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Unformatted text preview: 18 Reflecting plates, monopole antennas, corner reflectors TE reflection: k i k r k t 2 1 x z H i k 1 cos 1 k 1 sin 1 k 2 sin 2 Medium 1 Medium 2 1 E y r E y i = 2 cos 1 1 cos 2 2 cos 1 + 1 cos 2 E yt E y i = 2 2 cos 1 2 cos 1 + 1 cos 2 , TM reflection: k i k r k t 2 1 x z E i k 1 cos 1 k 1 sin 1 k 2 sin 2 Medium 1 Medium 2 1  E r E i = 2 cos 2 1 cos 1 2 cos 2 + 1 cos 1 E t E i = 2 2 cos 1 2 cos 2 + 1 cos 1 . In deriving the transmission and reflection rules for TE and TM modes summarized above we assumed lossless propagation media during the last two lectures. The equations can be easily modified as described next if either medium 1 or medium 2 or both have nonzero conductivities 1 and/or 2 . 1 In general, in the case of a noninsulating medium with a finite con ductivity , we expect a conduction current J = E , in which case the planewave form of Amperes law can be cast as j k H = E + j E , = j ( + j ) E . Since this equation differs from the nonconducting case only by having + j in place of , propagation parameters k = and = of nonconducting media are modified as k = ( + j ) and = + j , respectively, in homogeneous conducting media. In other wors a con ducting medium is treated as a dielectric with a permittivity + j . Consider the wavenumber k = ( + j ) in a medium with / . In that case poor conductor approxi 2 mation we can approximate k as k = ( j ) = (1 j ) (1 j 2 ) =  j 1 2 k j k , with k Re { k } Propagation constant and k  Im { k } 1 2 Attenuation constant . These terms are applicable since e j k r = e j k s = e j ( k k ) s = e k s e j k s clearly signify an attenuating planewave field with distance s measured in the direction of a unit vector k such that k introduced above relates to k = k j k as in k = k ( k j k ) ....
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 Fall '08
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 Electromagnet

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