Microwave Coupling Structures for Spectroscopy

The coupling of microwave resonators to transmission lines is described for inductive coupling, parallel capacitive coupling, and series capacitive coupling. Equations are presented for the calculation of inductance, capacitance, and resonant frequency of a loop-gap resonator from its physical dimensions. Equations are also given for the parameters of the coupling structure to achieve critical coupling for each of the three coupling methods. Suggestions for practical application of these equations are given.