Synthesis, design, and fabrication of filters with dual/multiple dangling nodes

A synthesis and design approach is proposed for filters with multiple transmission zeros generated using dual/multiple dangling nodes. It begins with the synthesis of the general characteristic polynomials. An analytical method is proposed to derive the coupling matrix from the polynomials. Two third-order-two-zero bandpass filters (BPFs) are first used to demonstrate the synthesis and design procedure. Two third-order-four-zero BPFs are then designed and prototyped using two pairs of mixed E/H-plane dual dangling nodes. The fabrication of the mixed E/H-plane complex filter structures are enabled by 3D printing technology. A monolithic filter is produced and tested. Excellent agreement between the measurement and the design substantially verifies the synthesis and design approach and demonstrates the capability of the additive manufacture technology.