Enhanced Gain Extrapolation

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.