In this article, we explore how acoustic wave filters starting with shunt resonator require particular reflection phase conditions to ensure that the synthesized filter is feasible. The position of transmission zeros (TZs) along with the phase of the objective filter function might lead to nonfeasible solutions where the first and last resonators require elements with positive reactance slope in the static branch, or equivalently, a nonphysical negative static capacitor. Since the reflection phase of a duplexer-oriented filter is fixed to reduce loading effects, the feasibility problem is solved by bringing the resonance frequency of the first resonator beyond the central frequency of the counter band. However, this entails surpassing the limits of the electromechanical coupling coefficient. We demonstrate how two reactive elements at the input overcome this resonance position limitation and provide a simple rule to decide the right topology. The position of the first TZ of duplexers will play an important role. Moreover, we provide rules on the reflection phase values that ensure that all resonators have a capacitive static branch.

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.

The use of classical symmetrical polynomial definition to synthesize fully canonical inline filters with an asymmetrical distribution of the transmission zeros along the topology leads to the occurrence of uneven admittance inverter in the main-line. This form introduces some limitations to transform such topology into a ladder network. Despite circuital transformation can be used to accommodate both technology and topology, it is usual that extra reactive elements are necessary to implement phase shifts required to achieve the complete synthesis. This article introduces a novel method able to determine the required phase correction that has to be applied to the characteristic polynomials in order to equalize all the admittance inverters in the main path to the same value. It has been demonstrated that a suitable pair of phase values can be accurately estimated using a developed hyperbolic model which can be obtained from the transmission and reflection scattering parameters. To experimentally validate the proposed method, a Ladder-type filter with asymmetrical polynomial definition has been synthesized, fabricated, and measured, demonstrating the effectiveness of the developed solution.