Coupling Matrix Decomposition of Acoustic Wave Ladder Filters in the Bandpass Domain

Abstract

The synthesis of acoustic wave (AW) filters based on lowpass prototype approximations is effective for narrowband filters, but it becomes less accurate as the fractional bandwidth (FBW) increases. To overcome this limitation, direct bandpass (DB) techniques have gained popularity to achieve precise wideband filter designs. While several works have successfully synthesized various sparse physical configurations by formulating the coupling matrix (CM) directly in the DB domain, no methodology has yet been established to obtain the AW ladder topology through the use of the CM in the DB domain. In addition, current CM-based methodologies suffer from numerical limitations, since the computation of the transversal CM in the DB domain becomes more sensitive to errors as either the filter order increases or the FBW decreases. This work presents a general and scalable methodology for synthesizing the reactance model of any AW ladder filter directly in the DB domain using the CM approach, regardless of filter order and FBW. The approach involves decomposing the ladder topology into smaller cascaded subnetworks, each corresponding to a resonator, using Householder transformations to modularize the desired order and arrangement of transmission zeros (TZs). To enhance the numerical stability during transversal CM computation, the process is performed using the roots of the rational functions rather than their coefficients, since the root values typically remain within a commensurate range of magnitude for the 16-digit precision of the double floating-point format. The effectiveness of the proposed CM-based approach in the DB domain is validated by comparing a synthesized fifth-order BAW ladder filter with a fabricated band 2 downlink, showing excellent agreement between simulated and measured responses. Finally, a fictitious 18th-order AW ladder filter is synthesized to demonstrate numerical stability.