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Unformatted text preview: 27 Parallelplate waveguides: example problems Summarizing the properties of guided modes of propagation in parallelplate waveguides: z x a σ = ∞ σ = ∞ • TE m and TE m modes with the transverse field phasors ˜ E = 2 j ˆ yE o e jk z z sin( k x x ) and ˜ H = 2ˆ yH o e jk z z cos( k x x ) , respectively, where k x = mπ a and k z = k 2 k 2 x = ω c 1 f 2 c f 2 = ω c 1 λ 2 λ 2 c , with cutoff frequencies and wavelengths f c = mc 2 a and λ 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, λ < λ c . – Nonpropagating modes are evanescent and have an attenuation constant  k z  . 1 • Also TE m and TE m mode fields have guide impedances η TE = E y H x = η o 1 f 2 c f 2 and η TM = E x H y = η o 1 f 2 c f 2 relating the transverse field components of the guided modes. All the results summarized above are for airfilled waveguides, but they can be readily modified, by replacing c and η o with c/n and η , respectively, in the case of dielectricfilled waveguides.the case of dielectricfilled waveguides....
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 Fall '08
 Staff
 Electromagnet, Frequency, Wavelength, Transmission line, group velocity

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