Two criteria of antenna synithesis by the amplitude radiation pattern are compared. They use the reactive power and weighted current nonn, respectively, both supplying the mean square difference betweenl the desired and obtained amplitude patterns. The technique based on the generating polynomial concept is applied to nonlinear integral equations in both eases. Numerical results are presented.IQ Introduction The mean square difference between the desired and obtained radiation pattems is usually used as ani optimization criterion in antenna synthesis problems. For the linear and plane antennas the integration domain is extended in the respective functionals by the complex angles introduced for describing the so-called reactive power I1]. Similar statements are used in the case when only amplitude pattern is given [2,3] The weighted current norm can be introduced into the functional instead of the reactive power [3]. Such a statement is applicable for other antennas, e.g., for the closed curvilinear ones, for which the concept of complex angles is inapplicable [23. In the problem statement the choice of the weight factor at the current norm is important.In the case of linear antenna, the standard formulation of the synthesis problem by the amplitude pattem permits analytical solutions expressible by generating polynomials [5]. Sucl an approach is generalized onto a wider class of nonliinear problems with free phase [6,7]. In this paper, the approach is applied to the fulnctionals of the second type (with weighted summands). In this case the problem is reduced to a finite set of equations, one of which is nonlinear integral one, and the other are transcendental.Numerical results are presented. The main purpose of calculations was to find the weight factor in the second formulation, which provides in the both statements the same values of the mean square deviation of the amplitude patterns in the real (visible) angle range.
Problem formulationThe functional to be minimized in the linear antenna synthesis problem by the amplitude radiation pattern has the form [2] 5(S)i(X -u(u'~J )IIf1(cM1)td, -cro(ut) + 11u112 -IfI~(Itla 5where u is the current on the antenna, 24
The antenna synthesis problem according to the prescribed power radiation pattern with the equality norm condition is solved by the approach based on the concept of generating polynomials. The variational formulation, supplied by the Lagrange method of multipliers, is applied. The modified Newton method is used for numerical solving of the respective integro-transcendental equation systems. The approach was numerically tested on the example of the antenna synthesis problem, recently solved directly by the Newton method. Numerical results are compared and analyzed. Index Terms-Power synthesis problem; linear antenna; nonlinear integral equation; polynomial representation of solutions; modified Newton method.
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