Help with Waveguide Transitions: Continuity, Amplitude Equations, and Fourier Ex

[Ahiya]

Hello everyone,

I’m working on an assignment involving a rectangular waveguide attenuator (composed of three sections) where the middle section is wide enough that the main TE10 mode experiences significant attenuation. I understand how to calculate the attenuation itself, but I’m struggling with the exact procedure to analyze the transitions between the different waveguide sections.

I’ve attached both the assignment and the explanatory notes from my instructor. These notes outline the geometric expression of the transitions and the continuity requirements for tangential fields at the boundaries. However, I’m unclear about:

From Continuity to Amplitude Equations: How do I move from the boundary continuity conditions (for both electric and magnetic tangential components) to the explicit amplitude equations for the reflected and transmitted modes?

Fourier Decomposition: I know I need a two-dimensional Fourier expansion (to handle the various possible TE/TM modes at each boundary), but how exactly should I set up this expansion? Which terms are essential, and how do I practically match them to obtain the reflection coefficients?

Step-by-Step Method: I’m looking for a more detailed, step-by-step explanation or reference—rather than just a general outline—that clearly shows how to apply these conditions, derive the amplitude relations for each mode, and then compute the reflection/transmission (and thus the attenuation) through each section.

Any concrete guidance, references, or illustrative examples would be greatly appreciated. Thanks in advance for your help!

https://math.stackexchange.com/questions/211689/real-valued-2d-fourier-series

[ahsrabrifat]

Sorry. Can't help much. This paper may help you. https://www.researchgate.net/publication/329466345_Mode_Matching_Method_for_the_Analysis_of_Cascaded_Discontinuities_in_a_Rectangular_Waveguide