Comparision of two optimization criteria in antenna problems with free phase pattern

Abstract

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

Application of modified Newton method to nonlinear integral equation of circular antenna synthesis problem

“…In the first case the increment is a smooth function of ϕ , in the second one it also has unexpected jumps. The solution 3 f starts at 2 2.56 c = from 0 f having already two sign alternations.…”

“…1 , ϕ ϕ are the angular coordinates of the points in the far-field zone, 0 J is the Bessel function of the first kind, c ka = is the variable parameter of the problem; a nonessential factor is omitted in (3). Analogous problem for the linear antenna was considered in [3] using the finite-polynomial presentation.…”

“…Analogous problem for the linear antenna was considered in [3] using the finite-polynomial presentation.…”

“…Such problems have non-unique solutions branching as a parameter varies, and their investigation has both the theoretical and practical interests. Recently a class of equations of such a type was found having semi-analytical solutions expressed by finite-order polynomials [1]- [3]. In general case, such equations can apparently be solved only by numerical methods.…”

Generalized nonlinear integral equation of hammerstein type

“…Such type of equations arises in the phase optimization problems of the antenna and transmitting lines with restrictions to the solution. The equation was first investigated in [1]. The problem was reduced to a system of transcendental equations and one nonlinear integral equation for the parameters of generating polynomial and an auxiliary real function.…”