350lect26 - 26 Parallel-plate waveguides TM m modes Last...

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Unformatted text preview: 26 Parallel-plate waveguides TM m modes Last lecture we discussed the TE m modes of propagation in parallel- plate waveguides. z x a = = These guided modes have y-polarized electric fields transverse to the propagation direction z and exhibit a standing wave pattern in x- direction with m half-wavelengths of variation between the guide plates at x = 0 and x = a . More specifically, the TE m modes have transverse electric field phasors E = 2 j yE o e- jk z z sin( k x x ) where k x = m a , m = 1 , 2 , and k z = k 2- k 2 x = c 1- f 2 c f 2 with cutoff frequencies f c = mc 2 a . Alternatively (and equivalently), k z = k 2- k 2 x = c 1- 2 2 c , 1 with cutoff wavelengths c = 2 a m . Above, the operation frequency f and operation wavelength satisfy f = c , and furthermore k = 2 = c is the operation wavenumber. The propagation characteristics of the guided mode, on the other hand, depends on k z , with v p = k z and g = 2 k z denoting the phase velocity and the wavelength of the guided mode when f > f c and, equivalently, < c , corresponding to propagation condition for a given mode. When f < f c and, equivalently, > c , the mode is evanescent....
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This note was uploaded on 09/27/2011 for the course ECE 450 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.

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350lect26 - 26 Parallel-plate waveguides TM m modes Last...

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