Differentiable Synthesis and Yield Optimization of Cross-Coupled Resonator Filters
Coupling-matrix synthesis of cross-coupled resonator filters is difficult when the desired topology is noncanonical. Automatic differentiation removes the need for problem-specific sensitivity expressions, but does not by itself overcome the nonconvex optimization landscape. This work develops a staged differentiable synthesis framework and identifies the importance of its initial objective through a controlled comparison that varies only the objective of the first optimization phase. For tenth- and sixteenth-order benchmarks, directly matching a frequency-sampled response under the prescribed topology reaches the target from $0$ of $24$ and $0$ of $12$ random starts, respectively. Replacing the first-stage objective with characteristic-polynomial matching increases the success rate to $18$ of $24$ and $12$ of $12$ (exact paired $p=7.6\times10^{-6}$ and $4.9\times10^{-4}$). The observed difference is not explained by local conditioning and is consistent with saturation of the bounded response residual far from the solution. A differentiable front end converts symmetric multiband specifications into target polynomials and, when applied end to end to a fabricated dual-band filter specification, finds a realization with one fewer cross-coupling than the published design. Finally, differentiating through Monte Carlo tolerance simulations enables yield-driven design centering, increasing the model-predicted yield from $50.9\%$ to $67.0\pm0.5\%$ under an additive coupling-error model, an improvement of $16.1$ percentage points.