# Mode matching technique for step transition in Rectangular to Circular Waveguide?

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#### mmrobles

##### Junior Member level 2
I've been designing step transitions for Rectangular to Circular waveguide, and I'm trying to search for any concepts regarding how to determine the optimal dimensions of the intermediate steps for this transition. From what I learned each step length should be kept at least to 1/4 of the guide wavelength, but for the height and width, I only found a solution for a single step transition model. However for more than 1 step, is there any convenient method or concept on how to predetermine the optimal dimensions theoretically before starting simulating the model in CST?
Any links or references or mathematical explanation would be greatly appreciated.

#### zhul3

##### Member level 5
back to basic always.

You know how to do a single step (lamda/4) transition, since you know the lamda/4 impedance matching formula, Zt^2=Zo*ZL

So same thing for multi-step transition, we can still choose lamda/4 for each step, and make the matching from load to the source. If you are lazy to calculate it, build a model in ADS etc, and optimize to find right impedance for each step.

The impedance for each step is determined by your waveguide width and height.

mmrobles

### mmrobles

Points: 2

#### mmrobles

##### Junior Member level 2
Thanks for your reply zhul3. I was thinking for that same formula as my reference as well, but not really sure for the exact mathematical expression for two-steps and above. So I'm asking for some references, coz I can't find any equation relating Zt and the height and width, aside from here (which is 1-step only): Circular to Rectangular conversion de K6BLG

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