Characterization of the lossy dielectric materials using contour mapping

The imaginary part of the complex permittivity of a lossy dielectric material is large and couples with its real part. The resonant frequency of a cavity with the sample depends not only on the real part of the complex permittivity of the sample but also the imaginary part, resulting in serious ambiguity in determining the sample's complex permittivity. This work proposes a contour mapping method to determine the complex permittivity. The full-wave simulation gives us the contours of the resonant frequency and the quality factor, which are functions of the relative dielectric constant and the loss tangent. By mapping the measured resonant frequency and the measured quality factor, one can uniquely determine the complex permittivity of the sample. Five liquids were examined, including three low-loss materials for benchmarking and two lossy materials. The measured complex permittivities of the three low-loss materials agree very well with the other methods. As for the lossy materials, the measured relative dielectric constant and the loss tangent of alcohol are 6.786 and 0.895, respectively. Besides, the measured dielectric constant of glycerin is 6.811, and its loss tangent is 0.562. The proposed contour mapping technique can be employed to measure the complex permittivity of liquids and solids from lossless to lossy materials.