Matrix Synthesis for Filters With Cascaded Extracted-Pole Sections

This letter proposes a direct matrix synthesis approach for filters with cascaded extracted-pole (EP) sections. The novel synthesis technique is based on the observation that an EP section is a special case of a singlet with a zero mainline coupling. With proper phase lengths inserted into a cross-coupled network, cascaded EP sections can be directly synthesized from the canonical wheel form by a sequence of elementary matrix operations. In this letter, the equation for the suitable phaselength is derived, and the matrix transformation strategy to synthesize cascaded EP sections is developed. Numerical synthesis examples are provided to validate the novel synthesis approach.