{
  "abstract": "Lumped-element networks give transparent, passive models of acoustic impedances whose low- and high-frequency limits can be read from the circuit, but a systematic, arbitrarily accurate construction for non-rational impedances is lacking. Continued fractions, one- and two-point Padé approximants and their identity with ladder networks and Cauer synthesis are introduced in tutorial form and applied to two examples: the radiation impedance of a baffled circular piston and the throat impedance of a horn with a piston mouth. The even contraction of the piston's continued fraction has positive coefficients, certified by interval arithmetic for the first 100 pairs, and yields a ladder of positive resistances, masses and compliances; with 14 elements the error is 4e-4 up to ka = 5. Beranek's four-element network is, to about 2%, the order-two two-point Padé approximant. A horn modelled as a cascade of waveguide sections is a continued fraction whose tail is the mouth impedance; the infinite exponential horn is a periodic continued fraction, an exact high-pass ladder. The piston networks are passive at every certified order (up to 202 elements) and are extended without changing existing elements; for a finite horn the error of the mouth network passes one to one to the throat impedance.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20371",
  "author_total": 1,
  "authors": [
    {
      "name": "Ronald M. Aarts"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f1vf4n3j8jms5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20371",
  "fulltext_url": null,
  "id": "f1vf4n3j8jms5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20371",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "eess.AS"
    ],
    [
      "arxiv",
      "physics.class-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.20371",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f1vf4n3j8jms5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.20371",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20371"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.class-ph",
      "subfield": "general"
    }
  ],
  "title": "Continued fractions and passive ladder networks for acoustic impedances: the baffled piston and the horn",
  "title_text": "Continued fractions and passive ladder networks for acoustic impedances: the baffled piston and the horn",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:31Z",
  "url": "https://research.draconitic.com/paper/f1vf4n3j8jms5",
  "venue": "arXiv",
  "versions": []
}