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

We introduce a novel procedure to retrieve the complex permittivity epsilon' - j epsilon '' 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 epsilon '' and such that the swept angle depends mostly on epsilon'. 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.