Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 86

In some microwave applications, ring-shaped cavity resonators with a very narrow center part are used. A cross section of such a resonator is shown in Fig. 10-27, in which d is very small in comparison with the resonant wavelength. Assuming that this resonator can be represented approximately by a parallel combination of the capacitance of the narrow center part and the inductance of the rest of the structure, find
a) the approximate resonant frequency,
b) the approximate resonant wavelength.