The Enhanced Gain Extrapolation Technique

Published

November 6, 2026

Author(s)

Joshua Gordon, Benjamin Moser

Abstract

We present an overview on a recently developed technique for performing antenna gain measurements with gain extrapolation that uses significantly fewer data points and at shorter distances than traditional gain extrapolation. This enhanced technique purposely incorporates third-order mutual coupling between antennas, which can be thought of as a useful homodyne signal, rather than an unwanted degradation of the antenna-to-antenna coupling signal as has been the historically accepted viewpoint. From Wacker's fundamental extrapolation equations, we give the development of the third-order signal which underpins this technique. From the third-order signal the framing of gain extrapolation can be approached as a measure of interference fringes, as opposed to a by-rote curve fitting problem, and thus provides ways of specifying the number of required data points and measurement distances so as to reduce both significantly from the traditional gain extrapolation approach. The truncation order of the full signal expansion, as it relates to the conditioning of the problem, is presented in light of the behavior of the design matrix that defines the gain extrapolation scenario and the orders of scattering, thus leading to fewer required samples. Along with considerations of the matrix conditioning, guidelines are presented from the thirdorder signal and interference fringes for sampling criteria and sampling accuracy criteria. These aid in choices of measurement system accuracy and precision requirements based on known values of the operating frequency, wavelength, and antenna dimensions. Bounds for gain uncertainty based on these sampling criteria are also given. Results comparing NIST reference antenna measurements made with the traditional gain extrapolation and enhanced gain extrapolation technique are presented. It is shown that the enhanced technique can produce gain values in agreement and within uncertainties of the traditional technique for the reference antennas.

Proceedings Title

48th​ ​Annual​ ​Meeting​ ​and​ ​Symposium​ ​of​ ​the Antenna​ ​Measurement​ ​Techniques Association

Citation

<i>48th​ ​Annual​ ​Meeting​ ​and​ ​Symposium​ ​of​ ​the Antenna​ ​Measurement​ ​Techniques Association</i> (48th​ ​Annual​ ​Meeting​ ​and​ ​Symposium​ ​of​ ​the Antenna​ ​Measurement​ ​Techniques Association, Austin , TX, US, 01-NOV-26 to 06-NOV-26)

Conference Dates

2026-11-01T00:00:00

Conference Location

Austin , TX, US

Conference Title

48th​ ​Annual​ ​Meeting​ ​and​ ​Symposium​ ​of​ ​the Antenna​ ​Measurement​ ​Techniques Association

Pub Type

Conferences

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Keywords

antenna measurements, gain extrapolation, gain measurements, sparse measurements, antenna gain, gain

Citation

Gordon, J. and Moser, B. (2026), The Enhanced Gain Extrapolation Technique, 48th​ ​Annual​ ​Meeting​ ​and​ ​Symposium​ ​of​ ​the Antenna​ ​Measurement​ ​Techniques Association, Austin , TX, US, [online], https://nps-ext.nist.gov/nps/nps_public_api/api/Publication/file/960021 (Accessed November 10, 2026)

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