{
  "abstract": "Every reconfigurable microwave device places a tuning element - a varactor, a diode, transistor, microelectromechanical or phase-change switch, a ferroelectric or liquid-crystal load - inside a fixed passive network. The network can make a small change of the element produce a large change of the response, and design practice often credits it with the device's tuning capability. This paper shows that a fixed, linear, passive network cannot add to that capability. Each tuning element carries a tuning budget, a dimensionless length computed from its own impedance trajectory, and a fixed passive network can transmit that budget or lose part of it, never enlarge it. The unit of the budget is the hyperbolic distance of the Smith chart: the distance from a match is the logarithm of the voltage standing-wave ratio, and the distance between two states sets their mutual mismatch and is the logarithm of their commutation quality factor. From one inequality we derive closed-form, ready-to-use limits for analog and digital phase shifters, true-time-delay lines, switches, attenuators, vector modulators, impedance tuners, tunable filters, reconfigurable antennas, metasurface cells and multiport networks; the two-state and attenuation limits are attained by explicit circuits, and the phase limit by a constant-loss trajectory. We introduce the $Λ$-chart, a Smith-chart companion on which budgets and requirements are read graphically, and apply it to four published microwave case studies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06279",
  "author_total": 3,
  "authors": [
    {
      "name": "Ali Nadarloo"
    },
    {
      "name": "Mohammad Javad Hajiahmadi"
    },
    {
      "name": "Mohammad Soleimani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/61fk9cj1dyj6b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06279",
  "fulltext_url": null,
  "id": "61fk9cj1dyj6b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06279",
  "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",
      "physics.app-ph"
    ],
    [
      "arxiv",
      "physics.optics"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06279",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/61fk9cj1dyj6b.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2611.06279",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06279"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.app-ph",
      "subfield": "applied-instrumentation"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    }
  ],
  "title": "A Design Rule for Passive Reconfigurable Microwave Devices",
  "title_text": "A Design Rule for Passive Reconfigurable Microwave Devices",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:20Z",
  "url": "https://research.draconitic.com/paper/61fk9cj1dyj6b",
  "venue": "arXiv",
  "versions": []
}