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ldeally the basis functions s**et** should r8~8mble and accurately represent the unknown current fundion. A limited number of basis s**et**s are used typically in pracüœ. the most popular being: a) Functions which are nonzero only over a part of the domain (surface of the scatterer) of the fundion g(p'). The surface of the scattemr is divided into N segments and the basis funcüon is defineci relaüvely to the limit of one or more segments. Typical shapes of these functions indude: the pulse type. the pieceWise Ynear or sinusoidal types. b) FunctÏons which are nonzero over the entire perim**et**er of aie scatt**et**er. They are usually sinusoids and their use is sirnilar to a Fourier series expansion of a function. D**et**ermining the best basis functions s**et** from aie ones listeâ in a) is not obvious. lt is believeâ [14] that increasing the sophistication of basis functions beyond the pulse shape wïll rep-nt more smoothly the current and hem- is mon, accurate. The priœ to pay hmver is computational complexity. In some cases also the use of sinusoid function could lead in an evaluation of the integral operator maiout nwnerical integration. The fundons listed in b) are usually used when the current distribution is known to have rnainly a sinusoidal distribution. In this wrk the pulse basis function was used because it is simple and. as explained in the next several trials with pulse basis and pieceWise sinusoid basis funcüons based codes were done in the early stage of this investigation: 80th codes have similar accuracy for radiation patterns and curent distributions. Equation 2.1 1 is useâ as thr, numencal tachnique to =Ive br the wmnt by satisfying the boundary condition (vanishing e1-c fields on the scatteror surface) only **et** discr**et**e poinîs. There is no guarante8 that behnieen these

points, the boundary conditions will be satisfkd. A mahod to force the boundary conditions (1 31 (in an average senci. at Ieast on the entire scatterer surface) is to use weighting funcüons in the domain of the integral. This means that equation 2.21 becomes (w~, R) ici an inner product which is a scalar operation. When both wigMing functions and basis functions are the sarne this is known as Galerkin m**et**hoci. In the literature [IS] this mcthod is considered adequate but not superior to a m**et**hod using weigMing and basis function not equal but of the same order. Again trials wiai two ditferent codes ( one using the Galerkin rn**et**hod and the other not) did not prove the superiority of one mahod over the other. It was beyond the scope of this work to investigate residuals of tangent electric field over the surface of the scatteren useâ. but from a aiment density and radiation pattern point of view. accurades of both codes (at least for the simple shape used) wiere sirnilar. The moment rn**et**hod codes created in this work use the point matching m**et**hod and pulse basis functions. It should be notexi that point matching is equivalent to using the impulse funmon as the wighting function. 2.4.3 Exp.rience with TDRS uid TEcn Two inâependent codes basad on the moment rn**et**hod mtre ubilizeà during this investigation in addition to the codes cmated especially for each scattering am. The first code. TDRS (Tm, Dimmsional Radiation and Scattering) was obtaind from [2]. It uses the integral qualion and moment maniod with equal

- Page 1 and 2: Evafuation of the Uniforrn Théory
- Page 3 and 4: ABSTRACT Evaluation of the Uniform
- Page 5 and 6: ACKNOWLEDGEMENT I am grateful to E.
- Page 7 and 8: TABLE OF CONTENTS (continued) 3.5.4
- Page 9 and 10: Figur, 3.6: Magnihrde of cummt dsns
- Page 11 and 12: Figur, 3.28: Magnihide of cunient d
- Page 13 and 14: LIST OF TABLES ....................
- Page 15 and 16: 60th TEz and TMz plane wave illumin
- Page 17 and 18: ISB 1 Figure 2.1 : UTD 2-D wdge dif
- Page 19 and 20: L=p for plane wave incidence or L-
- Page 21 and 22: the distance from each edge and the
- Page 23 and 24: 2.2 CHOlCE B€IWEEN UT D RADIATION
- Page 25 and 26: Ffgun, 2.2: Radiation pattern (Norm
- Page 27 and 28: 2.3 CWPARING UTD GENERAL FORMULATIO
- Page 29 and 30: and the final fomulation of equatio
- Page 31 and 32: If the lower limit of the integral
- Page 33 and 34: Sinœ we are dealing with the Tk ca
- Page 35 and 36: Figura 24: Magnitude of surface cun
- Page 37 and 38: 2.4 CHOEE OF AN INDEPENDENT METHOD
- Page 39 and 40: where, fZ&) is the incident field o
- Page 41: where VM = &(&) (known excitation f
- Page 45 and 46: form # n&Im-al s 2 & and x, king th
- Page 47 and 48: It should be noteâ that the penalt
- Page 49 and 50: Figure 2.7: Nmalized radiation patt
- Page 51 and 52: If we insert 2.29 in 2.28 w have: N
- Page 53 and 54: In two dimensional cases and at a c
- Page 55 and 56: In this chapter TG plane wavw are u
- Page 57 and 58: Figure 3.5 was proâuœd to &eck th
- Page 59 and 60: k- 3 3 2.5 - - 2- a 1.5e 3 O 1 0.5
- Page 61 and 62: 3 * L 1 I 1 1 1 1 I i 2.5 - 1 0.5 O
- Page 63 and 64: Figure 3.6: Magaitude of cument den
- Page 65 and 66: 3.2 STRlP SURFACE CURRENT USING UT0
- Page 67 and 68: Hi = incident field at B = (e -J~P
- Page 69 and 70: ii)On the lower surface: 3.2.2 Code
- Page 71 and 72: Fig 3.9: Magnitude of cwrent densit
- Page 73 and 74: Fig 3.1 1 : Magnitude of current di
- Page 75 and 76: + Z Lu 3 2.5 2 a 1.5 a 3 O 1 0.5 TE
- Page 77 and 78: 3 - I 2.5 - 1 I I 4 . l I l TE Plan
- Page 79 and 80: 3 2.5 2 l- Z W ai 1.5 3 O 1 Fig 3.1
- Page 81 and 82: t Z Ut 3 TG Plant wave 2.5 * 2 = 1-
- Page 83 and 84: 3 2.5 2 k Z W 1.5 K 3 O 1 0.5 TEz P
- Page 85 and 86: 3.3 STRlP SURFACE CURENT USING THE
- Page 87 and 88: - .Ir& = .Zrq + J- Srd = ~î&;-a) w
- Page 89 and 90: Figure 3.23: TEz plane wave inciden
- Page 91 and 92: To find the multiple difhaction ter
- Page 93 and 94:
Sdving equations 3.28 to 3.35 and u

- Page 95 and 96:
3.4.4 Code and Resub Based on the f

- Page 97 and 98:
0.5 - TEz plane wave Figure 3.25: M

- Page 99 and 100:
Figure 3.27: Magnitude of cumnt den

- Page 101 and 102:
Figure 3.29 : Magnitude of current

- Page 103 and 104:
RECTANGULAR CYLlNDER SURFACE CURREN

- Page 105 and 106:
Point m I Point m Figure 3.31 : Sca

- Page 107 and 108:
The 2, &mis are generally conputsd

- Page 109 and 110:
Figure 3.32 : Scattered field on AB

- Page 111 and 112:
Figure 3.33 : Scattered fields on B

- Page 113 and 114:
Figure 3.34 : Scattered fields on C

- Page 115 and 116:
where. = is fKwn equation 3.480 3.5

- Page 117 and 118:
where, Z,,,,, = is from equation 3.

- Page 119 and 120:
4 SCATTERING - TMz CASE EDGE SURFAC

- Page 121 and 122:
Equation 4.4 can ôe evaluated if i

- Page 123 and 124:
Usually subroutines will give the r

- Page 125 and 126:
2 2.5 3 RH0 in Lambdas ïMz plane w

- Page 127 and 128:
3' I I 1 1 1 1 1 I I O 0.5 1 1.5 2

- Page 129 and 130:
RH0 (in wavelengths) TMz plane wave

- Page 131 and 132:
4.2 STRIP SURFACE CURRENT USlNG UTD

- Page 133 and 134:
As shown in the previous section, c

- Page 135 and 136:
y the fact mat the wrrent density d

- Page 137 and 138:
Fig. 1.8: Magnitude of current dens

- Page 139 and 140:
Fg. 4.10: Magnitude of currcnt dens

- Page 141 and 142:
4.3 STRlP SURFACE CURRENT USlNG THE

- Page 143 and 144:
4.3.3 Code and Rnults The cornputer

- Page 145 and 146:
HL = v~sg'E' From image theory HP =

- Page 147 and 148:
from equation (4.21) On any surface