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# Class Note for ECE 6341 with Professor Jackson at UH

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COURSE
PROF.
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TYPE
Class Notes
PAGES
15
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KARMA
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This 15 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 13 views.

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Date Created: 02/06/15
EM Plane Wave Transformation Z A k E1 ZlEoe J Z Note The incident field will be represented using both Ar and Fr We use E to find A and i H to find Fr E i iEoianjn krPn 0056 an lt jgtquotlt2n 1 Its EM PlaneWave Transformation cont AA 1 sianosg 2 EO sin cos i anjn krPn cos 6 1120 I Not in the form of a sphericalwave expansion We need to put this in a form so that is matches with what we get from the Debye potential representation EM PlaneWave Transformation cont Try this i jkrcos Er E0 stcosgz e E0 cos ie jkrcos 1 86 jkr ijcowi anjnltkrgt12ltcos6gt EM PlaneWave Transformation cont Now use the integration formula Harrington notation Schaum s outline Eq 262 I Jinx 1 12 Note the 1 term is added to agree with the Harrington notation Hence Pnlx 1x2Pn39x EqE16in Harrington EM PlaneWave Transformation cont Thus we have a I P 0056 sin6 P 0056 66 n n sin 6Pn1cos 6 l 1 cos 6 2 1211005 6 Hence cos n anjn 10 an1 0039 EM PlaneWave Transformation cont Next use 3100 kl so E ngCOS ianLjnkVB11COS9 110 10 Now let Er w 8 6 2r 1624 Goal solve for c J U r EM PlaneWave Transformation cont Compare there two equations for incident radial field component gkiligcos ianjn kTPnlcose n an 1 2n 1 We need to put these in the same form 1 E Jams kZEO comic cm in 3n krpnl c059 n20 EM PlaneWave Transformation cont We now need to evaluate AH F J kr 3n kr To evaluate this use in x xjnx 3 x j x mix inquot x 1m m xjnquotx x 111x 21100 EM PlaneWave Transformation cont Hence Aquot Jn x Jn x x jnquot x 2 j x x jn x To simplify this use the spherical Bessel Eq 2quot x y 2xy39x2 nn1y0 1 n 2 i 2 1 0 or xy yxjx nn Jy Hence xjnquot x2jn39 x x2 nn1jn x EM PlaneWave Transformation cont Therefore 3 H 30 x lx2 nn1jn xxjnx x 1 xnn 1 x i2nn13 x x Hence E jail kZE0 cos 126413 0056 0102 nn 1 3n kr EM PlaneWave Transformation cont E0 jicosg icnnn13nkr 1cos n20 J39wa r2 Compare with the known expansion I klgcos ian3n k7PjcosQ E0 jams on jogn1 2 k2 an We see that EM PlaneWave Transformation cont SO EM PlaneWave Transformation cont C Hy 2n 1nn11 or or Hence EM PlaneWave Transformation cont Similarly to find Fr for the incident plane wave we use i 31 06 ij 77 39 A 39kz E xE e j E 0 2 051n6 sm e 1km 77 Note sin instead of cos andlfactorincluded 77 15 ECE 6341 Spring 2009 Prof David R Jackson ECE Dept Notes 26

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