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Unformatted text preview: 27 Parallel-plate waveguides: example problems Summarizing the properties of guided modes of propagation in parallel-plate waveguides: z x a = = TE m and TE m modes with the transverse field phasors E = 2 j yE o e- jk z z sin( k x x ) and H = 2 yH o e- jk z z cos( k x x ) , respectively, where k x = m a and k z = k 2- k 2 x = c 1- f 2 c f 2 = c 1- 2 2 c , with cutoff frequencies and wavelengths f c = mc 2 a and c = 2 a m , respectively, satisfy the zero tangential E boundary conditions on x = 0 and x = a plates of the guide. TE mode does not exist but TM =TEM does and it is disper- sionless. All TE m and TM m modes are dispersive for m 1 , and propagate only if f > f c , or, equivalently, < c . Non-propagating modes are evanescent and have an attenuation constant | k z | . 1 Also TE m and TE m mode fields have guide impedances TE = E y- H x = o 1- f 2 c f 2 and TM = E x H y = o 1- f 2 c f 2 relating the transverse field components of the guided modes. All the results summarized above are for air-filled waveguides, but they can be readily modified, by replacing c and o with c/n and , respectively, in the case of dielectric-filled waveguides.the case of dielectric-filled waveguides....
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- Fall '08