Arbitrary-order distributed-element narrowband reflectionless bandstop filter with canonical transmission response and broadband matching

In this article, we present a rigorous design method for a symmetric reflectionless bandstop filter with coupled lines. Analytic design equations and the detailed procedure for formulating narrowband reflectionless bandstop filter structures are given in this article. The presented design theory allows us to design a symmetric reflectionless bandstop filter with a predefined transmission response and an excellent impedance matching performance over a wide frequency range. Using the circuit formulation process with the closed-form design equations presented in this article, all circuit element values and the detailed physical dimensions of a filter can be obtained in a straightforward manner. In order to verify the design equations and the filter structure, a third-order Butterworth filter example has been designed, fabricated, and measured. Overall, the return loss was measured to be larger than 10 dB over a wide frequency range from dc to 4f{0} ( f{0} : center frequency).