On determination of the complex voltage ratio using the ellipse-fitting algorithm in the case of an ill-conditioned scattering matrix

Abstract

The article analyzes three modified versions of the standard ellipse fitting algorithm (EFA), which enables the determination of the complex voltage ratio (CVR) for extremely small values of the phase shift angle when the input scattering matrix of sampled data is poorly conditioned. The novelty of the method is in the use of EFA twice for the sequence of samples shifted by the same angle value, but with opposite signs. The results of the numerical simulation tests are confirmed by the results of measurements carried out in the sampling system using the NI PXI 4461 data acquisition module.