Range distance requirements for measuring low and ultralow sidelobe antenna patterns

Abstract

The effects of quadratic phase errors due to finite length pattern ranges on the measurement of low and ultralow sidelobe antennas are considered. The well-known <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2D^{2}/\lambda</tex> rule-of-thumb distance is shown to be adequate only for measuring patterns having moderately low sidelobes (i.e., down to about -30 dB). This distance is shown to be inadequate for measuring low (-30 to -40 dB) and ultralow (below -40 dB) sidelobe patterns if the near-in sidelobes are to be preserved within reasonable errors (e.g., less than 1 dB). A relationship between sidelobe errors and range distances is derived from calculated patterns for a number of one-dimensional amplitude distributions with various quadratic phase errors. This relationship is plotted on log-paper in terms of the change (error) in the highest sidelobe versus the range distances in multiples of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D^{2}/\lambda</tex> . This plot clearly shows the range distances required for various low sidelobe patterns and measurement tolerances. A corresponding plot of mainlobe directivity errors versus finite range distances is also presented. The results show that the effects of quadratic phase error on near-in pattern sidelobes diminishes rapidly with angular distance from the main beam. Thus for a given range length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ND^{2}/\lambda</tex> , the errors on the second and third sidelobes are significantly less than the error on the first sidelobe. This means that for many low and ultralow sidelobe antennas, practical range distances (such as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2D^{2}/\lambda</tex> .) can still be used to measure wide angle sidelobe levels accurately at the expense of "losing" the first one or two sidelobes.