Theory for pseudo-butterworth filter response and its application to bandwidth tuning

This paper presents a new class of filter responses called pseudo-Butterworth filter response. A detailed mathematical analysis on the pseudo-Butterworth response has been carried out. In addition, the comparison between the typical complete Butterworth response and the new pseudo-Butterworth response is provided. The theory for the pseudo-Butterworth filter response indicates that bandwidth tuning maintaining excellent return loss performance can be executed adjusting not all coupling structures of a filter. As an example, a bandwidth tuning method for a second-order filter is presented. For verifying the presented bandwidth tuning theory, a second-order substrate-integrated waveguide (SIW) resonator filter has been designed, fabricated, and measured. As an example of applications to higher order filters, a theory for the fourth-order pseudo-Butterworth responses and a bandwidth tuning method for the fourth-order filters have been developed. A fourth-order filter has also been fabricated and measured for verifying the presented bandwidth tuning technique.