General Synthesis Methodology for Acoustic Wave Ladder Filters in the Bandpass Domain

Abstract

In designing acoustic wave (AW) ladder filters, synthesis methods utilize the lowpass prototype (LP) representation to analyze bandpass responses in the normalized domain. This technique reduces the filter’s polynomial order and achieves asymmetric responses by incorporating frequency-invariant reactance (FIR) elements. While this technique is particularly effective for narrowband filter designs, it faces limitations with wideband filters due to errors that arise when transforming extracted LP elements to the bandpass domain. There are different approaches for the exact modeling of AW ladder filters in the real frequency domain. However, current direct bandpass (DB) techniques for AW ladder filters cannot be generalized, as they lack flexibility in characterizing frequency-dependent input and output (I/O) phases and suffer from numerical issues during parameter extraction due to excessively large polynomial coefficients in high-order or narrowband filter designs. This work aims to address both problems: first, to generalize the DB methodology for AW ladder filters by computing the transfer function while considering the asymptotic behavior at both the origin and infinity, as well as controlling the frequency-dependent I/O phases through complex reflection zeros (CRZs). Second, to enhance numerical accuracy during parameter extraction by relying on precise root-finding methods rather than interpolated coefficients. To validate the effectiveness of the proposed DB approach, the synthesized model has been compared with a manufactured LiNbO3 thin-film AW ladder filter, which features a wide fractional bandwidth (FBW) of 18% and demonstrates excellent agreement between the simulated and measured responses. Finally, an 18th-order AW ladder filter has been synthesized to validate numerical stability even for narrowband filters.