Scattering matrix solution for an ideal star-junction multiplexer based on ladder-type filters

Multiplexer design is a challenging task due to the high number of variables involved, raising the difficulty as the numbers of filters increase. Numerical computing tools provide a suitable environment to evaluate topologies and technologies before starting the long journey to the device. A direct scattering matrix solution for a star-junction multiplexer, based on the circuit theory, is presented in this work. The resulting star-junction matrix is introduced in a matrix system with the scattering matrix of each filter to evaluate the overall multiplexer response. This approach allows the acquisition of main multiplexer parameters like transmission, reflection, and cross-isolation response in a compact way, achieving a good starting point for the further full-wave optimization procedure. Furthermore, an approach for the design of a star-junction multiplexer is tackled based on the reflection coefficient phase. A triplexer under this interpretation is presented and evaluated using lumped elements.