Systematic Design of Planar Millimeter-Wave Filters Based on Hexagonal Barium Ferrite (BaM)

The design of magnetic filters for millimeter-wave (mmWave) applications is of interest due to the expanding demand for higher-frequency spectrum utilization. This article focuses on modeling and designing mmWave filters using M-type barium hexaferrite (BaM). A systematic design methodology is proposed, beginning with the construction and optimization of BaM resonators to achieve suitable energy coupling coefficients. These optimized resonators are subsequently coupled to form bandpass filters. An equivalent circuit model is developed to quantify the efficiency of coupling between electromagnetic (EM) waves and ferrimagnetic resonance (FMR), offering a robust performance metric for BaM resonators. The practical implementation involves planar printed-circuit-board (PCB)-based BaM resonators and filters. The fabricated bandpass filter, with in-plane dimensions of $3.8\times 2.7$ mm and an out-of-plane dimension of 0.51 mm, exhibits an insertion loss of 6 dB and achieves a 3-dB bandwidth of 190 MHz at 41.5 GHz. These results validate the feasibility and efficacy of the proposed design methodology, indicating significant potential for advancements in the development of high-performance magnetic filters.