Bounds on permittivity calculations using the TE01δ dielectric resonator

The use of both mode-matching and Rayleigh-Ritz numerical techniques for complex permittivity calculations using a TE_01δ mode dielectric resonator allows the determination of lower and upper bounds of the permittivity. The maximum difference of the relative permittivity obtained from the two techniques does not exceed 0.125% for a cavity-to-sample volume ratio from 1 to 64 and relative permittivity values in the range of 1 to 100. These results were obtained by employing 126 basis functions with the Rayleigh-Ritz technique and 10 basis functions with the mode-matching method. It is possible to increase the computational accuracy of the calculations by increasing the number of basis functions.