Synthesis of Cross-Coupled Filters with Frequency-Dependent Couplings

This paper presents a novel synthesis technique for coupled-resonator filters with frequency-dependent couplings. Unlike the works so far appeared in the literature, the proposed technique is not based on the optimization of a network with assigned topology, but it consists in the explicit synthesis of a folded prototype with frequency-dependent transversal couplings. The proposed procedure starts with the synthesis of a new type of canonical prototype with frequency-invariant couplings (the asymmetric lattice); this prototype is then suitably transformed by means of scaling and rotations of coupling and capacitance matrices for obtaining the new configuration with frequency-dependent couplings. Concerning the asymmetric lattice prototype, we show how this canonical network degenerates, in a special case, into the cul-de-sac form; this happens when the assigned reflection zeros are imaginary (or in pairs with opposite real part). This also implies that cul-de-sac is admissible only when reflection zeros satisfy this condition. The novel synthesis approach is illustrated with several examples. A test diplexer employing filters with frequency-dependent couplings has been designed and fabricated for validating the novel synthesis approach.