This study proposes a novel method for evaluating the transmission characteristics of a three-phase filter using the “Fortescue-mode S-parameters,” which are S-parameters whose variables are transformed into symmetrical coordinates (i.e., zero-/positive-/negative-phase sequences). The behavior of the filter under three-phase current, including its non-symmetry, can be represented by these S-parameters, without regard to frequency. This paper also describes a methodology for creating modal equivalent circuits that reflect Fortescue-mode S-parameters allowing the effects of circuit components on filter characteristics to be estimated. Thus, this method is useful not only for the measurement and evaluation but also for the analysis and design of a three-phase filter. In addition, the physical interpretation of asymmetrical/symmetrical insertion losses and the conversion method based on Fortescue-mode S-parameters are clarified.

We propose an accurate and efficient model of having an unbalanced differential line structure, where mode-conversion and frequency dependent loss effects are considered in above the GHz frequency range. To extract model parameters of the proposed unbalanced differential line model, we measured s-parameters of test patterns using a 2-port VNA and defined a new type of mixed-mode s-parameter. The model parameters were obtained and are described for various types of the unbalanced differential line structures. Finally, the validity of the proposed model and the model parameters were successfully confirmed by a series of time-domain measurements and a lattice diagram analysis.