A Direct Synthesis Approach of Bandpass Filters with Extracted-poles

A new direct coupling matrix synthesis approach for bandpass filters with extracted-poles is presented. Different from existing synthesis methods, the extracted-pole sections and the remaining cross-coupled resonators are synthesized in a unified approach. As a result, the coupling matrix synthesized contains both resonant and non-resonant nodes. Another distinct feature of the coupling matrix synthesized by the proposed approach is that its frequency response can involve certain phase offset, which can be determined from our synthesis approach.