Thickness-Independent Permittivity Determination of Nondispersive or Weakly Dispersive Materials Using Amplitude-Only Transmission Measurements

This article presents an attractive microwave technique for permittivity ($\varepsilon _{r} = \varepsilon _{r}^{\prime } {-} j \varepsilon _{r}^{\prime \prime }$) extraction of nondispersive or weakly dispersive dielectric materials. The technique uses amplitude-only transmission$|S_{21}|$measurements at multiple frequencies without requiring the information of sample thickness (d). To achieve this goal, the state transition matrix (STM) was first applied for determining$|S_{21}|$, and then the least minimum square (LMS) procedure was implemented to the derived objective function for unique$\varepsilon _{r}$determination. Numerical analyses were performed to validate the proposed extraction technique and evaluate the effect of inaccurate d information on$\varepsilon _{r}$determination by other similar techniques in the literature. Its performance is examined by numerical analyses based on the different number of frequency points M within a given frequency band and based on different frequency bands for the same M. Waveguide measurements at the S-band (2.60–3.95 GHz) and the G-band (3.95–5.85 GHz) of four low-loss nondispersive or weakly dispersive samples (dioxane, cyclohexane, polyethylene, and chloroform) and two lossy dispersive samples (ethanol and dimethyl sulfoxide) with different lengths were carried out to validate the proposed extraction technique and compare its accuracy against other similar methods in the literature. From measurements of low-loss nondispersive or weakly dispersive samples, it is noted that the accuracy of our extraction method does not change much with d. For instance, extracted$\varepsilon _{r}$of the cyclohexane (chloroform) sample with three different lengths differs from the reference value by less than 1% for$\varepsilon _{r}^{\prime }$and 3% for$\varepsilon _{r}^{\prime \prime }$. Although the accuracy of the proposed method lowers for dispersive samples, it can still find applications for low-cost accurate$\varepsilon _{r}$determination of nondispersive and/or weakly dispersive dielectric samples.

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