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# Class Note for ECE 6341 with Professor Jackson at UH 3

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This 26 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 12 views.

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Date Created: 02/06/15

ECE 6341 Spring 2009 Prof David R Jackson ECE Dept Notes 43 Overview In this set of notes we derive the SDI formulation using a more mathematical but general approach we directly Fourier transform Maxwell s equations This allows for all possible types of sources horizontal vertical electric and magnetic to be treated in one derivation General SDI Method Start with Ampere s law V x H Ji 2 nglj VVt 2 82 where Vt 23 3 x 6y General SDI Method cont A A 8 Hence we have ktg H211 jw8E 82 Next represent the field as 3151 13 2ltwgt2ltmgt Notethat A A A y ZXZZZ quot A A A A V zxzz Z X 2 x Take the 222 components of the transformed Ampere s equation General SDI Method cont 2 jkIIIv J waEZ A u V J 39wsE 82 M J u A F1 2 jktHZ 86 J ja8Ev Z Examine the TMZ field Ignore equation 1 392 TMZ Fields We wish to eliminate EZ To do this use Faraday s law Take the 2 component of the transformed Faraday s Law N 35 N N jkth 6 M java lt3gt Z TMZ Fields cont Substitute EZ from 1 into 3 to eliminate jktIIV ngEZ 1 N 5 jktEZ M jaqu 3 62 kt jl jktFlV 6E jwll l v jaw 62 0E k2 k or u Hvjaqu M 62 jaw 08 E Z TMZ Fields cont Note that 3 jamkf wzyg jCOS jCOS ngkf k2 1 ja8k2 k2 1k2 jcog Z Hence TMZ Fieidis cont Equations 2 and 4 are the final TMZ field modeling equations 10 Define We then have 61 62 aVW 62 ja8 VTM j 2 r JIMPM J08 L 08 Fields cont y Z Z l Telegrapher s Equation Allow for distributed 81 sources V v LAz VSdAZ at 8v 81 so L vd Telegrapher s Equation cont Hence in the phasor domain Also r z CAz z3AZ at so i C If 32 a 12 Telegrapher s Equation cont Compare field equations for TMZ fields with TL equations TM 61 a jagVTM J wCVIj 82 82 TM 2 62 39kz JITM M kt M 212 WMquot 2 10M Z 13 Telegrapher s Equation cont VVethenrnakethefoHomHngiden ca ons C25 2 szkZ 0 Hence 2 k2 zaALC 20 k 8 19 w 8 zTL Z 2 k2 0 C szgz we SO 15 Sources TMZ For the sources we have for the TMZ case Sources TMZ cont Special case planar surfacecurrent sources Assume 1Xayazls by 5Z lumped parallel current source lumped series voltage source 16 17 SQUtcasz count For a vertical electric current Assume xyz fxy 52 planar vertical current distribution Sources TMZ cont J x y z fx y 62 Vim j kxak me This corresponds to a lumped series voltage source 18 Sources TMZ cont Special case vertical electric dipole fxy 5x5y Use duality E gt 11 11 gt E I gt Mi M gt iquot 8 20 TE Fields 6HV 82 2 Z 3mm 9 111 62 as jaw 2 lt7 ja8Eu 2 Z aHu J M 9 Define We then identify 21 IE cont For the sources we have TEE cont 22 lumped series voltage source lumped parallel current source Sources TEZ cont For a vertical magnetic current Assume 3632 Z gx y 52 This corresponds to a lumped parallel current source Then we have 23 24 Sources TEZ cont Special case vertical magnetic dipole Assume gm y 5005 y 25 Summary cont Special case of planar vertical currents J fltxygt6ltzgt M gee y 52 lumped sources 26

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