2500-398-M RL # 854 TECHNICAL REPORT SUBJECT: A Bandwidth Enhancement Method for Microstrip Antennas FROM: P. B. Katehi Abstract: Bandwidth enhancement methods for electromagnetically coupled microstrip dipoles are discussed in this report. It is demonstrated that if parasitic metallic strips are incorporated in the structure either coplanar and parallel to the embedded microstrip transmission line open end, or between the transmission line and the microstrip dipole, then substantial bandwidth enhancement results. Experimental verification of this model is introduced for a bandwidth definition based on the frequency range which satisfies a VSWR < 2 criterion. Also, experimental E- and H-plane patterns verify the theoretical model which accounts for radiation from the microstrip dipole, the parasitics and the transmission line. RL-854 = RL-854

TABLE OF CONTENTS Page List of Figures ii Abstract 1 Technical Report 2 I. Introduction 2 II. Analytical Aspects of the Model 3 A. Current Distribution 4 B. Excitation Mechanism 7 C. Radiation Patterns 9 D. Numerical and Experimental Results 11 III. Conclusions 16 References 16 Computer Programs 31 Part a: Comments 32 Part b: User's Guide 46 Part c: List of Programs 52 JOBRUN 53 POLES 56 FINITE 61 INV33 106 GAIN 114 OUT1/DOUT 124 RESULT 133 RESGN 141 MUTUAL 145 Part d: Magnetic Tape Comments 157

I. Introduction It is well known that microstrip antennas exhibit very narrow bandwidth characteristics [1] through [3]. Various schemes have been proposed and/or implemented to reduce or eliminate this limitation with relatively promising results [4] through [6]. A dominant theme in these schemes is the introduction of additional capacitance which is accomplished by integrating parasitic metallic strips in the microstrip antenna structure. This is usually accomplished by stacking parasitic disks under a microstrip circular patch or a parasitic rectangular patch under the microstrip patch antenna and/or by increasing the overall substrate thickness. This work is concerned with the bandwidth improvement of electromagnetically coupled microstrip dipoles by adapting one or two parasitic metallic strips either in a stacked fashion between the embedded microstrip transmission line open end and the radiating microstrip dipole antenna or coplanar to and near the open end of the embedded microstrip transmission line. Both of the configurations just mentioned are shown for reference in Fig. 1. For both arrangements an optimization procedure may be carried out, as to the optimum position and size of the parasitics, in order to maximize bandwidth. The methodology adopted in this work for the evaluation and optimization of the electromagnetically coupled microstrip dipole bandwidth, accounts for all the substrate effects including surface wave propagation [7] through [12]. The embedded microstrip transmission line excitation is effectively taken into account by considering it as part of the antenna, i.e., the overall module of microstrip transmission line, its excitation and the microstrip dipole are treated as a radiating system. The model allows, in addition, finite conductor thickness. The transmission line and dipole

-3 - widths are taken to be a fraction of the free space wavelength x, so that the longitudinal current component is the dominant contributor to the radiating system characteristics. With this restriction the transverse current component is negligibly small and its effect is omitted without introducing appreciable error, as verified in [10]. The longitudinal current distribution Jx(x,y) is determined by applying Galerkin's method x in the x-direction of the system insuring that all interactions between the transmission line, microstrip dipole and parasitics are included; this will yield the x-dependence of Jx(x,y) as provided by the model. The y-dependence of Jz(x,y) is chosen to satisfy the edge condition at the effective width location [11]. Upon determining the current distribution, transmission line theory is invoked to evaluate the reflection coefficient and VSWR and their dependence on frequency. The bandwidth, defined here as the frequency range for which VSWR < 2, can be found therefore as a function of the characteristics of the strip dipoles and substrate parameters. Finally, an experiment is also carried out which verifies the model with good agreement. II. Analytical Aspects of the Model Success in the theoretical investigation of printed circuit antennas is contingent upon a variety of factors; two of the most important factors are the accuracy of the developed mathematical model and the usefulness of the derived results. The former factor is determined by the implemented analytical method, while the latter depends significantly on the assumptions adopted with respect to the excitation mechanism of the radiating system. The following sections describe the analytical method used for the computation of the current distribution as well as the assumptions involved for the excitation mechanism.

-4 - A. Current Distribution Evaluation The transmission line and the dipoles radiate an electric field Er given by r() + () = Jf G(r/r') a J(r')ds' (1) s where t.(r) is the impressed field at the point r = (r,e,d), G(r/r') is the dyadic Green's function and ~1(r') is the unknown current distribution at the point r' = (',e' = T/2,q'). The Green's function, pertinent to this problem, is given by the expression 00 G(r/r = f [kI + vv]. J (X - r'l)F(X) dx (2) 0 o where I is the unit dyadic, k = 27/X and F(x) a known dyadic function of the form A(x,cr,h) F(x) = f (x,c h)f (x,cr,h) * (3) In Eq. (3), A, f and f are analytic functions of the spatial frequency x, the relative dielectric constant Sr and the substrate thickness h, [lO]-[11]. Specifically, f and f are in the form 1 2 f (x,~r,h) = uo sinh(uh) + u cosh(uh) (4) 1 r 0 and f (Xc rh) = r u cosh(uh) + u sinh(uh) (5) 2 r r o with u = [x2 - k2]1/2 and u = [x2 - k2]1/2. (6)

-5 - The zeros of f (,cr,h) correspond to TE surface waves while the zeros of f (X,~,h) to TM surface waves respectively and their existence 2 r affects considerably the coupling between the dipoles and the microstrip line. The widths of the strip conductors are fractions of the wavelength in the substrate. For this reason, it can be assumed that the currents are unidirectional and parallel to the x-axis. Under this assumption, the current distribution in Eq. (1) may be written in the form (r) = xf(x')g(y'), (7) where f(x') is an unknown function of x' and g(y') is assumed to be given by g(y') = - 1 - ( )) -1/2 * (8) In Eq. (8), we is the effective strip width given by we = w + 26 with 6 the excess half-width. The effective strip width accounts for fringing effects due to conductor thickness [11]. From Eq. (1) the unknown current density J is evaluated by the application of the method of moments. Each section of the strip conductors is divided into a number of segments and the current is written as a finite sum N =(r') x g(y') Inf(x') (9) n=1

-6 - where N is the total number of segments considered. The expansion functions in Eq. (9) have been chosen to be piecewise sinusoidal and they are represented by sin[k (x' - x )] - x x x ' <X ' n-1 - n sin(ko)x) sin[ko(xn - x')] fn(X') n x < xi <x (10) n sin(kz n- - n+1 0, elsewhere with zX denoting the length of each subsection. The electric field given by Eq. (1) is projected along the axis y = 0, z = 0 using as weighting functions the basis functions (Galerkin's method). In this manner, Eq. (1) reduces to a matrix equation of the form [Zm [In = [V (11) mn n m NxN Nxl Nxl where [In] is the unknown vector and [Vm] is the excitation vector the latter depending critically on the impressed feed model. [Zmn] is the impedance matrix with elements given by w/2 z s(y)6(z) f-dy, mn (y)6() 1/2 -w/2 2+ 2 - * dx dx' xx + (F -F) fm(X)f (x') (12) C C

-7 - where 00 F 2( )4 ( j uh)) o) ( d (13) XX "4'k f J (Xi r,h) 0 0 r and f jw1uoosh(uh) sinh(uh) ', -u t = 2 )0 E - 1) r f (X.s=,h) )J (xp)e u dX 0 1 (-2 r (14) With this expression for the elements of the impedance matrix, one can solve equation (11) for the unknown coefficients of the current distribution I(r'). B. Excitation Mechanism One of the difficulties encountered in the solution of this problem is the implementation of a practical excitation mechanism which can be included in the mathematical model. In most applications the microstrip line is kept very close to the ground and is excited by a coaxial line of the same characteristic impedance. As a result, a unimodal field propagates under the transmission line and the current distribution on the line, beyond an appropriate reference plane, forms standing waves of a TEM-like mode (see Fig. 2(a)). Under this assumption and for the case of zero reflections from the coax-tomicrostrip transition, the microstrip line can be approximated by an ideal transmission line of the same characteristic impedance ZO terminated to an unknown self impedance Zs (see Fig. 2(b)). Furthermore, the coax can be substituted by a voltage generator VO with internal impedance Z0 as shown in Fig. 2(c). Since the reflection

-8 - coefficient is independent of the generator's internal impedance, the line at the excitation end is left open. From the above, one can see that a voltage gap generator placed near the end of an open microstrip line can serve as a very simple and very practical excitation (see Fig. 2(d)) for developing a useful model. Another method is to eject an incident TEM mode on the microstrip transmission line [14],[15]. The former excitation mechanism is adopted here for the solution of Pocklington's integral equation and results in an excitation vector [V ] = [.i ] with 1l, at the position of the gap generator im = 0, anywhere else The quasi-TEM mode considered on the microstrip line is related to the dominant component of the current distribution derived by the method of moments. If the origin of the x-coordinate is taken at the position of Z, then the self impedance, normalized with respect to the characteristic impedance at the position of the first current maximum dma, is given by maxm Z = 1 + r(O)e j2Bd 1 r(O)e max where SWR 1 jl max r(o) max (O =SWR + 1 and xmax is the position of a maximum. md~x

-9 - C. Radiation Patterns The electromagnetic field radiated by the microstrip dipole can be readily evaluated by a saddle point method of integration applied to the expression for the total electric field. The computation of the far field pattern involves the contribution not only from the microstrip dipole but also from the parasitic strip or strips and the embedded transmission line, i.e., from the entire module. The complete radiated electric field is therefore given by Ee = k: and E k k2- i 0~ where He = d + 1P + 1TL = e, 'e,~ e,~ Furthermore, the Hertzian potential is denoted by iIs 6,q d 11,6 =,p TL, (s = d for dipole), (s = p for parasitic), (s = TL for transmission line) with H 0 j'o -jrk -Jr e r cos(ko0x sin e cos p) - cos(k x) I 0 2 2 k sin(kzx) 1 - k- sin2 9 cos2 + L N S X E s (sr - 1)sin e SS(e)} * I n=l jk (f )sin e sin p jk as sin e cos (15). e o e o * cos p{cos e F (e) + jk (n x)sin e cos 4 e e

-1 0 - S IT~ rr k a -j rk0 e r N 5 nfl) Cas (k0zx sin e Gas fl- cos(kz x) ksnk k )1- - sin 2 e Gas2 k2 S sin p F (o' Is n jk0(nk X)sin e Gas cp e -%jk 0(fs)sin p sin e sin 6 Gas ~p ( 16 ) jk a e where I = w esin ~ i 2 2 7F u=cas' (w/ w )e Gas ky2 sin ~ sin e Gas a du 9 (1 7) Fd (e) Gas e 1 Gas 6 - i Ar - sin' e cat(k0V Er - sir'7Yh) (18) (19) d 0 d = F (e) sin e Er Gas e + i Ey- - Sin tan( k A- i ny e h ) sin(ka0 1/E11Yw sn2 F ( e) (h - 6)) Fd() (20) sin(ka A' - sin2 e h) 1. I sin(ka A'E - sin' -e (h 6)) d -s (e) (21 ) sin(kaE Er - sin' e h) sin(ka ErF - sin 62 (h - b ))d FTL (a) = 0 r Fd(6) (22) sin(ka E Cr - sin' o h)

-11 - and TL sin(k /i r - sinZ e (h - b )) d sTL(e) = S () (23) sin(ko / - sinz 6 h) In addition N + 1 - number of dipole subsections NS+ 1 = N + 1 - number of parasitic strip subsections N + 1 - number of transmission line subsections where kx denotes the length of each subsection and as the longitudinal displacement of the dipole or parasitic from the reference plane. For the particular applications under consideration in this article, fs is the offset of the dipole or parasitic strip longitudinal centerline from the transmission line centerline and here it is chosen to be fs = 0, i.e., all the metallic strips are aligned. Also, ad = ap = a and a = 0, while w and we denote the physical and effective strip widths, respectively. D. Numerical and Experimental Results Two different structures are investigated in this section for bandwidth improvement. The first case involves a parasitic strip located between the radiating dipole and the transmission line (see Fig. 1(a)) while the second case involves one or two parasitics embedded on the plane of the transmission line (see Fig. 1(c)). The bandwidth for these structures is defined by

-12 - f - f. BW = 2 max min f + f max min where fm fn denote the maximum and minimum frequencies for which max min VSWR < 2. For the computational results to be shown the substrate is duroid with er = 2.35 and the microstrip transmission line is kept at a distance 0.024 Xo from the ground plane. Case 2 With reference to Fig. l(a), the distance 6 is varied between zero and b. The VSWR and equivalent impedance are evaluated as functions of frequency for each 6. Figure 3 shows the observed variation in the normalized self impedance with and without the parasitic for different frequencies and 6. For these calculations h = 0.1 x, w = 0.05 x and the microstrip dipole and parasitic strip lengths are L = 0.280 x The bandwidth and the minimum achieved VSWR are plotted as functions of the ratio 6/bs for two different values of h (0.1 xo, 0.15 X ) with the corresponding dipole lengths equal to 0.280 Xo and 0.2906 xO respectively (see Fig. 4). From this figure, one can see that as the substrate becomes thinner the optimum bandwidth becomes smaller and the input match worse. Also, as the substrate thickness changes from 0.1 X to 0.15 Xo the range of 6 for VSWR < 2 becomes smaller and is shifted towards higher values. Therefore, there is a maximum value h such that for every h larger than h max max the VSWR is always larger than two. It is expected that the addition of another dipole between the parasitic and the printed dipole will further reduce the VSWR and will increase the bandwidth.

-13 - Case b. Parasitics of the Same Level with the Transmission Line Two different positions for the parasitic dipoles are investigated. At first, one dipole is placed along the transmission line as shown in Fig. 1(b). For this structure, the VSWR is evaluated as a function of the printed dipole length Ld, the parasitic dipole length L and the distance d. As an example, the variation of VSWR with Ld and d/Ld is shown in Fig. 5. However, the VSWR remains always larger than two. Subsequently, two parasitic dipoles are included and they are placed on each side of the transmission line (see Fig. 1(c)). The two parasitics have the same length, same width, same offset and overlap with respect to the transmission line. The VSWR and the self impedance Zs are evaluated as a function of the parasitic dipole length Lp and they are plotted in Figs. 6 and 7 for er = 2.35, h = 0.1x, b = 0.07587 X, w = 0.05 x and for three different lengths of the printed dipole at a frequency f = 10 GHz. From these figures, one can see that as the length of the parasitic becomes less than the printed-dipole length the VSWR goes asymptotically to values larger than two. However, there is a range of values for L which gives VSWR < 2 at f = 10 GHz. For six of these values and for Ld = 0.2906 x, the self impedance Zs is evaluated at different frequencies (9.37 to 10.41 GHz) as shown in Fig. 8. From these values, the bandwidth defined by VSWR < 2 is evaluated as a function of L and is plotted in Fig. 9. Figures 8,9 show that there is a specific L which will give VSWR = 1 at a frequency slightly above 10 GHz. An experiment has also been performed to corroborate the theoretical model. The test fixture in this case is a collection of

-14 - five duroid boards each with cr = 2.17. The overall thickness is roughly 120 mils and the boards are adhered together with vaseline. The embedded transmission line is at 30 mil, the parasitic dipole when present at 70 mil and the microstrip dipole at 120 mil from ground respectively. When there is no parasitic the bandwidth of the structure is zero, i.e., the requirement of VSWR < 2 is not satisfied throughout the frequency range of interest. If the parasitic is included (in this case of the same width and length as the microstrip dipole and directly beneath it) then the theoretically calculated bandwidth, for the parameters cited in Fig.10, is 11.6 percent, while the experimentally determined bandwidth is 10.4 percent. In addition, a frequency shift in the f and f points is observed between theory and experiment. Neverthe1 2 less, it is believed this is in very good agreement with the discrepancy between theory and experiment being attributed to tolerance errors in preparing the test fixture, the dissimilarity in ~r between the duroid boards and the vaseline used to adhere them together as well as due to the contribution of a standing surface wave pattern which arises as a result of the finiteness in size of the experimental substrate boards. In addition, some error may be introduced by the coax-to-microstrip transmission line transitions which is not accounted for in the theoretical model. Case C. Experimental Results —Radiation Patterns The E- and H-plane radiation patterns of the previously discussed test fixture have also been measured at a frequency f = 9.98 GHz and the results are shown in Figs. 11 and 12. The corresponding theoretically calculated patterns by using Eqs. (15) through (23) are also superimposed for comparison. It is observed

-15 - that the agreement between experiment and theory is nearly excellent in the H-plane while there is some discrepancy in the E-plane. It is important to note here that the theoretical model applies to an infinite substrate structure. The experimental structure, on the other hand, is finite in extent, as mentioned in the previous paragraph, and therefore diffraction from the edges will contribute to the shape of the E- and H-plane patterns. This contribution has been reduced by using absorbing material about the perimeter of the experimental fixture. Nevertheless, it is very difficult to eradicate these effects especially in the E-plane. The physical explanation for this comment is as follows. It has been demonstrated previously [11], [13] that the TM and the TE substrate surface waves excited by a microstrip dipole influence the E-plane and R-plane patterns, respectively. The relative permittivity constant and material thickness of the substrate used for this test allow only the fundamental TM surface wave mode to exist. This mode propagates in the x-direction (along the embedded transmission line-microstrip dipole axis) and diffracts at the substrate edges to influence the E-plane radiation pattern substantially. The R-plane radiation pattern is relatively clean since TE surface wave modes are not excited in this case and therefore there are no TE surface wave diffraction effects on this plane. The space wave diffraction effects at the board edges are much weaker than those due to surface waves and their contribution has been minimized substantially by the absorber layer affixed along the perimeter of the substrate board.

-16 - Conclusions A theoretical model to improve the bandwidth of electromagnetically coupled microstrip antennas has been developed. The model either incorporates parasitic metallic strips between the microstrip dipole and the excitation microstrip transmission line embedded in the substrate or it involves parasitic strips coplanar to and adjacent to the open end of the microstrip transmission line. Substantial bandwidth improvement has been obtained for either configuration. Experimental corroboration of the theoretical model has been obtained with very satisfactory results. References [1] A.G.Derneryd and A. G. Lind, "Extended analysis of rectangular microstrip antennas," IEEE Trans. on Antennas and Propagat., Vol. AP-27, November 1979, pp. 846-849. [2] J. H. Vandensonde and A. Van de Capelle, "Calculation of the bandwidth of microstrip resonator antennas," Proc. 9th European Microwave Conference, 1979, pp. 116-119. [3] Y. T. Lo, D. Solomon and W. F. Richards, "Theory and experiment on microstrip antennas," IEEE Trans. on Antennas and Propagat., Vol. AP-27, No. 2, March 1979, pp. 137-145. [4] H. G. Oltman and D. A. Huebner, "Electromagnetically coupled microstrip dipoles," IEEE Trans. Antennas Propagat., Vol. AP-29, January 1981, pp. 151-157. [5] R. S. Elliott and G. J. Stern, "The design of microstrip dipole arrays including mutual coupling, Part I: Theory," IEEE Trans. on Antennas and Propagat., Vol. AP-29, pp. 757-760.

-17 - [6] G. J. Stern and R. S. Elliott, "The design of microstrip dipole arrays including mutual coupling, Part II: Experiment," IEEE Trans. Antennas and Propagat., Vol. AP-29, September 1981, pp. 761-765. [7] P. B. Katehi and N. G. Alexopoulos, "On the effect of substrate thickness and permittivity on printed circuit dipole properties," IEEE Trans. on Antennas and Propagat., Vol. AP-31, January 1983, pp. 34-39. [8] P. B. Katehi and N. G. Alexopoulos, "Real axis integration of Sommerfeld Integrals with applications to printed circuit antennas," Journal of Mathematical Physics, Vol. 24, No. 3, March 1983, pp. 527 -533. [9] N. G. Alexopoulos, P. B. Katehi and D. B. Rutledge, "Substrate optimization for integrated circuit antennas," IEEE Trans. Microwave Theory and Techniques, Vol. Mtt-31, No. 7, July 1983,pp. 550-557. [10] P. B. Katehi, Ph.D. dissertation, University of California, Los Angeles, June 1984. [11] P. B. Katehi and N. G. Alexopoulos, "On the modeling of electromagnetically coupled microstrip antennas —The printed strip dipole," IEEE Trans. on Antennas and Propagat., Vol. AP-32, No.11, Novem. 1984, pp. 1179-1185. [12] P. B. Katehi and N. G. Alexopoulos, "Frequency-dependent characteristics of microstrip discontinuities in millimeter wave integrated circuits," IEEE Trans. on Microwave Theory and Techniques, Vol.33, No.10, October 1985, pp. 1029-1035. [13] N. G. Alexopoulos, D. R. Jackson and P. B. Katehi, "Criteria for nearly omnidirectional radiation patterns for printed antennas," IEEE Trans. on Antennas and Propagation, Vol. AP-33, No.2, Febr. 1985, pp. 195-205.

-18 - [14] J. Castaneda, "A frequency dependent characteristic impedance for an open-circuit transmission line," UCLA Integrated Electromagnetics Laboratory, internal memorandum, June 1984. [15] R.W Jackson and D. M. Pozar, "Full-wave analysis of microstrip openend and gap discontinuities," IEEE Trans. on Microwave Theory and Techniques, Vol. 33, No. 10, Oct. 1985, pp. 1036-1042. ACKNOWLEDGMENT The authors would like to thank G. Anttila and J. Castaneda for their help in the experimental part of this research. This research was supported by Northrop. Corp. under Research Grant 84-110-1006.

6 (a) } D,....... a..' ''', ' '':. '. ~ ~ ' d Ld I - -~ (. *. *. ' *.. (c ) / / / / / / / / / / /, / / / '/ '/ " L / Figure 1: Microstrip Configurations for Bandwidth Improvement.

I+ 29 I' I I:: I... I -'.I:.I.f.1. I I % I I I I I I.1. I I I I I I I I I I I t 2.0 * 1.6( - 1. 2? 0.8 *1 j.0.4 = 0.299xo I I I I.%...0 r- - - - - - -. I I I - I I I Ir9 I// // /.7/11 p 7, h (a) JY /I II I z 0 I I I I...1. I'I.. - V 0 I 1. I I I J..% 1. I %.0 z0F "I-" I I z 0 ~1z S (b) 1 I -.-a I I I I 1 V 0 If ff/ I / / 1 /!-I z 0 (C) I Ge I I I I...,.1..4 -. I I z s (d) Figure 2: Analytical Model for the Excitation Mechanism.

I - - -I —., 1, i I I i I — - - nr R s/z 77,, 7 7 7 7. 7 7, 7 7 7- ' A 0 R 10. 13 /II I; I 1 =1. 26mm \. ~Iz 2.0 p t. If-= R + JXs.86 —.o9. 79 I 6 = 1. 14mm 6 = 0. 96mm - —.e9. 49 GHz no parasitios 0.2 0.4 0.6 0.8 1.0 1.2 1.4 X5/Z0 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 Figur 3 NomlzdSl Imeac as a FunCtion1- of the Embedding Distance for Various Frequencies.

BW (%) 12 11 10 9 8 7. 6 5 4 3 2 1 VSWR 3 2 1 0.1 0.2 0.3 Figure 4: Bandwidth and Minimum for Two Values of the 0.4 0.5 0.6 0.7 0.8 0.9 1.0 6/ b Achieved V S W R as Fu Substrate Thickness h. nctions of the Ratio f/bs

VSWR 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 d/Ld 7 -____- - IL - --- 6 VSWR (d/Ld) / Ld = 8.4mm \ / Lp = 1.29mm 5 - \ / o \ / / / VSWR (Ld) \ d = 3.23mm \ Lp = 1.61mm 3- / d — I 2 -'... ~ 1 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 7.5 8.0 8.5 9.0 9.5 Ld(mm) Fiqure 5: VSWR as a Function of Ld and d/Ld for the Case of One Parasitic of the Same Level with the Transmission Line.

V SW P - - Z 7LZZZ72 r — -- - - -J1 5 Ld Lci=8. 4mm 4 3 2 1 N N L = 8.-72nmm ci * * --- — * S I/ S-10 Ia S0 Ld = 9.06mm. *-2& N.,. ---.*\, I I A.1. a. / a S N.. - I I I I 1T 2 3 4 5 8 9 6 7 Lp (mm) Figure 6: VSWR as a Function of Ld and LrI for the Case of Two Parasitics of the Same Level with the Transmission Line.

2.0 1.8 1.6 1.4 Ld = 8.72mm Ld = 9.06mm~ Ld = 8.4mm -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Xs/Zo Figure 7: Self Impedance as a Function of Ld and Lp for the Case of Two Parasitics of the Same Level with the Transmission Line.

R / Z Lp = 8. 72nmm - - L = 8.0 5mm p 0 L = 7. 38mm L 6.71mm o-o- L= 5.36mmf 1.8 1.6 1.4 10. 13GHz -9 10.27GHz -///" 9.87GHz X5 / Z -1. - 1.0 1-0.8 -0.6 -n 4 -fl 2 (>2 0.4 0.6 0.8 1.0 1.2 1. 4 1. 6 Fiqure 8: Self impedance as a Function of the Parasitic for Various Frequencies. Dipole Length LD

5 10 VSWR BW 4 BW VSWR 2 1 2 3 4 5 6 7 8 9 L (mm) p Figure 9: VSWR and Bandwidth as Functions of the Parasitic Dipole Length Ln for the Case of Two Pdrasitics of the Same Level with the Transmission Line. ( )

VSWR 8 7 6 5 4 3 2 1 --- Theoretical Results Experimental Results I,. ----r-~ ' I / I ^^ ----1 --- I I II....... 8.5 8.8 9.1 9.4 9.7 10.0 10.3 10.6 10.9 11.2 11.5 (GHz) Figure 10: VSWR as a Function of Frequency for the Case of Two Same Level with the Transmission Line. Parasitics of the

0 30 -30 60 -60 ( -120 120 Theoretical Experimenta h=120 mils <=50 mil -150 150 Figure 11: H-Plane Pattern for the Case of One Parasitic Between the Dipole and the Transmission Line.

-90______ / -- -- i. Theoretical Results h=120 mils \ / 6=50 mils \ 120 Theoretical Reu~Its Experimenta] Fe lts -150 Figure 12: E-Plane Pattern for the Case of One Parasitic Between the Dipole and the Transmission Line.

-31 - Part a: Part b: Part c: Part d: COMPUTER PROGRAMS Comments. User's Guide. List of Programs. Magnetic Tape Comments.

-32 - PART A " Comments About the Programs "

-33 - PART A; Comments about the programs. In order to evaluate the bandwidth for the radiating structures described in the technical report, one has to submit file JOBRUN as a batch job. This file is a collection of smaller batch jobs. Each of these jobs starts with a comment statement: $com JOBRUN1: Results for the bandwidth...f=... and evaluates the currents on the transmission line and dipoles at the frequency shown in the comment statement. Also, it evaluates the E- and Hplane radiation patterns at the same frequency. A list of such a batch jot) is shown in Table A.1. Preceding these jobs are a few commands which set the time limit for the whole job and create a temporary work file called DOUT. In line 1 of this program (see Table A.1), the command: $sig * route=unyn t=150 initiates a batch job of a maximum CPU time equal to 150secs and determines the destination of any punched or printed output (route=unyn). In line 3, the program creates a file called DOUT: $create dout and in line 4 it empties that file in case it existed already: $empty dout Each of the batch subjobs (JOBRUN1, JOBRUN2,...) is a collection of various JCL commands which perform different tasks. In line 5, the job excecutes the compiled version of program FINITE (see Part c) stored in file OFIN: $run ofin 5=*source* 6=dout(1) t=60 The program FINITE reads data from file "5" (=*source*=JOBRUN1), evaluates the elements of the impedance matrix which results from the application of the method of moments and stores these results in file DOUT starting at

-34 - line 1. The maximum CPU time for this program is 60 secs. The data given in lines 6 to 30 are in a format described in Part b. The command $endfile in line 31 denotes the end of the data. In the same manner, this job excecutes program FINITE ( stored in OFIN) two more times (lines 32 to 58 and 59 to 85) and stores all the results in file DOUT as shown in Part c. As it was mentioned previously,the results from these three different jobs are the elements of the impedance matrix stored in vectors Zll, Z31, Z33, Z21, Z22 and Z32. The elements of these vectors correspond to the following elements of the impedance matrix. Zll: Self-interaction elements of the printed dipole. Z22: Self-interaction elements of the parasitic dipoles. Z33: Self-interaction elements of the transmission line. Z21: Mutual-interaction elements between printed dipole and parasitics. Z31: Mutual-interaction elemets between transmission line and printed dipole. Z32: Mutual-interaction elements between transmission line and parasitics. In the case of two parasitics of the same level with the transmission line, there is one more vector given in the output as Z32 and it includes the mutual interaction elements between the two parasitics. In addition, the batch job excecutes program OINV33 (line 87) $run oinv33 1=*source* 2=dout(1) 3=resgn(1) 6=result(1) t=30 Program OINV33 is a compiled version of programm INV33 (see Part b). It takes as input the elements of vectors Z11,Z22,Z33,Z21,Z31 and Z32, fills out the impedance'matrix by using all the possible symmetries and inverts the matrix to get the current distribution on the strip conductors. The

-35 - program INV33 reads input from files 1 (=*source*=JOBRUN1) and 2 (=DOUT) and stores output in files 3 (=RESGN) and 6 (=RESULT). The results in file RESULT are in such a format that the user can read them easily recognizing the currents on the transmission line, the parasitic and printed dipoles (see Part c). The results in file RESGN are in such a form that can be fed as an input to program GAIN (see Part c). The input to program INV33 read through file 1 is shown in Table A.1 from line 88 to line 94. As soon as the excecution of program INV33 is complited, the content of file DOUT is copied to file OUT1, starting at line *1+1, for later possible use. In line 96, the batch job excecutes program OGAIN which is a compiled version of program GAIN: $run ogain 1=*source* 3=resgn 6=result(*l+l) t=20 This program reads data from files 1 (=*source*=JOBRUN1), 3 (=RESGN) and stores results in file 6(=RESULT) starting at the *1+1 line. The results of this file are the radiated E-, H-plane patterns of the structure under consideration. This program can give plots of these patterns when compiled by a VERSATEC compiler. The data given to this program have to be in a form which is explained in details in part b. Each of these batch subjobs (JOBRUN1, JOBRUN2,...) evaluates the currents and therefore the VSWR at some specified frequency. In order to compute the bandwidth of the radiating structure, the VSWR has to be evaluated over a range of frequencies and therefore various subjobs have to be excecuted one after the other through the batch job JOBRUN. As an example, for the evaluation of the bandwidth as shown in Figure 11 of the technical report, 14 batch subjobs had to be excecuted at the following frequencies: 9.1,9.25,9.4,9.55,9.7,9.85,10.0,10.15,10.30,10.45,10.60,10.75, 10.9 and 11.2 GHz.

-36 - TABLE A.1 " JOBRUN1 for the Case of One Parasitic Between the Transmission Line and the Printed Dipole".

-37 - 123456789 123456789 123456789 123456789 123456789 123456789 12345689 l:$sig * route=unyn t=150 2:$com...JOBRUN1...Results for bandwidth.. 3:$create dout 4:$empty dout 5:$run ofin 5=*source* 6=dout(1) t=60 6: 8 IIA 7: 15 IDA 8: 1 IOPT 9: 0 IFEED 10: 105 NTD 11: 25 ND 12: 116 NF 1:3: 0 NTE 14: 1 NTM 15: 2 IFIRST 16: 2.17 ER 17: 2.17 EER 18: 0.093080 H 19: 0.0697205 BS 20: 0.0310565 DEL 21: 0.0000895 T1 22: 0.0000895 T2 23: 0.0152125 DLX 24: 100.0 A 25: 3.14159265 26: 0.0647380 W 27: 0.0 OFFSET 28: 0.0000895 WDELTA 29: 6.61083218 POLTM PL 30: 6.61083218 POLES 31:$endfile 32:$run ofin 5=*source* 6=dout(*l+l) t=60 33: 8 IIA 34: 15 IDA 35: 2 IOPT 36: 0 IFEED 37: 105 NTP 38: 25 NP 39: 116 NT 40: 0 NTE 41: 1 NTM 42: 2 IFIRST 43: 2.17 ER 44: 2.17 EER 45: 0.093080 H 46: 0.0310565 DEL 47: 0.0310565 DEL 48: 0.0000895 T1 49: 0.0000895 T2 50: 0.0152125 DLX 51: 100.0 A.f=8.95GHz...

-38 - 123456789 123456789 123456789 123456789 123456789 123456789 123456789 52: 3.14159265 53: 0.064738 W 54: 0.0 OFPD 55: 0.0000895 WDELTA PO 56: 6.61083218 POLTM 57: 6.61083218 POLES 58:$endfile 59:$run ofin 5=*source* 6=dout(*l+1) t=60 60: 8 IIA 61: 15 IDA 62: 3 IOPT 63: 0 IFEED 64: 105 NTP 65: 25 NP 66: 116 NT 67: 0 NTE 68: 1 NTM 69: 2 IFIRST 70: 2.17 ER 71: 2.17 EER 72: 0.093080 H 73: 0.0697205 BS 74: 0.0310565 DEL 75: 0.0000895 T1 76: 0.0386640 BS-DEL 77: 0.0152125 DLX 78: 100.0 A 79: 3.14159265 80: 0.0647380 W 81: 0.0 OFTP 82: 0.0000895 WDELTA POLTE 83: 6.61083218 POLTM 84: 6.61083218 POLES 85:$endfile 86:$com...Parasitics with length=26*DLX... 87:$run oinv33 1=*source* 2=dout(1) 3=resgn(1) 6=result(1) t=30 88: 116 NT 89: 25 NP 90: 25 ND 91: 105 NTP 92: 1 NPD 93: 166 NOR 94: 17 NFEED 95:$endfile 96:$run ogain 1=*source* 3=resgn 6=result(*l+l) t=20 97: 0 IPLANE 98: 105 NTP 99: 116 NT 100: 25 NP1

-39 - 123456789 123456789 123456789 123456789 123456789 123456789 123456789 101: 0 NP2 102: 25 ND 103: 2.17 ER 104: 2.17 EER 105: 0.093080 H 106: 0.0697205 BS 107: 0.0310565 DEL 108: 0.0152125 DLX 109: 0.0647380 WIDTH 110: 0.0000895 WDELTA 111: 0.0 OFP1 112: 0.0 OFP2 113: 0.0 OFD 114:$endfile 115:$copy dout to outl(*l+1) 116:$empty dout 117:$signoff

-40 - Printedl Di pole Figure A.1: Microstrip Configuration for Bandwidth Enhancement. One Parasitic Between the Printed Dipole and the Transmission Line.

-41 - TABLE A.2 " JOBRUN1 for the Case of Two Parasitics of the Same Level with the Transmission Line".

-42 - 123456789 123456789 123456789 123456789 123456789 123456789 123456789 l:$sig *route=unyn t=150 2: com....JOBRUN1.....Results for bandwidth...f=8.95GHz... 3:$create dout 4:$empty dout 5:$run ofin 5=*source* 6=dout(1) t=60 6: 8 IIA 7: 15 IDA 8: 1 IOPT 9: 0 IFEED 10: 105 NTD 11: 25 ND 12: 116 NT 13: 0 NTE 14: 1 NTM 15: 2 IFIRST 16: 2.17 ER 17: 2.17 EER 18: 0.093080 H 19: 0.0697205 BS 20: 0.0 DEL 21: 0.0000895 T1 22: 0.0000895 T2 23: 0.0152125 DLX 24: 100.0 A 25: 3.14159265 26: 0.0647380 W 27: 0.0 OFTD 28: 0.0000895 WDELTAPO 29: 6.61083218 POLTM -- 30: 6.61083218 POLES 31:$endfile 32:$run ofin 5=*source* 6=dout(*l+l) t=60 33: 8 IIA 34: 15 IDA 35: 3 IOPT 36: 0 IFEED 37: 105 NTP 38: 25 NP 39: 130 NT 40: 0 NTE 41: 1 NTM 42: 2 IFIRST 43: 2.17 ER 44: 2.17 EER 45: 0.093080 H 46: 0.0697205 BS 47: 0.0 DEL 48: 0.0000895 T1 49: 0.0000895 T2

-43 - 123456789 123456789 123456789 123456789 123456789 123456789 123456789 50: 0.0152125 51: 100.0 52: 3.14159265 53: 0.064738 54: 0.07 55: 0.0000895 56: 6.61083218 57: 6.61083218 58:$endfile 59:$run ofin 5=*source: 60: 8 61: 15 62: 4 63: 0 64: 5 65: 25 66: 25 67: 0 68: 1 69: 2 70: 2.17 71: 2.17 72: 0.093080 73: 0.0697205 74: 0.0 75: 0.0000895 76: 0.0000895 /7: 0.0]52125 78: 100.0 79: 3.14159265 80: 0.0647380 81: 0.07 82: 0.0000895 83: 6.61U83218 84: 6.61083218 8b:$endfile 86:$run ofin 5=*source 87: 8 88: 15 89: 3 90: 0 91: 1 92: 25 93: 25 94: 0 95: 1 96: 2 97: 2.17 98: 2.17 99: 0.093080 100: 0.0697205 101: 0.0 102: 0.0000895 k DLX A W OFTP WDELTA POLTM POLES 6=dout(*l+l) t=60 IIA IDA IOPT IFEED NPD ND NP NTE NTM IFIRST ER EER H BS DEL T1 T2 DLX A w OFPD WDELTA POLTM POLES ----- POLTE * 6=dout(*l+l) t=60 IIA IDA IOPT IFEED NPP NP1 NP2 NTE NTM IFIRST ER EER H BS DEL T1

-44 - 123456789 123456789 123456789 123456789 123456789 123456789 123456789 103: 0.0000895 T2 104: 0.0152125 DLX 105: 100.0 A 106: 3.14159265 107: 0.0647380 W 108: 0.14 OFPP 109: 0.0000895 WDELTA ----— POLTE 110: 6.61083218 POLTM 111: 6.61083218 POLES 112:$endfile 113:$com...Parasitics with length 26*dlx... 114:$run omutual 1=*source* 2=dout(1) 3=resgn(1) 6=result(1) t=30 115: 116 NT 116: 25 NP1 117: 25 NP2 118: 25 ND 119: 105 NTP 120: 1 NPP 121: 1 NPD 122: 191 NOR 123: 12 NFEED1 124: 180 NFEED2 125:$endfile 126:$run ogain 1=*source* 3=resgn 6=result(*l+1) t=20 127: 0 IPLANE 128: 105 NTP 129: 116 NT 130: 25 NP1 131: 25 NP2 132: 25 ND 133: 2.17 ER 134: 2.17 EER 135: 0.093080 H 136: 0.0697205 BS 137: 0.0310565 DEL 138: 0.0152125 DLX 139: 0.0647380 WIDTH 140: 0.0000895 WDELTA 141: 0.07 OFP1 142: -0.07 OFP2 143: 0.0 OFD 144:$endfile 145:$copy dout to outl(*l+1) 146:$empty dout 147:$signoff

-45 - ( ProLsitic Dipole w I Trcxnsnmission Linne. -- -, c.I --- —,,, - y tt y j -" --- L - I Printed Dipole. ) Porcositic Dipole #.. Figure A.2: Microstrip Configuration for Bandwidth Enhancement. Two Parasitic Dipoles of the Same Level with the Transmission Line.

-46 - PART B " User's Guide"

-47 - Part B: User's Guide. i) Transfer the programs from the magnetic tape to your computer. On the tape there are 8 files. Five of them contain excecutable programs while the rest three are input and output data files. The files as shown on the tape are: -----------------------------------------— I --- —---- File name Type of file Description ------------------------------------------------------------ JOBRUN Excecutable program A group of JCL commands named JOBRUN. which lead to the evaluation of the bandwidth for either one of the structures under consideration.(see technical report). ------------------------------------------------------------ FOPTIONO Excecutable file This program evaluates the named POLES. poles of the Green's function and classifies them as TE and TM. ------------------------------------------------------------ FOPTION1 Excecutable file named FINITE. This program evaluates the elements of the impedance matrix. FOPTION2 Excecutable file This program inverts the named INV33. impedance matrix and evaluates the currents on all the strip conductors. It is good only for the case of one parasitic. FOPTION3 Excecutable file This program uses the currents named GAIN. to evaluate the E- and H-plane radiation patterns. FOPTION4 Data file named This is a permanent file that OUT1. contains the elements of the impedance matrix as they were evaluated by FINITE.

-48 - File name Type of file Description - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - I- - - - - - - FOPTION5 Data file named RESULT. This is a permanent file that contains the computed currents in a format easy to be read by the user. FOPTION6 Data file named This is a permanent file that RESGN. FOPTION7 Excecutable file named MUTUAL. contains the computed currents. This file is used as an input to program GAIN. This is a program that inverts the impedance matrix and evaluates the currents on the strip conductors. It is good only for the case of two parasitics of the same level with the T.L. (see technical report). ii) Run program POLES by substituting the rigth values for ER and H. This program gives as output the poles of the Green's function classified as TE and TM poles. Also, it gives the same poles ordered according to their magnitude. iii) Compile program FINITE and save it in a file named OFIN. Compile program INV33 or MUTUAL and save it in a file named OINV33 or OMUTUAL. Also, compile program GAIN and save it in a file named OGAIN. IDA, (see iv) In each run of the compiled program OFIN let the variables IIA, IOPT, IFEED, A and have exactly the same values as in the example Tables A.1,A.2). v) Change the rest of the variables so the correspond to the structure under consideration. The definition of each one of these variables is as follows: NTD: (NTD-1)*DLX= Distance of the leftend of the printed dipole from the left end of the Transmission line (see figure A.1).

-49 - NPD: (NPD-1)*DLX= Distance of the left end of the printed dipole from the left end of the parasitic dipole. NTP: (NTP-1)*DLX= Distance of the left end of the parasitic dipole from the left end of the transmission line. NPP:(NPP-1)*DLX= Distance of the left end of parasitic #1 from the left end of parasitic #2. NT: (NT+1)*DLX= Length of the transmission line. ND:(ND+1)*DLX= Length of the printed dipole. NP:(NP+1)*DLX= Length of the parasitic for the structure of figure A.1 NP1:(NP1+1)*DLX= Length of parasitic #1 for the structure of figure A.2 NP2:(NP2+1)*DLX= Length of parasitic #2 for the structure of figure A.2 NTE:Number of TE poles ( This number comes as an output from program POLES). NTM:Number of TM poles ( This number comes as an output from program POLES). IFIRST: This variable takes the values 0,1,2 0: The lowest pole is a TM one. 1: The lowest pole is a TE one. 2: There is only one TM pole. ER: Dielectric constant. EER: A variable which takes values between 1 and ER. It is suggested that this variable takes the value ER. H: Substrate thickness inj BS: Embedding distance of the transmission line in.2o DEL: Embedding distance of the parasitic/parasitics ino )0

-50 - T1: Conductor thickness of the printed and parasitic dipoles in A. 0 T2: Conductor thickness of the transmission line. It is suggested that you make T2 equal to T1. DLX: Subsection length in 9 ( 9= )0 /vEr )W: Width of the strip conductors. OFTD: Offset of the printed dipole with respect to the -/ transmission line. OFPD: Offset of the printed dipole with respect to the parasitics. OFTP: Offset of parasitic dipoles with respect to the transmission line. WDELTA: Correction to the width: we = w+2&. It is suggested that the value of is equal to T1 and T2. POLTE *: This is a vector having as elements all the TE poles ordered according to their magnitude. POLTM *: This is a vector having as elements all the TM poles ordered according to their magnitude. POLES *: This is a vector having as elements all the poles ordered accordig to their magnitude. NOR: Total number of unknown coefficients in the expression for the current in the integral equation (see technical report). NFEED NFEED*DLX= L = the distance of the gap generator from the left end of the microstrip transmission line. NFEED should have the following value INT(O.25/DLX). IPLANE: This variable determines wether the E- or H-plane patterns will be evaluated by program GAIN: 0: E-plane pattern 1: H-plane pattern. OFP1,2: Offset of the Ist,2nd parasitic dipoles with respect to Uie trailsa,ission line.

-51 - If there is only one parasitic, OFP2 should be equal to 0. OFD:This variable is equal to OFTD. vi) As an example, JOBRUN is shown as it should be submitted for the evaluation of the VSWR and radiation patterns at f=8.95GHz for the two structures discussed in the technical report. Specifically, the case of one parasitic between the printed dipole and the transmission line is treated in table A.1 while the case of two parasitics of the same level with the transmission line is treated in table A.2. * The elements of these vectors are given as output by the program POLES. ** All the lengths except of the subsection length are measured in Ao

-52 - PART C " List of Programs"

-53 - JOBRUN

-54 -$sig * route=unyn t=150 $com..... Results for Bandwidth..f=8.95GHz.. $create dout $ empty dout $run ofin 5=*source* 6=dout(1) t=60 8 15 1 0 105 25 116 0 1 2 2.17 2.17 0.093080 0.0697205 0.0310565 0.0000895 0.0000895 0.0152125 100.0 3.141592653 0.0647380 0.0 0.0000895 6.61083218 6.61083218 $endfile $run of in 5=*source* 6=dout(*l+1) t=60 8 15 2 0 1 25 25 0 1 2 2.17 2.17 0.093080 0.0310565 0.0310565 0.0000895 0.0000895 0.0152125 100.0 3.141592653 0.064738 0.0 0.0000895 6.61083218 6.61083218 $endfile $run of in 5=*source* 6=dout(*l+1) t=60 8

-55 -15 3 0 105 25 116 0 1 2 2.17 2.17 0.093080 0.0697205 0.0310565 0.0000895 0.0386640 0.0152125 100.0 3.141592653 0.0647380 0.0 0.0000895 6.61083218 6.61083218 $endfile $com.......Parasitics with length 26*dlx............ $run oinv33 1=*source* 2=dout(1) 3=resgn(1) 6=result(1) t=30 116 25 25 105 1 166 17 $endfile $run ogain 1=*source* 3=resgn 6=result(*1+1) t=20 0 105 116 25 0 25 2.17 2.17 0.093080 0.0697205 0.0310565 0.0152125 0.0647380 0.0000895 0.0 0.0 0.0 $copy dout to outl(*l+1) $empty dout $signoff

-56 - FOPTION.' ( POLES )

-57 -C THE NAME OF THIS FILE IS:.................POLES.................. C THE DOUBLE INTEGRATION IS PERFORMED FROM XK-1 TO XK C SAME THING WITH THE SINGLE INTEGRATION C C FROM 0 TO A WE PERFORM FIRST THE INTEGRATION WITH RESPECT TO X,X' C AND AFTER THAT THE INTEGRATION WITH RESPECT TO L C C FROM A TO ~ WE PERFORM FIRST THE INTEGRATION WITH RESPECT TO L C AND AFTER THAT THE INTEGRATION WITH RESPECT TO X,X' C C BUT DURING THIS SECOND INTGRATION WE ARE CAREFULL TO COMPUTE ANALY C TICALLY THE INTEGRALS WITH THE FAST VARYING INTEGRAND IMPLICIT REAL*8(A-H,O-Z) DIMENSION XR(40),XS(40) C.....................................9.0........ e....................... C ************************** COMMENTS ************************** C C ER:....DIELECTRIC CONSTANT C C DP:....HEIGHT OF THE DIELECTRIC SUBSTRATE C C C NE:....NUMBER OF ##TE## WAVES C C NM:....NUMBER OF ##TM## WAVES C C XS:....MATRIX OF POLES CONTRIBUTING TO TE WAVES C C XR:....MATRIX OF POLES CONTRIBUTING TO TM WAVES C C ERR:....ERROR IN THE COMPUTATION OF THE POLES C C COMMON/POLE/TPO(40),LOR(40) C...................e........ e................e..... eee......... ER=10.0 ER2=ER*ER PI=3.141592653589D0 PI2=PI*PI MAXE=5 ERR=0.00000001DO DO 12 IDP=1,1 DP=FLOAT(IDP)*0.10160 CALL POLES (ER,PI,DP,ERR,XS,XR,NE,NM) 12 CONTINUE STOP END C*************************************$$******!***$*********************** C THE NAME OF THIS FILE IS:................POLES.................... C THIS SUBROUTINE FINDS THE POLES OF THE GREEN'S FUNCTION C (TE AND TM SURFACE WAVES)

SUBROUTINE POLES(ER,PI, DP,ERR,TEZP,%MP,NE,NM) C C ER= DIELECTRIC CONSTANT C DP= HEIGHT OF THE DIELECTRIC SUBSTRATE NORMALIZED TO THE WAVELEC NGTH OF OPERATION C ERR= ACCURACY OF CALCULATION C NE= NUMBER OF TE POLES C NM= NUMBER OF TM POLES C IMPLICIT REAL*8 (A-H,O-Z) DIMENSION XS(40),XR(40),TEP(40),TMP(40) COMMON/POLE/TPO(40),LOR(40) C C PART I: TE MODES C AKO=2.DO*PI AK=DSQRT(ER)*AK0 XO=DP*DSQRT(AK**2-AKO**2) AN=XO/PI+0.5D0 NE=AN IF (NE.EQ.0) GO TO 310 DO 2 I=1,NE IF (XO-(2.DO*FLOAT(I)+1.DO)*PI/2.DO) 3,3,4 4 XSO=(2.DO*FLOAT(I)-1.D0)*PI/2.D0+ERR XS1=(2.DO*FLOAT(I)+1.DO)*PI/2.DO-ERR GO TO 5 3 XS0=(2.DO*FLOAT(I)-1.DO)*PI/2.DO+ERR XS1=XO 5 CONTINUE IF (DABS(XSO-XS1)-ERR) 22,7,7 7 XSA=(XSO+XS1)/2.DO Y=-DTAN(XSA)*DSQRT(XO**2-XSA**2)-XSA IF (Y) 8,9,10 9 XS(I)=XSA GO TO 222 8 XS1=XSA GO TO 5 10 XSO=XSA GO TO 5 22 XS(I)=(XSO+XS1)/2.DO 222 XS(I)=DSQRT(AK**2-XS(I)**2/DP**2) 2 CONTINUE WRITE (6,301) ER,DP 301 FORMAT('1',10X,'1) THE TE MODES THAT CAN BE EXCITED IN A DIELECT *RIC SUBSTRATE WITH'/10X,'ER=',D16.9,5X,'DP=',D16.9/10X,'ARE GIVEN *BY:'//) DO 302 I=1,NE TEP(I)=XS(I) WRITE (6,303) I,TEP(I) 303 FORMAT (10X,'ORDER OF MODE=',I4,5X,'SURFACE TE WAVE AT L=',D16.9) C 302 CONTINUE IF (NE.NE.0) GO TO 312 310 WRITE (6,311) 311 FORMAT('1',10X,'1) THERE IS NOT ANY TE SURFACE WAVE'/1OX,'.... *............... **.......*. ' ) C 312 CONTINUE C C END OF PART I

-59 -C C C PART II: TM MODES C AN=XO/PI+1.DO NM=AN IF (NM.EQ.0) GO TO 320 DO 13 I=1,NM IF (XO-(2.DO*FLOAT(I)+1.D0)*PI/2.D0) 14,14,15 15 XS1=FLOAT(I)*PI-PI/3.DO-0.01DO GO TO 16 14 XS1=XO 16 XSO=FLOAT(I-1)*PI+ERR 17 CONTINUE IF (DABS(XSO-XS1)-ERR) 113,19,19 19 XRA=(XSO+XS1)/2.DO Y=DSQRT(ER)**2*(1.DO/DTAN(XRA))*DSQRT(XO**2-XRA**2)-XRA IF (Y) 20,21,24 21 XR(I)=XRA GO TO 333 20 XS1=XRA GO TO 17 24 XSO=XRA GO TO 17 113 XR(I)=(XSO+XS1)/2.DO 333 XR(I)=DSQRT(AK**2-XR(I)**2/DP**2) 13 CONTINUE WRITE (6,304) ER,DP 304 FORMAT (//10X,'2) THE TM MODES THAT CAN BE EXCITED IN A DIELECT *RIC SUBSTRATE WITH'/10X,'ER=',D16.9,5X,'DP=',D16.9/20X,'ARE GIVEN *BY:'//) DO 305 I=1,NM TMP(I)=XR(I) WRITE (6,306) I,XR(I) 306 FORMAT (10X,'ORDER OF MODE=',I4,5X,'SURFACE TM WAVE AT L=',D16.9) C 305 CONTINUE IF (NM.NE.0) GO TO 322 320 WRITE (6,321) 321 FORMAT (10X,'2) THERE IS NOT ANY TM SURFACE WAVE'/10X,'......... *...e....................... 0 ) C 322 CONTINUE C NK=NE+NM DO 411 IQW=1,NE TPO(IQW)=TEP(IQW) LOR(IQW)=0 411 CONTINUE DO 412 IQW=1,NM TPO(NE+IQW)=TMP( IQW) LOR(NE+IQW)=1 412 CONTINUE DO 515 IIL=1,NK WRITE (6,516) IIL,TPO(IIL),LOR(IIL) 516 FORMAT ( OX,'IIL=',14,5X,'TPO=',D16.9,5X,'LOR=',I4/) 515 CONTINUE C IF (NK.EQ.1) GO TO 416 NNK=NK-1

-60 -DO 415 IIP=1,NNK IK=IIP+1 DO 413 IIF=IK,NK QWR=TPO(IIP) IIW=LOR(IIP) IF (TPO(IIP).LT.TPO(IIF)) GO TO 413 TPO(IIP)=TPO(IIF) LOR(IIP)=LOR(IIF) TPO(IIF)=QWR LOR(IIF)=IIW 413 CONTINUE 415 CONTINUE C 416 CONTINUE WRITE (6,418) (TPO(IR),LOR(IR),IR=1,NK) 418 FORMAT (/12X,'TPO-MATRIX',10X,'LOR-MATRIX'/12X,' - ------ ' 10X'* --- —--— '//20(10X,D16.9,5X,I4/)) RETURN END

-61 - FOPTIONi_ (FINITE

-62 - C.................... FINITE....................................... C C THIS PROGRAM EVALUATES THE ELEMENTS OF THE MATRIX AND VECTOR C IN THE MATRIX EQUATION FOR THE FOLLOWING PROBLEM: C "EXCITATION OF A DIPOLE ON THE AIR-DIELECTRIC C INTERFACE WITH A FEEDING LINE EMBEDDED IN C THE SUBSTRATE-GAP GENERATOR" C C THIS PROGRAM IS GOOD FOR ANY EMBEDDING DISTANCE OF THE C TRANSMISSION LINE C C MNUM= 1 WHEN OFFSET = 0.0 C 2 WHEN OFFSET > 0.0 C C IMPLICIT REAL*8 (A-H,O-Z) COMPLEX*16 Z1GT(150),Z2GT(160),Z2LT(190),CI DIMENSION VSPE(20),VTPE(20),VSPM(20) COMMON/OUT/G1GT (150),G2GT(160),G2LT(190) COMMON/MAT/PLI,IWRITE COMMON/PUT/SSJO (150),SAJO (150),YSIN,YCOS COMMON/ADON/DIST(10,150,10),SERS(5),SERA(5),DARG(10,10,4),SN(10,2) *,WREAL,NSER,MNUM COMMON/DAT/ER,H,BS,TT1,TT2,DLX,A,TPI,TPI2,PI,W,E1,E2,E3,E4,E5,EER, *AK0,AK,AKK,FA,FA0,BW,BWW,BWWW,B4W,B5W,OFFSET,WDELTA,NS,NF,ND,IFEED COMMON/DATT/COAL(20),POINT(20),CN(51),BM(51),POLTM(20),POLTE(20) *,AM(41),DM(41),POLES(40),NPOINT,NKO,MA,NTM,NTE,NKOK,IFIRST COMMON/COEF/RX(5),XX(5),RZ(5),XZ(5),FRX(5),FRZ(5),F1XX,F1ZX,F2XXG, *F2ZXG,F2XXL,F2ZXL,FlXXL,F1ZXL,F2XL,F2ZL CALL DATA(IOPT) WREAL=W W=W* (1.DO+2.DO*WDELTA/W) CI=(0.DO,1.DO) C C FOR THE NORMALIZATION OF THE CURRENT ALONG THE Y AXIS CVON=W*PI/2.DO C C --- --------------------------------------— + C STEP 1: EVALUATION OF VECTOR CN C IT GIVES THE END POINTS OF THE C INTERVALS CONSIDERED IN (0,KO) C --- —--------------------------------------— + DELTA=AKO/FLOAT(NKO) CN(1)=0.DO DO 1 I=1,NKO CN(I+1)=DELTA*FLOAT(I) 1 CONTINUE C --- —-------------------------------------- C STEP 1: EVALUATION OF VECTOR BM C IT GIVES THE END POINTS OF THE C INTERVALS CONSIDERED IN (K,A) C --- —--------------------------------------— + DELTA=(A/DSQRT(EER)-AK)/FLOAT(MA)

-63 - BM (1)=AK DO 2 I=1,MA BM(I+1)=DELTA*FLOAT(I)+AK 2 CONTINUE C --- —------------------------------------— + C STEP 1: EVALUATION OF THE VECTORS AM,DM C "AM" GIVES THE END POINTS AROUND C THE TM POLES C "DM" GIVES THE END POINTS AROUND C THE TE POLES C C IFIRST= 2 ONLY ONE TM POLE C 1 TEO<TMO C 0 TM0<TEO C --- — - -----------------------------------------— + AM(1)=AKO DM(1)=AKO NMAX=NTE+NTM-1 IF (IFIRST.EQ.2) GO TO 3 DO 4 I=1,NMAX AM(I+1)=(POLES (I+1)+POLES (I))/2. DO DM(I+1)=AM(I+1) 4 CONTINUE AM(NMAX+2)=AK DM(NMAX+2)=AK IF (IFIRST.EQ.1) GO TO 5 DM(NMAX+1)=AM(NMAX+2) DO 6 I=1,NMAX DM(NMAX-I+1)=AM(NMAX-I+2) 6 CONTINUE GO TO 7 5 AM(NMAX+1) =DM(NMAX+2) DO 8 I=1,NMAX AM(NMAX-I+1)=DM(NMAX-I+2) 8 CONTINUE GO TO 7 C 3 DELTA=(AK-AKO)/FLOAT(NKOK) AM(1)=AKO DO 9 I=1,NKOK AM(I+1)=DELTA*FLOAT(NKOK)+AKO 9 CONTINUE 7 CONTINUE C --- —-------------------------------------------— + C STEP 2: EVALUATION OF VECTORS VSPE,VTPE C --- —------------------------ ------------------— + IF (IFIRST.EQ.2) GO TO 10 DO 11 I=1,NTE ARG=POLTE(I) VSPE(I)=WSPE(ARG) VTPE(I)=WTPE(ARG) 11 CONTINUE 10 CONTINUE C --- —----------------------------------— + C STEP 2: EVALUATION OF VECTOR VSPM

-64 - C --- —- --------------- + DO 12 I=1,NTM ARG=POLTM(I) VSPM(I)=WSPM(ARG) 12 CONTINUE C --- —-------------------------------------------------— + C EVALUATION OF THE COEFFICIENTS FOR THE C FF'S FUNCTIONS C --- —----------------------------------------------— + F1XX=O.5D0/(1.DO-E2) FlZX=(FXX-1.DO/ ((ER+1.DO)*(1.DO-E3))) F2XXG=O. 5D0/ (1 DO+E4) F2ZXG=(F2XXG-1.DO/((ER+1.DO)*(1.DO+E6))) F2XXL=0.5D0*E4/(1.DO+E4) F2ZXL=(F2XXG-1.DO*ER/((1.DO+ER)*(1.DO+E6))) IF (IFEED.NE.1) GO TO 75 F2XXG=F lXX F2ZXG=F1ZX F2XXL=F1XX F2ZXL=F1ZX 75 F1XXL=F2XXG F1ZXL=F2ZXL F2XL=F2XXL F2ZL=F2ZXL C --- —------------------------------------------------— + C STEP 2: EVALUATION OF VECTORS Z1GT,Z2GT, C Z2LT,ZOGT,ZOLT,ZOO C --- —----------------------------------------------— + Vl=AKO *AKO V2=1.DO-EER V3=ER-EER IF (IFEED.EQ.1) V3=V2 ER1=ER-1.DO YSIN=DSIN (AKK*DLX) YCOS=DCOS(AKK*DLX) SS 1N2=YS IN*YS IN WS S IN= (2. D O /AKK) * S S IN2 YSIN2=SSIN2 /AKK WCOS=(l.DO-YCOS) *AKK NMAX=NS +ND CALL ARIS MMAX=NMAX+2 DO 16 I=1,NPOINT NTTM=NTM IADD=1 IF (IFIRST.NE.2) GO TO 15 NTTM=NKOK IADD=O 15 AI=COAL(I) TI=POINT (I) C --- —-----------------------------------------------— + C STEP 3: EVALUATION OF INTERVALS 1 AND 2 C --- —-----------------------------------------------— + DO 17 N=1,NKO X=CN(N+1)-CN(N)

-65 - Y=CN (N+1) +CN (N) ALI=0.5D0* (TI*X+Y) C + --- —------------------ C I EVALUATION OF GXX'S I C ----------------------- CALL RGRI (ALI) GCON=AI *>X FCON=GCON GXXR1=GCON* (RX (1) -FRX (1)) GXXX1=GCON*XX (1) GXXR2=GCON* (RX (2) -FRX (2)) GXXX2=GCON*XX (2) GXXR3=GCON* (RX (3) -FRX (3)) GXXX3=GCON*XX (3) C ------------------------ C I EVALUATION OF GZX'S I C + --- —------------------— + GCON=GCON*ER1 GZXR1=GCON*RZ (1) -FCON*FRZ (1) GZXXl=GCON*XZ (1) GZXR2=GCON*RZ (2) -FCON*FRZ (2) GZXX2=GCON*XZ (2) GZXR3=GCON*RZ (3) -FCON*FRZ (3) GZXX3=GCON*XZ (3) C -- + --- —--------------------------— + C I REFORMULATION OF GXX'S GZX'S I C + --- —--------------------------— + VARX=Vi* (V2*GXXR1+EER*GZXR1) VARZ=AKK* (GXXR1-GZXR1) GXXR1=VARX GZXR1=VARZ VARX=Vl* (V2*GXXX1+EER*GZXX1) VARZ=AKK* (GXXX1-GZXX1) GXXX1=VARX GZXX1=VARZ VARX=V1* (V2*GXXR2+EER*GZXR2) VARZ=AKK* (GXXR2-GZXR2) GXXR2=VARX GZXR2 =VARZ VARX=Vi* (V2 *GXXX2+EER*GZXX2) VARZ=AKK* (GXXX2-GZXX2) GXXX2=VARX GZXX2 =VARZ VARX=VI* (V3*GXXR3+EER*GZXR3) VARZ=AKK* (GXXR3-GZXR3) GXXR3=VARX GZXR3=VARZ VARX=V1 * (V3 *GXXX3+EER*GZXX3) VARZ=AKK* (GXXX3-GZXX3) GXXX3=VARX GZXX3=VARZ PLI=ALI CALL ADONIS (MMAX) DO 34 K=1,NMAX Sl=GXXR2*SSJO (K) +GZXR2*SAJO (K)

-66 - S2=GXXX2*SSJO (K) +GZXX2*SAJO (K) Z2GT (K) =Z2GT (K) +S1-CI*S2 IF (K.GT.NF) GO TO 35 Sl=GXXR3*SSJO (K) +GZXR3*SAJO (K) S2=GXXX3*SSJO (K) +GZXX3*SAJO (K) Z2LT (K) =Z2LT (K) +Sl-CI*S2 35 IF (K.GT.ND) GO TO 34 Sl=GXXR1*SSJO (K) +GZXR1*SAJO (K) S2=GXXX1*SSJO (K) +GZXX1*SAJO (K) ZlGT (K) =Z1GT (K) +Sl-CI*S2 34 CONTINUE 17 CONTINUE C --- —----------------------------------------------— + C STEP 3 EVALUATION OF INTERVAL 3 C --- —----------------------------------------------— + IND=-IADD DO 18 N=lNTTM IND=IND+IADD+1 X=AM (IND+l) -AM (IND) Y=AM (IND+1) +AM (IND) ALI=O 5D0* (TI*X+Y) C + --- —-----------------— + C I EVALUATION OF GXX'S I C + --- —-----------------— + NPOL=N IF (IFIRST.EQ.2) NPOL=l XTM=POLTM JNPOL) CALL WGXZ (ALIXTM) GCON=AI *X FCON=GCON GXXR1=GCON* (RX(l)-FRX(l)) GXXR2=GCON* (RX (2) -FRX (2) ) GXXR3=~GCON* (RX (3) -FRX (3)) C + --- —-----------------— + C I EVALUATION OF GZX'S I C + --- —-----------------— + TMTM= (2.DO*POLTM(NPOL) -Y) /X TTI=TI GCON=2.DO*AI*ER1/ (TTI-TMTM) GZXR1=GCON*RZ (1) -FCON*FRZ (1) GZXR2=GCON*RZ (2) -FCON*FRZ (2) GZXR3=GCON*RZ (3) -FCON*FRZ (3) C + --- —--------------------------— + C I REFORMULATION OF GXX'S GZX'S I C + --- —--------------------------— + VARX=V1* (V2 *GXXR1+EER*GZXR1) VARZ=AKK* (GXXR1-GZXR1) GXXR1=VARX GZXR1=VARZ VARX=V1* (V2 *GXXR2 +EER*GZXR2) VARZ=AKK* (GXXR2-GZXR2) GXXR2=VARX GZXR2 =VARZ VARX=Vl* (V3*GXXR3+EER*GZXR3) VARZ-AKK* (GXXR3-GZXR3)

-67 - GXXR3=VARX GZXR3=VARZ PLI=ALI CALL ADONIS (MMAX) DO 36 K=1,NMAX S=GXXR2*SSJO(K) +GZXR2*SAJO(K) Z2GT(K)=Z2GT(K)+S IF (K.GT.NF) GO TO 37 S=GXXR3*SSJO(K) +GZXR3*SAJO(K) Z2LT(K)=Z2LT(K)+S 37 IF (K.GT.ND) GO TO 36 S=GXXR1*SSJ0(K)+GZXR1*SAJO(K) Z1GT(K)=Z1GT(K)+S 36 CONTINUE 18 CONTINUE C --- —--------- ----------------------— + C STEP 3: EVALUATION OF INTERVAL 4 C --- —-- ------------- -----------------— + IND=-IADD DO 19 N=1,NTTM ALI=POLTM(1) FAN1=VSPM(1) IF (IFIRST.EQ.2) GO TO 20 ALI=POLTM(N) FAN1=VSPM(N) 20 IND=IND+IADD+1 X=AM(IND+1) -AM(IND) Y=AM(IND+1) +AM(IND) TM=(2.D0*ALI-Y)/X C + --- --------------— + C I EVALUATION OF GZX'S I C I GXX'S =0.DO C + --- —----------------— + CALL WGZTM (FAN1,ALI) TTI=TI IF (DABS(TI-TM).LT.1.D-6) TTI=TI+1.D-5 GCON=-2.DO*AI*ER1/(TTI-TM) GZXR1=GCON*RZ(1) GZXR2=GCON*RZ(2) GZXR3=GCON*RZ(3) C + --- — -----------------------— + C I REFORMULATION OF GXX'S,GZX'S C + --- —-----------------------— + VARX=Vl*EER*GZXR1 VARZ=-AKK*GZXR1 GXXR1=VARX GZXR1=VARZ VARX=V1 *EER*GZXR2 VARZ=-AKK*GZXR2 GXXR2=VARX GZXR2=VARZ VARX=V1*EER*GZXR3 VARZ=-AKK*GZXR3 GXXR3=VARX GZXR3=VARZ

-68 - PLI=ALI CALL ADONIS(MMAX) DO 38 K=1,NMAX S=GXXR2*SSJO(K)+GZXR2*SAJO(K) Z2GT(K)=Z2GT(K)+S IF (K.GT.NF) GO TO 39 S=GXXR3*SSJO(K)+GZXR3*SAJO(K) Z2LT(K)=Z2LT(K)+S 39 IF (K.GT.ND) GO TO 38 S=GXXR1*SSJO(K)+GZXR1*SAJO(K) Z1GT(K)=Z1GT(K)+S 38 CONTINUE 19 CONTINUE IADD=2 C --- —------- -----------------------------------— + C STEP 3: EVALUATION OF INTERVAL 5 1 C --- —------------------------------------------— + IND=-1 IF (IFIRST.EQ.2) GO TO 21 DO 21 N=1,NTE IND=IND+IADD X=DM(IND+1) -DM(IND) Y=DM(IND+1)+DM(IND) ALI=0.5D0*(TI*X+Y) C + --- —----------------— + C I EVALUATION OF GXX'S | C + --------- ----— + FCON=AI*X CALL WGXZE(ALI,POLTE(N)) TMTE= (2.DO*POLTE (N) -Y)/X GCON=2.DO*AI/(TI-TMTE) GXXR1=GCON*RX(1)-FCON*FRX(1) GXXR2=GCON*RX (2) -FCON*FRX (2) GXXR3=GCON*RX(3)-FCON*FRX(3) C + --- —-----------------— + C I EVALUATION OF GZX'S I C + --- —-----------------— + GCON=GCON*ER1 GZXR1=GCON*RZ(1)-FCON*FRZ(1) GZXR2=GCON*RZ(2)-FCON*FRZ(2) GZXR3=GCON*RZ(3)-FCON*FRZ(3) C + --- —-------------------------— + C I REFORMULATION OF GXX'S,GZX'S I C + --- —-------------------------— + VARX=V1 * (V2*GXXR1+EER*GZXR1) VARZ=AKK* (GXXR1-GZXR1) GXXR1=VARX GZXR1=VARZ VARX=V1*(V2*GXXR2+EER*GZXR2) VARZ=AKK*(GXXR2-GZXR2) GXXR2=VARX GZXR2=VARZ VARX=V1*(V3*GXXR3+EER*GZXR3) VARZ=AKK*(GXXR3-GZXR3) GXXR3=VARX

-69 - GZXR3=VARZ PLI=ALI CALL ADONIS(MMAX) DO 40 K=1,NMAX S=GXXR2*SSJO(K)+GZXR2*SAJO(K) Z2GT(K)=Z2GT(K)+S IF (K.GT.NF) GO TO 41 S=GXXR3*SSJO(K)+GZXR3*SAJO(K) Z2LT(K)=Z2LT(K)+S 41 IF (K.GT.ND) GO TO 40 S=GXXR1*SSJ0(K)+GZXR1*SAJO(K) Z1GT(K)=Z1GT(K)+S 40 CONTINUE 21 CONTINUE C ---------------------------------------— + C STEP 3: EVALUATION OF INTERVALS 6,9,11 C --- —------------------------------------------— + IND=-1 IF (IFIRST.EQ.2) GO TO 22 DO 22 N=1,NTE ALI=POLTE (N) IND=IND+IADD X=DM (IND+1) -DM(IND) Y=DM(IND+1) +DM(IND) TM= (2.D0*ALI-Y) /X C + --- —-------------— + C I EVALUATION OF GXX'S I C + --- —-----------------— + TTI=TI IF (DABS(TI-TM).LT.1.D-6) TTI=TI+1.D-5 FAN1=VSPE(N) FAN2=VTPE(N) CALL WGXZTE (FAN1,FAN2,POLTE(N)) GCON=-2.DO*AI/(TTI-TM) GXXR1=GCON*RX(1) GXXR2=GCON*RX(2) GXXR3=GCON*RX(3) C + --- —----------------— + C | EVALUATION OF GZX'S I C + --- —--------------— + GCON=GCON*ER1 GZXR1=GCON*RZ(1) GZXR2=GCON*RZ(2) GZXR3=GCON*RZ(3) C + --- —---------------------— + C | REFORMULATION OF GXX'S,GZX'S I C + --- —------------------------— + VARX=V* (V2*GXXR1+EER*GZXR1) VARZ=AKK* (GXXR1-GZXR1) GXXR1=VARX GZXR1=VARZ VARX=V1* (V2*GXXR2+EER*GZXR2) VARZ=AKK*(GXXR2-GZXR2) GXXR2=VARX GZXR2=VARZ

-70 - VARX=V1*(V3*GXXR3+EER*GZXR3) VARZ=AKK*(GXXR3-GZXR3) GXXR3=VARX GZXR3=VARZ PLI=ALI CALL ADONIS(MMAX) DO 42 K=1,NMAX S=GXXR2*SSJO (K) +GZXR2*SAJO (K) Z2GT(K)=Z2GT(K)+S IF (K.GT.NF) GO TO 61 S=GXXR3*SSJO(K)+GZXR3*SAJO(K) Z2LT(K)=Z2LT(K)+S 61 IF (K.GT.ND) GO TO 42 S=GXXR1*SSJO(K)+GZXR1*SAJO(K) Z1GT(K)=Z1GT(K)+S 42 CONTINUE IF (I.LT.NPOINT) GO TO 22 VLOG=DLOG((1.DO-TM)/ (1.DO+TM)) C ----- ----------- C I EVALUATION OF GXX'S I C + --- —---------------— + GCON1=2.DO*VLOG GCON2=2.DO*PI GXXR11=GCON1*RX(1) GXXR21=GCON1*RX(2) GXXR31=GCON1*RX(3) GXXR12=GCON2*RX(1) GXXR22=GCON2*RX(2) GXXR32=GCON2*RX(3) C + --- —----------------— + C I EVALUATION OF GZX'S I C + --- —-----------— + GCON1=GCON1*ER1 GCON2=GCON2*ER1 GZXR11=GCON1*RZ(1) GZXR21=GCON1*RZ(2) GZXR31=GCON1*RZ(3) GZXR12=GCON2*RZ(1) GZXR22=GCON2*RZ (2) GZXR32=GCON2*RZ(3) C + --- —----------------------— + C I REFORMATION OF GXX'S,GZX'S I C + --- —-------------- VARX=V1*(V2*GXXR11+EER*GZXR11) VARZ=AKK* (GXXR11-GZXR11) GXXR11=VARX GZXR1 1=VARZ VARX=V1* (V2*GXXR21+EER*GZXR21) VARZ=AKK*(GXXR21-GZXR21) GXXR21=VARX GZXR21=VARZ VARX=V1*(V3*GXXR31+EER*GZXR31) VARZ=AKK*(GXXR31-GZXR31) GXXR31=VARX GZXR31=VARZ

-71 - VARX=V1*(V2*GXXR12+EER*GZXR12) VARZ=AKK*(GXXR12-GZXR12) GXXR12=VARX GZXR12=VARZ VARX=V1*(V2*GXXR22+EER*GZXR22) VARZ=AKK*(GXXR22-GZXR22) GXXR22=VARX GZXR22=VARZ VARX=V1*(V3*GXXR32+EER*GZXR32) VARZ=AKK*(GXXR32-GZXR32) GXXR32=VARX GZXR32=VARZ C DO 43 K=1,NMAX S1=GXXR21*SSJO(K)+GZXR21*SAJO(K) S2=GXXR22*SSJO (K) +GZXR22*SAJO (K) Z2GT (K)=Z2GT (K) +S1-CI*S2 IF (K.GT.NF) GO TO 62 S1=GXXR31*SSJO(K)+GZXR31*SAJO(K) S2=GXXR32*SSJO (K) +GZXR32*SAJO (K) Z2LT(K)=Z2LT(K)+S1-CI*S2 62 IF (K.GT.ND) GO TO 43 Sl=GXXR11*SSJO(K)+GZXR11*SAJO(K) S2=GXXR12*SSJO(K)+GZXR12*SAJO(K) Z1GT(K)=Z1GT(K)+S1-CI*S2 43 CONTINUE 22 CONTINUE C --- —-----------------------------------------— + C STEP 3: EVALUATION OF INTERVAL 7 1 C --- —------------------------------------------— + DO 23 N=1,MA X=BM(N+1)-BM(N) Y=BM(N+1)+BM(N) ALI=0.5D0* (TI*X+Y) C + --- —----------------— + C I EVALUATION OF GXX'S I C + --- —----------------— + CALL PGXZ(ALI) GCON=AI*X FCON=GCON GXXR1=GCON* (RX (1) -FRX (1)) GXXR2=GCON*(RX(2)-FRX(2)) GXXR3=GCON*(RX(3)-FRX(3)) C ---------------------— + C I EVALUATION OF GZX'S I C + — ---------------------— + GCON=GCON*ER1 GZXR1=GCON*RZ(1)-FCON*FRZ(1) GZXR2=GCON*RZ (2) -FCON*FRZ (2) GZXR3=GCON*RZ(3)-FCON*FRZ(3) C + --- —------- ------------------— + C I REFORMULATION OF GXX'S,GZX'S I C + --- —-------------------------— + VARX=V1*(V2*GXXR1+EER*GZXR1) VARZ=AKK* (GXXR1-GZXR1)

-72 - C GXXR1=VARX GZXR1=VARZ VARX=V1 * (V2 *GXXR2+EER*GZXR2) VARZ=AKK* (GXXR2-GZXR2) GXXR2=VARX GZXR2=VARZ VARX=V1 * (V3 *GXXR3+EER*GZXR3) VARZ=AKK* (GXXR3-GZXR3) GXXR3=VARX GZXR3=VARZ PLI=ALI CALL ADONIS(MMAX) DO 45 K=1,NMAX S=GXXR2*SSJO (K) +GZXR2*SAJO (K) Z2GT (K) =Z2GT (K) +S IF (K.GT.NF) GO TO 63 S=GXXR3*SSJO (K) +GZXR3*SAJO (K) Z2LT(K)=Z2LT(K)+S IF (K.GT.ND) GO TO 45 S=GXXR1*SSJO (K) +GZXR1*SAJO (K) Z1GT (K) =Z1GT (K) +S 63 45 CONTINUE 23 CONTINUE 16 CONTINUE C --- —------------------------------------------— + C STEP 3: EVALUATION OF INTERVALS 8,10 1 C --- —-------------------------------------------------— + IND=- 1 IADD=2 DO 25 24 26 C C C N=1,NTM IF (IFIRST.NE.2) GO TO 24 TM=(2.DO*POLTM(1)-(AK+AK0) ) / (AK-AKO) ALI=POLTM (1) GO TO 26 ALI=POLTM (N) IND= IND+IADD X=AM (IND+1) -AM (IND) Y=AM(IND+1) +AM(IND) TM=(2.DO*ALI-Y) /X CONTINUE + --- —-----------------— + EVALUATION OF GZX'S I + --- —-----------------— + FAN1=VSPM (N) CALL WGZTM (FAN1,ALI) GCON1=2.DO*ER1*DLOG ((1.DO-TM)/(1.DO+TM)) GCON2=2.DO*ER1*PI GZXR11=GCON1*RZ(1) GZXR21=GCON1*RZ(2) GZXR31=GCON1*RZ(3) GZXR12=GCON2*RZ(1) GZXR22=GCON2*RZ(2) GZXR32=GCON2*RZ(3) + --- —--------------------------— + C

-73 - C I REFORMULATION OF GXX'S,GZX'S C -------------------------------- VARX=V1 *EER*GZXR11 VARZ=-AKK*GZXR1 1 GXXR1 1=VARX GZXR1 1=VARZ VARX=V1 *EER*GZXR2 1 VARZ=-AKK*GZXR2 1 GXXR2 1=VARX GZXR2 1=VARZ VARX=V1*EER*GZXR3 1 VARZ=-.AKK*GZXR3 1 GXXR31=VARX GZXR3 1=VARZ VARX=V1 *EER*GZXR12 VARZ=-AKK*GZXR12 GXXR12=VARX GZXR12=VARZ VARX=V1 *EER*GZXR22 VARZ=-AKK*GZXR2 2 GXXR22=VARX GZXR2 2=VARZ VARX=V1 *EER*GZXR32 VARZ= —AKK*GZXR32 GXXR3 2=VARX GZXR32=VARZ C " —PLI=ALI CALL ADONIS(MMAX) DO 47 K=1,NMAX S1=GXXR21*SSJO (K) +GZXR21*SAJO (K) S2=GXXR22*SSJO(K)+GZXR22*SAJO(K) Z2GT (K) =Z2GT (K) +S1-CI*S2 IF (K.GT.NF) GO TO 64 Sl=GXXR31*SSJO(K)+GZXR31*SAJO(K) S2=GXXR32*SSJO (K) +GZXR32*SAJO (K) Z2LT (K) =Z2LT (K) +S1-CI*S2 64 IF (K.GT.ND) GO TO 47 S1=GXXR11*SSJO (K) +GZXR11*SAJO (K) S2=GXXR12*SSJO (K) +GZXR12*SAJO (K) ZlGT(K)=Z1GT(K)++S1CI*S2 47 CONTINUE 25 CONTINUE C CALL TAIL C CONST1= (1.DO/CVON) *15.DO*DSQRT (EER) / (P* *(YSIN*YSIN) *100.DO) CONST2=CONST1/ER IF (IOPT.NE.1) GO TO 100 WRITE (6, 66) 66 FORMAT ('............................. TF (IFEED.EQ.1) CONST2=CONST1 WRITE (6,67) ND 67 FORMAT (11X,I4) DO 50 K=1,ND

-74 - Z1GT(K)=Z1GT(K)*CONST1 G1GT(K)=G1GT(K)*CONST1 Z1GT(K)=(Z1GT(K)+G1GT(K))*CI WRITE (6,51) Z1GT(K) 51 FORMAT(11X,E14.7,4X,E14.7) 50 CONTINUE 100 CONTINUE IF(IOPT.EQ.1) WRITE(6,101) 101 FORMAT('........ Z31....................... Z31. ') IF (IOPT.EQ.2) WRITE(6,102) 102 FORMAT('.............................. Z21. ') IF(IOPT.EQ.3) GO TO 103 WRITE (6,67) NMAX DO 52 K=1,NMAX Z2GT(K)=Z2GT(K)*CONST1 G2GT (K)=G2GT (K) *CONST1 Z2GT (K) = (Z2GT (K) +G2GT (K)) *CI WRITE (6,51) Z2GT(K) 52 CONTINUE 103 CONTINUE IF (IOPT.EQ.1) WRITE (6,104) 104 FORMAT('........ Z33.................... Z33. ') IF(IOPT.EQ.2) WRITE(6,105) 105 FORMAT('........ Z22......................' ) IF (IOPT.EQ.3) WRITE(6,106) 106 FORMAT ('...........32................Z32 WRITE (6,67) NF DO 54 K=1,NF Z2LT(K)=Z2LT(K)*CONST2 G2LT (K)=G2LT (K) *CONST2 Z2LT(K)= (Z2LT(K)+G2LT(K))*CI WRITE (6,55) Z2LT(K) 55 FORMAT(11X,E14.7,4X,E14.7) 54 CONTINUE STOP END C WGXZTE SUBROUTINE WGXZTE(F1,F2,XTE) IMPLICIT REAL*8 (A-H,O-Z) COMMON/DAT/ER,H,BS,TT1,TT2,DLX,A,TPI,TPI2,PI,W,El,E2,E3,E4,E5,EER, *AKO,AK,AKK,FA,FA0,BW,BBWW,BWWW,B4W,B5W,OFFSET,WDELTA,NS,NF,ND,IFEED COMMON/COEF/RX(5),XX(5),RZ(5),XZ(5),FRX(5),FRZ(5),F1XX,F1ZX,F2XXG, *F2ZXG,F2XXL,F2ZXL,F1XXL,F1ZXL,F2XL,F2ZL C X=XTE X2=X*X AK2=AK*AK AK02=AK0 *AK0 R1=DSQRT (AK2-X2) R2=DSQRT (X2-AK02) R3=R1*H R4=R2*TT1 R5=R1*(H-BS)

-75 - R6=Rl* (H-BS+TT2) R7=Rl* (BS-TT2) R8=Rl* (H-BS-TT2) R9=R1l*BS Sl=DSIN (R3) C1=DCOS (R3) S2=DSTN (R5) S3=DSIN (R6) S4=DSIN (R7) S5=2.DO*S1*Cl S6=DSIN (R8) S7=DSIN (R9) C5=DCOS (R9) C4=DCOS (R7) EX=DEXP (-R4) EX1=DEXP (-R2 *DABS (TT2-BS)) C RX (1) =X*EX* S1 *F 1 RX (2) =X*EX*S2*F1 RX (3) =X* (S2 /Rl) * (R1 *C4+R2 *s4) *Fl IF (IFEED.EQ.1) RX(3)=X*EX1*S2*Fl C CQ 1=AK2 / (X2 -AK2) + 1.DO RZ (1) =X*EX*R2*O 5DO*S5'*F2 RZ (2) =X*EX*R2*S2*Cl*F2 RZ (3) =X*R1*S2*S3*F2 IF (IFEED.EQ.1) RZ(3)=X*EX1*R2*S2*C1*F2 RETURN END C PGXZ SUBROUTINE PGXZ (ALI) IMPLICIT REAL*8 (A-HO-Z) COMMON/DAT/ERHBSrTTlTT2,DLXATPITPI2,PIWElE2,E3,E4,E5,EERI COMMON/COEF/RX(5),XX(5),RZ (5),XZ (5),FRX(5),FRZ (5),FlXX,fF1ZXF2XXG., *F2ZXG, F2XXL, F2ZXL, FlXXL, FlZXL, F2XL, F2ZL C X=ALI X2=X*X AK2=AK*AK AKO2=AKO *AKO R1=DSQRT (X2-AK2) R2=DSQRT (X2-AKO2) R3=Rl*H R4=R2 *TT1 R5=Rl*BS R6=R1* (BS-TT2) R7=Rl* (BS+TT2) E~X=DEXP (R3) TAN1= (EX-1l.DO/EX) /(EX+1.DO/EX) EX=DEXP (R6) COSH1=O 5D0* (EX+1.DO/EX) SINH1=O 5D0* (EX-1l.DO/EX)

-76 - R6=R1* (H-BS+TT2) R7=R1* (BS-TT2) R8=Rl* (H-BS-TT2) R9=R1l*BS Sl=DSIN (R3) C1=DCOS (R3) S2=DSIN (R5) S3=DSIN (R6) S4=DSIN (R7) S5=2.DO*S1*Cl S6=DSIN (R8) S7=DSIN (R9) C5=DCOS (R9) C4=DCOS (R7) EX=DEXP (-R4) EX1=DEXP (-R2 *DABS (TT2 -BS)) C RX (1) =X*EX*S1*Fl RX (2) =X*EX*S2*Fl RX (3) =X* (S2 /Rl) * (Ri *C4~R2 *S4) *Fl IF (IFEED.EQ.1) RX(3)=X*EX1*S2*F1 C. CQ 1=AK2 / (X2 -AK2) + 1.DO RZ (1) =X*EX*R2 *0 5D0 * S5 *F2 RZ (2) =X*EX*R2*S2*Cl*F2 RZ (3) =X*Rl*S2*S3*F2 IF (IFEED.EQ.1) RZ(3)=X*EX1*R2*S2*Cl*F2 RETURN END C PGXZ SUBROUTINE PGXZ (ALI) IMPLICIT REAL*8 (A-H O —Z) COMMON/DAT/ERHBSTTlTT2,DLXATPITPI2,PIWEiE2,E3,E4,E5,EER, *AKOAK,rAKK,,FAFAOBWBWWBWWWB4WB5WOFFSETWDELTANSNFND, IFEED COMMON/COEF/RX(5),XX(5),RZ (5),XZ (5),FRX(5),FRZ (5),F1XXFlZXF2XXG, *F2ZXG, F2XXL, F2ZXL, FlXXL, F1ZXL, F2XL, F2ZL C X=ALI X2=X*X AK2=AK*AK AKO2=AKO *AKO R1=DSQRT (X2-AK2) R2=DSQRT (X2-AKO2) R3=Rl*H R4=R2 *TT1 R5=Ril*BS R6=Rl* (BS-TT2) R7=R1* (BS+TT2) EX=DEXP (R3) TAN1==(EX-il.DO/EX) /(EX+1.DO/EX) EX=DEXP (R6) COSH1=0.5D0* (EX+1.DO/EX) SINH1=O 5D0* (EX-1l.DO/EX)

-77 - EX=DEXP (R5) COSH2=0.5D0* (EX+1.DO/EX) SINH2=0.5D0O (EX-1l.DO/EX) EX=DEXP (R7) SINH3=0. 5DO* (EX-1l.DO/EX) COSH3=0.5D0O (EX+1.DO/EX) EX=DEXP (-R4) EX1=DEXP (-R2 *DABS (TT2 -BS)) EXA=DEXP (-X*TT1*FAO) *FAO EXB=DEXP (-X*BW*FA) *FA EXC=DEXP (-X*TT2*FA) *FA EXD=DEXP (-X*BWWW*FA) *FA EXE=DEXP (-X*BWW*FA) *FA EXF=DEXP (-X*B4W*FA) *FA EXG=DEXP (-X*B5W*FA) *FA C IF ((X-AK).LT.l.D-6) GO TO 1 CQ1=R2 *TAN1+Rl CQ2=ER*R2+R1l*TAN1 CQ3=TAN1 *COSH2-S INH2 RX (1) =EX*TAN1 *X/CQ1 FRX (1) =FlXX*EXA RX (2) =EX*CQ3*X/CQ1 FRX (2) =F2XXG*EXB RX(3)=CQ3*X*(Rl*COSH1+R2*SINH1)/(Rl*CQ1) FRX (3) =0. 5DO*EXC-F2XXL*EXD IF (IFEED.EQ.1) RX(3)=EX1*CQ3*X/CQ1 IF (IFEED.EQ.1) FRX(3)=F2XXL*EXE C CQ4=CQ1 *CQ2 CQ5=AK2/ (X2-AK2) +1.DO RZ (1) =EX*R2*TAN1*X/CQ4 FRZ (1) =FlZX*EXA RZ (2) =EX*CQ3*R2*X/CQ4 FRZ (2) =F2ZXG*EXB RZ (3) =-CQ3* (TAN1f*COSRl-SINH1) *Rl*X/CQ4 FRZ (3) =F2ZXL*EXD IF (IFEED.EQ.1) RZ(3)=EX1*CQ3*R2*X/CQ4 IF (IFEED.EQ.1) FRZ(3)=F2ZXL*EXE RETURN C 1 CQ1=R2*H+1.DO CQ2=ER*R2 CQ4=CQ1*CQ2 RX (1) =EX*H*X/CQ1 FRX (1) =FlXX*EXA RX(2)=EX* (H-BS) *X/CQ1 FRX (2) =F2XXG*EXB RX(3) =X* (H-BS) * (1.DO+R2* (BS-TT2) )/CQ1 FRX (3) = 0. 5DO0* EXC-F2 XXL *EXD IF (IFEED.EQ.1) RX(3)=EX1* (H-BS) *X/CQ1-F2XXL*EXE IF (IFEED.EQ.1) FRX(3)=F2XXL*EXE C RZ (1) =EX*R2*H*X/CQ4 FRZ (1) =FlZX*EXA

-78 - RZ (2) =EX*R2* (H-BS) *X/CQ4 FRZ (2) =F2ZXG*EXB RZ (3) =0.DO FRZ (3) =F2ZXL*EXD IF (IFEED.EQ.1) RZ(3)=EX1*R2*(H-BS)*X/CQ4 IF (IFEED.EQ.1) FRZ(3)=F2ZXL*EXE RETURN END C WGXZE SUBROUTINE WGXZE (ALIXTE) IMPLICIT REAL*8 (A-HO-Z) COMMON/DAT/ERHBSrTTlTT2,DLXATPITPI2,PIWE1,E2,E3,E4,E5rEER, *AKOAKAKKFAFAOBWBWWBWWWB4WB5WOFFSETWDELTANSNFND, IFEED COMMON/COEF/RX(5),XX(5),RZ (5),XZ (5),FRX(5),FRZ (5),F1XXFlZXF2XXG,f *F2ZXG, F2XXL, F2ZXL, FlXXL, F1ZXL, F2XL, F2ZL C X=ALI X2=X*X AK2=AK*AK AK02=AKO *AKO~j R1=DSQRT (AK2-X2) R2=DSQRT (X2-AK02) R3=Rl*H R4=R2 *TT1 R5=Rl*(H-BS) R6=Rl* (BS-TT2) R7=Rl* (H-BS+TT2) R8=R1* (H-BS-TT2) R9=R1l*BS Sl=DSIN (R3) Cl=DCOS (R3) C3=DCOS (R6) C4=DCOS (R9) S2=DSIN (R5) S3=DSIN (R6) S4=2.DO*Sl*Cl S5=DSIN (R7) SG=DSIN (R8) S7=DSIN (R9) EX=DEXP (-R4) EX1=DEXP (-R2 *DABS (TT2-BS)) EXA=DEXP (-X*TT1*FAO) *FAO EXB=DEXP (-X*BW*FA) *FA EXC=DEXP (-X*TT2*FA) *FA EXD=DEXP (-X*BWWW*FA) *FA EXE=DEXP (-X*BWW*FA) *FA EXF=DEXP (-X*B4W*FA) *FA EXG=DEXP (-X*B5W*FA) *FA C IF ((AK-X).LT.1.D-6) GO TO 1 CQ1=R2 *S1+Rl1Cl SL= (X-XTE) /CQ1 RX (1) =X*EX*Sl*SL

-79 - FRX (1) =F1XX*EXA RX (2) =X*EX*S2*SL FRX (2) =F2XXG*EXB RX (3) =X* (S2 /Rl) * (Rl*C3+R2 *S3) *SL FRX (3) =0 5DO*EXC-F2XXL*EXD IF (IFEED.EQ.1) RX(3)=X*EX1*S2*SL IF (IFEED. EQ. 1) FRX (3) =F2XXL*EXE C CQ2=ER*R2 *C1-Rl*Sl CQ3=AK2/ (X2-AK2) +1.DO TL= (X-XTE) /(CQ1*CQ2) RZ (1) =X*EX*R2*05DS4T FRZ (1) =F1ZX*EXA RZ (2) =X*EX*R2*S2*Cl*TL FRZ (2) =F2ZXG*EXB RZ (3) =Rl*S2*S5*X*TL FRZ (3) =F2ZXL*EXD IF (IFEED.EQ.1) RZ(3)=X*EX1*R2*S2*C1*TL IF (IFEED.EQ.1) FRZ(3)=F2ZXL*EXE RETURN C 1 S L= (X-XTE) / (R2 *H+ 1. DO) RX (1) =X*EX*H*SL FRX (2.) =FlXX*EXA RX (2) =X*EX* (H-BS) *SL FRX (2) =F2XXG*EXB RX (3) =X*EX*S2*SL FRX (3) =0. 5D0*EXC-F2XXL*EXD IF (IFEED.EQ.1) RX(3)=X*EX1*(H-BS)*SL IF (IFEED.EQ.1) FRX(3)=F2XXL*EXE C TL=SL/ (ER*R2) RZ (1) =X*EX*R2*H*TL FRZ (1) =FlZX*EXA RZ (2) =X*EX*R2* (H-BS) *TL FRZ (2) =F2ZXG*EXB RZ (3) =0.DO FRZ (3) =F2ZXL*EXD IF (IFEED.EQ.1) RZ(3)=X*EX1*R2*(H-BS)*TL IF (IFEED.EQ.1) FRZ(3)=F2ZXL*EXE RETURN END C WGZTM SUBROUTINE WGZTM (F, XTM) IMPLICIT REAL*8 (A-HO-Z) COMMON/DAT/ER,HrBSTT1,TT2,DLXrATPITPI2,PI,WrE1,E2,E3,E4,E5,EER, *AKOAKAKKFAFAOBWBWWBWWWB4WB5W,OFFSETWDELTANSrNFND, IFEED COM4MON/COEF/RX(5),XX(5),RZ (5),XZ (5),FRX(5),FRZ (5),FlXXFlZXF2XXG, *F2ZXG, F2XXL, F2ZXL, FlXXL, FlZXL, F2XL, F2ZL C X=XTM X2=X*X AK2=AK*AK

-80 - AKO2=AKO *AKO Rl=DSQRT (AK2-X2) R2=DSQRT (X2-AKO2) R3=R1l*H R4=R2 *TT1 R5=R1* (H-BS) R6=Rl* (H-BS+TT2) R7=R1* (H-BS-TT2) S1=DSIN (R3) C1=DCOS (R3) S2=2.DO*S1*C1 S3=DSIN (R5) S4=DSIN (R6) S5=DSIN (R7) EX=DEXP (-R2*TT1) EX1=DEXP (-R2 *DABS (TT2-BS)) C CQ 1=AK2 / (X2 -AK2) + 1.DO RZ (1) =X*EX*R2 *0 D *2* RZ (2) =X*EX*R2*S3*Cl*F RZ (3) =X*Rl*S3*S4*F IF (IFEED.EQ.1) RZ(3)=X*EX1*R2*S3*C1*F RETURN END o WGXZ SUBROUTINE WGXZ (ALIXTM) IMPLICIT REAL*8 (A-HO-Z) COMMON/DAT/ERHBSTTlTT2,DLXA,,TPITPI2,PIWElE2rE3rE4,E5,EERr *AKOAK,fAKK,fFAFAOBWBWWBWWWB4WB5WOFFSETrWDELTANSNFND, IFEED COMMON/COEF/RX(5),XX(5),RZ (5),XZ (5),FRX(5),FRZ (5),F1XXFlZXF2XXG, *F2ZXG, F2XXL, F2ZXL, FlXXL, FlZXL, F2XL, F2ZL C X=ALI X2=X*X AK2=AK*AK AKO2=AKO *AKO Rl=DSQRT (AK2-X2) R2=DSQRT (X2-AKO2) R3=R1l*H R4=Rl* (H-BS) R5=Rl* (BS-TT2) R6=Rl* (H-BS+TT2) R7=Rl* (H-BS-TT2) R8=R1l*BS S1=DSIN (R3) Cl=DCOS (R3) S2=DSIN (R4) S3=DSIN (R5) C3=DCOS (R5) EX=DEXP (-R2*TT1) E~X1=DEXP (-~R2 *DABS (TT2-BS)) S4=2.DO*Sl*Cl S5=DSIN (R6)

-81 - S6=DSIN (R7) S7=DSIN (R8) C4=DCOS (R8) EXA=DEXP (-X*TT1*FAO) *FAO EXB=DEXP (-X*BW*FA) *FA EXC=DEXP (-X*TT2*FA) *FA EXD=DEXP (-X*BWWW*FA) *FA EXE=DEXP (-X*BWW*FA) *FA EXF=DEXP (-X*B4W*FA) *FA EXG=DEXP (-X*B5W*FA) *FA IF ((AK-X).LT.l.D-6) GO TO 1 CQ1=R2 *Sl+R1l*01 RX (1) =EX*Sl*X/CQ1 FRX (1) =F1XX*EXA RX (2) =EX*S2*X/CQ1 FRX (2) =F2XXG*EXB RX (3) =S2* (Rl*C3+R2*S3) *(/ (CQ1*R1) FRX (3) =0.5D0*EXC-F2XXL*EXD IF (IFEED.EQ.1) RX(3)=EX1*S2*X/CQ1 IF (IFEED.EQ.1) FRX(3)=F2XXL*EXE CQ2=ER*R2 *C1-R1*Sl CQ3=AK2/ (X2-AK2) +1.DO SL= (X-XTM) / (CQ1 *CQ2) RZ (1) =X*EX*R2*0.5D0*S4*SL FRZ (1) =FlZX*EXA RZ (2) =X*EX*R2*S2*Cl*SL -FRZ (2) =F2ZXG*EXB RZ (3) =X*Rl*S2*S5*SL FRZ (3) =F2ZXL*EXD IF (IFEED.EQ.1) RZ(3)=X*EX1*R2*S2*C1*SL IF (IFEED.EQ.1) FRZ(3)=F2ZXL*EXE RETURN CQ1=R2*H+1.DO RX (1) =EX*H*X/CQ1 FRX (1) =FlXX*EXA RX (2) =EX* (H-BS) *X/CQ1 FRX (2') =F2XXG*EXB RX(3) =(H-BS) * (1.DO+R2* (BS-TT2) )*X(/CQ1 FRX (3) =0.5D0*EXC-F2XXL*EXD IF (IFEED.EQ.1) RX(3)=EX1*(H-BS)*X/CQ1 IF (IFEED.EQ.1) FRX(3)=F2XXL*EXE CQ2=ER*R2 SL=(X-XTM) /(CQ1*CQ2) RZ (1) =X*EX*R2*0.5D0*H'*SL FRZ (1) =FlZX*EXA RZ (2) =X*EX*R2* (H-BS) *SL FRZ (2) =F2ZXG*EXB RZ (3) =0.DO FRZ (3) =F2ZXL*EXD IF (IFEED.EQ.1) RZ(3)=X*EX1*R2*(H-BS)*SL IF (IFEED.EQ.1) FRZ(3)=F2ZXL*EXE RETURN

-82 - END O RGRI SUBROUTINE RGRI (ALT) IMPLICIT REAL*8 (A-HO-Z) COMMON/DAT/ERKBSTTlTT2,DLXrA,TPITPI2,PIWE1,E2,E3,E4,E5,EER, *AKOA(,AKKFAFAOBWBWWBWWWB4WB5WOFFSETWDELTANSNFND, IFEED COMMON/COEF/RX(5),XX(5),RZ (5),XZ (5),FRX(5),FRZ (5),F1XXFlZXF2XXG,f *F2ZXG, F2XXL, F2ZXL, F1XXL, FlZXL, F2XL, F2ZL C X=ALI X2=X*X AK2=AK*AK AKO2=AKO *M(O Rl=DSQRT (AK2-X2) R2=DSQRT (AKO2-X2) R3=R1l*H R4=R2 *TT1 R5=Rl* (H-BS+TT2) R6=R1* (-BS+TT2) R7=Rl* (H-BS) R8=Rl* (H-BS-TT2) Sl=DSIN (R3) S 12=Sl*'Sl1 Cl=DCOS (R3) C12=Cl*Cl S2=DSIN(R4) C2=DCOS (R4) S3=2.DO*Sl*Cl S4=DSIN (R7) S5=DSIN (R6) C3=DCOS (R5) S6=DSIN (R5) C4=DCOS (R6) S7=DSIN (R8) C5=DCOS (R7) S8=DSIN (Ril*BS) CQ1=R2*R2+AKO2* (ER-i1.DO) *012 EXA=DEXP (-X*TT1*FAO) *FAO EXB=DEXP (-X*BW*FA) *FA EXC=DEXP (-X*TT2*FA) *FA EXD=DEXP (-X*BWWW*FA) *FA EXE=DEXP (-X*BWW*FA) *FA EXF=DEXP (-X*B4W*FA) *FA EXG=DEXP (-X*B5W*FA) *FA C RX (1) = (R2*S2*Sl2+0.5D0*Rl*C2*S3) *X/CQ1 XX(1)=(R2*C2*Sl2+O.5D0*Rl*S2*S3)*X/CQl FRX (1) =FiXX*EXA C RX(2)=S4* (-R2*Si*S2+Rl*C2*Cl) *X/CQi XX(2)=S4* (R2*Sl*C2+R1*S2*Ci) *X/CQi FRX (2) =F2XXG*EXB C

-83 -IF (IFEED.NE.1) GO TO 1 RX (3) =S4* (-R2*S1*S5+R1*C4*C1) *X/CQ1 XX(3)=S4*(R2*S1*C4+R1*S5*C1)*X/CQ1 FRX (3) =F2XXL*EXE GO TO 2 1 RX(3)=(S4/R1)*(R1*R1*C3+AK02*(ER-1.DO)*S1*S5)*X/CQ1 XX(3)=S4*R2*S6*X/CQ1 FRX (3) =0.5DO*EXC-F2XXL*EXD C 2 CQ2=R1*R1+(ER*AK02*(ER-1..DO) X2*(ER*ER-1.DO) ) *Cl2 CQ3=1.DO- (1.DO+ER) *C12 CQ4=0. 5D0 (2.DO*AK2 —X2* (1.DO+ER)) CQ5=AK2/(X2-AK2)+1.DO CQ6=CQ1*CQ2 RZ(1)=-0.5DOD*R2*S3*(R*R2*CQ3*C2+CQ4*S2*S3)*X/CQ6 XZ(1)=0.5DO*R2*S3* (CQ4*S3*C2-R*R2*CQ3*S2)*X/CQ6 FRZ (1) =F1ZX*EXA C RZ (2) =R2*S4* ( R1*R2*C2*CQ3-CQ4*S2*S3) *X*cl/CQ6 XZ(2)=R2*S4* (R1*R2*S2*CQ3+cQ4*C2*S3) *X*Cl/CQ FRZ(2)=F2ZXG*EXB C IF (IFEED.NE.1) GO TO 3 RZ (3) =R2*S4* ( R1*R2*C4*CQ3-CQ4*S5*S3) *X*C1/CQ6 XZ(3)=R2*S4*(-R1*R2*S5*CQ3+CQ4*C4*S3)*X*Cl/CQ6 FRZ(3)=F2ZXL*EXE GO TO 4 3 RZ(3)=-CQ4*S4*S6*S3*X*R1/CQ6 XZ(3)=-R2*R1*R1*S4*S6*CQ3*X/CQ6 FRZ (3) =F2ZXL*EXD C 4 CONTINUE RETURN END C FUNCTIONS WSPE,WTPEWSPM FUNCTION WSPE(X) IMPLICIT REAL*8 (A-llO-Z) COMMON/DAT/ERHBSTT1,TT2,DLXATPITPI2,PIWrE1,E2,E3,E4,E5,EERf *AK0,AKAKKFAFA0,BWBWWBWW WB4WB5WOFFSETWELTANSNFND IFEED C X2=X*X AKO2=AKO *AKO AK2=AK*AK R1=DSQRT (AK2-X2) R2=DSQRT (X2-AK02) R3=R1 *H R4=R2*H SX1=DSIN(R3) /R2-DCOS (R3) /R1 SX2=1.DO/(X*(1.DO+R4)) WSPE=SX2/SX1 RETURN END C

-84 - C C FUNCTION WTPE (X) IMPLICIT REAL*8 (A-H, O-Z) COMMON/DAT/ERHBSTT1,TT2,DLXAfTPITPI2,PI,WElE2,E3,E4,E5,EERf *AKOAKAKKFAFAOBWBWWBWWWB4WB5WOFFSETrWDELTANSNFND, IFEED C X2=X*X AKO2=AKO *AKO AK2=AK*AK Rl=DSQRT (AK2-X2) R2=DSQRT (X2-AKO2) R3=Rl *H R4=R2*H S3=DSIN (R3) C3=~DCOS (R3) SX1=l1.DO/ (X* (1.DO+R4)) SX2=S3/R2-C3/Rl SX3=ER*R2 *C3-R1l*S3 WTPE=SX1/ (SX2*SX3) RETURN END C C C C FUNCTION WSPM(X) IMPLICIT REAL*8 (A-HO-Z) COMMON/DAT/ERrHBS, TTlTT2,DLXA TPI, TPI2,PIW, El, E2, E3,E4,E5,EER, C X2=X*X AKO2=AKO *AKO AK2=AK*AK Rl=DSQRT (AK2-X2) R2=DSQRT (X2-AKO2) R3=Rl *H R4=R2 *H S3=DSIN (R3) C3=DCOS (R3) SX1=R2 *S3+Rl *C3 SX2=( (ER+R4) *C3/R2+(l.DO+ER*R4) *53/Ri) *X WSPM=1.DO/ (SX1*SX2) RETURN END

-85 - C ARIS SUBROUTINE ARIS IMPLICIT REAL*8 (A-HO-Z) DIMENSION AMK(4),LMK(4) COMMON/DAT/ERH,BSTT1,TT2,DLXAATPI,TPI2,PI,W,E1,E2,E3,E4,E5,EER *, AKO, AK, AKK, FA, FAQ, BW, BWW, BWWW, B4W, B5W, OFFSET, WDELTA, NS, NF, ND, *IFEED COMMON/ADON/DIST(l0,150,10),SERS(5),SERA(5),DARG(l0,10,4),S(l0,2),f *WREAL, NSER, MNUM COMMON/COEF/RX(5),XX(5),RZ (5),XZ (5), FRX(5),FRZ (5),F1XXF1ZXF2XXG, *F2ZXG, F2XXL, F2ZXL, FlXXL, FlZXL, F2XL, F2ZL COMMON/DATT/COAL(20),POINT(20),CN(51),FBM(51),POLTM(20),POLTE(20) *,pAM(41),DM(41),POLES(40),NPOINTNKOMA,NTMNTENKOK,IFIRST C C + --- —-----------------------------------------— + C I FORMATION OF VECTORS MATRICES DIST, C FUN2,FUN4,FUN6,FUN8 C I C + --- —-----------------------------------------— + W2=W/2.DO W4=W2*W2 NMAX=ND+NS+2 MNUM=2 DELTA=PI/ (2.DO*FLOAT (MNUM)) DO 10 M=IMNUM FM1=FLOAT(M-1)*DELTA FM2=FM1+DELTA X=0.5D0* (FM2-FM1) Y=0.5D0* (FM2+FM1) DO 11 J=1,NPOINT FI=X*POINT (J) +Y AS=DSIN (FI) AC=DCOS (FI) DARG (M, J, 1) =W2*AC DARG (M, J, 2) =AC DARG (M, J, 3) =AS DARG (M, J, 4) =X DO 1 K=1,NMAX AXN=FLOAT (K-2) *DLX DIST (M, K, J) =AXN*AS 1 CONTINUE 11 CONTINUE 10 CONTINUE C C + --- —--------------------------------— + C I FORMATION OF THE SERIES S C + --- —--------------------------------— + C U=WREAL/W U=DATAN(DSQRT(1.DO/(U*U)-1.DO)) Ul=2.DO*U/FLOAT (NSER) DO 2 JN=iNSER S2= (2.DO*FLOAT (JN) -1.DO)

-86 - S2=S2/(2.DO*FLOAT(NSER)) S3=DCOS(S2*U) S (JN, 2) =S3*w/2.DO S (JN, 1)=Ul 2 CONTINUE C C + --- —---------------------------------------------— + C FORMATION OF THE SERIES S(DLX); STORAGE IN C VECTORS SERS(5),SERA(5) C + --- —------------------------------------------— + ADL=AKK*DLX ADL2=ADL*ADL ADL3=ADL2 *ADL ADL4=ADL3 *ADL ADL5=ADL4 *ADL ADL6=ADL5 *ADL YSIN=DSIN (ADL) YCOS=DCOS (ADL) C SER1=(1.DO-YCOS)*2.DO/AKK SER2=-YSIN/3.DO+ADL*YCOS/4.DO+ADL2*YSIN/10.DO-ADL3*YCOS/36.DO ADL4 * *YSIN/168.D0+ADL5*YCOS/960.DO+ADL6*YSIN/6480.DO SER3=YSIN/60.DO ADL*5.DO*YCOS/360.DO ADL2*YSIN/168.DO+ADL3*YCOS/56 O.DO+ADL4*YSIN/2592.DO-ADL5*YCOS/12960.DO-ADL6*YSIN/9504O.DO SER4=-YSIN/2520.DO+ADL*YCOS/28 80.DO+ADL2 *YSIN/ 6480.DO ADL3*YCOS/21 6 6O0.DO-ADL4*YSIN/9504O.DO+ADL5*YCOS/518400.DO SER5=YSIN/181440.DO ADL*YCOS/201600.D0O ADL2*YSIN/443520.DO+ADL3*CC OS/1442775.9D0 C SERS (1)=SER1*SER1 SERS(2)=DLX*2.DO*SER1*SER2 SERS(3)=DLX*(DLX*SER2*SER2+2.DO*SER1*SER3) SERS(4)=DLX*(2.DO*SER1*SER4+2.DO*DLX*SER2*SER3) SERS(5)=DLX*(DLX*SER3*SER3+2.DO*DLX*SER2*SER4) C SERA(1)=SER1 SERA (2) =DLX*SER2 SERA (3) =DLX*SER3 SERA (4) =DLX*SER4 SERA (5) =DLX*SER5 RETURN END C ADONIS SUBROUTINE ADONIS(NMAX) IMPLICIT REAL*8 (A-HO-Z) DIMENSION BJ(10,10),DERIV(9,3) C.OMMON/ADON/DIST(10,150,10),SERS(5),SERA(5),DARG(10,10,4),S(10,2), *WREAL, NSER, MNUM COMMON/PUT/SSJO (150),SAJO (150),YSINYCOS COMMON/DAT/ERHKBSTT1,TT2,DLXATPITPI2,PIWElE2,E3,E4,E5,EER, *AK0,AKAKKFAFAOBWBWWBWWWB4W,35WOFFSETWDELTANSNFND, IFEED COMMON/MAT/PLI, IWRITE COMMON/BSS/ARG(10, 10)

-87 - COMMON/COEF/RX(5),XX(5),RZ(5),XZ(5),FRX(5),FRZ(5),F1XX,F1ZX,F2XXG, *F2ZXG,F2XXL,F2ZXL,F1XXL,F1ZXLF2XL,F2ZL COMMON/DATT/COAL(20),POINT(20),CN(51),BM(51),POLTM(20),POLTE(20) *,AM(41),DM(41),POLES(40),NPOINT,NKO,MA,NTM,NTENKOKIFIRST C W1=2.DO*YCOS PR1=PLI*DLX PR2=PR1*PR1 PR4=PR2*PR2 PR6=PR4*PR2 PR8=PR6*PR2 DO 11 M=1,MNUM DO 10 J=1,NPOINT ARG (M, J) =PLI*DARG (M, J, 1) 10 CONTINUE 11 CONTINUE DO 1 K=1,NMAX SSJO(K)=0.DO SAJO(K)=0.DO 1 CONTINUE CALL BESS(BJ) SUMD=O.DO DO 23 M=1,MNUM DO 20 J=1,NPOINT ASIN=W*DARG(M,J, 4) *COAL(J) AROF=PLI*OFFSET*DARG(M,J,2) COFF=DCOS(AROF) DO 21 NK=1,5 DERIV(NK,1)=0.DO DERIV(NK, 2)=0.DO 21 CONTINUE SSUM=0.DO DO 4 JN=1,NSER ARAF=PLI*S (JN,2) *DARG(M,J, 2) CAFF=DCOS (ARAF) SSUM=SSUM+S (JN, 1) *CAFF 4 CONTINUE DO 3 K=1,NMAX SIN11=DARG (M,J, 3) *DARG (M,J, 3) DO 22 NK=1,5 DERIV (NK,1) =DERIV (NK, 2) DERIV (NK,2) =DERIV (NK, 3) 22 CONTINUE COS1=DCOS(PLI*DIST (M,K,J)) TERM=COFF*(BJ(M,J)-SSUM/PI)*COS1 DERIV (1,3)=TERM SIN1=SIN11 DERIV(2,3) =-TERM*SIN1 SIN1=SIN1*SIN11 DERIV(3,3)=TERM*SIN1 SIN1=SIN1*SIN11 DERIV(4,3)=-TERM*SIN1 SIN1=SIN1*SIN11 DERIV(5,3)=TERM*SIN1 C

-88 - IF (K.LT.3) GO TO 3 SUMS=SERS (1) *DERIV (1,r2) -PR2 *SERS (2) *DERIV (2,2) +PR *4 *SERS (3) *DERIV (3,2) -PR6 *SERS (4) *DERIV (4 2) + *PR8 *SERS (5) *DERIV (5,r2) C CH1=SERA (1) *(DERIV (l11) +DERIV (1, 3) -Wl*DERIV (1,2)) CH2=SERA (2) *(DERIV (2,f1) +DERIV (2,3) -Wl*DERIV (2, 2)) * *PR2 CH3=SERA(3) *(DERIV(3 1) +DERIV(3, 3) -Wl*DERIV(3, 2)) * *PR4 CH4=SERA (4) *(DERIV (4,f1) +DERIV (4 r3) -Wl*DERIV (4, 2)) * *PR6 CH5=SERA (5) * (DERIV (5,r 1) +DERIV (5,3) -W1 *DERIV (5,2)) * *PR8 SUMA=CHl-CH2+CH3-CH4+CH5 KJ=K-2 SSJO (KJ) =SSJO (KJ) +ASIN*STJMS SAJO (KJ) =SAJ0O(KJ) +ASIN*SUMA 3 CONTINUE 20 CONTINUE 23 CONTINUE RETURN END C BESS SUBROUTINE BESS (BJ) IMPLICIT REAL*8 (A-HO-Z) DIMENSION BJ(10,10) COMMON/COEF/RX(5),XX(5),RZ (5),XZ (5),FRX(5),FRZ (5),F1XX,rFlZX,fF2XXG, *F2ZXG, F2XXL, F2ZXL, FlXXL, F1ZXL, F2XL, F2ZL COMMON/ADON/DIST(10,150,10),SERS(5),SERA(5),DARG(10,10,f4),S(10,2), *WREAL, NSERrMNUM COMMON/BSS/ARG (10, 10) COMMON/DATT/COAL(20),POINT(20),CN(51),BM(51),rPOLTM(20),POLTE(20) *,AM(41),DM(41),POLES(40),NPOINT,rNK0,MANTM.,NTENKOKIFIRST C C PI=3. 141592653589D0 DO 20 M=lMNUM DO 1 IJ=lNPOINT X=ARG (M, IJ) IF (X.GT.0.001D0) GO TO 10 X3=X/3.DO X32=X3 *X3 X3 4=X32 *X32 X3 6=X3 4*X32 BJ0=1.DO-2.2499997D0*X32+1.2656208D0*X34-0.3163866D0*X36 BJ (MIJ) =BJ0 GO TO 1 10 IF (X.GT.3.DO) GO TO 12 X3=X/3.DO X32=X3*X3 X3 4=X32 *X32 X3 6=X3 4*X32

-89 - X38=X3 6*X32 X310=X38*X32 X312=X310*X32 BJO=1.DO-2.2499997D0*X32+1.2656208D0*X34-0.3163866D0 *X36+0.0444479D0*X38-0.0039444D0*X310+0.00021000 * DO*X312 BJ (M, IJ) =BJO GO TO 1 12 CONTINUE X3=3.DO/X X32=X3 *X3 X33=X32*X3 X34=X33*X3 X35=X34*X3 X3 6=X35*X3 FJO=0.79788456D0-0. 00000077D0*X3-0.00552740D0*X32-0.0000 9512D0*X33+0.00137237D0*X34-0.00072805D0*X35+0.00014 476D0*X36 TJO=X-0. 78539816D0-0. o4166397D0*X3-0. 00003954D0*X32+0.00 * 262573D0*X33-0.00054125D0*X34-0.00029333D0*X35+0.000 * 13558D0*X36 WCON=DSQRT (1.DO/X) BJ(M, IJ)=WCON*FJO*DCOS (TJO) 1 CONTINUE 20 CONTINUE RETURN END C TAIL CONTRIBUTION SUBROUTINE TAIL IMPLICIT REAL*8 (A-HO-Z) DIMENSION Z(6),C(6),S1(4,150),Dl(4,150),D2(4,150), *T1 (3, 150),1T2 (3,150),T3 (3, 150),T4 (3, 150) C COMMON/OUT/G1GT ( 150) G2GT ( 160) G2LT ( 190) COMMON/DAT/ERHBSTT1,TT2,DLXATPITPI2,PIWE1,E2,E3,E4,E5,EERI *AKOAKAKK, FAFAOBWBWWBWWWB4WB5WOFFSETWDELTANSNFND IIFEED COMMON/INT/XNS(40), CNS(40),XND(20,2),CND(20),XNT(40, 3) *,CNT (40),MAX(3, 6), IMAX(3),NDP, NTPINSP COMMON/ADON/DIST(10,150,10),SERS(5),SERA(5),DARG(10,10,r4),SN(10,2) *, WREAL, NSERMNUM C C C This vector contains the values of t in the integrals hO C Z(1)=TT1 Z (2) = (1.DO+2.DO*E4) *TT1+BS IF (IFEED.EQ.1) Z(2)=TT1+BS*(1.D0-2.DO*E2) Z(3)=TT2 Z (4) =2. DO*BS-TT2 IF (IFEED.EQ.1) Z(4)=TT2-2.DO*BS*E2 Z(5)=BS+TT2 Z (6) =2. DO*BS+TT2 C

-90 - C This vector contains the values of the coefficient C in C the integrals hO C C(1)=FAO C(2)=FA C(3) =FA C(4) =FA C(5) =FA C(6)=FA C C This vector contains the values of the coefficient A in C the integrals hO C AKK=TPI MMAX=ND+NS+6 IF ((ND+NS).LT.NF) MMAX=NF+6 C C W2=W/2.DO THMIN=WREAL/W THMIN=DATAN(DSQRT(1.DO/THMIN**2-1.DO)) THMAX=PI-THMIN IF (OFFSET.LT.l.D-6) THMAX=PI PI2=PI/2.DO PI4=PI/4.DO DLX2=DLX/2.DO DLX4=DLX2 *DLX2 DSP=(THMAX-THMIN)/4.DO DDP=DSP*DLX2 DTP=DSP*DLX4 COEF1=(THMAX-THMIN)/2.DO IF (OFFSET.LT.1.D-6) COEF1=(PI/2.DO-THMIN)/2.DO COEF2= (THMAX+THMIN) /2.DO IF (OFFSET.LT.1.D-6) COEF2=(PI/2.DO+THMIN)/2.DO C YCOS=DCOS (AKK*DLX) CCS=DCOS(2.DO*AKK*DLX) YSIN=DSIN (AKK*DLX) SSN=DSIN(2.DO*AKK*DLX) C C + --- —-----------------------------— + C | Evaluation of S1,S2,S3,S4,S5,S6 C I (Single Integrals) C + --- —----------------------------— + C ZP1=Z(1)*C(1) ZP2=Z(2) *C(2) ZP3=Z(3) *C(3) ZP4=Z(4)*C(4) ZP5=Z(5)*C(5) ZP6=Z(6)*C(6) C ZP12=ZP1*ZP1 ZP22=ZP2*ZP2 ZP32=ZP3*ZP3

-91 - ZP42=ZP4*ZP4 ZP52=ZP5*ZP5 ZP62=ZP6*ZP6 NMAX=IMAX(1) DO 10 I=1,NSP THI=COEF1*XNS (I)+COEF2 C1=DCOS(THI) C2=W2*C1 C2=OFFSET-C2 CW=C2 *C2 ASIN=CNS (I) *DSP DO 11 N=1,NMAX XN=FLOAT (N-3) *DLX RAD2=XN*XN+CW TRAD1=DSQRT (RAD2+ZP12) TRAD2=DSQRT (RAD2+ZP22) TRAD3=DSQRT (RAD2+ZP32) TRAD4=DSQRT (RAD2+ZP42) IF (N.GT.MAX(1,1)) GO TO 12 Si (1,N) =Sl (1,N) +DLOG (2.DO* (TRAD1+XN) ) *ASIN 12 S1 (2,N) =S1 (2, N) +DLOG (2. D 0 * (TRAD2 +XN) ) *AS IN IF (N.GT.MAX(1,3)) GO TO 13 S1(3, N) =S 1(3,rN) +DLOG(2.D0*(TRAD3+XN) ) *AS IN 13 S 1 (4, N) =S 1 (4, N) +DLOG (2.D O * (TRAD 4 +XN) ) *AS IN 11 CONTINUE 10 CONTINUE C -------------------------------------------------------------- C I EVALUATION OF D1,D2,D4,D5 C + --- —---------------------------------------------------------------— + NMAX=IMAX (2) DO 20 I=1,NDP THI=COEF1*XND (I, 1)+COEF2 XI=DLX2 * (XND (I, 2) + 1.D0) C1=DCOS(THI) C2=W2 *01 C2=OFFSET-C2 CW=C2 *C2 ASIN=CND (I) *DDP SV1=DS IN (AKK* (DLX-XI)) SV2=-SV1 SV4=DSIN (AKK*XI) C2=DCOS (AKK* (DLX-XI)) DO 21 N=1,NMAX XNP=XI+FLOAT(N-2)*DLX XNM=-XI+FLOAT (N-2) *DLX RADP2=XNP *XNP+CW RADM2=XNM*XNM+CW TRAP1=DSQRT (RADP2+ZP12) TRAP2=DSQRT (RADP2+ZP22) TRAP3=DSQRT (RADP2+ZP32) TRAP4 =DSQRT (RADP2+ZP 42) C TRAM1=DSQRT (RADM2+ZP12) TRAM2=DSQRT (RADM2+ZP22) TRAM3=DSQRT (RADM2+ZP32)

-92 - TRAM4=DSQRT (RADM2+ZP42) C XA1=AKK*XNP XA2=AKK*XNM XAP=DSIN (XA1) XAM=DSIN (XA2) C SANP1=XAP * DLOG (2. DO* (TRAP 1 +XNP) ) SANP2=XAP*DLOG (2. DO* (TRAP2+XNP) ) SANP3=XAP*DLOG (2.DO* (TRAP3+XNP)) SANP4=XAP*DLOG (2.DO* (TRAP4+XNP)) C SANM1=XAM*DLOG (2. DO* (TRAM1+XNM)) SANM2=XAM*DLOG (2.DO* (TRAM2+XNM)) SANM3=XAM*DLOG (2.DO* (TRAM3+XNM)) SANM4=XAM*DLOG (2.DO* (TRAM4+XNM)) C XAP=DSIN (XA1/2.DO) XAM=D S IN (XA2 /2. DO) SONP 1=XAP /TRAP 1 SONP2=XAP /TRAP2 SONP3=XAP/TRAP3 SONP 4=XAP /TRAP 4 C SONM1=XAM/ TRAM1 SONM2=XAM/ TRAM2 SONM3=XAM/TRAM3 SONM4=XAM/TRAM4 C Y1=-XNM/2.DO-DLX Y2=-XNP/2.DO+DLX CY1=DCOS(AKK*Y1) CY2=DCOS (AKK*Y2) SY1=DSIN(AKK*Y1) SY2=DSIN (AKK*Y2) C IF (N.GT.MAX(2,1)) GO TO 22 Dl (1,N) =Dl (1,N) + (SANP1+SANM1) *SV2*ASIN D2 (1,N)=D2 (1,N)+(CY1*SONP1-CY2*SONM1) *ASIN 22 D1 (2, N) =D 1 (2, N) + (SANP 2 +SANM2) * SV2 *AS IN D2(2,N)=D2(2,N)+(CY1*SONP2-CY2*SONM2) *ASIN 25 IF (N.GT.MAX(2,3)) GO TO 23 D2 (3,N) =D2 (3,N) + (CY1*SONP3-CY2*SONM3) *ASIN 23 D1 (4, N) =D 1 (4, N) + (SANP 4+SANM4) *SV2 *AS IN D2 (4, N) =D2 (4, N) + (CY 1 * SONP 4 -CY2 * SONM4) *AS IN 21 CONTINUE 20 CONTINUE C + --- —-----------------------------------— + C I EVALUATION OF T1,T2,T3,T4 C + --- —-----------------------------------— + C NMAX=IMAX (3) DO 30 I=1,NTP THI=COEF1*XNT (I, 1)+COEF2 XI=DLX2* (XNT (If2) +1.DO)

-93 - XIP=DLX2* (XNT (I, 3) +1.DO) C1=DCOS(THI) C2=W2*C1 C2=OFFSET-C2 CW=C2*C2 SV1=DSIN(AKK* (DLX-XI)) SV2=-SV1 SV3=DSIN(AKK* (DLX-XIP) ) ASIN=DTP*CNT ( I ) DO 31 N=1,NMAX XNPP=(XI+XIP) +FLOAT (N-1) *DLX XNPM= (XI-XIP) +FLOAT (N-1) *DLX XNMP= (-XI+XIP) +FLOAT (N-l) *DLX XNMM= (-XI-XIP) +FLOAT (N-1) *DLX RADPP2=XNPP *XNPP+CW RADPM2=XNPM*XNPM+CW RADMP 2 =XNMP *XNMP+CW RADMM2 =XNMM*XNMM+CW TAPP =DSQRT (RADPP2+ZP12) TAPP2=DSQRT(RADPP2+ZP22) TAPP4=DSQRT(RADPP2+ZP42) TAPM1=DSQRT (RADPM2+ZP12) TAPM2=DSQRT (RADPM2+ZP22) TAPM4=DSQRT (RADPM2+ZP42) TAMP1=DSQRT (RADMP2+ZP12) TAMP2=DSQRT (RADMP2+ZP22) TAMP4=DSQRT (RADMP2+ZP42) TAMM1=DSQRT (RADMM2+ZP12) TAMM2=DSQRT (RADMM2+ZP22) TAMM4=DSQRT (RADMM2+ZP42) CST1=DCOS(AKK*(XNPM/2.DO+DLX) ) *DSIN(AKK*XNPP/2.DO) CST2=DCOS(AKK* (-XNMP/2.DO+DLX) ) *DSIN(AKK*XNMM/2.DO) CST3=DCOS(AKK*(XNMM/2.DO+DLX) ) *DSIN(AKK*XNMP/2.DO) CST4=DCOS(AKK*(-XNPP/2.DO+DLX) ) *DSIN(AKK*XNPM/2.DO) IF (N.GT.MAX(3,1)) GO TO 32 Tl (,N)=T1 (,N)+SV2*ASIN*CST1/TAPP1 T2 (1,N)=T2 (1,N)+SV1*ASIN*CST2/TAMM1 T3(1,N)=T3(1,N)+SV1*ASIN*CST3/TAMP1 T4 (1,N)=T4 (1,N) +SV2*ASIN*CST4/TAPM1 32 Tl(2,N)=T1(2,N)+SV2*ASIN*CST1/TAPP2 T2(2,N)=T2(2,N)+SV1*ASIN*CST2/TAMM2 T3(2,N)=T3(2,N)+SV1*ASIN*CST3/TAMP2 T4(2,N)=T4(2,N)+SV2*ASIN*CST4/TAPM2 IF (N.GT.MAX(3,4)) GO TO 31 T1 (3,N) =T1 (3,N)+SV2*ASIN*CST1/TAPP4 T2(3,N)=T2(3,N)+SV1*ASIN*CST2/TAMM4 T3(3,N)=T3(3,N)+SV1*ASIN*CST3/TAMP4 T4(3,N)=T4(3,N)+SV2*ASIN*CST4/TAPM4 31 CONTINUE 30 CONTINUE CONST1=FAO CONST2=FA C C +- --------------------— + C I EVALUATION OF G1NI> I

-94 - C + - - -- - - -- - - --- + C 1=3 IF (IFEED.EQ.1) I=4 WCS=(TPI2/EER) * (1.DO/(1l.DO-E2) -2.DO*EER/ ((1.DO+ER) * (1.DO-E3))) WCA=TPI*2.DO/ ((1.DO+ER) * (1 DO-E3)) CS=WCS CA=WCA NMIN=i NMAX=ND DO 60 N=NMIN,NMAX NP 1=N+2 NO=N+i NMi=N ST1=-D1 (1, NP 1) +2.DO *YCOS *D1 (1,INO) -Dl (1, NM1) ST2=2.DO* (Ti (1, N) +T2 (1, N) -T3 (iN) -T4 (1, N)) ST=STi+ST2 C MP2=N+4 MPi=N+3 MO=N+2 MMi=N+l MM2=N SINP2=DSIN (AKK*FLOAT (N+i) *DLX) S INP 1=DS IN (AKK*FLOAT (N) *DLX) SINO=DSIN (AKK*FLOAT (N-i) *DLX) S INMi=DS IN (AKK*FLOAT (N-2) *DLX) S INM2=DS IN (AKK*FLOAT (N-3) *DLX) ATi=SINP2*Si (i,MP2) -4.DO*YCOS*SINPi*Si (i,MPi) +2.DO* (2.DO+CCS * )*SINO*Si(iMO)-4.DO*YCOS*SINMi*Si(iMM1)+SINM2*Si(iMM2) AT2=-2. D O* (D2 (1, NP 1) -2. D O*YCOS *D2 (1, NO) +D2 (1, NM1)) AT=ATi+AT2 GiGT (N) =W* (CS *ST+CA*AT) *CONSTi 60 CONTINUE C + --- —------------------— + C I EVALUATION OF G2NI> I C + --- —------------------— + C DS=1.DO/(l.DO+E4)-2.DO*EER/((i.DO+ER)*(i.DO+E6)) DT=2.DO/ ((i.DO+ER) * (i.DO+E6)) CS=TPI2*DS/EER IF (IFEED.EQ.i) CS=WCS CA=TP I *DT IF (IFEED.EQ.i) CA=WCA NMIN=i NMAX=NS+ND DO 6i N=NMINNMAX NP i=N+2 NO=N+i NMi=N ST=-Di (2, NPi) +2.DO*YCOS*Di (2, NO) -Di (2,NMi) +2.DO* (Ti (2,fN) +T2 * 2,N)-T3(2,N)-T4(2,N)) MP2=N+4 MPi=N+3 MO=N+2

-95 - MM 1=N+1 MM2=N SINP2=DSIN (AKK*FLOAT (N+l) *DLX) SINPi=DSIN (AKK*FLOAT (N) *DLX) SINO=DSIN (AKK*FLOAT (N-i) *DLX) SINMi=DSIN (AKK*FLOAT (N-2) *DLX) SINM2=DSIN (AKK*FLOAT (N-3) *DLX) AT1=SINP2*Si (2,MP2) -4.DO*YCOS*SINP1*S1 (2,MPi) +2.DO* (2.DO+CCS * )*SINO*Sl(2,MO)-4.DO*YCOS*SINM*S1*(2,MM1)+SINM2*Sl(2, MM2) AT2=-2.DO* (D2 (2,NPi) -2.DO*YCOS*D2 (2,NO) +D2 (2,NMi)) AT=AT 1 +AT2 G2GT (N) =W* (CS*ST+CA*AT) *CONST2 61 CONTINUE C C + --- —------------------— + C I EVALUATION OF G2NI< C + --- —-------------------— + C DS1=ER*E4/ (1.DO+E4) +EER*2.DO*ER/ ((1.DO+ER) * (1.DO+E6) ) -EER CS=- (TPI2/EER) *DS1 IF (IFEED. EQ. 1) CS=WCS CA=TPI IF (IFEED.EQ.1) CA=WCA CWW=1.DO-2.DO*ER/ ((1.DO+ER) * (1.DO+E6)) IF (IFEED.EQ.1) CWW=O.DO CAA=TP I *CWW NMIN=1 NMAX=NNF DO 62 N=NMINNMAX NP 1=N+2 NO=N+1 NM1=N ST=-D1 (4,NP1) +2.DO*YCOS*Dl (4, NO) -Dl (4,NM1) +2.DO* (Ti (3,N) +T2 3,N)-T3(3,N)-T4(3,N)) C MP2=N+4 MP1=N+3 MO=N+2 MM1=N+1 MM2=N SINP2=DSIN (AKK*FLOAT (N+1) *DLX) SINP1=DSIN (AKK*FLOAT (N) *DLX) SINO=DSIN (AKK*FLOAT (N-i) *DLX) S INM1=DS IN (AKK*FLOAT (N-2) *DLX) SINM2=DSIN (AKK*FLOAT (N-3) *DLX) AT1=SINP2*S1 (I,MP2) -4.DO*YCOS*SINP1*Si (I,MP1) +2.DO* (2.DO+CCS * )*SINO*S1(IMO) 4.DO*YCOS*SINM*S1(II)MM1+SINM2*S1(IMM2) AAI=SINP2*Sl (4,MP2) -4.DO*YCOS*SINP1*S1 (4,MP1) +2.DO* (2.DO+CCS )*SINO*Sl(4,MO) 4.DO*YCOS*SINM1*Sl(44JMM1)+SINM2*S1l(4 JMM2) AT2=-2. DO * (D2 (I, NP 1) -2.DO *YCOS *D2 (I, NO) +D2 (I, NMi) ) AA2=-2.DO* (D2 (4,NPl) -2.DO*YCOS*D2 (4,NO) +D2 (4,NM1) ) AT=AT 1+AT2 AA=AA1+AA2 G2LT (N) =W* (CS *ST+CA*AT-CAA*AA) *CONST2 62 CONTINUE

-96 - RETURN END C The name of this subroutine is DATA C and gives all the data used by the main program and the other C subroutines. SUBROUTINE DATA(IOPT) IMPLICIT REAL*8 (A-H,O-Z) DIMENSION IAXX(10),DAXX(50) COMMON/COEF/RX(5),XX(5),RZ(5),XZ(5),FRX(5),FRZ(5),F1XX,F1ZX,F2XXG, *F2ZXG,F2XXL,F2ZXL,F1XXL,F1ZXL,F2XL,F2ZL COMMON/DATT/COAL(20),POINT(20),CN(51),BM(51),POLTM(20),POLTE(20) *,AM(41),DM(41),POLES(40),NPOINT,NK0,MA,NTM,NTE,NKOK,IFIRST COMMON/DAT/ER,H,BS,T1,T2,DLX,A,TPI,TPI2,PI,W,El,E2,E3,E4,E5,EER, *AK0,AK,AKK,FA,FA0,BW,BWW,BWWW,B4W,B5W,OFFSET,WDELTA,NS,NF,ND,IFEED COMMON/INT/XNS(40),CNS(40),XND(20,2),CND(20),XNT(40,3) *,CNT (40),MAX(3, 6),JMAX(3),NDP,NTP,NSP COMMON/ADON/DIST(10,150,10),SERS(5),SERA(5),DARG(10,10,4),S(10,2), *WREAL, NSER, MNUM C +- -- -----------------------------------------— + C I VARIABLES FOR THE GEOMETRY. I C I C I IFEED= 1: FEED LINE ON THE INTERFACE C I 0: FEED LINE IN THE DIELECTRIC C + --- —-------------------------------------— + READ(5,80) IIA 80 FORMAT(5X,I4) READ(5,80) IDA DO 66 I=1,IIA READ(5,67) IAXX(I) 67 FORMAT (5X,I4) 66 CONTINUE DO 68 I=1,IDA READ(5,69) DAXX(I) 69 FORMAT (5X,D16.9) 68 CONTINUE IOPT=IAXX(1) IFEED=IAXX(2) NS=IAXX(3) ND=IAXX(4) NF=IAXX(5) NTE=IAXX(6) NTM=IAXX(7) IFIRST=IAXX(8) ER=DAXX(1) EER=DAXX(2) IF (IFEED.EQ.1) EER=1.DO H=DAXX (3) *DSQRT (EER) BS=DAXX(4) *DSQRT (EER) DEL=DAXX(5)*DSQRT(EER) T1=DAXX (6) *DSQRT (EER) T2=DAXX(7) *DSQRT (EER) DLX=DAXX(8) A=DAXX(9)

-97 - PI=DAXX(10) W=DAXX (11) *DSQRT (EER) OFFSET=DAXX(12) *DSQRT (EER) WDELTA=DAXX (13) *DSQRT (EER) IF (NTE.EQ.0) GO TO 71 NPTE=13+NTE DO 72 NE=14,NPTE INE=NE-13 POLTE (INE) =DAXX (NE) /DSQRT (EER) C WRITE (6,101) INE,POLTE(INE) 101 FORMAT(10X,'INE=',I4,5X,'POLTE=',D16.9/) 72 CONTINUE 71 NRTM=13+NTE+1 NPTM=1 3+NTE+NTM DO 73 NM=NRTM,NPTM INM=NM-NRTM+1 POLTM(INM)=DAXX(NM)/DSQRT(EER) C WRITE (6,102) INM,POLTM(INM) 102 FORMAT (10X,'INM=',I4,5X,'POLTM=',D16.9/) 73 CONTINUE NMN=13+NTE+NTM+1 NMX=13+2* (NTM+NTE) DO 74 NP=NMN,NMX NII=NP-NMN+1 POLES (NII) =DAXX (NP) /DSQRT (EER) C WRITE (6,103) NII,POLES(NII) 103 FORMAT (10X,'NII=',I4,5X,'POLES=',D16.9/) 74 CONTINUE IF (IOPT.NE.1) GO TO 91 WRITE (6,90) ER,H,BS,T1,DLX,W,PI,WDELTA 90 FORMAT (10X,E14.7/lOX,E14.7/lOX,E14.7/lOX,E14.7/10X,E14.7/lOX, *E14.7/10X, E14.7/10X,E14.7/) 91 CONTINUE C.................................................................. TPI=2.DO*PI TPI2=TPI*TPI C + --- —-----------— + C I ERROR FUNCTIONS I C + --- —--------------- C AA1=A/TPI AA2=AA1 *AA1*EER E1=0.5D0/(AA2-1.DO) E2=0.25D0* (ER-1.DO) / (AA2-1.DO) E3=2.DO*E2/(1.DO+ER) E4=0.25D0*(ER-1.DO) / (AA2-ER) E5=0.5D0*ER/(AA2-ER) E6=2.DO*ER*E4/(1.DO+ER) C AKO=2.DO*PI/DSQRT(EER) AKK=2.DO*PI AK=AKO*DSQRT (ER) FA=DSQRT (1.DO+ER/(AA2-ER)) FAO=DSQRT (.DO+1.DO/ (AA2-1.DO))

-98 - FA=1.DO/FA FAO=1.DO/FAO IF (IFEED.EQ.1) FA=FAO BW=BS+T1*(1.D0+2.DO*E4) IF (IFEED.EQ.1) BW=T1+BS*(1.DO-2.DO*E2) BWW=T2-2.DO*BS*E2 BWWW=2.DO*BS-T2 B4W=BS+TT2 B5W=2.DO*BS+TT2 C + --- —----------------------------------------------— + C DATA FOR THE POLES C | IFIRST= 0: DOMINANT MODE IS TM WAVE (MANY POLES) C 1: DOMINANT MODE IS TE WAVE (MANY POLES) C 2: ONLY ONE TM SURFACE WAVE C + --- —------ ---------------------------------------— + C + --- —----------------------- -----------------— + C Data for the Dipoles C I C NS = Distance between the first points of C the two dipoles in dlx C ND = Length of the upper dipole in dlx C NF = Length of the lower dipole C (feeding line) in dlx C + --- —---- ---- ---------------------------------------— + C C VECTOR OF THE MAXIMA C --- ---------- C MAX(1,1)=ND+4 MAX(1,2)=ND+NS+4 MAX(1,3)=NF+4 IF (IFEED.EQ.1) MAX(1,3)=0 MAX(1,4)=NF+4 MAX(1,5)=ND+NS+4 MAX(1,6)=NF+4 JMAX (1)=MAX(1,2) C MAX(2,1)=ND+2 MAX(2,2)=ND+NS+2 MAX(2,3)=NF+2 IF (IFEED.EQ.1) MAX(2,3)=0 MAX(2,4)=NF+2 MAX(2,5)=ND+NS+2 MAX(2,6)=NF+2 JMAX(2)=MAX(2,2) C MAX(3,1)=ND MAX(3,2)=ND+NS+1 MAX(3,4)=NF+1 JMAX(3)=MAX(3,2) C C -------------------------— + C I Data for the Integration I C + --- —---------------— + NKO=20

-99 - NKOK=1 MA=20 NPOINT=10 NSER=10 C C VECTOR COAL C --- —------ COAL(1)=0.0666713443D0 COAL(2)=0.14945134915D0 COAL(3)=0.21908636251D0 COAL(4)=0.26926671931D0 COAL(5)=0.29552422471D0 COAL(6)=COAL(5) COAL(7)=COAL(4) COAL(8)=COAL(3) COAL(9)=COAL(2) COAL(10)=COAL(1) C C VECTOR POINT C --------- POINT(1)=0.973906528517D0 POINT(2)=0.865063366688D0 POINT(3)=0.679409568299D0 POINT(4)=0. 433395394129D0 POINT(5)=0.148874338981D0 POINT(6)=-POINT(5) -POINT(7)=-POINT(4) POINT (8)=-POINT (3) POINT(9)=-POINT(2) POINT(10)=-POINT(1) C C SINGLE INTEGRATION C ----------- C NSP=31 RS1=0.99708748181D0 RS2=0. 98468590966D0 RS3=0.96250392509D0 RS4=0.93075699789D0 RS5=0. 88976002994D RS6=0.83992032014D0 RS7=0.78173314841D0 RS8=0. 71577678458D0 RS9=0. 64270672292D0 RS10=0.56324916140D0 RSll=0.47819378204D0 RS12=0.38838590160D0 RS13=0.29471806998D0 RS14=0.19812119933D0 RS15=0.09955531215D0 RS16=0.DO C XNS (1)=RS1 XNS (2)=RS2 XNS(3)=RS3

-100 - XNS (4) =RS4 XNS (5) =RS5 XNS(6)=RS6 XNS(7)=RS7 XNS(8)=RS8 XNS (9)=RS9 XNS(10)=RS10 XNS(11)=RS11 XNS(12)=RS12 XNS(13)=RS13 XNS(14)=RS14 XNS(15)=RS15 XNS(16)=RS16 XNS(17)=-RS15 XNS(18)=-RS14 XNS(19)=-RS13 XNS(20)=-RS12 XNS(21)=-RS11 XNS(22)=-RS10 XNS(23)=-RS9 XNS(24)=-RS8 XNS(25)=-RS7 XNS(26)=-RS6 XNS (27) =-RS5 XNS(28)=-RS4 XNS(29)=-RS3 XNS(30)=-RS2 XNS(31)=-RS1 C CNS(1)=0.0074708315792D0 CNS(2)=0.0173186207903D0 CNS(3)=0.0270090191849D0 CNS(4)=0.0364322739123D0 CNS(5)=0.0454937075272D0 CNS (6)=0.0541030824249D0 CNS(7)=0.0621747865610D0 CNS(8)=0.0696285832354D0 CNS(9)=0.0763903865987D0 CNS(10)=0.0823929917615D0 CNS(11)=0.0875767406084D0 CNS(12)=0.0918901138936D0 CNS(13)=0.0952902429123D0 CNS(14)=0.0977433353863D0 CNS(15)=0.0992250112266D0 CNS (16) =0. 0997205447934D0 CNS(17)=CNS(15) CNS(18)=CNS(14) CNS (19)=CNS (13) CNS(20)=CNS(12) CNS(21)=CNS(11) CNS(22)=CNS(10) CNS(23)=CNS(9) CNS (24)=CNS(8) CNS (25)=CNS(7) CNS(26)=CNS(6)

-101 - CNS (27) =CNS (5) CNS (28)=CNS (4) CNS(29)=CNS(3) CNS (30)=CNS(2) CNS(31)=CNS(1) C C C C 2) Double Integration C --------------- C NDP=16 R1=DSQRT((15.DO-2.DO*DSQRT(30.D0))/35.D0) R2=-R1 Sl=QRT((15DDDSQRT((15.D+2.D*DSQRT(30.D0))/35.D0) S2=-S1 A1=4.DO*(59.DO+6.DO*DSQRT(30.DO) )/864.DO A2=4.DO*(59.D0-6.DO*DSQRT(30.D0))/864.D0 A3=4.DO*49.D/864.DO C XND(1,1)=R1 XND(1,2)=R1 CND(1)=A1 C XND(2,1)=R2 XND(2,2)=R1 CND(2)=A1 C XND (3,1)=R1 XND(3,2)=R2 CND(3)=A1 C XND(4,1)=R2 XND(4,2)=R2 CND(4)=A1 C XND(5, 1)=S1 XND(5,2)=S1 CND(5)=A2 C XND(6,1)=S1 XND(6,2)=S2 CND (6)=A2 C XND(7,1)=S2 XND(7,2)=S1 CND(7)=A2 C XND(8,1)=S2 XND(8,2)=S2 CND(8)=A2 C XND(9,1)=R1 XND(9,2)=S1 CND (9)=A3

-102 - C XND (10,r1) =R1 XND (10,2) =S2 CND (10) =A3 C XND (11,1) =Sl XND (11,2) =Rl CND (11) =A3 C XND (12,1) =S2 XND (12,2) =R1 CND (12) =A3 C XND (13,1) =R2 XND (13,2) =S1 CND (13) =A3 C XND (14,1) =R2 XND (14,2) =S2 CND (14) =A3 C XND (15,1) =S1 XND (15,2) =R2 OND (15) =A3 C XND (16,1) =S2 XND (16,2) =R2 CND (16) =A3 C o 3) Triple Integration C - - - - - - - - - C NTP=34 RS1=0. 9317380000D0 RS2=-RS1 UU1=0.916744177 9D0 UUJ2=-UJU1 SS1=0.408 60038 00D0 SS2=-SS1 TT1=0.739852 9500D0 TT2=-TT1 B1=8.D0*0.035581808 96D0 B2=8.D0*0.012478 92770D0 B3=8.DO*0.0528 6772 991D0 B4=8.DO*0.02672752182D0 C XNT (1,1)=RSl XNT (1,2) =0.DO XNT (1,3) =0.DO ONT (1) =B1 C XNT (2, 1)=RS2 XNT (2,,2) =0.DO XNT (2,,3) =0.DO CNT (2) =B1

-103 - C XNT(3, 1) =0.DO XNT (3,2) =RS1 XNT (3,3) =0.DO ONT (3)=Bl C XNT (4,1) =0.DO XNT (4,2) =RS2 XNT (4,f3) =0.DO CNT (4)=B1 C XNT(5, 1) =0.DO XNT (5,2) =0.DO XNT (5,3) =RS1 CNT (5) =Bl C XNT (6,1) =0.DO XNT (6,2)=0.DO XNT (6,3)=RS2 CNT (6) =B1 C XNT (7,1) =UU1 XNT (7,2) =UU1 XNT (7,f3) =0.DO CNT (7)=B2 C XNT (8, 1)=IJU2 XNT (8,2) =IU1 XNT (8,3) =0.DO CNT (8) =B2 C XNT(9, 1)=UU1 XNT (9,2) =UU2 XNT (9,3)=0.DO CNT(9)=B2 C XNT (10,1) =UU2 XNT (10,2) =UU2 XNT (10, 3)=0.DO ONT (10) =B2 C XNT (11,1) =~U1 XNT (11, 2) =0.DO XNT (11,3) =UU1 CNT (11) =B2 C XNT (12,1) =UU1 XNT (12,,2) =0.DO XNT (12, 3) =UU2,CNT (12) =B2 C XNT (13,1) =UU2 XNT (13, 2) =0.DO XNT (13,,3) =UU1 CNT (13) =B2

-104 - C XNT (14, 1) =1U2 XNT (14,2) =0.DO XNT (14,3)=TJU2 CNT (14) =B2 C XNT (15,1) =0.DO XNT (15,2) =UU1 XNT (15,3) =UU1 CNT (15) =B2 C XNT (16,1) =0.D0 XNT (16,2)=UJI1 XNT (16,3) =UU2 CNT(16)=B2 C XNT (17, 1) =0.DO XNT (17,2) =UU2 XNT (17,3) =UU1 CNT (17) =B2 C XNT (18, 1) =0. DO XNT (18,2) =UU2 XNT (1 8,r3) =UU12 CNT (18) =B2 C XNT (19,1) =SS1 XNT (19,2) =SS1 XNT (19,3) =SS1 CNT (19) =B3 C XNT (20,1) =SS1 XNT (20,2) =SS1 XNT (20,f3) =SS2 CNT (20) =B3 C XNT (21,1) =SS1 XNT (21,2) =SS2 XNT (21,3) =SS1 CNT (21) =B3 C XNT (22,1) =SS1 XNT (22,,2) =SS2 XNT (22,3) =SS2 CNT (22) =B3 C XNT (23,1) =SS2 XNT (2"3,2)=SS1 XNT (23,3) =SS1 CNT (23) =B3 C XNT (24,1) =SS2 XNT (24,2) =SS1 XNT (24, 3) =SS2 ONT (24) =B3

-105 - c XNT(25,1)=SS2 XNT(25,2)=SS2 XNT(25,3)=SS1 CNT(25)=B3 C XNT(26,1)=SS2 XNT(26,2)=SS2 XNT(26,3)=SS2 CNT(26)=B3 C XNT(27,1)=TT1 XNT(27,2)=TT1 XNT(27,3)=TT1 CNT(27)=B4 C XNT(28,1)=TT1 XNT(28,2)=TT1 XNT(28,3)=TT2 CNT(28)=B4 C XNT(29,1)=TT1 XNT(29,2)=TT2 XNT(29,3)=TT1 CNT(29)=B4 C XNT(30,1)=TT1 XNT(30,2)=TT2 XNT(30,3)=TT2 CNT(30)=B4 C XNT(31,1)=TT2 XNT(31,2)=TT1 XNT(31,3)=TT1 CNT(31)=B4 C XNT(32,1)=TT2 XNT(32,2)=TT1 XNT(32,3)=TT2 CNT(32)=B4 C XNT(33,1)=TT2 XNT(33,2)=TT2 XNT(33,3)=TT1 CNT(33)=B4 C XNT(34,1)=TT2 XNT(34,2)=TT2 XNT(34,3)=TT2 CNT(34)=B4 RETURN END

-106 - FOPTJON2 ( INV33 )

-107 - C The name of this file is.............. INV33................... C It solves the problem of three strip dipoles. Two of them parasiC tic and the third excited. One on the interface and two in the C dielectric. The exciter is in the dielectric IMPLICIT REAL*4 (A-H,O-Z) COMPLEX*8 CUR (170), ZIN COMPLEX*8 BMATR,Zll(200),Z22(200),Z33(200),Z21(200),Z32(200) *,Z31(200) DIMENSION IB(170),IA(170),IDATA(10),RDATA(20) COMMON/MAN/BMATR (170,170) C DATA C......................................................................... DO 180 ID=1,7 READ (1,100) IDATA(ID) 180 CONTINUE NOEL3=IDATA(1) NOEL2=IDATA(2) NOEL1=IDATA(3) NS2=IDATA(4) NS1=IDATA (5) NOR=IDATA(6) NFEED=IDATA(7) C 100 FORMAT (10X, I4) DO 190 ID=1,8 READ (2, 200) RDATA(ID) 190 CONTINUE ER=RDATA (1) H=RDATA (2) BS=RDATA(3) T1=RDATA (4) DLX=RDATA (5) W=RDATA (6) PI =RDATA (7) WDELTA=RDATA(8) 200 FORMAT(1OX,E14.7) READ(2,310) N11 310 FORMAT(/11X,I4) WRITE (6,330) 330 FORMAT(/, '**************************************************** '/) DO 500 I=1,N11 READ(2,400) Zll(I) C WRITE (6,320) I,Zll(I) 320 FORMAT (2X, 'Zll(',I4, ')=',E14.7,3X, E14.7) 500 CONTINUE READ(2,310) N31 DO 530 I=1,N31 READ(2,400) Z31(I) C WRITE (6,323) I,Z31(I) 323 FORMAT (2X, 'Z31 (',I4, ')=',E14.7, 3X, E14.7) 530 CONTINUE READ(2,310) N33 DO 540 I=1,N33 READ(2,400) Z33(I) C WRITE (6,324) I,Z33(I) 324 FORMAT (2X, 'Z33(',I4, ') =', E14.7, 3X, E14.7) 540 CONTINUE

-108 -READ(2,310) N21 DO 510 I=1,N21 READ(2,400) Z21(I) C WRITE (6,321) I,Z21(I) 321 FORMAT(2X, 'Z21(', I4, ')=',E14.7,3X,E14.7) 510 CONTINUE READ(2,310) N22 DO 520 I=1,N22 READ(2,400) Z22 (I) C WRITE (6,322) I,Z22(I) 322 FORMAT(2X, 'Z22(', I4, ')=', E14.7, 3X, E14.7) 520 CONTINUE READ(2,310) N32 DO 550 I=1,N32 READ(2,400) Z32(I) C WRITE (6,325) I,Z32(I) 325 FORMAT(2X, 'Z32(',14, ')=',E14.7,3X,E14.7) 550 CONTINUE 400 FORMAT (11X,E14.7,4X,E14.7) H=H/SQRT (ER) BS=BS/SQRT (ER) DEL=DEL/SQRT (ER) W=W/SQRT (ER) T1=T1/SQRT (ER) T2=T2/SQRT (ER) OFFSET=OFFSET/SQRT(ER) WDELTA=WDELTA/SQRT(ER) C................................................. C WRITE (6,1) 1 FORMAT (//'l',1OX,'A strip dipole at the interface EM coupled '//1 *OX, 'to another printed dipole in the dielectric which'//10X,'is ex *cited by a gap generator'///) WRITE (6,3) ER,H,BS,T1,T2,DLX,W, OFFSET,WDELTA,DEL 3 FORMAT(/10X,'ER=',E14.7,5X,'H=',E14.7/10X,'BS=',E14.7,5X,'T1=',E14 *.7/10X,'T2=',E14.7,5X,'DLX=',E14.7/10X,'W=',E14.7/10X,'OFFSET=',E1 *4.7,5X, 'WDELTA=',E4.7/10X, 'DELTA=',E14.7///) C C Diagonal Matrices C NS3=NS2+NS1-1 INI=NOEL3 IMIN=1 IMAX=INI DO 4 I=IMIN,IMAX IXN=0 DO 5 KI=I,IMAX IXN=IXN+1 BMATR(IXN,KI)=Z33(I) BMATR (KI, IXN) =BMATR (IXN, KI) 5 CONTINUE 4 CONTINUE IMIN=NOEL3+1 IMAX=NOEL3+NOEL2 DO 6 I=IMIN,IMAX IXN=INI DO 7 KI=I,IMAX IXN=IXN+1 BMATR(IXN, KI)=Z22 (I-INI) BMATR (KI, IXN) =BMATR(IXN, KI)

-109 -7 CONTINUE 6 CONTINUE INI =NOEL3+NOEL2 IMIN=INI +1 IMAX=NOEL3+NOEL2 +NOEL1 DO 8 I=IMIN,IMAX IXN=INI DO 9 KI=I,IMAX IXN=IXN+1 BMATR (IXN, KI) =Zll (I - INI) BMATR (KI, IXN) =BMATR (IXN, KI) 9 CONTINUE 8 CONTINUE C C...1... First off-diagonal matrix C C 1) Upper Part C IMIN=NOEL3+1 IMAX=NOEL 3 +NOEL2 DO 10 I=IMIN,IMAX IXN=0 LXN=NS2 +I -IMIN DO 11 KI=I,IMAX IXN=IXN+1 BMATR (IXN, KI) =Z32 (LXN) BMATR (KI, IXN) =BMATR (IXN, KI) 11 CONTINUE 10 CONTINUE C C 2) Lower Part C IMI=NOEL3-NOEL2+2 KIMIN=IMIN I IMAX=IMAX IMIN=2 IMAX=NOEL3 DO 12 I=IMIN,IMAX IXN=I-1 KIMAX=I IMAX IF (I.GE.IMI) KIMAX=IIMAX-(I-IMI+1) LXN=IABS (NS2-I) +1 DO 13 KI=KIMIN,KIMAX IXN=IXN+1 BMATR (IXN, KI) =Z32 (LXN) BMATR (KI, IXN) =BMATR (IXN, KI) 13 CONTINUE 12 CONTINUE C C....2.... First off-diagonal matrix C C 1) UPPER PART C IMIN=NOEL 3 +NOEL 2 +1 I MAX=NOEL 3 +NOEL 2 +NOEL 1 DO 14 I=IMIN, IMAX IXN=NOEL3 LXN=NS1+I - IMIN DO 15 KI=I,IMAX IXN=IXN+1

-110 -BMATR (IXN, KI) =Z21 (LXN) BMATR (KI, IXN) =BMATR (IXN, KI) 15 CONTINUE 14 CONTINUE C C 2) Lower Part C IMI=NOEL2 -NOEL1+ 2 NOEL3 KIMIN=IMIN I IMAX=IMAX IMIN=NOEL3+2 IMAX=NOEL 3+NOEL 2 DO 16 I=IMIN,IMAX IXN=I-1 KIMAX=I IMAX IF (I.GE.IMI) KIMAX=IIMAX-(I-IMI+1) LXN=IABS (NS1-I+NOEL3) +1 DO 17 KI=KIMIN,KIMAX IXN=IXN+1 BMATR (IXN, KI) =Z21 (LXN) BMATR (KI, IXN) =BMATR (IXN, KI) 17 CONTINUE 16 CONTINUE C C....1.... Second off-diagonal matrix C C 1) UPPER PART IMIN=NOEL3+NOEL2+1 IMAX=NOEL 3+NOEL2 +NOEL1 DO 18 I=IMIN,IMAX IXN=0 LXN=NS3+I - IMIN DO 19 KI=I,IMAX IXN=IXN+1 BMATR (IXN, KI) =Z31 (LXN) BMATR (KI, IXN) =BMATR (IXN, KI) 19 CONTINUE 18 CONTINUE C C 2) Lower part C IMI=NOEL3-NOEL1+2 KIMIN=IMIN IIMAX=IMAX IMIN=2 IMAX=NOEL3 DO 20 I=IMIN,IMAX IXN=I-1 KIMAX=IIMAX IF (I.GE.IMI) KIMAX=IIMAX-(I-IMI+1) LXN=IABS (NS3-I) +1 DO 21 KI=KIMIN,KIMAX IXN=IXN+1 BMATR (IXN, KI) =Z31 (LXN) BMATR (KI, IXN) =BMATR (IXN, KI) 21 CONTINUE 20 CONTINUE C C C IMIN=1

-111 -C IMAX=NOEL 3+NOEL2 +NOEL1 C DO 22 I=1,IMAX C WRITE (6,23) I, (BMATR(I,J),J=l,IMAX) C 23 FORMAT (I2,2X,I2,1X,I2,1X,I2,1X,I2,1X,I2,lX,I2,1X, I2,1X C *,12, X,I2, X,I2, X,I2, X,I2, X,I2,1X,I2, X, 12, X C *, I2, X, I2, X, I2, X, I2, X, I2, X, I2, X, I2, X, 2, 1X C *,I2, X,I2, iX,I2, X,I2,IX,I12, X, I2, 2,,12, X/) C 22 CONTINUE C GO TO 1000 C 1001 CALL MINVCD (NOR,NOR,DETA, IB, IA) C DO 25 IQQ=1,NOR CUR(IQQ)=BMATR(IQQ,NFEED)/100.00 25 CONTINUE ZIN=1.00/CUR (NFEED) WRITE (6,701) ZIN 701 FORMAT (///10X, 'ZIN=',(E14.7,2X,E14.7)//) WRITE (6,30) 30 FORMAT (///1OX,'Current distribution on the t.l.'///) WRITE (3,40) NOEL3 40 FORMAT(10X,14) IMIN=1 IMAX=NOEL 3NOEL 2 +NOEL1 DO 31 IQQ=IMIN,IMAX RECUR1=REAL (CUR (IQQ)) ABCU1=CABS (CUR (IQQ)) AICUR1=AIMAG (CUR (IQQ)) PHCUR1=ATAN2 (AI CUR1, RECUR1) PHCUR1=180. 00*PHCUR1/PI IF (IQQ.EQ. (NOEL3+1)) WRITE (6,36) 36 FORMAT(///10X, 'Current on the first parasitic dipole'////) IF (IQQ.EQ. (NOEL3+1)) WRITE (3,46) NOEL2 46 FORMAT(10X,14) IF (IQQ.EQ.(NOEL3+NOEL2+1)) WRITE (6,37) 37 FORMAT(///10X, 'Current on the second parasitic dipole'////) IF (IQQ.EQ. (NOEL3+NOEL2+1)) WRITE (3,47) NOEL1 47 FORMAT(10X,14) WRITE (6,32) IQQ,CUR(IQQ),ABCU1,PHCUR1 32 FORMAT (7X, 'CURR(',I4, ')=(', (E14.7,', ',E14.7),5X,E14.7,5X, * E14.7/) WRITE (3,45) CUR(IQQ) 45 FORMAT(10X,E14.7,1X,E14.7) 31 CONTINUE 1000 CONTINUE STOP END C*********************************************************************** C THIS SUBROUTINE INVERTS A SQUARE COMPLEX MATRIX C************************************************************************ SUBROUTINE MINVCD (IA,MA,DETA,IR,IC) IMPLICIT REAL*4 (A-H,O-Z) COMPLEX*8 A,PIV,DETA,TEMP,PIV1 DIMENSION IR (MA),IC(MA) COMMON/MAN/A(170,170) DO 1 I=1,MA IR(I)=0 1 IC(I)=0 C DETA=(1.00,0.00) S=0.00

-112 -R=MA 2 CALL SUBMCD(IA,IA,MA,MA, IR, IC, I,J) PIV=A(I, J) C DETA=PIV*DETA Y=CABS (PIV) IF (Y.EQ.O) GO TO 17 IR(I)=J IC (J) =I PIV= (1.00,0.00)/PIV A(I,J)=PIV DO 5 K=1,MA 5 IF (K.NE.J) A(I,K)=A(I,K)*PIV DO 9 K=1,MA IF (K.EQ.I) GO TO 9 PIV1=A (K, J) 6 DO 8 L=1,MA 8 IF (L.NE.J) A(K,L)=A(K,L) -PIV1*A(I,L) 9 CONTINUE DO 11 K=1,MA 11 IF (K.NE.I) A(K,J)=-PIV*A(K,J) S=S+1. 00 IF (S.LT.R) GO TO 2 12 DO 16 I=1,MA K=IC (I) M=IR (I) IF (K.EQ.I) GO TO 16 C DETA=-DETA DO 14 L=1,MA TEMP=A (K, L) A(K,L)=A(I,L) 14 A(I,L)=TEMP DO 15 L=1,MA TEMP=A (L, M) A (L, M) =A (L, I) 15 A(L,I)=TEMP IC (M) =K IR (K) =M 16 CONTINUE RETURN 17 WRITE (6,18)I,J 18 FORMAT (10X, 'MATRIX IS SINGULAR'/10X, 'I=', 4,5X, 'J=', 4) RETURN END C*** ** ************************************** ******************** ******** SUBROUTINE SUBMCD (IA, JA, MA, NA, IR, IC, I, J) IMPLICIT REAL*4 (A-H,O-Z) COMPLEX*8 A DIMENSION IR (MA), IC (NA) COMMON/MAN/A (170,170) I=O J=0 TEST=0.00 DO 5 K=1,MA IF (IR(K).NE.O) GO TO 5 DO 4 L=1,NA IF (IC(L).NE.0) GO TO 4 X=CABS (A (K, L)) IE(X.LT.TEST) GO TO 4

-113 -I=K J=L TEST=X 4 CONTINUE 5 CONTINUE RETURN END

-114 - FOPTJON3 (GAIN )

-115 -C THE NAME OF THIS PROGRAM IS: GAIN C IT COMPUTES THE RADIATION PATTERN OF DIPOLES **************************************************************** ******** IMPLICIT REAL*4 (A-H,O-Z) COMPLEX*8 ETH, EFI, CUR1, CUR2, CUR3, CUR4 DIMENSION THETA(203),RGAIN(203),X(203),Y(203),XB(203),XC(203), *YB(203),YC(203), XPOS1(7),XPOS2(7),YPOS1(7),YPOS2(7),XA(203), *YA(203),XPOS3(3),XPOS4(4),YPOS3(3),YPOS4(4),ARG(201),CUR1 (100), *CUR2(50),CUR3(50),CUR4(50),RTHETA(203) COMMON/DAT/PI,DLX,ER,EER,H,BS,CUR1,CUR2, S (20,2),WIDTH, *WREAL, NSER, ICON, CUR3, CUR4 COMMON/PAR/OF2,OF3, OF4, NS,N1, N2,N3, N4,A2,A3,A4, DEL C SLOWER......Minimun dBs fo the radiation pattern you want to plot C DIV.........dBs per subdiv yow want to plot C TC1.........coef which determines the number of dB for the second C subdiv circle C TC2.........coef which determines the number of dBs for the first C subdiv circle C WARNING!!!! after you change this parameters be carefull to change C appropriately the corresponding symbol statements C C ICON= 0 both transmission line and dipoles are included C C 1 only dipoles are included C C -1 only transmission line is included C C IPLANE= 0 E-plane radiation pattern C C 1 H-plane radiation pattern C.......................................................................... ICON=0 SLOWER=-50.0 DIV=10.0 TC1=2.0 TC2=1.0 C READ(1,400) IPLANE READ(1,400) NS 400 FORMAT(5X, 14) READ(1,400) N1 READ(1,400) N2 READ(1,400) N3 READ(1,400) N4 C PI=3.1415926535890 READ(1,300) ER 300 FORMAT(5X,E14.7) READ(1,300) EER READ(1,300) H READ(1,300) BS READ(1,300) DEL READ(1,300) DLX READ(1,300) WIDTH READ (1,300) WDELTA C READ(1,300) OF2

-116 -READ(1,300) OE3 READ(1,300) OF4 C IFEED=0. 25/DLX A2=FLOAT (NS) *DLX A3=A2 A4=FLOAT (NS) *DLX C WREAL=WIDTH WIDTH=WIDTH* (1.DO+2. DO*WDELTA/WIDTH) C IF (IPLANE.EQ.1) GO TO 500 C C E-plane pattern FI=0.00 IFI=0 GO TO 501 C 500 CONTINUE C C H-plane pattern FI=PI/2.00 IFI=1 C 501 CONTINUE C C Current distribution on the trans.line C READ (3,100) NOEL1 100 FORMAT(/I4) DO 110 I=1,NOEL1 READ(3,120) CUR1(I) 120 FORMAT(/E14.7,1X,E14.7) 110 CONTINUE C C Current distribuitons on the 1st parasitic dipole C READ (3,100) NOEL2 DO 140 I=1,NOEL2 READ(3,120) CUR2(I) 140 CONTINUE C C Current distribuitons on the 2nd parasitic dipole C IF (N3.EQ.0) GO TO 502 READ (3,100) NOEL3 DO 140 I=1,NOEL3 READ(3,120) CUR3(I) 140 CONTINUE 502 CONTINUE C C Current distribution on the printed dipole C READ (3,100) NOEL4 DO 160 I=1,NOEL4 READ(3,120) CUR4(I) 160 CONTINUE C NSER=10 U= (WREAL/WIDTH)

-117 -U=ATAN (SQRT (1.0/(U*U) -1.0)) Ul=2.D0*U/FLOAT (NSER) DO 3 JN=1,NSER S2=2.DO*FLOAT (JN)-1.DO S2=S2/(2.DO*FLOAT(NSER)) S3=COS(S2*U) S (JN, 2) =S3*WIDTH/2.DO S (JN, 1) =U1 3 CONTINUE THMIN=-PI/2.0 THMAX=PI/2.0 MTHETA=201 DELTH= (THMAX-THMIN) /FLOAT (MTHETA-1) C DO 2 ITH=1,MTHETA THETA (ITH) =THMIN+FLOAT (ITH-1) *DELTH RTHETA(ITH) =180.00*THETA(ITH)/PI CALL EFIELD (THETA(ITH),FI,ETH,EFI) ACURR=CABS (CUR1 (IFEED)) IF (ICON.EQ.1) ACURR=CABS(CUR2 (IFEED)) ATH1=WREAL/WIDTH ATH1=ATAN (SQRT (1. / (ATH1*ATH1) -1.0)) ATH2=PI -ATH1 CURIN= (1.DO/PI) * (ATH2-ATH1) ACURR=ACURR*CURIN ARG(ITH)=(960.0/EER) * (CABS (ETH) **2+CABS (EEI) **2)/ACURR ALARG=10. 0*ALOG10 (ARG (ITH)) BLARG=180. 0*ITHETA (ITH)/PI BLARG=90. 0-ABS (BLARG) WRITE (6,4) BLARG,ARG(ITH),ALARG 4 FORMAT(10X,E14.8,5X,E14.8,5X,E14.8) 2 CONTINUE C........................................................................ C THIS PART FINDS THE MAXIMUM ELEMENT OF THE MATRIX ARG C........................................................................ KMAX=1 R1=ARG(1) M1=I+1 DO 6 K=2,MTHETA R2=ARG(K) IF (ABS(R2).LT.ABS(R1)) GO TO 6 R1=R2 KMAX=K 6 CONTINUE ANORM=ARG (KMAX) C C........................................................................ C THIS PART FINDS THE MINIMUM ELEMENT OF THE MATRIX ARG C........................................................................ LMAX=1 R1=ARG(1) DO 21 K=2,MTHETA R2=ARG(K) IF (ABS(R2).GT.ABS(R1)) GO TO 21 R1=R2 LMAX=K 21 CONTINUE BNORM=ARG (LMAX) /ANORM CNORM=10. 0*ALOG10 (BNORM) IF (ABS(CNORM).GE.ABS(SLOWER)) CNORM=SLOWER

-118 -C THIETA1 —HETA (KMAX) RMAX=10. D0*ALOG10 (ANORM) DO 15 I=1,MTHETA ARGUM=ARG (I) /ANORM SPOWER=10. 0*ALOG10 (ARGUM) IF (ABS (SPOWER). GT.ABS (SLOWER)) SPOWER=SLOWER RGAIN(I)=SPOWER XZ= (SPOWER-CNORM)/ABS (CNORM) X (I) =XZ*SIN (THETA (I) ) Y (I) =XZ*COS (THETA (I)) 15 CONTINUE RTHET1=180.00*THETA1/PI WRITE (6, 7) RTHET1,RMAX 7 FORMAT (10X, 'MAXIMUM GAIN OCCURS AT ANGLE: ',lX,E14.8,1X, *//10X, 'MAXIMUM GAIN IN DB: ',lX,E14.8////10X, 'ANGLE-THETA IN RAD', *10X, 'NORMALIZED GAIN IN DB',1OX, 'X-MATRIX',10X, 'Y-MATRIX'//) C C DO 8 I=1,201 WRITE (6,9) RTHETA(I),RGAIN(I) 9 FORMAT (10X,E14.8,10X,E14.8) 8 CONTINUE FC=ABS (CNORM)/DIV FC1=TCl/FC FC2=TC2/FC C........................................................................ C PLOTTING OF THE RADIATED POWER IN RECTANGULAR COORDINATES C....................................................................... C CALL PLOTS (0,0,0) C C CALL PLOT (0.,-2.,-13) C CALL PLOT (0.,3.,-13) C CALL PLOT (-2.,0.,-13) C CALL PLOT (3.,0.,-13) C CALL NEWPEN (1) C CALL SCALE (THETA,5.,201,1) C CALL SCALE (RGAIN,4.,201,1) C CALL AXIS(0.,0.,'ANGLE-THETA IN RADIANS',-22,5.,O0.,TETA(202),THE C *TA(203)) C CALL AXIS (O.,0.,'RADIATED POWER IN DB',20,4.,90.,RGAIN(202),RGAI C *N(203)) C CALL GRID (0.,0.,10,0.5,8,0.5,3333) C CALL NEWPEN (5) C CALL LINE (THETA,RGAIN,201, 1, 0,5) C CALL NEWPEN (1) C IF (IFI.EQ.0) CALL SYMBOL (0.,4.,0.15,' E-PLANE PATTERN ',0.,17) C IF (IFI.EQ.1) CALL SYMBOL (0.,4.,0.15,' H-PLANE PATTERN ',0.,17) C CALL PLOT(0.,O.,+999) C........................................................................ C PLOTTING OF RADIATED POWER IN POLAR COORDINATES C........................................................................ C DO 11 I=1,201 C XA(I)=SIN(THETA(I)) C XB(I)=XA(I)*(1.0-FC2) C XC(I)=XA(I)*(1.0-FC1) C YA(I)=COS(THETA(I)) C YB(I)=YA(I)*(1.0-FC2) C YC(I)=YA(I)*(1.0-FC1) C 11 CONTINUE

C C CALL PLOTS (0,0,0) C CALL FACTOR (0.5) C CALL PLOT (0.,-2.,-13) C CALL PLOT (0.,4.,-13) C CALL PLOT (-2.,0.,-13) C CALL PLOT (4.,0.01-13) C X(202)=-1.0 C X(203)=2.0/10. C Y(202)=Y(l) C Y(203)=1.0/5.0 C XA(202)=X(202) C XA(203)=X(203) C XB(203)=X(203) C XC(202)=X(202) C XC(203)=X(203) C YA(202)=Y(202) C YA(203)=Y(203) C YB(202)=Y(202) C YB(203)=Y(203) C YC(202)=Y(202) C YC(203)=Y(203) C C CALL NEWPEN (1) C CALL HLINE(0.,10.,0.,ZFFFF) C CALL VLINE (0.,5.,5.,ZFFEF) C CALL NEWPEN (5) C CALL LINE(X,Y,201,1,0,3) C CALL NEWPEN (1) C CALL L INE (XA, YA, 2 01,1, 0,3) C CALL L INE (XB, YB, 2 01, 1,0,3) C CALL LINE (XCYC,201,1,0,3) C C DO 12 I1=7 C ARGU=-PI/2.+PI *FLOAT (I-1) /6. C XPOS1 (I) =5. 5*SIN (ARGU) +5. C XPOS2 (I)=7.*SIN (ARGU) +5. C YPOS1 (I)=5. 5*COS (ARGU) C YPOS2 (I)=7.*COS (ARGU) C 12 CONTINUE C C DO 13 I=1,3 C ARG1=-~PI/2.+PI*FLOAT(I-1)/6.~PI/100. C ARG2=-ARG1 C XPOS3 (I) =6. 75*SIN (ARGi) +5. C YPOS3 (I) =6. 75*COS (ARGi) C XPOS4 (I) =5. 75*SIN(ARG2) +5. C 13 YPOS4(I)=5.75*COS(ARG2) C XPOS4(4)=4.8 C YPOS4 (4) =5.75 C C CALL PLOT (5.,0.,+13) C CALL PLOT (XPOS1 (1),YPOS1 (1),-'13) C CALL PLOT (XPOS2(1),.YPOS2(l),-f12) C CALL SYMBOL (XIPOS 3(1),YPOS 3(1) 0. 15, 'THETA= -9 0'0.9) C XPO=0.0 C YPO=-0.25 C C-ALL T SYMBnOL (XPOYPO,0n.15nODBn, —) C XPO=5.0*FC2 C YPO=-0. 25

-120 -C CALL SYMBOL (XPO,YPO,0.15.,'-lODB'.0..,5) C )CPO=5.0*FC1 C CALL SYMBOL (XPO.,YPO,0.15,1-20DB',0..,5) C C CALL PLOT (5.,0.,+13) C CALL PLOT (XPOSl(2),YPOSl(2),-'-13) C CALL PLOT (XPOS2(2).,YPOS2(2)..+12) C CALL SYMBOL (XPOS3(2),YPOS3(2),0.15, 'TF{ETA=-60',330.,,9) C C CALL PLOT (5.,0..+13) C CALL PLOT (XPOSl(3),YPOS1(3),-I13) C CALL PLOT (XPOS2(3),YPOS2(3),,~l2) C CALL SYMBOL (XPOS3(3),,YPOS3(3)~.0.l5, 'THETA=-30',300.,9) C C CALL PLOT (5.,0.,-i13) C CALL PLOT (X1POSl(4),,YPOS1(4),+l3) C CALL PLOT (XP052(4),YPOS2(4),+12) C CALL SYMBOL (XPOS4(4),YPOS4(4),0.15,'THETA=0' 90.,7) C C CALL PLOT (5.,0.,-i13) C CALL PLOT (XPOS1(5),YPOS1(5),,+13) C CALL PLOT (XPOS2(5).,YPOS2(5),+12) C CALL SYMBOL (XPOS4(3)2(YP054(3).,0.15. 'TEIETA=30',,60.,8) C C CALL PLOT (5..,0.,~13) C CALL PLOT (XPOSl(6),YPOSl(6),+13) C CALL PLOT (XPOS2(6),,YPOS2(6),,+12) C CALL SYMBOL (XPOS4(2),,YPOS4(2),O.15, 'THETA=601,30.,8) C C CALL PLOT (5.,0.,+13) C CALL PLOT (XPOSl(7),YPOSl(7).,~l3) C CALL PLOT (XPOS2(7).,YPOS2(7),,+l2) C CALL SYMBOL (XPOS4(l).,YPOS4(l),0.152'TBETA=901',0.,8) C XPO=10. C YPO=-0.25 C CALL SYMBOL (XPO,YPO,0.1520'DB'..0.,3) C XIPO=10.0-~5.0*FC2 C YPO=-0.25 C CALL SYMBOL (XIPO,YPO,0.151,'-10DB',0.,5) C XPO=10.0-~5.0*FCl C CALL SYMBOL (XPO,YPO,0.15,'1-20DB'..0.,5) C IF (IFI.EQ.0) CALL SYMBOL (2.,,7.8,,0.1521 E-PLANE PATTERN '.,0.4,7) C IF (IFI.EQ.l) CALL SYMBOL (2.,7.8.,0.l5,1 H-PLANE PATTERN ',0...17) C CALL SYMBOL (4.,f7.3,0.l5,#'ER=2.45 H=0.1l27 BS=0.088 W=O.c500',,oc., C *34) C CALL PLOTS (0.,0.,+999) 2000 CONTINUE STOP END C The name of this subroutine is: EFIELD C It evaluates the far field of a dipole SUBROUTINE EFIELD (THETA,El, ETHI, EFl) IMPLICIT RE-AL *4(A-H, O-Z) COMPLEX*8 W,WN,ETH3, EEI,WEL,WSL,WED,WSD,WTL,WTD,WNL,WND,WWE',WWS. *W8,CURl1(100),CUR2 (50),CUR3(50),CUR4(50),WND2,WND3,WNID4 *J WEP, WSP, WTP, WNP COMMON/DAT7P I.DLX, ER,EER, H,BS, CUR1, CUR 2,S (20, 2), WIDTHI

-121 -*WREAL, NSER, ICON, CUR3, CUR4 COMMON/PAR/OF 2, OF 3, OF4, NS, Ni, N2, N3, N4, A2, A3, A4, DEL C CKO=2. 0*PI CKK=CKO*SQRT(EER) ARG= (CKO*WIDTEI/2.DO) *SIN(FI) *SIN(THETA) CALL BESS(ARG,BJ) SSUM=0.DO DO 5 JN=i,NSER ARAF=CKO *S (JN, 2) *SIN (EI) *SIN (THETA) CAFF=COS (ARAF) SSUM=SSUM~S (JN, 1) *CAMF 5 CONTINUE TERMI= (BJ-SSUM/PI) C R1=CKO*SQRT (ER-SIN (THETA) **2) RSi=Ri/CKO R2=Ri *H R3=R2 Si=SIN (R2) SS1=SIN(Ri* (H-BS)) SS2=SIN(Ri *(H-DEL)) S2=Si S3=SIN (THETA) S4=SIN (FI) Ci=COS (R3) C2=COS (THETA) C3=COS (EI) C W=(0.0,1.0) WWF=C2*TERMI/ (C2*S2-W*RSi*Ci) WWS=S53*Cl*C2*TERMI/ ( (C2*S2-W*RSi*Ci) * (C2*ER*Ci~W*RSi*S2)) WFL=SS1 *WWFq WFP=SS2 *~WW WFD=Si*~WWF WSL=SSi*WWS WSP=SS2 *WWS WSD=S *WWS C WTL=C2*WFL+ (ER-i. 00) *S3*WSL WTP=C2*WFP+ (ER-i. 00) *S3*WSP WTD=C2*WFD+ (ER-i.00) *S3*WSD C C For the transmission line C WNL= (0. 0, 0.0) DO i I=i,Ni R8=CKO* (FLOAT (I) *DLX) *S3*C3 W8=COS (R8) ~SIN (R8) *W WNL=WNL+CURi(I) *W8 1 CONTINUE C C For dipole #2 C WND2=(0.0,0.0) DO 10 I=i,N2 R8=CKO* (FLOAT (I) *DLX) *S3*C3 W8=COS (R8) -sSIN(R8) *W WND2=WND2+CUR2 (I) *W8 10 CONTINUE

-122 -R8=CKO *A2 *S3*C3 W8=COS (R8) +SIN (R8) *W, WND2=WND2 *W8 R8=CKO *0F2 *S4*S3 W8=COS (R8) +SIN (R8) *W~ WND2=WND2 *W4 C C For dipole #3 C IF (N3.EQ.0) GO TO 503 WND3= (0.0,0.0) DO 11 I=1,N3 R8=CK0*FLOAT (I) *DLX*S3*C3 W8=COS (R8) +SIN (R8) *W WND3=WND3+CUR3 (I) *W8 11 CONTINUE R8=CKO *A3*S3*C3 W8=COS (R8) -iSIN (R8) *W WN3=WND3 *W8 R8=CKO*0F3*S4*S3 W8=COS (R8) +SIN (R8) *W WND34fWND3 *W8 C For dipole #4 C 503 CONTINUE WND4= (0.0,0.0) DO 12 I=1,PN4 R8=CKO*FLOAT (I) *DLX*S3*C3 W8=COS (R8) +SIN (R8) *1 WND4=WND4+C`UR4 (I) *W8 12 CONTINUE R8=CKO *A4*S3*C3 W8=COS (R8) +SIN (R8)*14 N44WNTD4 *W8 R8=CKO *0F4*S4*S3 W8=COS (R8) ~SIN (R8)*14 WND4=WNTD4*W8 C WNP=WND2 +WND3 IE(N3.EQ.0) WNP=WND2 WND=-WND4 C IE(ICON.EQ.1) WNL=(0.DO,0.DO) IF(ICON.EQ.-l) WND=(0.DO,0.DO) IF (ABS(FI).GT.1.E-4) GO TO 2 TR=ABS (ABS (ThETA) -PI/2. 0) IF (THER.GE.1.E-4) GO TO 2 IF (ABS(EER-1.00).LT.l.E-6) GO TO. 3 2 R6=COS (CKO*DLX*S3*C3) -COS (CKK*~DLX) R7=SIN(CKK*DLX) *(1.00- (CKO*S3*C3/CKK) **2) C ETFI=W* (-1.0) *C3*R6* (WL*WN+WP*WP+WTD*WND) /R7 EFI=W*S4*R6* (WFL*WNL+IWFP*WNP+WFD*WND) /R7 RETURN C 3 RIO=DLX*CKO/2.0 ETH= (-1.0) *C3* (WT*WN4'WTP*WNP~WflD*4NTD) *RlO EFI=S4* (WL*WN~WFP*WP+WFD*WND) *R1O C WRITE (6,4) ETHI,EFI

-123 -4 FORMAT (5X,'ETH=',(E14.8,5X,E14.8),5X,'EFI=',(E14.8,5X,E14.8)) C RETURN END * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * ***** C BESS C********************************** *************************************** SUBROUTINE BESS(X,BJ) IMPLICIT REAL*4 (A-H,O-Z) C PI=3.14159265358900 IF (X.GT.0.00100) GO TO 10 X3=X/3.00 X32=X3*X3 X34=X32*X32 X36=X34*X32 BJ=1.00-2.249999700*X32+1.265620800*X34-0.316386600*X36 GO TO 1 10 IF (X.GT.3.00) GO TO 12 X3=X/3.00 X32=X3*X3 X34=X32*X32 X36=X34*X32 X38=X36*X32 X310=X38*X32 X312=X310*X32 BJO=1.00-2.249999700*X32+1. 265620800*X34-0.316386600 * *X36+0.044447900*X38-0.003944400*X310+0.00021000 * 00*X312 BJ=BJO GO TO 1 12 CONTINUE X3=3.00/X X32=X3*X3 X33=X32*X3 X34=X33*X3 X35=X34*X3 X36=X35*X3 FJ0=0.7978845600-0.0000007700*X3-0.0055274000*X32-0.0000 * 951200*X33+0.0013723700*X34-0.0007280500*X35+0.00014 * 47600*X36 TJO=X-0.7853981600-0.0416639700*X3-0.0000395400*X32+0.00 * 26257300*X33-0.0005412500*X34-0.0002933300*X35+0.000 * 1355800*X36 WCON=SQRT(1.00/X) BJ=WCON*FJO*COS(TJO) 1 CONTINUE RETURN END

-124 - FOPTJON4_ ( OUTi / DOUT )

U. 2170000E+01 0. 1371154E+00 0. 1027047E+00 0. 1318417E-03 0. 1521250E-01 0.9536503E-01 0.3141593E+01 0. 1318417E-03........... Zll.. 25 0.4375703E-03 0.4372342E-03 0.4362269E-03 0.4345515E-03 0.4322130E-03 0.4292185E-03 0.4255770E-03 0.4212995E-03 0.4163987E-03 0.4108895E-03 0.4047883E-03 0. 3981133E-03 0. 3908846E-03 0. 3831235E-03 0. 3748532E-03 0. 3660982E-03 0. 3568842E-03 0. 3472384E-03 0. 3371890E-03 0. 3267654E-03 0. 3159978E-03 0. 3049174E-03 0. 2935560E-03 0. 2819462E-03 0. 2701209E-03............ Z31 130 0. 1197214E-03 0. 1196309E-03 0. 1193598E-03 0. 1189089E-03 -125 - -0.1661283E+01 0.3532292E+00 0.2472233E+00 0.9749434E-01 0.5504017E-01 0.3476495E-01 0.2315949E-01 0.1604274E-01 0.1160677E-01 0.8839811E-02 0.7027479E-02 0.5676763E-02 0.4544296E-02 0.3597179E-02 0.2886684E-02 0.2419244E-02 0.2112645E-02 0.1849440E-02 0.1561405E-02 0.1265194E-02 0.1023717E-02 0.8757187E-03 0.7982550E-03 0.7300448E-03 0.6270357E-03 -0.5197332E-02 -0.4600093E-02 -0.3074783E-02 -0.1220961E-02

0.1182795E-03 0.1174735E-03 0.1164933E-03 0.1153419E-03 0.1140227E-03 0.1125396E-03 0.1108971E-03 0.1091000E-03 0.1071537E-03 0.1050638E-03 0.1028367E-03 0.1004788E-03 0.9799706E-04 0.9539871E-04 0.9269133E-04 o.8988277E-04 o. 8698112E-04 o. 8399473E-04 o.8093213E-04 0.7780202E-04 o.746132 3E-04 o. 7137472E-04 o.6809551E-04 o. 6478465E-04 o.6145124E-04 o.5810433E-04 o. 5475293E-04 0.5140597E-04 o.4807227E-04 o.4476052E-04 o.4147921E-04 0.3823667E-04 0.3504097E-04 0.3189996E-04 0.2882119E-04 0.2581191E-04 0.2287906E-04 0.2002923E-04 0.1726862E-04 0.1460308E-04 0.1203805E-04 0.9578526E-05 0.7229109E-05 0.4993940E-05 0.2876706E-05 0.8806384E-06 -0.9915038E-06 -0.2737433E-05 -0.4355337E-05 -0.5843882E-05 -0.7202210E-05 -0.8429936E-05 -0.9527148E-05 -0. 1049439E-04 -0.1133268E-04 -0.11204345E-04 -0.1262861E-04 -0. 1309045E-04 -0.1343169E-04 -0. 1365545E-04 -126 -0.4122365E-03 0.1549654E-02 0.2172842E-02 0.2396465E-02 0.2362587E-02 0.2188393E-02 0.1953351E-02 0.1704640E-02 0.1467288E-02 0.1252935E-02 0.1065655E-02 0.9053170E-03 0.7695368E-03 0.6549821E-03 0.5583032E-03 0.4766426E-03 0.4077025E-03 0.3495403E-03 0.3003695E-03 0.2585427E-03 0.2226798E-03 0.1917731E-03 0.1651376E-03 0.1422379E-03 0.1225339E-03 0.1054588E-03 0.9051556E-04 0.7737407E-04 0. 6586448E-04 0.5587287E-04 0.4723490E-04 0.3971903E-04 0.3310098E-04 0.2724763E-04 0.2212755E-04 0.1774105E-04 0.1403868E-04 0. 1090304E-04 0.8204418E-05 0.5871302E-05 0.3907480E-05 0.2342382E-05 0.1165070E-05 0. 3043443E-06 -0.3298236E-06 -0.7868898E-06 -0.1055813E-05 -0.1101321E-05 -0.9191041E-06 -0.5569956E-06 -0.8437438E-07 0.4581213E-06 0.1079714E-05 0.1812920E-05 0.2666986E-05 0.3606538E-05 0.4574481E-05 0.5535256E-05 0.6496413E-05 0.7489060E-05

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0.3273687E-05 0.3150827E-05 0.30132 28E-05 0.2861678E-05...................... Z21 26 0.3070108E-03 0.3067773E-03 0.3060775E-03 0.3049135E-03 0.3032889E-03 0. 3012084E-03 0. 2986784E-03 0.2957065E-03 0.2923014E-03 0. 2884735E-03 0.2842341E-03 0.2795959E-03 0.2745726E-03 0.2691792E-03 0.2634316E-03 0.2573468E-03 0.2509427E-03 0.2442379E-03 0.2372521E-03 0.2300057E-03 0. 2225195E-03 0.2148150E-03 0.2069145E-03 0.1988404E-03 0.1906156E-03 0.1822631E-03...................... Z22 25 0.2156319E-03 0.2154694E-03 0.2149826E-03 0.2141729E-03 0.2130427E-03 0.2115954E-03 0.2098353E-03 0.2077677E-03 0.2053987E-03 0.2027355E-03 0.1997859E-03 0.1965586E-03 0.1930634E-03 0.1893104E-03 0.1853107E-03 0.1810761E-03 0.1766191E-03 0.1719525E-03 0.167090 OE-03 0.1620457E-03 0.1568341E-03 0.1514701E-03 0.1459691E-03 0. 1403466E-03 0.1346185E-03...........e...........Z32 -130 -0.7104707E-05 0.4457888E-06 -0.5131084E-05 -0.4832633E-05 -0.5240 316E-01 -0.3716714E-01 -0.9469705E-02 0. 8399848E-02 0.1449135E-01 0.1455873E-01 0. 1259615E-01 0.1031939E-01 0.8313972E-02 0.6708082E-02 0. 5456517E-02 0.4467567E-02 0. 3665454E-02 0.3009858E-02 0. 2484292E-02 0.2073846E-02 0.1752953E-02 0.1490432E-02 0.1263105E-02 0.1063669E-02 0.8959795E-03 0. 7631298E-03 0.6593909E-03 0.5722814E-03 0.4913286E-03 0.4146210E-03 -0.1212243E-401 0.2567733E+00 0.1797817E~00 0.7149411E-01 0.4123373E-01 0.2666213E-01 0.1802873E-01 0.1254659E-01 0.9106259E-02 0.7017869E-02 0.5677413E-02 0.4622736E-02 0.3648396E-02 0.2787972E-02 0.2158871E-02 0.1796604E-02 0.1603533E-02 0.1428847E-02 0.1188040E-02 0.9122948E-03 0.6942644E-03 0.5905598E-03 0.5708609E-03 0,r.516402EA n-03-^ - 0.4738459E-03

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-0.7924815E-05 -o.8348444E-05 -0.8686603E-05 -0.8941151E-05 -0.911422OE-05 -0.9208202E-05 -0.9225733E-05 -0.9169688E-05 -0.9043158E-05 -0.8849440E-05 -0.8592020E-05 -0.8274555E-05 -0.7900860E-05 -0. 7474887E-05 -0.7000710E-05 -0.6482505E-05 -0.5924533E-05 -0.5331123E-05 -0.4706649E-05 -0.4055518E-05 -0.3382147E-05 -0.2690947E-05 -0.1986302E-05 -0.1272557E-05 -0.5539957E-06 0.1651747E-06 0.8808392E-06 0.1588992E-05 0.2285749E-05 0.2967368E-05 0. 3630255E-05 0.4270983E-05 0.4886302E-05 0.5473148E-05 0.6028658E-05 0.6550176E-05 0.7035263E-05 0.7481702E-05 0.7887508E-05 0.8250930E-05 0.8570457E-05 0.8844822E-05 0.9073000E-05 0.9254215E-05 0. 9387934E-05 0.9473870E-05 0.9511978E-05 0.9502454E-05 0.9445725E-05 0. 9342453E-05 0.9193519E-05 0.9000022E-05 0.8763273E-05 0.8484777E-05 0. 8166234E-05 0.7809523E-05 0.7416691E-05 -132 -0.5582907E-05 0.6330278E-05 0.6738780E-05 0.6982085E-05 0.7396274E-05 0.8149983E-05 0.9090107E-05 0.9900275E-05 0. 1040644E-04 0.1073196E-04 0.1116109E-04 0.1185333E-04 0.1268767E-04 0.1338084E-04 0.1375754E-04 0.1391015E-04 0.1410 006E-04 0.1450311E-04 0.1504558E-04 0.1548231E-04 0.1563351E-04 0.1555046E-04 0.1545655E-04 0.1552845E-04 0.1573047E-04 0.1585587E-04 0.1572751E-04 0.1536221E-04 0.1494680E-04 0.1465766E-04 0.1450067E-04 0.1431939E-04 0.1395282E-04 0. 1338515E-04 0.1274819E-04 0.1218607E-04 0.1172154E-04 0.1125122E-04 0.1066292E-04 0.9950179E-05 0.9210385E-05 0.8536643E-05 0.7920651E-05 0.7268076E-05 0.6508315E-05 0.5681192E-05 0.4905795E-05 0.4258939E-05 0.3688104E-05 0.3054941E-05 0.2275284E-05 0.1418686E-05 0.6610227E-06 0.1240331E-06 -0.2485011E-06 -0.6530843E-06 -0.1251186E-05

-133 - FOPTJON5_ (RESULT )

-134 - 1 A strip dipole at the interface EM coupled to another printed dipole in the dielectric which is excited by a ER= 0.2170000E~01 BS= 0.6972045E-01 T2=-0.4745267E-76 W= 0.6473798E-01 OFFSET=-0.4745267E-76 DELTA=-0.4745267E-76 H= 0.9307998E-0l T1= 0.8949997E-04 DLX= 0.1521250E-01 WDELTA= 0.8949997E-04 ZIN= 0.1390856E+02 -0.1946242E~02 Current distribution on the t.l. CURR ( CURR ( CURR ( CURR ( CURR ( CURR CURR CURR ( CURR ( CURR CURR CURR ( 1) = 2) = 3) = 4) = 5) = 6) = 7) = 8) = 9) = ( 11)> = ( 12) - o.5529810E-02, 0.7913578E-02, 0.1035526E-O1, 0.1256970E-Ol, o. 1463460E- Oll 0.1653551E-01, 0.1826459E-0l, 0.1981271E-01, 0.2117016E-01, 0.2232717E-0l, 0.2327523E-01, 0.2400661E-01, 0.6086718E-02 o. 8723304E-02 0.1142906E-01 0.1389077E-Ol 0.1 619454E-OL 0.1832530E-01 0.2027472E-01 0.2203275E-01 0.2358915E-0l 0.2493553E-01 0.2606709E-01 0.2698093E-01 0.8223556E —02 0.1177797E —Ol o. 1542 254E- 01 0. 1873368E-O1 0.2182738E-01 0.2468278E-01 0.2728845E-01 0.2963082E-01 0.3169580E-01 0.3347063E-01 0.3494609E-01 0.3611492E-01

CURR CURR CUPRR CURR CURR CURR CURR CURER CURR. CURR. CURR CURE. CURE. CURE. CURE. CURE. CURE. CURE. CURE. CURE. CURR. CURE. CURE. CURE. CURE. CURE. CURE. CURR CURE. CURE. 13) = 15) = ( 22) = 25) = 30) = 31) = ( 0.2451679E-01, 0.2480210E-01, 0. 2486178E-01, 0. 2469550E-01, 0.2430572E-01, 0.2369601E-01, 0.2287227E-01, 0.2184313E-01, 0.2061787E-01, 0.1920843E-01, 0.1762706E-01, 0. 1588852E-01, 0.1400849E-01, 0. 1200465E-01, 0. 9895012E-02. -135 -0.2768240E-01 0.2816359E-01 0.2860489E-01 0.2839100E-01 0. 3401132E-01 0.2534669E-01 0.2254402E-01 0.1914320OE-01 0.1578638E-01 0.1232169E-01 0.8782301E-02 0.5188957E-02 0.1567575E-02 -0.2054288E-02 -0.5646870E-02 0.3697821E-01 0.3752775E1-01 0.3789918E7-01 0.3762867E7-01 0.4180356E-01l 0.34698061>01O 0.3211500E-01l 0.2904452E-01 0.2596740E-01l 0.2282077E-01l 0.1969370E7-01 0.1671436E"-01 0.1409592E"-01 0.1217915E"-01 0.1139291E"-01 0.1198000EI'-01 0.1374011E.-01 0.1624136E'-01 0.1912 256E-01 0.2215095EI-01 0.2518284E:-01 0.2812261E:-01 0.3090466E:-01 0.3347825E:-01 0.3580449E:-01 0.3785237E-01 0.3959512E.-01 0.4101305E-01 0.4208855E-01 0.4281049E-01 0.7698670E-02, -0.9178828E-02 0.5435623E-02, -0.1261922E-01 0. 3126045E-02, -0.1593769E-01 0.7909655E-03,.-0.1910619E-01 32) =(-0. 1548504E-02, -0. 2209676E-01 33) =(-0. 3871198E-02, -0. 2488352E-01 34) =(-0. 6156076E-02, -0. 2744056E-01 35)=(-0.8382879E-02, -0.2974601E-01 36) =(-0.1053148E-01, -0.3177864E-01 37) =(-0. 1258259E-01, -0.3352074E-01 38) =(-0.1451793E-01, -0.3495757E-01 39) =(-0.1631971E-01, -0.3607548E-01 40) =(-0.1797234E-01, -0.3686550E-01 41) =(-0.1946057E-01. -0.3731932E-01 42) =(-0.2077153E-01, -0.3743370E-01

CURR CURR CURR CURR CURR CURR CURR CURR CURR CUIRR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR -136 -43) =(-0.2189320E-Ol, -o. 3720727E-O1 44) =(-0. 2281630E-0l, -o. 3664362E-01 45) =(-0.2353165E-01, -o. 3574622E-01 46)=(-0.2403376E-O1. -O.3452448E-01 47) =(-0.2431779E-Ol, -o. 3298843E-01 48) =(-0. 2438155E-Ol, -o. 3115239E-Ol 49) =(-0. 2422509E-0l, -o. 2903360E-Ol 50) =(-0.2384919E-O1l -0. 2665045E-O1 51) =(-0. 2325809E-01, -O.2402529E-Ol 52) =(-0. 2245648E-01, 53) =(-0. 2145283E-01, 54) =(-0. 2025533E-01, 55) =(-0. 1887581E-01, 56) =(-0. 1732635E-01L 57) =(-0. 1562117E-01, 58) =(-0. 1377605E-01, 59) =(-0. 1180728E-01, 60) =(-0. 9733178E-02, 61) =(-0. 7572234E-02, 62) =(-0.5344339E-02, 63) =(-0. 3069290E-02, 64) =(-0. 7677733E-03, 65)=( 0.1539489E-02, 66)=( 0.3831622E-02, 67)=( 0.6088078E-02, 68)=( 0.8288421E-02, 69)=( 0.1041317E-01, 70)=( 0.1244302E-01, 71)=( 0.1436022E-01, 72)=( 0.1614732E-01, -0. 2118091E-01 -0.1814394E-01 -0.1494094E-01 -0.1160165E-01 -0.8156050E-02 -0.4635349E-02 -0. 1071388E-02 0. 2503756E-02 0.6057687E-02 0. 9557996E-02 0. 1297331E-01 0.1627221E-01 0.1942547E-01 0.2240423E-01 0.2518150E-01 0.2773252E-01 0.3003322E-01 0.3206373E-01 0.3380474E-01 0.3524167E-01 0.3636054E-01 0.4317050E-01 0.4316641-E-01 0.4279638E-01 0.4206615)E-01 0.4098281.E-01 0.3955921E-01 0.3781276,E-01 0.3576353E-01 0.3343879E-01 0.3086947E-01 0.2809673E-01 0. 2516963E-01 0.22156131E-01 0.19150 03E-01 0. 1629440E-01l 0.1381765E-01l 0.1206982E1 —01 0.1146431E-01 0.1219401E-01 0.140 3099E-01 0.1655915EI-01 0. 1944063E.-01 0.2245706E-01 0.2547134E:-01 0. 2839291E,-01 0.3115594E-01 0.3371227E-01 0. 3602207E-01 0.3805510E-01 0.3978472E-01

CURR CURR CURR CURR CURR CURR CUPRR CURR CURR CURR CURR CURR CURR CURR CURR CUPR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CUIRR CURR CURR 74) = 77) =( 79) =( 80) =( 81) =( 782) = 83) =( 85) =( 86) = 87) = 88) = 90) =( 91) =( 92) =( 93) = 94) = 895) = 96) =( 97) =( 0.1778847E-01, 0.1926944E-01, 0.2057667E-014 0. 2169960E-01, 0.2262778E-01,1 0.2335395E-01, 0.2387122E-01, 0. 2417680E-01, 0. 2426766E-01, 0. 2414458E-01, 0. 2380930E-01, 0. 2326557E-01, 0. 2252033E-01, 0.2158127E-01, 0.2045841E-01, 0.1916457E-01, 0. 1771324E-01, 0.1612000E-01, 0.1440319E-01, 0.1258180E-01, 0.1067721E-01, 0.8712891E-02, 0. 6713960E-02, 0.4707947E-02, 0. 2725505E-02, 0.8004336E-03, -137 -0.3715133E-01 0. 3760728E-01 0.3772321E-01 0.3749960E-01 0.3693730E-01 0. 3604240E-01 0. 3482158E-01 0.3328777E -01 0.3145348E-01 0.2933664E-01 0.2695629E-01 0.2433395E-01 0.2149462E-01 0.184640 OE-01 0.1527042E-01 0.1194447E-01 0.8517347E-02 0.5021736E-02 0. 1491607E-02 -0. 2038496E-02 -0.5532678E-02 -0. 8954588E-02 -0.1226678E-01 -0. 1543095E-01 -0. 1840834E-01 -0. 2115661E-01 -0. 2363015E-01 -0.2577736E-01 -0. 2753685E-01 -0.2883789E-01 0.4119042E-01 0.4225658E-01 0.4297022SE-01 0.4332542E-01 0.4331721.E-01 0.4294719E-01 0.4221822E-01 0.4114114E-01 0. 3972708E-01 0. 3799473E-01 0.3596560E-01 0.3366642E-01 0. 3113171E-01 0.2840194'E-01 0.2552905E-01 0.2258209E-01 0.1965462E-01 0.1688408E7-01 0.1448022E7-01 0.1274586E7-01 0.1202553E-01 0.1249396E-01 0.1398396E-01 0.1613317E.-01 0.1860902E.-01 0.2117174FE-01 0.2365251E:-01 0.2591992E-01 0.2785612E,-01 0.2934601E-01 99) =(-0.1028201E-02, 100) =(-0. 2714849E-02, 101) =(-0.4205409E-02,1 102) =(-0.5437352E-02,1

CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR -138 -103)=(-0.6348044E-02. -0.2960837E-01 104)=(-0.6900232E-02, -0.2980108E-01 105)=(-0.7117171E-02,1-0.2943631E-01 106) =(-0.7079169E-02, -0.2860190E-01 107)=(-0.6871171E-02,f-0.2739449E-01 108)=(-0.6548587E-02, -0.2588402E-01 109)=(-0.6139353E-02,f-0.2411075E-01 110)=(-O.5658176E-02, -O.2210324E-01 111)=(-0.5113490E-02,-0.1988231E-01 112)=(-0.4512072E-02. -O.1746885E-01 113)=(-0.3859175E-02,-0.1488047E-01 114) =(-0.3162184E-02, -0.1214405E-01 115)=(-0.2401073E-02,-0.9183709E-02 116) =(-0.1663873E-02, -0.6333020E-02 0.3028124E-01l 0.3058950E7-01 0.3028449E7-01 0.2946495E1 —01 0.2824306E7-01 0.2669955E-01-O 0.2488011E-01 0.2281597E7-01 0.2052934E-01 0. 18042151E-01 0.1537275E"-01 0.12548991E-01 -0.94923971E-02 0.6547946E7-02 Current on the first parasitic dipole CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR 117)=(-0.7535733E-02, -0.8758638E-02 118) =(-0.1014305E-01, -0.1219982E-01 119) =(-0.1276311E-01, -0.157152.?6E-01 120) =(-0.1505901E-01, -0.1888525E-01 121) =(-0.1717950E-01, -0.2185617E-01 122) =(-0.1911406E-01, -0. 2460676E-01 123) =(-0.2085138E-01,-0.27~L1692E-01 124) =(-0.2237806E-01. -0.2936493E-01 125) =(-0.2368199E-01, -0.3132947E-01 126) =(-0.2475377E-01, -0.3298987E-01 127) =(-0.2558015E-01, -0.3431433E-01 128) =(-0.2614281E-01, -0. 3525246E-01 0.1155426E-01 0.1586559E-01 0.2024516E:-01 0.241542 2E:-01 0.2779977E:-01 0.3115830E:-01 0.342 0683E:-01 0.3691987E:-01 0. 3927305E:-01 0.4124416E:-01 0.4279973E,-01 0.4388829E-01

CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR CURR -139 -129) =(-0.2642066E-01, -o. 3573780E-01 130) =(-0.2639570E-01, -0. 3571354E-O1 131) =(-0.2606665E-O1, -O. 3517430E-O1 132) =(-0.2544660E-01, -0. 3416147E-01 133) =(-0.2455183E-01, -O. 3272875E-O1 134) =(-0. 2339638E-O1, -0. 3092249E-O1 135) =(-0.2199185E-O1, -O. 2877880E-O1 136) =(-0.2034729E-O1, -0. 2632468E-01 137) =(-0.1847406E-01, -0.2358643E-01 138) =(-0. 1637485E-01, -0. 2057878E-01 139) =(-0. 1405190E-01, -0. 1731761E-01 140) =(-0.1131796E-01, -0.1361610E-01 141)=(-0.8545324E-02,-0.9938192E-02 0.4444368E-01 0.4440934E-01 0.4378016E-01 0.4259736E-01 0.4091409E-01 0.3877617E-01 0.3621962E-01 0.3327162E-01 0.2996015E-01 0.2629870E-01 0.2230147E-01 0.1770577]E-01 0.1310688E7-01 Current on the second parasitic dipole CUJRR CURR CURR CUPRR CURR CURR CURR CURR CURR CURR CURR CURR CURR 142)=(-0.4317302E-02, -0.1699954E-02 143)=(-0.5430728E-02,-0.1728756E-02 144)=(-0.6494038E-02, -0.1697618E-02 145)=(-0.7342964E-02, -0.1578550E-02 146)=(-0.8093011E-02, -0.1447108E-02 147)=(-0.8752242E-02,#-0.1316910E-02 148) =(-0.9327009E-02, -0.1197289E-02 149)=(-0.9818468E-02, -0.1093740E-02 150) =(-0.1022789E-01, -0.1010995E-02 151)=(-0.1055577E-01, -0.9528201E-03 152)=(-0. 1080253E-01, -0.9221481E-03 153) =(-0.1096762E-01, -0.9207914E-03 154) =(-0.1104936E-01,-0.9493500E-03 0.4639927E7-02 0. 5699243E-02 0.6712258E-02 0.7510722E:-02 0.8221366E:-02 0.8850761E:-02 0.9403542E:-02 0.9879194E:-02 0.1027773EI-01 0. 1059868E-01 0. 1084182E-01 0.110 0621E-01 0.11090 06E-01

CURR ( CURRE( CURR ( CURR ( CURR ( CURRE. CURRE. CURRE. CURRE. CURRE. CURRE. CURE.( -140 -155) =(-0. 1104738E-01 -o0. 1007952E-02 156) =(-0.1096119E-01, -o0.1095505E-02 157) =(-0. 1079034E-01 -o0. 1209857E-02 158) =(-0.1053413E-O1, -o0.1347447E-02 159) =(-0.1019086E-01, -o0.1503473E-02 160)=(-O.9757549E-02. -0.1671682E-02 161) =(-0. 9231780E-02 -o0. 1845369E-02 162)=(-0.8610032E-02, -0.2016632E-02 163)=(-0.7884189E-02,-0.2173728E-02 164) =(-0.7042494E-02 -o0. 2299465E-02 165)=(-0.5952518E-02, -0.2299824E-02 166) =(-0.4793983E-02, -o. 2219521E-02 o0.1109327E-01 o0.1101580E-O1 o0.1085795E-01 o0.1061996E-O1 o0.1030116E-O1 0.9899706E-02 o0.9414405E-02 0.8843042E-02 0.8178353'E-02 0.7408388'E-02 0. 6381352]E-02 0.5282853E"-02

-141 - FOPTION6_ (RESGN

-142 - 116 0.5529810E-02 0.7913578E-02 0.1035526E-01 0.1256970E-01 0.1463460E-01 0.1653551E-01 0.1826459E-01 0.1981271E-01 0.2117016E-01 0.2232717E-01 0.2327523E-01 0.2400661E-01 0.2451679E-01 0.2480210E-01 0.2486178E-01 0.2469550E-01 0.2430572E-01 0.2369601E-01 0.2287227E-01 0.2184313E-01 0.2061787E-01 0.1920843E-01 0.1762706E-01 0.1588852E-01 0.1400849E-01 0.1200465E-01 0.9895012E-02 0.7698670E-02 0.5435623E-02 0.3126045E-02 0.7909655E-03 -0.1548504E-02 -0.3871198E-02 -0.6156076E-02 -0.8382879E-02 -0.1053148E-01 -0.1258259E-01 -0.1451793E-01 -0.1631971E-01 -0.1797234E-01 -0.1946057E-01 -0.2077153E-01 -0.2189320E-01 -0.2281630E-01 -0.2353165E-01 -0.2403376E-01 -0.2431779E-01 -0.2438155E-01 -0.2422509E-01 -0.2384919E-01 -0.2325809E-01 -0.2245648E-01 -0.2145283E-01 -0.2025533E-01 -0.1887581E-01 -0.1732635E-01 -0.1562117E-01 -0.1377605E-01 -0.1180728E-01 0.6086718E-02 0.8723304E-02 0.1142906E-01 0.1389077E-01 0.1619454E-01 0.1832530E-01 0.2027472E-01 0.2203275E-01 0.2358915E-01 0.2493553E-01 0.2606709E-01 0.2698093E-01 0.2768240E-01 0.2816359E-01 0.2860489E-01 0.283910OE-01 0.3401132E-01 0.2534669E-01 0.2254402E-01 0.1914320E-01 0.1578638E-01 0.1232169E-01 0.8782301E-02 0.5188957E-02 0.1567575E-02 -0.2054288E-02 -0.5646870E-02 -0.9178828E-02 -0.1261922E-01 -0.1593769E-01 -0.1910619E-01 -0.2209676E-01 -0.2488352E-01 -0.2744056E-01 -0.2974601E-01 -0.3177864E-01 -0.3352074E-01 -0.3495757E-01 -0.3607548E-01 -0.3686550E-01 -0.3731932E-01 -0.3743370E-01 -0.3720727E-01 -0.3664362E-01 -0.3574622E-01 -0.3452448E-01 -0.3298843E-01 -0.3115239E-01 -0.2903360E-01 -0.2665045E-01 -0.2402529E-01 -0.2118091E-01 -0.1814394E-01 -0.1494094E-01 -0.1160165E-01 -0.8156050E-02 -0.4635349E-02 -0.1071388E-02 0.2503756E-02

-0.9733178E-02 -o. 7572234E-02 -o. 5344339E-02 -0.3069290E-02 -0.7677733E-03 0.1539489E-02 0.3831622E-02 0.6088078E-02 0.8288421E-02 0.1041317E-01 0.1244302E-01 0.1436022E-01 0.1614732E-01 0.1778847E-01 0.1926944E-01 0.2057667E-01 0.2169960E-01 0.2262778E-01 0.2335395E-01 0.2387122E-01 0.2417680E-01 0.2426766E-01 0.2414458E-01 0.2380930E-01 0.2326557E-01 0.2252033E-01 0.2158127E-01 0.2045841E-01 0.1916457E-0i 0. 1771324E-01 0.1612000E-01 0.1440319E-01 0.1258180E-01 0.1067721E-01 0.8712891E-02 0.6713960E-02 0.4707947E-02 0.2725505E-02 0.8004336E-03 -0.1028201E-02 -0. 2714849E-02 -0.4205409E-02 -0.5437352E-02 -0.6348044E-02 -0.6900232E-02 -0.7117171E-02 -0. 7079169E-02 -0.6871171E-02 -0.6548587E-02 -0.6139353E-02 -0.5658176E-02 -0.5113490E-02 -0.4512072E-02 -0.3859175E-02 -0.3162184E-02 -0.2401073E-02 -0.1663873E-02 25 -0.7535733E-02 -0.1014305E-01 -143 -0.6057687E-02 0.9557996E-02 0.1297331E-01 0.1627221E-01 0.1942547E-01 0.2240423E-01 0.2518150E-01 0.2773252E-01 0.3003322E-01 0.3206373E-01 0.3380474E-01 0.3524167E-01 0. 3636054E-01 0.3715133E-01 0.3760728E-01 0.3772321E-01 0.3749960E-01 0.3693730E-01 0.3604240E-01 0.3482158E-01 0.3328777E-01 0.3145348E-01 0.2933664E-01 0.2695629E-01 0.2433395E-01 0.2149462E-01 0.184640OE-01 0.1527042E-01 0.1194447E-01 0.8517347E-02 0.5021736E-02 0.1491607E-02 -0.2038496E-02 -0.5532678E-02 -0.8954588E-02 -0.1226678E-01 -0.1543095E-01 -0.1840834E-01 -0.2115661E-01 -0.2363015E-01 -0.2577736E-01 -0.2753685E-01 -0.2883789E-01 -0.2960837E-01 -0.2980108E-01 -0. 2943631E-01 -0.2860190E-01 -0.2739449E-01 -0.2588402E-01 -0.2411075E-01 -0.2210 324E-01 -0.1988231E-01 -0.1746885E-01 -0.1488047E-01 -0.1214405E-01 -0.9183709E-02 -0.6333020E-02 -0.8758638E-02 -0.1219982E-01

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-145 - FOPTJON7 (MUTUAL

-146 -C The name of this file is.............. MUTUAL................. C It solves for the mutula coupling between two dipoles C excited by microstrip transmission lines embedded in the C dielectric. C C It also solves for the bandwidth of a dipole printed on a C dielectric substrate and excited by a microstrip transmission C line embedded in the dielectric in the presence of two other C parasitics on the same level of the transmission line C******************************************************************** IMPLICIT REAL*4 (A-H,O-Z) COMPLEX*8 CUR(170,3) COMPLEX*8 BMATR,Z11(100),Z44(100),Z12(200),Z23(200),Z34(200), *Z24(200),Z14(200),Z13(200) DIMENSION IB(160),IA(160),IDATA(10),RDATA(20) COMMON/MAN/BMATR(160,160) C.................................................................. C DATA C.................................................................. DO 180 ID=1,10 READ (1,100) IDATA(ID) 180 CONTINUE NOEL1=IDATA(1) NOEL2=IDATA(2) NOEL3=IDATA(3) NOEL4=IDATA(4) NS12=IDATA(5) NS23=IDATA(6) NS34=IDATA(7) NOR=IDATA(8) NFEED1=IDATA(9) NFEED4=IDATA(10) WRITE (6,222) NOEL1,NOEL2,NOEL3,NOEL4,NS12,NS23,NS34 222 FORMAT (10X, 'NOEL1=',I4/10X, 'NOEL2=',I4/10X, 'NOEL3=',I4/ *10X,'NOEL4=',I4/O1X,'NS12=',I4/10X,'NS23=',I4/10X, 'NS34=', *I4,//////) 100 FORMAT(10X,14) DO 190 ID=1,11 READ(2,200) RDATA(ID) 190 CONTINUE ER=RDATA (1) H=RDATA(2) BS=RDATA(3) T=RDATA (4) DLX=RDATA(5) W=RDATA(6) OF12=RDATA(7) OF34=RDATA(8) DIEL=RDATA(9) PI=RDATA(10) WDELTA=RDATA (11) 200 FORMAT(1OX,E14.7) READ(2,310) N44 310 EORMAT(/11X,I4) WRITE (6,330) 330 FORMAT(/, '**************************************************' DO 500 I=1,N44 READ(2,400) Z44(I) C WRITE (6,320) I,Z44(I)

-147 -320 FORMAT (2X, 'Z44(',14,')=',E14.7,3X,E14.7) 500 CONTINUE READ(2,310) N14 DO 510 I=1,N14 READ(2,400) Z14(I) C WRITE (6,321) I,Z14(I) 321 FORMAT(2X, 'Z14(', 4, ')=',E14.7, 3X, E14.7) 510 CONTINUE READ(2,310) Nll DO 520 I=1,Nll READ(2,400) Zll(I) C WRITE (6,322) I,Z11(I) 322 FORMAT(2X, 'Z11 (', I14, ')=',E14.7, 3X, E14.7) 520 CONTINUE NOEL2 3=NOEL 2 +NOEL 3 IF (NOEL23.EQ.0) GO TO 299 READ (2,310) N12 DO 530 I=1,N12 READ (2,400) Z12(I) Z13 (I) =Z12 (I) C WRITE (6,323) I,Z12(I) 323 FORMAT(2X, 'Z12(',14,')=',E14.7,3X,E14.7) 530 CONTINUE READ (2,310) N24 DO 540 I=1,N24 READ(2,400) Z24(I) C WRITE (6,324) I,Z24(I) 324 FORMAT(2X,'Z24(',I4, ')=',E14.7,3X,E14.7) 540 CONTINUE READ (2,310) N23 DO 550 I=1,N23 READ(2,400) Z23(I) C WRITE (6,325) I,Z23(I) 325 FORMAT (2X, 'Z23(',I4, ')=',E14.7,3X, E14.7) 550 CONTINUE READ (2,310) N34 DO 560 I=1,N34 READ(2,400) Z34(I) C WRITE (6,326) I,Z34(I) 326 FORMAT(2X, 'Z34(',I4, ')=',E14.7,3X, E14.7) 560 CONTINUE 299 CONTINUE 400 FORMAT (11X,E14.7,4X,E14.7) H=H/SQRT (ER) BS=BS/SQRT (ER) T=T/SQRT (ER) W=W/SQRT (ER) OF12=OF12/SQRT (ER) OF34=OF34/SQRT (ER) DI EL=DI EL/SQRT (ER) WDELTA=WDELTA/SQRT (ER) C WRITE (6,1) 1 FORMAT (//'',10X, 'Mutual coupling between two strip dipoles' */10X,'excited by two embedded transmission lines'/lOX,'OR'/ *10X,'Bandwidth of a printed dipole in the presence of two'/ *10X, 'parasitics on the same plane with thw embedded line'/// */) WRITE (6, 3) ER,H, BS,T,W, OF12, OF34,DIEL,WDELTA, DLX

-148 -3 FORMAT(/10X,'ER=', E14.7/10X,'H=',E14.7/10X,'BS=',E14.7/10X, 'T=' *,El4.7/10X, 'W=',El4.7/10X,'OFFSET12=',E14.7/10X,'OFFSET34=', *El4.7/10X,'DIEL=', El4.7/10X, 'WDELTA=',El4.7/10X,'DLX=',E14.7 C C..... First Diagonal Matrix........ C IMIN=1 IMAX=NOEL1 DO 4 I=IMIN,IMAX IXN=0 DO 5 KI=I,IMAX IXN=IXN+l BMATR(IXN,KI)=Zll (I) BMATR (KI, IXN) =BMATR (IXN, KI) 5 CONTINUE 4 CONTINUE IF (NOEL23.EQ.0) GO TO 300 C C....... Second Diagonal Matrix........ C C INI =NOEL1 IMIN=NOEL1+1 IMAX=NOEL1+NOEL 2 DO 6 I=IMIN,IMAX IXN=INI DO 7 KI=I,IMAX IXN=IXN+l BMATR(IXN,KI)=Zll (I-INI) BMATR (KI, IXN) =BMATR (IXN, KI) 7 CONTINUE 6 CONTINUE C C......Third Diagonal Matrix..... C C INI=NOEL1+NOEL2 IMIN=INI+l IMAX=INI+NOEL3 DO 8 I=IMIN,IMAX IXN=INI DO 9 KI=I,IMAX IXN=IXN+l BMATR(IXN, KI)=Zll1 (I-INI) BMATR (KI, IXN) =BMATR (IXN, KI) 9 CONTINUE 8 CONTINUE 300 CONTINUE C C.....Fourth Diagonal Matrix..... C C INI=NOEL1 +NOEL2+NOEL3 IMIN=INI+1 IMAX=INI+NOEL4 DO 10 I=IMIN,IMAX IXN=INI DO 11 KI=I,IMAX IXN=IXN+l

-149 -BMATR (IXN, KI) =Z44 (I -INI) BMATR (KI, IXN) =BMATR (IXN, KI) 11 CONTINUE 10 CONTINUE IF (NOEL23.EQ.0) GO TO 301 C C...1... First off-diagonal matrix C C 1) Upper Part C IAI =NOEL1 -NOEL2 IMI=IABS (IAI) +1 IMIN=NOEL1+1 IMAX=NOEL1 +NOEL 2 DO 12 I=IMIN,IMAX IXN=0 LXN=NS12+I - IMIN IF (IAI.LT.0) GO TO 13 KIMIN=I KIMAX=IMAX GO TO 14 13 KIMIN=I KIMAX=I +NOEL1 IF ((I-IMIN+1).GE.IMI) KIMAX=IMAX 14 DO 15 KI=KIMIN,KIMAX IXN=IXN+1 BMATR (IXN, KI) =Z12 (LXN) BMATR (KI, IXN) =BMATR (IXN, KI) 15 CONTINUE 12 CONTINUE C C...... 2) lower Part.............. C IMIN=2 IMAX=NOEL1 DO 16 I=IMIN,IMAX IXN=I-1 LXN=IABS (NS12-I) +1 IF (IAI.GT.0) GO TO 17 KIMIN=NOEL1+1 KIMAX=2*NOEL1-I+IMIN-1 GO TO 18 17 KIMIN=NOEL1+1 KIMAX=NOEL1+NOEL2 IIMI=I-IMIN+2 IF (IIMI.GE.IMI) KIMAX=NOEL1+NOEL2-IIMI+IMI 18 DO 19 KI=KIMIN,KIMAX IXN=IXN+1 BMATR (IXN, KI) =Z12 (LXN) BMATR (KI, IXN) =BMATR (IXN, KI) 19 CONTINUE 16 CONTINUE C C....2.... First off-diagonal matrix C C... 1) Upper Part....... C IAI =NOEL2 -NOEL 3 IMI=IABS (IAI) +1 IMIN=NOEL1 +NOEL 2 +1

-150 -IMAX=NOEL1+NOEL 2 +NOEL3 DO 20 I=IMINJIMAX IXN=NOEL1 LXN=IABS (NS23) +I-IMIN+l IF (IAI.LT.0) GO TO 21 KIMIN=I KIMAX=IMAX GO TO 22 21 KIMIN=I KI MAX= I +NOEL 2 - 1 IF ((I-IMIN+1).GE.IMI) KIMAX=IMAX 22 DO 23 KI=KIMIN,KIMAX IXN=IXN+1 BMATR (IXN, KI) =Z23 (LXN) BMATR (KI, IXN) =BMATR (IXN, KI) 23 CONTINUE 20 CONTINUE C C 2) Lower Part C IMIN=NOEL1+2 IMAX=NOEL1 +NOEL 2 DO 24 I=IMIN,IMAX IXN=I -1 LXN=IABS (NS23-I+IMIN-1) +1 IF (IAI.GT.0) GO TO 25 KIMIN=NOEL1 'NOEL2 +1 KIMAX=NOEL1+2*NOEL2- (1-IMIN) -1 GO TO 26 25 KIMIN=NOEL1+NOEL2+1 KIMAX=NOEL1+NOEL2 +NOEL3 IIMI=I -IMIN+2 IF (TIMI.GE. IMI) KIMAX=NOEL1~NOEL2 NOEL3-IIMI+IMI 26 DO 27 KI=KIMIN,KIMAX IXN=IXN+1 BMATR (IXN, KI) =Z23 (LXN) BMATR (KI, IXN) =BMATR (IXN, KI) 27 CONTINUE 24 CONTINUE C C...3.... First off-diagonal matrix C C 1) Upper Part C IAI =NOEL3 -NOEL4 IMI=IABS (IAI) +1 IMIN=NOEL1~NOEL2 +NOEL3+1 IMAX=NOEL1 -NOEL 2 -NOEL3~NOEL4 DO 28 I=IMIN,IMAX IXN=NOEL1+NOEL2 LXN=IABS (NS34) +I-IMIN~1 IF (IAI.LT.0) GO TO 29 KIMIN=I KIMAX=IMAX GO TO 30 29 KIMIN=I KIMAX=I +NOEL3- 1 IF ((I-IMIN-i-1).GE.IMI) KIMAX=IMAX 30 DO 31 KI=KIMINKIMAX IXN=IXN+l

-151 -BMATR (IXN, KI) =Z34 (LXN) BMATR (KI, IXN) =BMATR (IXN, KI) 31 CONTINUE 28 CONTINUE C C...2)... Lower Part C IMIN=NOEL1+NOEL2+2 IMAX=NOEL1+NOEL2 +NOEL 3 DO 32 I=IMIN,IMAX IXN=I-1 LXN=IABS(NS34-I+IMIN-1)+1 IF (IAI.GT.O) GO TO 33 KIMIN=NOEL1 +NOEL 2 +NOEL3+1 KIMAX=NOEL1+NOEL2+2*NOEL3-(I-IMIN)-1 GO TO 34 33 KIMIN=NOEL1+NOEL2+NOEL3+1 KIMAX=NOEL1 +NOEL 2 +NOEL 3 +NOEL4 IIMI=I-IMIN+2 IF (IIMI.GE. IMI) KIMAX=NOEL1+NOEL2+NOEL3+NOEL4-IIMI+IMI 34 DO 35 KI=KIMIN,KIMAX IXN=IXN+1 BMATR (IXN, KI) =Z34 (LXN) BMATR (KI, IXN) =BMATR (IXN, KI) 35 CONTINUE 32 CONTINUE C C....1.... Second off-diagonal matrix C C 1) Upper Part C NS13=NS12+NS23 IAI=NOEL1-NOEL3 IMI=IABS(IAI) +1 IMIN=NOEL1+NOEL2+1 IMAX=NOEL1+NOEL 2 +NOEL3 DO 36 I=IMIN,IMAX IXN=O LXN=NS13+I-IMIN IF (IAI.LT.O) GO TO 37 KIMIN=I KIMAX=IMAX GO TO 38 37 KIMIN=I KIMAX=I +NOEL1-1 IF ((I-IMIN+1).GE.IMI) KIMAX=IMAX 38 DO 39 KI=KIMIN,KIMAX IXN=IXN+1 BMATR (IXN, KI) =Z13 (LXN) BMATR (KI, IXN)=BMATR (IXN, KI) 39 CONTINUE 36 CONTINUE C C 2) Lower part C IMIN=2 IMAX=NOEL1 DO 40 I=IMIN,IMAX IXN=I-1 LXN=IABS (NS13-I) +1

-152 -IF (IAI.GT.0) GO TO 41 KIMIN-NOEL1+NOEL2 +1 KIMAX=2 *NOEL1+NOEL2- I +IMIN- 1 GO TO 42 41 KIMIN=NOEL1+NOEL2+1 KIMAX=NOEL1-+NOEL2 +NOEL 3 IIMI=I-IMIN+2 IF (IIMI.GE. IMI) KIMAX=NOEL1+NOEL2+NOEL3-IIMI+IMI 42 DO 43 KI=KIMIN,KIMAX IXN=IXN+i BMATR (IXN, KI) =Z13 (LXN) BMATR (KI, IXN) =BMAIR (I XN, KI) 43 CONTINUE 40 CONTINUE C C...2... Second off-diagonal matrix C C 1) Upper Part C NS24=NS23-+NS34 IAI=NOEL2 -NOEL4 IMI=IABS (IAI) +1 IMIN=NOEL1-+NOEL2 +NOEL3+1 IMAX=NOEL1 +NOEL2 +NOEL 3+NOEL4 DO 44 I=IMIN, IMAX IXN=NOEL1 LXN=IABS (NS24) +I-IMIN+1 IF (IAI.LT.0) GO TO 45 KIMIN=I KIMAX=IMAX GO TO 46 45 KIMIN=I KIMAX=I +NOEL2 -1 IF ((I-IMIN+1).GE.IMI) KIMAX=IMAX 46 DO 47 KI=KIMIN,KIMAX IXN=IXN+i BMATR (IXN, KI) =Z24 (LXN) BMATR (KI, I XN) =BMATR (I XN, KI) 47 CONTINUE 44 CONTINUE C C 2) Lower Part C IMIN=NOEL1+2 IMAX=NOEL1 +NOEL2 DO 48 I=IMIN,IMAX IXN=I-1 LXN=IABS (NS24-I+IMIN-1) +1 IF (IAI.GT.0) GO TO 49 KIMIN=NOEL1 +NOEL 2 +NOEL 3+1 KIMAX=NOEL1+2 *NOEL2+NOEL3- I +-IMIN- 1 GO TO 50 49 KIMIN=NOEL1-+NOEL2 +NOEL3+1 KIMAX=NOEL1 +NOEL 2 +NOEL3+NOEL4 I IMI=- IMIN+2 IF (IIMI.GE. IMI) KIMAX=NOEL1+NOEL2+NOEL3+NOEL4-IIMI+IMI 50 DO 51 KI=KIMIN,KIMAX IXN=IXN+i BMATR (IXN, KI)=Z24 (LXN) BMATR (KI, IXN) =BMATR (IXN, KI)

-153 -51 CONTINUE 48 CONTINUE 301 CONTINUE C C...1... Third off-diagonal matrix C C 1) Upper part C NSl4=NSl2+NS2 3+NS34 IAI =NOEL1 -NOEL4 IMI=IABS (IAI) +1 IMIN=NOEL1+NOEL2 +NOEL3+1 IMAX=NOEL1 +NOEL 2 +NOEL3+NOEL4 DO 52 I=IMIN,IMAX IXN=O LXN=NS14+I - IMIN IF (IAI.LT.0) CO TO 53 KIMIN=I KIMAX=IMAX GO TO 54 53 KIMIN=I KIMAX=I +NOEL1 -1 IF ((I-IMIN+1).GE.IMI) KIMAX=IMAX 54 DO 55 KI=KIMINKIMAX IXN=IXN+1 BMATR (IXN, KI) =Z14 (LXN) BMATR (KI, IXN) =BMATR (IXN, KI) 55 CONTINUE 52 CONTINUE C C 2) Lower Part C IMIN=2 IMAX=NOEL1 DO 56 I=IMIN,IMAX IXN=I-1 LXN=IABS (NS14-I) +1 IF (IAI.GT.O) GO TO 57 KIMIN=NOEL1+NOEL2 -NOEL3+1 KIMAX=2 *NOEL1+NOEL2~NOEL3- I ~IMIN- 1 GO TO 58 57 KIMIN=NOEL1+NOEL2 +NOEL3+1 KIMAX=NOEL1 +NOEL 2 ~NOEL3~NOEL4 IIMI=I -IMIN~2 IF (IIMI.GE. IMI) KIMAX=NOEL1+NOEL2+NOEL3+NOEL4-IIMI+IMI 58 DO 59 KI=KIMINKIMAX IXN=IXM+1 BMATR (IXN, KI) =Z14 (LXN) BMATR (KI, IXN) =BMATR (IXN, KI) 59 CONTINUE 56 CONTINUE C C C IMIN=1 C IMAX=NOEL1 ~NOEL2 ~NOEL3+NOEL4 C JMIN-1 C DO 60 K=1,4 C DO 61 I=1,IMAX C IF (K.EQ.1) WRITE (6,62) (BMATR(IJ),J=1,12) C IF (K.EQ.2) WRITE (6,63) (BMATR(IJ),J=13,17)

-154 -C IF (K.EQ.3) WRITE (6,64) (BMATR(I,J),J=18,21) C IF (K.EQ.4) WRITE (6,65) (BMATR(I,J),J=22,33) C 62 FORMAT(12 (14, 2X)/) C 63 FORMAT (5 (4, 2X)/) C 64 FORMAT (4 (4, 2X)/) C 65 FORMAT(12 (14, 2X)/) C 61 CONTINUE C 60 CONTINUE C C GO TO 1000 C 1001 CALL MINVCD (NOR,NOR,DETA,IB,IA) C DO 70 IQQ=1,NOR C CUR(IQQ, 1) = (BMATR (IQQ, NFEED1) +BMATR(IQQ, NFEED4) )/100. 00 C CUR (IQQ, 2)=(BMATR (IQQ, NFEED1) -BMATR(IQQ,NFEED4))/100.00 CUR (IQQ, 3) =BMATR (IQQ, NFEED1) /100.00 70 CONTINUE C WRITE (6,71) 71 FORMAT (///1X, 'Current distribution on the strip conductors', *////) IMIN=1 IMAX=NOEL4+NOEL3+NOEL2+NOELL1 DO 72 K=3,3 IF (K.EQ.1) WRITE(6,73) IF (K.EQ.2) WRITE(6,74) IF (K.EQ.3) WRITE(6,75) 73 FORMAT(////1OX,'Current Distribution for EVEN excitation', ////) 74 FORMAT(////1OX,'Current Distribution for ODD excitation', ////) 75 FORMAT(////1OX,'Current Distribution for UNEVEN excitat.', ////) DO 76 IQQ=IMIN,IMAX RECUR1=REAL (CUR (IQQ, K)) ABCU1=CABS (CUR (IQQ, K)) AICUR1=AIMAG (CUR (IQQ, K) ) PHCUR1=ATAN2 (AI CUR1, RECUR1) PHCUR1=180. 00*PHCUR1/PI IF (IQQ.EQ.1) WRITE (6,77) 77 FORMAT(///1OX, 'Current on the first Transmiss. line', ///) IF (NOEL23.EQ.0) GO TO 302 IF (IQQ.EQ. (NOEL1+1)) WRITE (6,78) 78 FORMAT(///10X, 'Current on the first parasit.dipole', ///) IF (IQQ.EQ. (NOEL1+NOEL2+1)) WRITE (6,79) 79 FORMAT(///1OX, 'Current on the second paras. dipole', ///) 302 CONTINUE IF (IQQ.EQ. (NOEL1+NOEL2+NOEL3+1)) WRITE (6,80) 80 FORMAT(///1OX, 'Current on the printed dipole', ///) WRITE (6,81) IQQ,CUR(IQQ,K),ABCU1,PHCUR1 81 FORMAT (1X, 'C(',I4, ')=',(E14.7, ',',E14.7),2X, * E14.7,1X,E14.7/) 76 CONTINUE 72 CONTINUE 1000 CONTINUE

-155 -STOP END C THIS SUBROUTINE INVERTS A SQUARE COMPLEX MATRIX SUBROUTINE MINVCD (IAMA.DETA,IR,IC) IMPLICIT REAL*4 (A-HO-Z) COMPLEX*8 APIVDETA,TEMP,PIV1 DIMENSION IR(MA),IC (MA) COMMON/MAN/A(160,160) DO 1 I=1,MA IR (I)=0 1 IC(I)=0 C DETA=(1.00,0.00) S=0 00 R=MA 2 CALL SUBMCD(IA,IA,MA,MA,,IR, IC, I,J) PIV=A(I,J) C DETA=PIV*DETA Y=CABS (PIV) IF (Y.EQ.0) GO TO 17 IR(I)=J IC (J) =I PIV (1.00,0.00)/PIV A(I,J)=PIV DO 5 K=1,MA 5 IF (K.NE.J) A(I,K)=A(I,K)*PIV DO 9 K=1,MA IF (K.EQ.I) GO TO 9 PIV1=A(K,J) 6 DO 8 L=1,MA 8 IF (L.NE.J) A(K,L)=A(K,L)-PIV1*A(IL) 9 CONTINUE DO 11 K=1,MA 11 IF (K.NE.I) A(K,J)=-PIV*A(KJ) S=S+1.00 IF (S.LT.R) GO TO 2 12 DO 16 I=1,MA K=IC (I) M=IR (I) IF (K.EQ.I) GO TO 16 C DETA=-DETA DO 14 L=1,MA TEMP=A(K,L) A (K, L) =A(I, L) 14 A(IL)=TEMP DO 15 L=1,MA TEMP=A(L,M) A (L, M) =A.(L, I) 15 A(L,I)=TEMP IC(M) =K IR(K)=M 16 CONTINUE RETURN 17 WRITE (6,18)I,J 18 FORMAT (lOX, 'MATRIX IS SINGULAR''/10X, 'I='f 14, 5X,'J=',14) RETURN END C..............................................................................

-156 -************************************************************** ********** SUBROUTINE SUBMCD (IA, JA, MA, NA, IR, IC, I, J) IMPLICIT REAL*4 (A-H,O-Z) COMPLEX* 8 A DIMENSION IR (MA), IC (NA) COMMON/MAN/A (160,160) I=0 J=0 TEST=0.00 DO 5 K=1,MA IF (IR(K).NE.0) GO TO 5 DO 4 L=1,NA IF (IC(L).NE.0) GO TO 4 X=CABS (A (K, L)) IF(X.LT.TEST) GO TO 4 I=K J=L TEST=X 4 CONTINUE 5 CONTINUE RETURN END

-157 - PART D " Magnetic Tape Comments"

-158 - Tape name= *T* 16:18:59 4 Jan. 1986 ANSI labeled 6250-bpi 9TP Volume= BANDW2 Owner= PISTIKATEHI Rack#= C9366J LP=on BLK=in DTCHK=on RETRY=10 File Data set Block Record Tapelen Record Expires name count count (feet) format - - - -.-.-.-. —.-i -.-.-. —. — - - - - - - - - - - - - - - - - - - - - - - - - - 1 2 3 4 5 6 7 8 9 JOBRUN FOPTION 0 FOPTION1 FOPTION2 FOPTION3 FOPTION4 FOPTION5 FOPTIONS FOPTION7 20 34 64 31 45 39 32 26 52 116 199 2357 367 529 458 384 307 622 1.74 2.17 5.28 2.27 2.82 2.58 2.32 2.07 3.11 FB(500,80) FB(500,80) FB(3000,80) FB(1000,80) FB(1000,80) FB(1000,80) FB(1000,80) FB(1000,80) FB(1000,80) 31 31 31 31 31 31 31 31 31 Dec. Dec. Dec. Dec. Dec. Dec. Dec. Dec. Dec. '99 '99 '99 '99 '99 '99 '99 '99 '99 Total Tape Length = 24.37 feet