Permittivity measurement of the substrate by using the corrected differential phase method and quick-press test fixture

Abstract

Permittivity is critical for analyzing electromagnetic propagation in the substrate. The differential phase method is desirable to measure the permittivity of the substrate. The actual measurement is usually required to be started at a low frequency to avoid the S21-phase ambiguity problem. To get rid of this problem, the unwrapped S21-phase is calculated accurately at any measurement frequency range. In the classical method of calculating the real permittivity from the effective permittivity, the calculation error increases gradually with increasing frequency, especially in an ultra-wide frequency range. To effectively reduce the error, the ratio of the calculated and real permittivity is used in the permittivity correction, which is a function with respect to frequency, dimension, and permittivity of the microstrip line. A two-step fitting process is proposed to reduce the dimension of the ratio function from three-dimension to two-dimension. Furthermore, a quick-press test fixture is designed for a more convenient measurement, which is characterized by no soldering requirement and ultra-wide frequency range. Compared with the stripline resonant method, in the proposed method, the maximum deviations of the four substrates are 0.035, −0.04, 0.07, and 0.13, in the frequency range of 1–40 GHz.