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Antenna local phase center and its hodograph: methodology and calculation technique


Yu. I. Choni – Ph.D. (Eng.), Associate Professor, Kazan National Research Technical University n.a. A.N. Tupolev – KAI

Interest in the phase structure of the radiation field of antennas was associated primarily with the development and enhancement of horn or other types of feeds for parabolic reflectors. It is very important that the feed forms a spherical wave, the center of which, so-called phase center, should be placed in the focus of the reflector. Wide analytical studies were carried out, methods and means for ex-perimental determination of the phase center position were developed many years ago. With the advent of satellite positioning systems, high accuracy of which is due to phase measurements on the carrier frequency, the requirements for the stability of the phase center and the accuracy of its control have multiplied. This gave rise to a second wave of research on this subject these days using digital modeling and modern antenna measurement tools.
For real antennas, with rare exceptions, there is no phase center in the strict sense of the word. Therefore, they introduce the concept of a local phase center as the center of a spherical surface that reproduces a sufficiently small portion of the phase front of the emitted field in the vicinity of the remote observation point. In most works, the local phase center is identified with the center of curvature of the phase-front curve in the main cross sections of the radiation pattern. This is far from always applicable, since the curvature of the phase front in mutually perpendicular cross sections can differ significantly. The article is devoted to the analysis of methodological and computational aspects of the universal computing algorithm to find the position of a local phase center by the best mean square approximation. In it, there are closed expressions for the coefficients of the corresponding set of linear algebraic equations of the fourth order: three coordinates of the local phase center and the radius of the approximating sphere. While the angular coordinates (θ, φ) of the observation point change, the local phase center moves, forming a surface in three-dimensional space, called a 3D hodograph. In some cases (a linear antenna, for example), this hodograph is a surface of rotation and one can confine ourselves to analyzing the principal curve, that is a 2D hodograph.
A circle antenna array, whose elements have the cardioids pattern, used as a test example to compare several computational algorithms. For cases of zero and first phase variations of the excitation distribution, 3D hodographs are presented for a different number of antenna elements. They are shown by an axonometric projection of the set of local phase center points that correspond to directions (θi, φj) with spacing of 5 degree. The shape of many of these hodographs is unpredictable and curious. It is found that the calculation of the local phase center as the center of curvature of the phase front curve leads to erroneous results that contradict the physical meaning.

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