An Efficient and Frequency-Scalable Algorithm for the Evaluation of Relative Permittivity Based on a Reference Data Set and a Microstrip Ring Resonator

In this paper, a fast and efficient algorithm for the evaluation of relative permittivity of a solid dielectric sample, when measured by a microstrip ring resonator, is proposed. It is verified for permittivity values up to 10 and material-under-test thicknesses up to 8 mm, which cover a wide range of prospective materials that may be used in electronics and communications. The algorithm was tested on 11 samples of various permittivity values and thicknesses and showed a very good agreement with their nominal permittivity values. The maximum error was within 10% even for the sample thicker than 7 mm, while the results for the four standard laminates (TLX8-060, RF60A-0300, RF60A-0620, and FR4) showed an average error of 2.34%. Attractive features of the proposed algorithm are that the results contained in the reference set are frequency-scalable, applicable to many pairs of unknown permittivity and sample thickness values, unbiased, and easily appendable with additional reference points if higher accuracy is sought.