A Graphical Aid for the Complex Permittivity Measurement at Microwave and Millimeter Wavelengths

We introduce a novel procedure to retrieve the complex permittivity ϵ^´-jϵ^´´ of dielectric materials. It is a variant of the well-known waveguide method, and uses as input the one-port reflection data from a vector network analyzer connected to a short-circuited rectangular waveguide filled with a dielectric sample of known length. Here, it is shown that for low to moderate loss materials, the locus of the reflection coefficient in the complex plane versus frequency is approximately a circumference arc with curvature radius that depends mainly on ϵ^´´ and such that the swept angle depends mostly on ϵ^´. It is proven that fitting the theoretical circumference arc with the measured data not only allows identifying possible measurement errors but also enables estimating the complex permittivity with good accuracy. A graphical based implementation of the method is described and validated experimentally.