It might have several different reasons: the formula has some assumptions that the simulation does not fulfill; the parameters you used might be different from simulation. for example, are r1, and r2 and power attentuation coefficient accurate and they are the same with simulation?
Please refer this post for more possible causes:
Ansys Insight: Why my simulation result is different from published paper or experiment?
It might be easier to use the theory and simulation for smaller ring which you can use FDTD for verification.
If the theoretical analysis can accurately predict final result, we would not need to simulate it.
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