Question: Two rectangular waveguides are joined end-to-end. The guides have identical dimensions, where a = 2b. One guide is air-filled; the other is filled with a

Two rectangular waveguides are joined end-to-end. The guides have identical dimensions, where a = 2b. One guide is air-filled; the other is filled with a lossless dielectric characterized by ∈'_r.

(a) Determine the maximum allowable value of r such that single-mode operation can be simultaneously assured in both guides at some frequency.

(b) Write an expression for the frequency range over which single-mode operation will occur in both guides; your answer should be in terms of ∈'_r, guide dimensions as needed, and other known constants.

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