Waveguide H-plane step modal analysis question

[szoftveres]

Hi All,

I'd like to calculate the reactance of an H-plane step, according to Pozar 4.6, Modal Analysis of an H-Plane Step in Rectangular Waveguide

What is unclear to me is the Imn integral - For TE10 mode primary excitation, for which m and n values does this integral need to be evaluated? Also how does N relate to m and n?
If there was a Matlab code example implementation somewhere, that would also help a lot.

[yl3akb]

Imn is so called coupling integral and in this case 'mn' are not indexes seen in usual mode numbering convention such as TEmn (if that confuses You), but instead m is index of all possible modes in waveguide with dimension 'a' and n is index of modes in waveguide with dimension 'c'.

In case of H plane step and TE10 excitation only modes TEx0 = TE10, TE20, TE30,... are excited, so 'm' indexes modes TEx0 in waveguide a and 'n' indexes modes TEx0 in waveguide c. The Imn theoretically has to be evaluated for all possible mode couplings, but truncated to N terms in practice like this (prefix '_a' and '_c' identifies waveguide with dimension a or c):

I(TE10_a, TE10_c) I(TE20_a, TE10_c) I(TE30_a, TE10_c) ... I(TEN0_a, TE10_c)
I(TE10_a, TE20_c) I(TE20_a, TE20_c) I(TE30_a, TE20_c) ... I(TEN0_a, TE20_c)
I(TE10_a, TE30_c) I(TE20_a, TE30_c) I(TE30_a, TE30_c) ... I(TEN0_a, TE30_c)
.
.
.
I(TE10_a, TEN0_c) I(TE20_a, TEN0_c) I(TE30_a, TEN0_c) ... I(TEN0_a, TEN0_c)


Term I11 here is first term (or N = 1) in the coupling matrix or coupling between the TE10 in waveguide 'a' and TE10 in waveguide 'c'. Of course, You should use N >> 1 to for solution to converge.