A Quantitative Approach for Direct Synthesis of Bandpass Filters Composed of Transversal Resonators

Abstract

This brief aims to propose a quantitative approach for direct synthesis of bandpass filters (BPFs) composed of a few transversal resonators. In conventional synthesis of these BPFs, coupling coefficients between input/output port and resonators are converted to external quality factor ( Qe ), ignoring inherent characteristics of resonators, such as impedance or reactance/susceptance slopes. As a result, the physical dimensions of resonators could only be determined qualitatively. In this brief, a transversal lowpass prototype derived from coupling matrix is transformed into a bandpass circuit at first, then the coupling coefficients between input/output port and resonators in these BPFs are quantitatively derived as an accurate relationship between ${J}$ inverter and susceptance slope of resonators instead. Hence, the physical dimensions of an entire BPF could be directly synthesized by solving the values of ${J}$ inverters and susceptance slope in addition to the resonant frequency of resonators. In order to verify the theory, a proof-of-concept example using cross-shaped resonator is designed and fabricated. The measured results are found in good agreement between the synthesized and simulated ones.