Differentiable Synthesis and Yield Optimization of Cross-Coupled Resonator Filters
Abstract
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=7.6×10−6 and 4.9×10−4). 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±0.5% under an additive coupling-error model, an improvement of $16.1$ percentage points.
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BibTeX
@misc{georgiou2026differentiable,
title = {{Differentiable Synthesis and Yield Optimization of Cross-Coupled Resonator Filters}},
author = {Orion Georgiou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22310},
eprint = {2609.22310},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22310},
}
RIS
TY - UNPB
TI - Differentiable Synthesis and Yield Optimization of Cross-Coupled Resonator Filters
AU - Orion Georgiou
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.22310
UR - https://arxiv.org/abs/2609.22310
AB - 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=7.6×10^−6 and 4.9×10^−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±0.5% under an additive coupling-error model, an improvement of $16.1$ percentage points.
ER -