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# Cavity Modes

## Cavity Modes

(OP)
I have been searching my microwave textbooks for information on rectilinear cavity modes and have found very little practical information. For standard rectangular waveguide we have simple rules like the height is half the width making the next pair of modes 2:1 above the dominant mode. A cubic cavity seems like a very poor idea as the number of degenerate modes is large.

What I am after is the idiot’s guide to cavity modes. It seems that TE101 is the lowest mode.

My ultimate goal is to make a cavity oscillator using a MMIC. Initially I thought I could "play" with the idea by doing this at some low frequency (a few GHz) so the probe/launcher dimensional tolerances are not such an issue.

If I use a 25mm wide waveguide, 12mm high, then the cutoff frequency is f= c/lambda = 3E8/(2*25E-3) = 6GHz. So aiming for 7GHz, for example, how long should the cavity be?

It seems that for TE cavity modes, 1/lambda= sqrt(  (m/2a)^2 + (n/2b)^2 + (p/2d)^2 )

and it is best to make one of m, n or p zero.

If the cavity is 25mm x 12mm x 25mm, I get 6GHz * sqrt(2)= 8.48GHz, which is reasonable.

I don’t have an equation for the TM cavity modes.

So the real question is what ratio of sides should I use to get the highest ratio between the lowest mode and the next higher modes?

I would think that this was a standard textbook result, just not in any of my textbooks!

### RE: Cavity Modes

You need to find a graph called a "mode chart".  You might find one somewhere on the web.  Older microwave engineering books like Ramo, Whinnery, and Van Duzer have them.

### RE: Cavity Modes

Alternatively, it would be pretty easy to make your own mode chart on Matlab or Mathcad.

### RE: Cavity Modes

(OP)
Ramo, Whinnery and Van Duzer (third ed) only has a small section (10.4) on this subject, without a mode chart. I did find a chart in Very High Frequency Techniques (c.1947) which shows it nicely so I recreated the chart in Mathcad.

The cavity I had in an earlier amplifier design was 29mm x 20mm and I easily got this to oscillate at 7.15GHz, 14.29GHz, 21.43GHz, 28.58GHz. Unfortunately the lowest cavity mode is 9.11GHz.

The only thing I can think is that the ceramic tile covering the base of the cavity is slowing down the mode in some difficult to calculate way.

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