Two rectangular waveguides with different major side lengths (a 1 < a 2 ) along the x-axis

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Two rectangular waveguides with different major side lengths (a1 < a2) along the x-axis and equal minor sides (b1 = b2) along the y-axis are butt-joined in the z = 0 plane.Waveguide 1 propagates a TE10 mode (only) in the +z-direction toward waveguide 2. Find the amplitude of the various modes excited in waveguide 2 if the two guides share a corner at x = y = 0 and the open portion of the larger guide in the x-y plane is closed by a perfect conductor. Check the a1 = a2 limit.

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