Unique Permittivity Determination of Low-Loss Dielectric Materials From Transmission Measurements at Microwave Frequencies

Abstract

Abstract-A non-resonant microwave method has been proposed for accurate complex permittivity determination of low-loss materials. The method uses two measurement data of the magnitude of transmission properties of the sample. While the first datum must correspond to a frequency point resulting in a maximum magnitude of transmission properties, the other can be any datum at a frequency different than the first datum and not far distant from the first datum. Two closed-from expressions are derived for a good initial guess using the above data. The limitations of each expression are discussed. The method has been validated by transmission measurements at X-band (8.2-12.4 GHz) of a low-loss sample located into a waveguide sample holder.

Microwave Method for Thickness-Independent Permittivity Extraction of Low-Loss Dielectric Materials From Transmission Measurements

“…In the literature, various methods based on complex S 21 measurements have been proposed for stable ε r measurement of highloss and low-loss dielectric materials [30][31][32][33][34][35][36][37][38]. While the method in [30] assumes that the sample is low-loss and thin, the method in [31] uses a second-order approximation to derive a one-variable objective function for fast ε r measurements.…”

“…Although the technique in [37] is attractive and applicable to low-loss samples, it is not appropriate for thin samples with lower dielectric constants. To eliminate this drawback, the method in our recently published paper [38] can be employed. However, the discussed methods in [34][35][36][37][38] need precise knowledge of the sample thickness.…”

“…To eliminate this drawback, the method in our recently published paper [38] can be employed. However, the discussed methods in [34][35][36][37][38] need precise knowledge of the sample thickness. Elimination this necessity is very crucial in the extraction of electrical properties of low-loss materials, as will be discussed in Results Section of the paper.…”

“…In addition, any inhomogeneity or irregularity present in the second sample also lowers the measurement accuracy. Besides, swept-frequency phase measurements [34,35] or magnitude measurements [36][37][38] of S 21 over a broadband can be directly utilized to obtain unique ε r . While the formulation in [34], sometimes, requires at least three measurements at different frequencies for a correct initial guess of ε r , those in [35] are complex in nature.…”

“…Assuming e jωt time convention, between calibration planes in Fig. 1, the normalized S 21 can be expressed as [24,38] …”