{
  "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 $p=7.6\\times10^{-6}$ 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22310",
  "author_total": 1,
  "authors": [
    {
      "name": "Orion Georgiou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b3ejcphkca9a6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22310",
  "fulltext_url": null,
  "id": "b3ejcphkca9a6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22310",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "eess.SP"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2208|Microwave Engineering and Waveguides"
    ]
  ],
  "openalex": "W7214026666",
  "pdf_url": "https://arxiv.org/pdf/2609.22310",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b3ejcphkca9a6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22310",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22310"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Differentiable Synthesis and Yield Optimization of Cross-Coupled Resonator Filters",
  "title_text": "Differentiable Synthesis and Yield Optimization of Cross-Coupled Resonator Filters",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/b3ejcphkca9a6",
  "venue": "arXiv",
  "versions": []
}