Hello All: Which formula for the characteristic impedance of rectangular waveguides (air filled, and operating in TE10) applies when attempting to determine the impedance mismatch that occurs when one waveguide abruptly transitions to another?

Using the familiar "wave impedance" formula doesn't make sense because that implies that the impedance depends only on the waveguide width. If that were the correct formula to use to calculate the mismatch between two waveguides, then if one waveguide transitioned abruptly in to another of equal width but different height, there would be no reflection. Intuitively, it is obvious that that cannot be true, because if it were, then a stub or iris placed along the broad face of a waveguide (which effectively shortens the waveguide at that point, but does not affect its width) would have no effect.

Edit: I should point out that I am only interested in reflection coefficients, so I only need to know the best way to determine the proportionality of the waveguide impedances, not necessarily the absolute values. As long as I have a way of determining Z2/Z1 based on their dimensions, I can easily determine: Rho=(Z2/Z1-1)/(Z2/Z1+1).

The "wave impedance" formula effectively sets the impedance of a waveguide proportional to Lambda_g which, at any particular frequency, is determined only by the width, not the height. But I have also seen a formula for impedance proportional to (b/a)*Lambda_g, and another proportional to b*Lambda_g.

Thanks very much for any assistance.