Let's say you know the resonant frequencies of a rectangular microwave resonator and that you are only considering TE_0np modes. However, you do not know which values of (n,p) belong to which frequency.
How would you approach this problem?
Please bear in mind that you may have different materials in the resonator, thus you cannot use the analytical solution of a homogeneously-filled resonator
Any thoughts on the matter are appreciated!
It's not clear what you mean by "know the resonant frequencies?" Do you know them from measurements? Are these modes degenerate in (n,p)?
Hi Paul,
I am using circuital analysis to find these resonant frequencies. Through this technique, you split your problem into simpler networks, then you calculate the admittance and scattering matrices of each network and finally find the frequencies at which the determinant of their product becomes zero. This, however, merges the effect of all modes:
Let's say you plot the resulting equation for different frequencies, and you observe there are resonances at 0.6, 1.0 and 1.2 GHz. So, now you have three resonances but do not have information about the values of n,p they are associated to.
Hope this helps clarify my question a little bit further.
Thanks again for your comments!
On the one hand you have an approximate circuit model and on the other the mode numbers, n and p. There must be an invertible connection between the circuits and the individual modes(cavity fields) from which it should be possible to extract modal coefficients. If I were doing a cavity problem I would probably try a modal analysis. For rectangular guides this is straight forward since the modes are known in closed form and are simple sines and cosines. With the modal expansion of the fields setup a system of eigenvalue equations which include the dielectrics. Solving this problem will then yield the resonance frequencies and corresponding expansion coefficients.
"Please bear in mind that you may have different materials in the resonator, thus you cannot use the analytical solution of a homogeneously-filled resonator"
Without specifying the resonator structure it would be nearly impossible to answer your question.
But in general the exact solutions exists even for inhomogeneously filled resonators thus circuit model approach is not recommended.
Well the easy way out would be simulate this structure in an FEM program where a modal analysis can be done (sweep a set of modes and see which one resonants).
Other than this, I would first try to estimate the average wavelength in the structure for these specific resonant frequencies at different modes. Then compare the length of the structure this and look for something that is an N/2 multiple where N is an integer.
As a note, the 1.2 resonant frequency is probably the same mode as the 0.6 but with the "p" value doubled. For instance, if the 0.6 corresponds to TE012, then the 1.2 should be TE014 (assuming the wave is propagating/ oscillating in the z direction).
Without knowing more about the structure, this is all I can think of.
Hi.
I think,if you could separate your structure into some homogenous sections you can find propagated modes in each sections by means of checking propagation constant.
I hope this help you.
An universal method is the visualization of electromagnetic fields at the resonance frequencies
https://www.researchgate.net/publication/275212649_TELECOMMUNICATION_MILLIMETER_FILTERS_BASED_ON_WAVEGUIDE_JUNCTIONS_%28in_Russian%29
Article TELECOMMUNICATION MILLIMETER FILTERS BASED ON WAVEGUIDE JUNC...
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