Simple calibration plane-invariant method for complex permittivity determination of dispersive and non-dispersive low-loss materials

Abstract

Complex scattering parameter measurements generally require meticulous measurements of materials since (a) the measured phase generally differs from the actual value, (b) a shift in calibration (reference) plane results in large errors and (c) the phase uncertainty of the reflection scattering parameters of low-loss materials greatly increases when the material thickness is of integer multiples of one-half guided wavelength. To overcome all these drawbacks, the authors propose an amplitude-only method for complex permittivity determination of dispersive and non-dispersive medium- and low-loss materials. The method utilises amplitude-only measurements of two identical samples where the length of the second sample is twice as long as that of the first. There are three main advantages of this method. First, it eliminates multi-valued terms that produce multiple solutions in the process of extracting the complex permittivity and, thus, allows one to measure unique complex permittivity. Secondly, it removes the dependency of the calibration plane on measurements and phase uncertainty in the measurements of the reflection scattering parameters. Thirdly, it uses an objective function, which depends on only one variable for its goal. This is very important since fast, dynamic and accurate computations could be achieved by using this objective function. The method is verified by amplitude-only and complex scattering parameter measurements of two low-loss samples fitted into a waveguide section in the X-band (8.2–12.4 GHz).