VSIE-Based Scattering Parameter Analysis for a Tunable Bandpass Filter With a PET-Controlled Magnetodielectric Perturber

Electromagnetic analysis with $S$ -parameter characteristic is carried out for a tunable bandpass filter with a magnetodielectric perturber controlled by a piezoelectric transducer. The filter consists of a hairpin-like microstrip resonator and a perturber as a superstrate, which is composed of thin ferrite film with a high permeability and Rogers dielectric material with a high permittivity in a sandwich style. The structure is of multiscale feature because the thickness of the thin film is very small but cannot be ignored and also of multimaterial property because there are three strongly different materials. The problem can be governed through surface integral equations in the integral equation approach, but we use volume-surface integral equations to formulate it so that the conditioning of impedance matrix can be improved in the method of moments (MoM) solution. In addition, the dyadic Green´s function is kept in its original form in the implementation of MoM and thus the problems in the traditional MoM can be overcome. Numerical examples are presented to illustrate the approach and good results can be observed.