Estimation of the propagation constant in multilayer microwave circuits using a low cost multiline system

For microwave circuits and planar antennas, complex multilayer structures pose a challenge for the designer since different materials for substrates, bonding films and coating have different frequency behaviour. Furthermore, the traditional measurement techniques for the complex permittivity rely on different field distributions than those of a transmission line making it hard to account for non-isotropic materials. This paper presents a method of measuring complex propagation constant γr, eff and the effective permittivity ϵr, eff with low cost set of simple transmission lines. It uses parts of the Multiline Calibration Technique which was developed for the calibration of vector network analyzers. An implementation in MATLAB as well as a study on the performance of the algorithm using simulated lines with added noise are presented.