One of the features of the CST Microwave studio is the ability to use variables and equations instead of hardcoded values for dimensions. The variables can then be swept across a range and, with a robust enough model, simulation can be done at each point.
In this case, I varied the large and small diameter of the cavity and the height to see what affect it had on the frequency of the TE0,1,1 mode. With three variable and three points each, the result was 27 different simulations, i.e. hold the height constant and vary the small diameter across three points, then the large diameter across three points.
CST can also do distributed computation and I had two computer going for two days, one an eight core AMD and the other a six, both with better than 16GBs of memory running three simulations simultaneously.
And the results are.. promising.
The first result was to vary one parameter up to 2cm either side of ideal while holding the other two parameters at ideal values. The results were
- Varying the large diameter meant the frequency of TE0,1,1 mode only varied from 445Mhz to 437Mhz.
- Varying the small diameter meant the frequency varied by the same amount, 445Mhz to 437Mhz
- Varying the height had a larger affect and it wasn’t symmetrical: having a height 2cm too small made the frequency of the TE0,1,1 mode jump to 458Mhz, outside the 70cm Ham radio band. However, 2cm too large and the frequency only fell to ~438Mhz, just a couple Mhz lower than 440Mhz.
Now let us keep the height ideal:
- With the small and large diameter 2cms higher than ideal, the TE0,1,1 mode was at ~464Mhz (bad)
- With the small and large diameter 2cms lower than ideal, the TE0,1,1 mode was at ~453Mhz (bad)
To conclude – the resonant frequency will stay around the target 440Mhz as long as the height is ideal or less than 2cm larger and the large and small diameters are within 1cm.