Adv Electromag Waves
Adv Electromag Waves ECE 6341
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This 17 page Class Notes was uploaded by Karolann Wiegand on Saturday September 19, 2015. The Class Notes belongs to ECE 6341 at University of Houston taught by David Jackson in Fall. Since its upload, it has received 108 views. For similar materials see /class/208289/ece-6341-university-of-houston in Electrical Engineering at University of Houston.
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Date Created: 09/19/15
ECE 6341 Spring 2009 Prof David R Jackson ECE Dept Notes 15 Arbitrary Line Current Z TMZ AZ Z 0 I Z Introduce Fourier Transform A 102 1zeszzdz Arbitrary Line Current cont View this as a collection of phased line currents dIz 10 e szz 10 imng 27 Then I 6112 H02 kpp e czz from Notes 11 0 1 2 39kZz 4j j1kzdeHo kppe J Arbitrary Line Current cont Hence from superposition the total magnetic vector potential is Example Uniform phased line current 10 272509 kzo 6x j e kax dkx Example cont Hence AZ 2 l Mew kppe szzdkz 1 87 0j 027 502 kzoH02k2pe jk dkz OO u 2 IkZOZ g0j1027rIIO kpope J I Z Z 11 H52 kpope szo 1 where kpo k2 202 5 Example cont where 1 kpo k2 4902 x Example Dipole l 209 11 Example cont AZ 1kZH 2kppe szzdkz 00 Hence Also from 6340 Example cont Hence Sommerfeld identity A spherical wave is thus expressed as a collection of cylindrical waves FarField Identity This identity is useful for calculating the farfield of finite 3D sources in cylindrical coordinates 1 12 Note we assume that the current decays at Z i 00 fast enough so that the 3D far field exists FarField Identity cont Z 1 12 Exact solution FarField Identity cont From 6340 as I gt 00 4f iglt6 gt F 216 J iZI61H Sin6005 y39Sin sin z39cos dx3901le V 00 I V 1Zvekz costZ39 7239 oo 739 Hence FarField Identity cont Hence comparing these two 39kr 0 00 2 ijZ 0 e j k H k e dk 8W Z 0 pp Z 474 I j k 00549 or Far Field Identity cont To generalize this identity use Hence FarField Identity cont Therefore we have X3 jkr f 1kZHEzkppekZdeZ 2 e j k cos 9 m 7 Note this is valid for 0 gt 00 Hence this is valid for FarField Identity cont Since the current function is arbitrary we can write
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