Coupling Matrix Synthesis for the Cascaded Filters

This paper presents a method using N+4 coupling matrix to represent cascaded filters. With additional columns and rows (corresponding to the transmission line) added to the conventional N+2 coupling matrix, the N+4 coupling matrix can be developed. It can also be used to calculate the S-parameter responses of filters cascaded through transmission lines. A cascaded bandpass filter is demonstrated using lumped LC components, and the synthesized coupling matrix is verified by the excellent agreement between simulated and calculated results.