Chebyshev-Polynomial-Based Synthesis Algorithm for Pass-Band Acoustic Wave Filters

This work presents a complete synthesis framework for bandpass ladder filters based on acoustic resonators using a generalized Chebyshev filtering function. The method proceeds in four major steps: (i) generating the Chebyshev polynomials that define the target filter behavior in terms of reflection and transmission; (ii) extracting the ladder network filter parameters (iii) optimize the pole placement and return losses for feasibility constraints. The routine formalizes the intrinsic trade-offs between in-band and Out-Of-Band (OOB) performance and adapts the transmission zeros placement consistently with the constraints, relaxing Return Loss (RL) only when necessary. A case study of a fifth-order band-pass filter centered at 14 GHz with 8% Fractional Bandwidth (FBW) illustrates the approach. Naïve synthesis yields unrealistically high $k_t^2$, whereas the feasibility-aware iteration converges to masks-compliant responses under a technology ceiling, producing a manufacturable set of resonators. The resulting parameters are then mapped directly to device geometry and layout generation, shortening the path from RF specification to fabrication. The framework is compatible with alternative topology choices and can be extended to cross-coupled networks, duplexers, and yield-aware multi-objective design under process variation.