Rigorous Design of Input-Reflectionless Filter With Chebyshev Response and Exact Approach to Increase Reflectionless Range

This article presents a rigorous design method for a one-port-reflectionless filter with a Chebyshev response. In particular, we, for the first time, present inverter-coupled resonator filter topologies capable of having a Chebyshev response with zero reflection at all frequencies in theory. This work demonstrates a systematic approach for filter synthesis to find the normalized coupling (inverter) values without employing optimization methods or heuristic approaches. In addition, it provides closed-form design formulas in terms of a target frequency for the design of a one-port-reflectionless filter of coupled-line structure. We also present an exact approach to increase the reflectionless range of a distributed-element filter. Distributed-element bandpass filter structures formulated by this work are capable of producing a predefined canonical transmission response and a reflectionless feature over the entire frequency range at the same time, which has never been reported up to date. The presented topologies, synthesis results, and design methods have been applied to the design of second- and third-order filters for demonstration.