A Lumped Equivalent Circuit Model for Symmetrical T-Shaped Microstrip Magnetoelectric Tunable Microwave Filters

Based on microwave transmission theory and the ferromagnetic resonance mechanism, a lumped equivalent circuit model for a symmetrical T-shaped microstrip magnetoelectric (ME) tunable microwave filter was established by combining a straight microstrip ME device and a coupling microstrip ME device. Assuming the electrical tunable equivalent factor of the piezoelectric layer, equivalent circuit parameters were derived where the filter was equivalent to a straight microstrip resonator. Using the magnetostatic surface wave transmission mechanism, a new unit radiation impedance formula was introduced where the filter was equivalent to a coupling microstrip bandpass filter. The corresponding equivalent circuit parameters were calculated and a lumped equivalent circuit of the ME tunable coupling microstrip bandpass filter was established. The insertion loss of the symmetrical T-shaped ME tunable microwave filter was predicted using the lumped equivalent circuit under varied magnetic and electric fields. The comparisons with the simulated results and the experimental results of the electromagnetic field indicated that those were in good agreement, both qualitatively and quantitatively, verifying the validity of the lumped equivalent circuit. The influence of the ME laminate's size and the external bias magnetic field on the filter's performance was predicted by the lumped equivalent circuit, which supports the design of ME tunable microwave devices.