A modified indirect algorithm for extracting real permittivities from measured resonant frequencies has been developed. It is based on the perturbation theory along with the Newton iteration method, and improves the speed of the calculation with a factor of 2-4. It is superior, especially when system matrices under calculation are large. Based on the complementary advantages of the modified algorithm and a direct algorithm, a mixed algorithm of high speed and accuracy has been described. A real measurement system incorporating the linear fractional curve-fitting method and the mixed algorithm has been built to measure complex permittivities of high-Q materials.
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Fan et al. (2005) studied this question.
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