Differing Circuit Models for Cavity Resonators

I've been trying to reconcile two circuit models of cavity resonators.

Background:
Its commonly known in order to measure a cavity resonator, one has to "load" the resonator with however you wish to excite it (probe, loop, etc.). Parameters such as the length of your probe or size of your loop will affect the measured Q and f0. But these are the loaded Q and resonant frequency, whereas many designers are concerned with the unloaded Q and resonant frequency (Q0 and f0).

My understanding is that when it comes to taking measurements to find unloaded resonator properties, a good authority is Q Factor Measurements Using MATLAB by Prof Darko Kajfez. This useful work takes smith chart measurements and finds unloaded resonator properties. It does so by assuming the following circuit model for the loaded cavity resonator:


Where the unloaded resonant frequency is given by L1 and C1 and the unloaded Q is just a function of R1 and L1 and f0. The complex impedance Z1 can detune the resonant frequency and lower the measured Q, resulting in loaded measurements. This is of course only valid at one mode near the resonant frequency.

However, another there is another circuit model detailed in "Equivalent circuit of a cavity coupled to a feeding line and its dependence on the electric or magnetic nature of output coupling structure" by P. Couffignal et. al. (I'm sure this isn't the only source to use this circuit model but I can't find it anywhere else). I find THIS circuit model to be very useful for designing the cavity probe later after I've determined (or at least confident I've determined) unloaded resonator properties.


In Couffignal's circuit model, there is electrical coupling (mutual capacitance Cm) between the probe (modeled as lumped capacitor Cp) and the unloaded cavity.

My question is, are BOTH of these circuit models valid for probe excited cavities? It feels fishy to me that I model a cavity one way for measurement and another way later down the design path, but things seem to be working out. Kajfez's model certainly seems to work for measurement purposes according to the larger microwave engineering community, yet Couffignal's seems more intuitive to me and closer to the actual physics of whats happening, a single probe coupling energy via electric fields to a resonator. Thoughts?

in your second model, the lumped equivalent circuits shown in the pink box look like the Z1 of the first model. So, to a first order they are the same.

I personally think the 2nd model is a little more useful, since it has elements that correspond to the physical reality of a probe coupling. i.e. there will be fringing capacitance to ground, an equivalent coupling capacitor to the resonator, etc.

but it is not fully detailed enough. such as if the probe has some inductance, is that shown?

also, a resonator can have higher order modes of resonance, and of course the coupling model will be drastically different for each of those higher modes. So the 2nd model is only good for a "narrowband" simulation

in your second model, the lumped equivalent circuits shown in the pink box look like the Z1 of the first model. So, to a first order they are the same.

Click to expand...

I'm glad you think so! I was suspecting that myself, but I suppose what I would really like would be an equation relating Z1 to the lumped elements Cp and Cm (this way I can continue using Kajfez's code to measure a cavity that I'm then going to simulate using Couffignal's circuit). Maybe I'll try comparing the networks.

but it is not fully detailed enough. such as if the probe has some inductance, is that shown?

Click to expand...

Possible! I suppose really I simply know the probe has some reactance at a particular mode and I represent that with a lumped capacitor, seeing as I really am mostly interested in behavior at or near the resonant frequency.