Direct Synthesis of Acoustic Wave Multiplexers Built on Fully Canonical Multiport Functions

Abstract

This work proposes the first analytical method for the direct synthesis of multiplexers based on acoustic wave (AW) ladder filters connected in a star junction topology. It describes the computation of the polynomial representation of a multiport ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K} +$ </tex-math></inline-formula> 1 ports) network with fully canonical (FC) channels and derives a set of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> distorted channel polynomials from which each of the AW ladder filters is synthesized. The channel polynomials are distorted in a way such that when connected together at the star junction, the desired multiplexer response is obtained avoiding degradation due to channel loading. The method allows to freely set the fractional bandwidth (FBW), return loss (RL), and transmission zeros (TZs) of each channel enabling the search for multiplexers that fulfill the technological requirements of AW technology in terms of electromechanical coupling coefficient and area occupancy among others. Moreover, since the multiport network polynomials incorporate the complete effects of the loading between channels as, for example, additional TZs, the synthesized multiplexers depict an improvement of isolation when compared with a design based on only controlling the reflection phase of each channel filter. The proposed method is rigorously demonstrated by means of a synthesized multiplexer example providing the Butterworth–Van Dyke (BVD) elements of each channel filter. This approach avoids intensive optimization procedures and represents a useful technique for the design of carrier aggregation (CA) filter modules in a direct and controlled manner.