- — -— - — --------- -- ---- - --- ----- eOO i 2 4 le00 j. 2 44 2e00 k. 2 4 A Xk fS elO, ' A. 28 deg lelO x~lcosA. 21 2el0 xsainA. 2'3eO3 xi-. 22 ft. 4ew x6 -. 2d8 deg 5elo x7 = 1. 2l12 ft. 6elo x - h. 2 ft. 7elO x5 " 28 deg ell y7. 2 1 ell YT'2 lell Y6. 2 1 -e8 2ell Y25 28 -8 3eU Y26. 2 4ell 2. 2 1 5ell y28. 2-1 - f- ----— ----— — - ----------- ----- ------------—.*-. ---— -5.____ bOO 251 0 2e00 2e00 2eOO0 2e00 too 001 d39 0 c02 lc02 2e00 -001 bOl aOO 0 fi ri ba A call in part I a36 a37 2e00 all an cn su fi 0 -> Cb is k > 16? is k > 46? o -> k forced clear c, faa36 2e00 2c02 e02 ml k A6. 2-8 k 0f +k )2-8 3c02 e02 4el0 ad (x x + k Ax6) fOO -0 a38 cm forced ' faa37 faa38 faa39 2e00 5c02 2e00 b34 e02 e02 fOO 4c02 e02 8c02 -001 '7c02 9c02 -e04 e02 4elO e02 -001 eO2 a39 -e03 ml ad sn -fi ad ex -ad k 26 0 2-8 (x6 X" 6 kA2x6 (2k). 24 file cb and clear -8.2 set up xfer order sin-cos x6. 2

All fab34 fab24 fab25 -001 0 4e11 5ell le02 le02 12o02 3el0 2e03 lelO lOaO2 10c02 lelO 10c02 e02 2e05 b28 f00 fOO fOO leO2. 2eo3 b28 fOO f00 18c02 e02 e02 e02 4ell le03 002 4095m 1e03 eO3 4e02 4e02 5el0 4e02 2e03 e02 e02 le02 ie02 11e02 e02 001 511 -0 13o02 11c02 leO2 001 511 -0 13c02 5ell 3e03 2e02 3e02 le10 a39 -001 1e02 4e02 eO2 1e02 4eO2 3eO3 e02 2e03 e02 leO2 le02 b20 510 b27 2e02 b21 2e02 b22 510 b27 3e02 b23 e02 e02 e02 e02 e02 4e02 ba Sa-a x6. 2' 1 ba reset a mr Y27 Y30 mr Y28 Y9 2 d (Y31 27 Y+ Y8 Y29) 2 (su 27 - 30o 28 ^29) mr (i * X) o 2 dv (y3*3- I 7 /x3). 2 la(r35.1 ' Y~) ' rL' mr (x15). 23 mr tly3.) * 33) (y33 1 ti le) ' 2'3 mr (x132). 2-3 su- (y 1 - 32). 2 on is Y33 > e? mr (36 ' 35 Y33) ' 2: fi file -> asie/ ad- (y3g - sia y36/y6) * 2" oM forced ad 1 2 ^ an is >34 e? mr (37 "?'3~ ) ' 29 fi file -> Sinr/9/ ad- (y 8 l sin y3/y^) - 21 ox forced ad 1 2.2 1 ar (k28). 29 mr [( " ) 35.13 * 2 mr 38 *2 \, )(38. 2 mr- (YO k 328 1039) * 2'23 mr (YhO ). 2. sn Y3o 22 fab20 fab21 fab22 fab23 19o02 le02

A12 fab29 fab30 fab 32 1e02 le02 le02 e03 le02 le02 2e03 e02 e02 20c02 4e02 e02 e02 e02 4e02 3e02 3e02 3e02 22c02 3e02 511 511 2e02 4e02 b31 511 2e02 2e02 3e02 -e12 6c02 -001 4e02 le02 2ell 2elO le02 3ell 3e03 0 4e02 4e02 6c02 2eO2 e02 21c02 0 2e02 2e02 21c02 0 2e02 leO2 2e02 e02 0 1e02 le02 2e02 001 25c02 26c02 3e02 23c02 24c02 2e00 04 / IeO2 le02 2e03 le02 leO2 3e03 3e02 4e02 e02 4e02 4eO2 4e02 e02 2e02 e02 4e02 3e02 2e02 3e02 2e02 511 le02 511 2e02 2e02 lb31 3e02 2e02 3e02 -el2 -e12 2e00 a35 Su -2 8u l(Y " Y0 -v Y2 27 mr (Y42 - 2 mr (Y43 4225 2 mr (Y44 y295) 22 mr ( - ) 2 -mr (Y46 Y5Y26) 2'2 mr 2-(23-px) y140 px P'x (y0)2 sn y 2 -2(23-px)+PX su- (23p - x px] 224 mr y47(1A8603) 2-12 px Px" (Y47) sn Y 2(12pxf) su (12 - px) 244 2 p(2+-px) +px mr (y47y40) px Px"'(yo7y40) sn- (y4 2-0) 2-8+px+px+ su (12 - px" - px"') 244 ad-K I exponent of (y47y0) fi file -> log2 routine sn log2 28 sn 2 -" adsu (12-y7y0)) 2 sn-, ]l (g) 2-58+px+ ~' + ~,' d 1~2 (Y4?Lo )'(Zlog2 ) 2'8 m*r- )[Y48 101glogy47Y4o - l -'lOloglll86.312. _ ~ -10gl6.312 ad ba 1 + k -> k Repeat l6 timbs

A13 fOO O0 bl4 om forced -> rollback fab27 14c02 510 4e02 mr (/w). 29 4e02 15002 4e02 sn (/2w). 20 (rev) frao. part 16e02 *e02 511 mr Q. 2'3 (rad) b26 001 lb26 fi file -> sin rout. 511 17e02 4eO2 an (sin@). 210 510 4e02 511 dv sin2/~. 2 fab28 fOO -O 0 om exit fab26 da041 b26 sin rout 01901aOOOod 0181ffOO2ac Olclfflff85 lff01900a6d lff0190036d lff0191ff44 013014002ed O18lfflff84 lfft04o0564 01001201ee5 lffoofold6l OOeOlolffc5 OOdOOeff4ed OOflffOlaab 00b009004e5 018018019e9 0100091ffe5 0171fflff89 lffOOflff45 fffoo7fff~5 ffe04ffded 0121fflff89 003004feaed rffoof0ff45 lffOl51ff45 -00000000000 00000100000 80000000000 3243f6a8886 96cbe3f9991 c90fdaa2217 6487ed5110c 00000074f6a -0001e28998 000541dad70 -00996964021 Oa335e3357c -52aef3988ae

c90fdaa2211 0 0 fab31 da032 b31 log2 rzot 40001oooo06 lffOleO126o rlfflblff48 lff0ll01b64 lffOlOOlb65 OlaO19019eb OOfO18018eb 017017018e9 40000900365 40000dlff45 IffI0151ff49 rooolorrres fffOlOfffe5 ffeOO5ffded 0olofflff89 lffOelff44 40000 ff026 lff00olff45 lffOrllff45 -OOllffOOOOf 5a827999fof 2beo3330189 00000004a32 ooooobofO6 00001e44962 00059f73f4f 013e5a65819 7ebbe72c5fe 000001 8 0 0 def fac02 2d.44b.46.2.0.5 - 45.1 2d -44b Id -8b Od Ob eo2 16.2"' lcO 46.2^*2 2102 Ax 2.20 3c02x x' 0 6 5e02 x = -45.2 6Sc2.2 -6c02 1.2 1 Id -8b 2d -8b Id - 44b cd 0 eO4 0 ri 7c02 initial sin add. 8c02 21.2' def.2 ~ 21 2d.44brc

daOO1 def daOOl def daOOl def daOO1 def 00OOfff.1.1 Oa90fdaa221.1 517cclb7272.8 90fdaa2217.128988 -.1.23 00o5367686.12,3010299957 -.8 o36 ld 1d fd -3b -40b -lb 9c02 p ext, 10c02 1.2"3 11c02 1o2'~ * o 12c02 v.22 13c02 1.24 l4e02 (1/w).2~ 15c02 8.2 id 2d Id 24 44b -8b -44b Ob -44b -4b -# b -41b -44b 16c02 17c02 18c02 19c02 20c02 21c02 22c02 23c02 2aco02 25c02 26c02 2n.2-3 k.9 2. 244 k3.2 -1.2 4 -23.24 (1/186.3) 12 2. 10( o 2).2~ 6.3 2?12 -8.2 36.244 ain-cos X6. fae04 da0O92 0000000000 80000000000 047796327e0 7fee09e2ffc 08ede7b6b51 7fb02dc5c3f Od61304d9e2 7f4c7e53e19 ld06e968d7 7ecllaa4c25 163ala7e0b6 7e0e2e32047 la9cd9ac426 7d33f0c9e80 lef74bf2e4a 7c32a67de6e 234815ba651 7bOa9f8d79e eO04 91e04

278dde6e5fe 79bc584dll# 2bo750e9140 7847d90948b 2ff31bddeb3 76adf5e65f2 340ff2420c1 74efOebbfe0 381o8bb57c0 730baeed58e 3 17a4e848b 71046d3db49 tffffffffff 6ed9eba1614 496af3elf13 68d9f964561 5246dd48f03 620dbe8b3d5 5a827999fof 5a827999fcf 620dbe8b3d2 5246dd48f07 68d9f964561 496af3elfl3 6ed9eba16l4 3ffffffffff 74o01e40b75 36185aee6f5 7847d90948b 2bc750e9141 7ba3751d22e 2120fb83262 7e0e2e32046 163ala7eOb6 7f854edo605 Ob27eb5o616 80000000000 -00000000005 7r834edo605 -Ob27eb5c616 7eOe2e32045 -163ala7e0ba 7ba3751d22e -2120fb83262 7847d90948a -2bG750e9144 7401e4oOb75 -36185aee6f5 6ed9ebal612 -4000000003 68d9f96455f -496af3elfl7 620dbe8b3d2 -5246dd48f07 5a827999fob -5a827999fd2 5246dd48fO0 -620dbe8b3d5 - 496af3elfof

A17 -68d9f964564 3ffffffrfff -6ed9ebal614 36185aee6f0 -7401e4O0b77 2bo750e9140 -7847d90948b 2120fb8325e -7ba3751d22f 165ala7eob6 -7e0e2e32047 Ob27eb5o611 -7fr84ed0605 -0000000000..8oooooooooo -80000000000 ed faall 3e15 fOO eO0 faa13 a12 fOO -001 -001 ~00 -007 faa16 -e12 -e12 f00 fOo ~00 fOO -oo faal7 -e12 511 511 a20 faal9 a12 foo 3e15?el5 7.15 3oOl 001 510 002 3ool 001 510 002 e15 11O01 GeOl 6o01 6c*01 001 8c01 -001 001 510 3e15 6e15 511 lal2 -*115 a13 511 la12 *4e15 al1 002 -e12 a17 3e15 4e15 5el5 la20 511 511 511,001 la12 - e35 Su ad sn fi -ad ba rn fl -ad ba ro -ad - C 0 -> p0o c.r. - j:.0o set up i for p.o;:file *> digit store store i for p... ba 2 times set up J for p.o. file -* digit store store j for p.o. ba 2 tims print i and 3 (punch) round ak to 2 dea. i ke a, 100? tuA '\%... W ad ( x -> tl ad em foreed -mr ak 212/1io bd cony. 511 sn convy no. 2' -fl file cb and fi file -> digI 'ad dlo (d -> 3 3 4 -6 clear lt store tl (t,) "' - LL f

faa20 fab35 fab36 -001 0 -el2 fOO -004 fO0 fO0 -005 -001 -002 2e00 12c01 fOO 002 4095m cOl 7el5 3e15 -0 9c01 3e15 o46 7e15 2eOO 2e00 leOO -0 A18 a19 -001 b35 6e15 002 b36 6e15 002 a16 002 2e00 le00 aO0 ba ba -On ad ro cm ad ro ba ro su ad 0m ba 2 times k -> & is ak O? c,r. -> p.o. print + ak forced -> p.o. print -ak ba 46 times print c.r. and stop code 0 -> k 1 + J -> j forced __, _ __ I. --- ---- ------------------------------— ~ --- cd faa12 fOO 511 cO0 511 fO0 -0 IcOl 2c01 -0 0 510 511 511 a12 em exit ex b1-b6 510 ex -> bl -6 sn shift 511 (+4) bite cm forced -> exit facOl daOO07 -0 fc 00000000004 00000000022 fff o64 cOl -0 lcOl bl-b6 ext 2c01 4.24 3c01 31*.2^ 4cO1 ~( ext. 5c01 100.2 12 6c01 x 7c01 212/10o, 20 8c01 6.2-4 9co1 ( lOcOl 1 2-8 5c def da004.4096 0ooooooooo6 60000000000 Od Ob 01

4eo fael5 daOO9 fa e02 ae5e02 faeO3 aa4e03 fae12 boaOl OOOOd.1 04 0 A19 -##b Id 0 0 0 8. 80 1col d.220 %1o"2 12cOl 1.2'4.15 ~.r 2 5to l3* t 3e02 t1 Ie% tg 6e1$ c.r. or G 7e3$ c4r' 8e15 stop code e02.to le02 t1 2e02 t 3e02 t 4e02 t4 e03 y. 2' 2.03 2 3e03 y35. ' 2 4.12 2

U INICSl/A\5 F IIFIIELO - UNIVERSITY OF MICHIGAN - APPENDIX B 5The followiner are the values of the antenna gain for the types of anteinas as listed in the headings. The constants used are' K 1i28.988 6 10 o-~ 2-1Q't e.or.u. Each. table gives the value of the anterna gain for the!i6 values of, as listed in the table of parameter variations. The values of A and f are listed in the heading. The first tword of each table is an idenltity word, indlicatinu the value of L and f as listed in the table of parameter variations, (Table II). ~~~~~~~~~~~~~. _.o UJIN~L/4llF E E

B2 TYPE C f = 2 me A=2 4 6 8 10 00000 01000 02000 03000 04000 491- 429- 390- 361- 336 -479- 419.- 383- 356- 332 -455- 400- 367- 343- 322 -432- 379- 349- 327- 309 -412- 361- 32- 312- 296 -396- 345- 317- 298- 283 -382- 331- 304- 286- 272 -370- 319- 293- 275- 261 -359- 309- 283- 265- 252 -55- 300- 274- 256- 243 -342- 292- 265- 248- 236 -335- 285- 258- 241- 228 -328- 278- 252- 235- 222 -322- 272- 246- 229- 216 -317- 267- 241-. 223- 211 -312- 262- 236- 219- 206 -303- 253- 226- 209- 196 -296- 246- 219- 201- 188 -292- 241 214- 196- 183 -291- 240- 212- 194- 181 -292- 240- 213- 194- 181 -296- 244- 216- 197- 183 -303- 251- 222- 203- 189 -314 261- 232- 212- 198 -328- 275- 245- 225- 210 -347- 293- 263- 243- 227 -372- 318- 287- 267- 251 -405- 351- 320- 298- 282 -453- 397- 365- 343- 325 -532- 476 442- 418- 398 -697- 650- 635- 645- 699 -539- 483- 453- 434- 421 -505- 449- 418- 397- 382 -497- 440- 408- 387- 371 -503- 445- 413- 391- 374 -521- 463- 430- 407- 390 -555- 496- 463- 439- 420 -622- 562- 527- 501- 480 -773- 724- 707- 715- 769 -600- 543- 512- 491- 478 -551- 493- 461- 439- 424 -525- 466- 433- 411- 395 -508- 450- 416- 394- 377 -498- 439- 406- 383- 367 -493- 434- 400- 378- 361 -491- 432- 399- 376- 359 - 12 14 16 18 05000 06000 07000 08000 315- 295- 276- 259 -312- 293- 275- 258 -304- 287- 270- 254 -293- 278- 263- 249 -282- 268- 26- 243 -271- 259- 247- 236 -260- 249- 239- 228 -250- 240- 231- 221 -241- 232- 223- 214-, 233- 224- 215- 207 -225- 217- 209- 201 -218- 210- 202- 195 -212- 204- 196- 189 -206- 198- 191- 184 -201- 193- 186- 179 -196- 188- 181- 174 -186- 178- 171- 165 -178- 170- 163- 157 -173- 165- 158- 151 -170- 162 154- 148 -170- 161- 154- 147 -172- 163- 155- 149 -177- 16- 160- 153 -186- 176- 168- 161 -198- 188- 180- 172 -215- 205- 196 188 -238- 227- 217- 209 -268- 256- 246- 237 -311- 298- 287- 277 -381- 365- 351- 337 -739- 600- 535- 489 -413- 408- 407- 409 -371- 363- 357- 354 -358- 349- 342- 336 -361- 351- 342- 336 -376- 365- 355- 348 -405- 39- 582- 73 -463- 447- 4- 21 -809- 669- 605- 561 -469- 465- 464- 467 -413- 405- 400- 398 -383- 374- 368- 364 -365- 356 349- 44 -354- 345- 337- 332 -348- 338- 331- 326 -346- 336- 329- 324 - 20 09000 243 -242 -239 -235 -230 -224 -218 -212 -206 -199 -194 -188 -183 -178 -173 -168 -159 -151 -146 -142 -141 -143 -147 -155 -166 -181 -202 -229 -267 -325 -454 -416 -352 -333 -331 -341 -365 -410 -526 -475 -398 -362 -341 -329 -322 -320 -

33 TYPE C f = 2 mc A=22 24 26 28 30 32 34 36 38 40 OaOOO ObOO OcOOO OdOOO Oe000 OfOO 10000 11000 12000 13000 228 214- 200- 188- 176 165- 155- 145- 16- 128 -227- 213- 200- 188- 176- 165- 155- 145- 136- 128 -225- 212- 199- 187- 175- 164- 154- 145- 136- 128 -222- 209- 197- 185- 174- 163- 153- 144- 135- 127 -218- 206- 194- 185- 172- 162- 152- 143- 135- 127 -213- 202- 191- 180- 170- 160- 151- 142- 134- 126 -208- 198- 187- 177- 167- 158- 149- 141- 132- 125 -202- 195- 183- 174- 165- 156- 147- 139- 131- 124 -197- 188- 179- 171- 162- 153- 145- 137- 130- 123 -191- 183- 175- 167- 159- 151- 143- 135- 128 121 -186- 179- 171- 163- 156- 148- 141- 133- 127- 120 -181- 174- 167- 160- 152- 145- 138- 131- 125- 119 -176- 169- 163- 156- 149- 142- 136- 129- 123- 117 -171- 165- 159- 2- 146- 140- 133- 127- 121- 116 -167- 161- 155- 149- 143- 137- 131- 125- 120- 114 -163- 157- 151- 146- io- 134- 129 123- 118- 113 -153- 148- 143- 138- 133- 128- 123- 119- 114- 110 -146- 141- 136- 132- 127- 123- 119- 115- 111- 107 -141- 136- 131- 127- 123- 119- 115- 112- 108- 105 -137- 133- 128- 124- 121- 117- 113- 110- 107- 104 -136- 132- 127- 124- 120- 117- 113- 110- 108- 105 -138- 133- 129- 125- 122- 118- 115- 112- 110- 107 -142- 17- 133- 129- 126- 122- 119- 117- 114- 112 -149- 144- 140- 136- 132- 129- 126- 123- 121- 118 -160- 155- 150- 146- 142- 139- 1 6- 13- 1 0- 127 -175- 170- 165- 160- 156- 152- 148- 145- 142- 139 -195- 189- 184- 178- 174- 169- 165- 161- 158- 154 -222- 215- 209- 203- 197- 192- 187- 182- 177- 173 -258- 250- 242- 235- 22 - 221- 215- 208- 203- 197 -515- 301- 291- 280- 270- 261- 252- 243- 235- 227 -424- 398- 376- 356- 338- 321- 306- 292- 279- 267 -427- 448- 484- 573- 560- 460- 410- 375- 347- 325 -353- 356- 362- 371- 385- 405- 440- 514- 565- 441 -330- 330- 331- 334- 339- 347- 358- 374- 398- 439 -327- 324- 323- 323- 325- 328- 334- 342- 353- 369 -336- 332- 329- 327- 327- 327- 330- 34-. 540- 349 -358- 352- 347- 343- 341- 339- 39- 340- 342-. 547 -400- 390- 382- -375- 369- 36 360- 358- 357- 3559 -498- 475- 455- 438- 423- 411- 400- 392- 86- 383 -489 511- 550- 642- 6- 536- 491- 462 441- 427 -401- 4o6- 414- 426- 444- 469 508- 588-. 646- 530 -362- 364- 368- 375- 384- 396- 412- 435- 466- 516 -340- 341- 343- 348- 354- 362- 374- 389- 4o8- 45533 -327- 327- 329- 332- 337- 344- 353- 365- 380- 400 -320- 320- 321- 323- 328- 334- 342- 353- 367- 384 -318- 317- 318- 321- 325- 331- 339- 350- 363- 379 -

TYPE C f = 2 ma A=42 45 50 55 60 65 70 75 80 85 14000 15000 16o000 120- 110- 096 -120- 110- 096 -120- 110- 096 -120- 110- 096 -119- 109- 096 -119- 109- 095 -118- 108- 095 -117- 108- 095 116 107- 094 115- 106 o094 -114- 105- 094 -113- 105- 093 -112- 104 093 -110- 103- 092 -109- 102- 092 -108- 101- 092 -105- 099- 091 -103- 098- 091 -102- 097- 091 -101- 098- 092 -103- 099- 095 -105- 102- 098 -110- 107- 103 -116- 113- 109 -125- 122- 117 -136- 133- 127 -151- 146 140 -169- 163- 154 -192- 184- 172 -220- 209- 193 -256- 240- 217 -305- 281- 247 -388- 338- 284 -546 445- 331 -394- 476- 401 -363- 397- 57 -355- 376- 78 -362- 374- 432 -382- 386. 423 -417- 411- 430 -486- 454- 451 -632- 550- 486 -469- 57~- 548 -425- 42- 716 -406- 452- 623 -400- 444- 590 - 17000 o86 -086 -o85 -085 -o85 -085 -o85 -085 -085 -085 -085 -085 -o85 -085 -085 -085 -085 -086 -087 -089 -091 -095 -100 -106 -114. 123 -1 4 -147 -161 -178 -198 -220 -246 -275 -309 -350 -400o 465 -569 -692 -598 -6oi. 645 -787 -720 -682 - 18000 19000 laOO0 lbOOO 079- 076- 076- 081 -079- 076- 076- 081 -079- 076. 076- o8l079- 076- 076- 081 -079- 076- 077- 081 -079- 076- 077- 081 -079- 076- 077- 081 -079- 076- 077- 082 -079- 076- 077- 082 -079- 077- 078- 082 -079- 077- 078- 083 -079- 077- 078- 083 -079- 077- 079- 083 -080- 078- 079- 084 -080- 078- 080- 084 -080- 079- 080- 085 -081- 080- 082- 086 -082- 082- 084- 088 -084- 084- o86. 090 -087- 087- 089- 093 -090- 090- 092- 096 -094- 094- 095- 099 -o99- o98- 100- 102 -104- 104 0- 106 -111- 110- 110- 110 -120- 117- 116- 115 -129- 125- 122- 120 -140- 134- 129- 125 -152- 144 17- 131 -166- 155- 145- 137 -181- 166- 154- 145 -198- 179- 163- 149 -216- 192- 173- 156 -236- 207- 182- 162 -258- 221- 192- 169 -281- 236- 202- 175 -305- 251- 212- 182 -330- 266- 222- 187 -354- 280- 230- 193 -377- 293- 2 9- 198 -397- 304- 246- 202 -413- 314- 252- 206 -425- 322- 257- 209 -432- 327- 260- 211 -436- 331- 262- 212 -437- 332- 263- 213 - IcOOO ldOOO o89- 102 -o89- 102 -089- 102 -090- 103 -090o 103 -090- 103 -090. 103 -ogo- 103 -090- 103 -091- 103 -091- 10 -091- 104 092- 104 -092- 104 -092- 104. 093- 105 -094- 105 -096. 106 -097- 107 -099- 109 -102- 110 -104- 111 -107- 11 109-. 114 112- 116 -116- 117 -119- 119 -123- 121 -126- 123 -130- 125 -134- 126 -138- 128 -142- 130 -146. 132 -150- 134 153- 135 -157- 137 -160- 138 -163- 139 -166- 141 -168- 142 -170- 142 -172- 145 -173- 144 -174- 144 174- 144 -

UNIVERSITY OF MICHIGAN 3 9015 02844 0678