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Computation and measurement of the resonant frequencies and Q factors of high-permittivity dielectric resonators

This paper describes the measurement and computation of the resonant frequencies and the associated Q factors of dielectric parallelepipeds made of high-permittivity, low-loss ceramic materials. The radar cross-section(RCS) is measured separately near each resonance peak with a fine frequency step. A curve-fitting method is used to accurately estimate the resonant frequency and the 3 dB bandwidth from the measured RCS. The calculation uses the finite-difference time-domain method to compute the initial portion of the backscattered field as a function of time, due to a Gaussian pulse plane wave. The transient response is then extended in time to zero value by Prony's method. and the Fourier transform is used to obtain the RCS as a function of frequency. The measured and computed resonant frequencies and Q factors are compared for parallelepiped resonators of permittivity 37.84 and 79.46.