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  "ediid": "ark:/88434/mds2-3813",
  "version": "1.0.0",
  "doi": "doi:10.18434/mds2-3813",
  "title": "Enhanced Gain Extrapolation",
  "contactPoint": {
    "fn": "Josh Gordon",
    "hasEmail": "mailto:josh.gordon@nist.gov"
  },
  "modified": "2025-04-23",
  "status": "available",
  "landingPage": "https://data.nist.gov/od/id/mds2-3813",
  "description": [
    "We present an overview on a recently developed\ntechnique for performing antenna gain measurements with gain\nextrapolation that uses significantly fewer data points and at\nshorter distances than traditional gain extrapolation. This enhanced\ntechnique purposely incorporates third-order mutual\ncoupling between antennas, which can be thought of as a useful\nhomodyne signal, rather than an unwanted degradation of the\nantenna-to-antenna coupling signal as has been the historically\naccepted viewpoint. From Wacker\u2019s fundamental extrapolation\nequations, we give the development of the third-order signal\nwhich underpins this technique. From the third-order signal the\nframing of gain extrapolation can be approached as a measure\nof interference fringes, as opposed to a by-rote curve fitting\nproblem, and thus provides ways of specifying the number\nof required data points and measurement distances so as to\nreduce both significantly from the traditional gain extrapolation\napproach. The truncation order of the full signal expansion,\nas it relates to the conditioning of the problem, is presented\nin light of the behavior of the design matrix that defines the\ngain extrapolation scenario and the orders of scattering, thus\nleading to fewer required samples. Along with considerations of\nthe matrix conditioning, guidelines are presented from the thirdorder\nsignal and interference fringes for sampling criteria and\nsampling accuracy criteria. These aid in choices of measurement\nsystem accuracy and precision requirements based on known\nvalues of the operating frequency, wavelength, and antenna\ndimensions. Bounds for gain uncertainty based on these sampling\ncriteria are also given. Results comparing NIST reference antenna\nmeasurements made with the traditional gain extrapolation\nand enhanced gain extrapolation technique are presented. It is\nshown that the enhanced technique can produce gain values in\nagreement and within uncertainties of the traditional technique\nfor the reference antennas."
  ],
  "keyword": [
    "antenna measurements",
    "gain extrapolation",
    "gain measurements",
    "sparse measurements",
    "antenna gain",
    "gain"
  ],
  "theme": [
    "Advanced Communications: Wireless (RF)",
    "Electronics: Electromagnetics",
    "Metrology",
    "Metrology: Electrical/electromagnetic metrology"
  ],
  "topic": [
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      "tag": "Advanced Communications: Wireless (RF)"
    },
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      "tag": "Electronics: Electromagnetics"
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      "tag": "Metrology"
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      "scheme": "https://data.nist.gov/od/dm/nist-themes/v1.1",
      "tag": "Metrology: Electrical/electromagnetic metrology"
    }
  ],
  "accessLevel": "public",
  "license": "https://www.nist.gov/open/license",
  "publisher": {
    "name": "National Institute of Standards and Technology",
    "@type": "org:Organization"
  },
  "language": [
    "en"
  ],
  "bureauCode": [
    "006:55"
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  "programCode": [
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