A canonical prototype for coupled-resonator filters with frequency-dependent couplings

We present in this paper a novel canonical folded prototype circuit with some couplings varying linearly with the normalized frequency. The derivation of this prototype is based on a suitable transformation of an asymmetric lattice network, generated through a sequence of matrix rotations of the coupling matrix of the folded canonical prototype. It is shown that the lattice network is a generalization of the canonical cul-de-sac form, which is obtained when the reflection zeros are all imaginary. We have also verified that the cul-de-sac forms are possible only when the reflection zeros are all imaginary (or in para-conjugate pairs). The lattice network (or the one with frequency-dependent couplings) represents a possible alternative to the cul-de-sac forms in the synthesis of star-junction multiplexers, when the synthesized filters exhibits complex reflection zeros.