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Hello, I assume you are familiar with transmission line resonators and their RLC representation.
Do an Internet search on patch antenna transmission line model (without quotes). Once you have a transmission line model, you can convert that to a RLC model (over narrow frequency range). You may narrow down your search by adding LC or LCR.
You will find that a probe fed or edge fed half wave resonating patch behaves more or less as a parallel resonant circuit with a parallel loss resistance. The loss resistance is because of ohmic loss and radiation.
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