Synthesis of extracted-pole filters without fixed-phase lengths

A synthesis method for extracted-pole filters is presented. As previous methods, it is based on successive extractions of simple elements, particularly what are called extracted-pole sections, composed of one non-resonant node and a resonator that is coupled exclusively to it. The difference with other methods is that this one does not require the inclusion of fixed-phase sections of transmission line, even as an auxiliary tool. Therefore, the network is composed solely of coupled resonators and non-resonant nodes. A detailed synthesis example of a fourth order filter with three prescribed transmission zeros shows that the resulting network contains reactive elements at the ports, related to its phase response. These reactive elements can be easily cancelled once computed the complete coupling matrix.