N. N. Voitovich. Antenna synthesis according to prescribed amplitude radiation pattern (V.V.Semenov's method). Radio Engineering and Electronic Physics, v.17, No.12, 1972 (Transl. from Radiotekhnika i Elektronika, v.17, No.12, 1972, p. 2491-2497).

Abstract. A method of antenna synthesis is described, which is a development of the method proposed before for quasioptical problems solving. The mean square difference between the given and obtained amplitude patterns in the sum with the reactive power is used as optimization criterion. The problem is reduced to a nonlinear integral equation solved by an iterative method. The solutions of this equation are nonunique, some of them are minimal points and some only stationary points of the minimized functional. Numerical results are presented. The method is used also in the case when the pattern is expressed in the form of a linear combination of partial ones.

N. N. Voitovich, P. A. Savenko. Generalized criterion of pattern proximity in the problem of antenna synthesis by V.V.Semenov's method. Radio Engineering and Electronic Physics, v. 18, No.9, 1973 (Transl. from Radiotekhnika i Elektronika, v. 18, No.9, 1973, p. 1794-1798).

Abstract. An optimization criterion proposed before for the antenna synthesis according to prescribed amplitude pattern is generalized by introduction in the norm definition a weight function characterizing different demands to proximity degree in different angle directions. In the case of even prescribed amplitude patterns, a new kind of solutions are obtained. These solutions give even amplitude patterns and odd phase ones andprovide in some parameter ranges the best proximity to prescribed pattern than completely even patterns. Numerical results for linear antenna with various prescribed patterns are presented.

N. N. Voitovich, P. A. Savenko. An integral equation of antenna synthesis theory. Matematicheskiye Metody i Fiziko-Mekhanicheskiye Polya, v.2, 1975, p. 161-163 (In Russian).

Abstract. A homogeneous linear integral equation is considered. The equation arises when the branching of solutions of nonlinear equation of antenna synthesis theory is investigated. Eigen functions of the linear equation are written in the analytical form for the case of linear antenna. The branching points could be calculated from simple transcendental equations.

N. N. Voitovich, P. A. Savenko. Branching of solutions of the antenna synthesis problem based on a specified amplitude radiation pattern. Radio Engineering and Electronic Physics, vol. 20, June 1975, p. 1-8. (Transl. from Radiotekhnika i Elektronika, v. 21, No.4, p. 723-729).

Abstract. A nonlinear integral equation arising in the antenna synthesis problem according to prescribed amplitude pattern is considered. The equation have nonunique solutions branching when physical parameters are changed. Transcendental equations for branching points are obtained for the case of linear antenna. Numerical results are presented.

N. N. Voytovich, P. A Savenko. A method for solving the antenna synthesis problem by given amplitude directivity pattern. 31st All-Union Scient. Session Dedicated to Radio Day (Proc.), Moscow, 1976, p. 63-64 (In Russian)

N. N. Voytovich, P. A Savenko. Synthesis of antennas from a specified amplitude pattern and related problems in quasioptics (review). Radio Engineering and Electronic Phys., v. 24, No.8, 1979 (Transl. from Radiotekhnika i Elektronika, v. 24, No.8, 1979, p. 1485-1500).

Abstract. A method of the antenna synthesis according to prescribed amplitude pattern, proposed by authors before, as well as some its applications are described in the review form. The method is based on minimization of the sum of mean square difference between given and obtained amplitude patterns and power coming out the given angles including reactive power. The problems considered in the paper are following: optimization of complete current distribution or of phase one only in linear antennas and arrays, forming the given field distributions by two-aperture quasioptical system, combined synthesis of the quasioptical feeder tract together with the mirror or lens antenna. Mathematical description of the method as well as numerical results regarding some concrete problems are presented.

N. N. Voitovich, P. A. Savenko. Antenna synthesis at prescribed amplitude pattern. Direct and Inverse Problems of Diffraction Theory, Inst.Radioeng.&Electr., Moscow, 1979, p.142-166 (In Russian).

M. I. Andriychuk, Ya. V. Vasilkiv, N. N. Voitovich, A. M. Kovalchuk, B. M. Podlevskiy, P. O. Savenko. Sythesis of radiating systems by prescribed amplitude pattern. Wave and Diffraction, Inst.Radioeng.&Electr., Moscow, 1981, v.1, p. 11-14 (In Russian).

P. A. Savenko, N. N. Voitovich. . Radiating system synthesis by the prescribed amplitude pattern. Proc. of VII Colloq. on Microw. Commun., Budapest, 1982, v.1.

M. I. Andriychuk, N. N. Voitovich. . Synthesis of closed plane antenna according to prescribed amplitude pattern. Radiotekhnika i Elektronika, v. 30, No. 2, 1985, p. 276-281 (In Russian).

Abstract. A plane curvilinear antenna is considered. The current distribution on the antenna is found, which minimizes a functional as the sum of mean square difference (with a function as weight factor) between the given and obtained amplitude patterns and the current norm (with a constant weight factor). Problem is reduced to a nonlinear integral equation. A modification of the conjugate gradient method for direct functional minimizing is proposed. Numerical results regarding antennas of circular and elliptic shape are presented.

N. N. Voitovich. Synthesis of closed plane antenna with limitations at field in near zone. Radiotekhnika i Elektronika, v. 30, No. 3, 1985, p. 458-462 (In Russian).

Abstract. A method for calculation of the two-dimensional curvilinear antenna shape and current distribution on it is proposed, when the amplitude pattern as well as amplitude of field distribution on some circle are given. Optimization criterion is a functional having the form of the sum of two functional-weighted mean square differences between the given and obtained amplitude patterns and between the field distributions, respectively. The problem is solved in two step. In the first step, a field distribution on the circle minimizing the functional is defined. In the second step, the antenna shape and current distribution are calculated. Numerical results are given.

M. I. Andriychuk, I. P. Bolotova, N. N. Voitovich, O. F. Zamorskaya, Yu. V. Semenyuk, V. P. Tkachuk, Yu. P. Topolyuk, I. V. Chmyga. Calculation of antennas with synthesed semitransparent surfaces. Wave and Diffraction - 85, Tbilisi, 1985, v. 1 (In Russian)

M. I. Andriychuk, V. P. Tkachuk, Yu. P. Topolyuk, N. N. Voitovich. Numerical solution of non-linear problems of constructive antenna synthesis. Proc. of URSI Int. Sympos. on Electromagn. Theory, Budapest, 1986, Part A, p. 121-123.

Abstract. Methods of solving three problems of constructive antenna synthesis are discussed. The resonant antenna shape or its walls transparency are found. The functional in the form of mean-square deviation of the created amplitude pattern from the prescribed one is minimized. All the problems are nonlinear and are solved by the successive approximation method.

N. N. Voitovich, B. Z. Katsenelenbaum, E. N. Korshunova, L. I. Pangonis, A. N. Sivov, A. D. Shatrov. Electrodynamical bases of constructive antenna synthesis. Antenny. Radio i Svyaz' Publ., v.33, 1986, p. 21-41 (In Russian).

Abstract. A new approach to the problem of synthesis of the antenna with semitransparent surfaces is described in the review form. The approach is grounded on the generalized eigen oscillation method. It permits to find the shapes of exterior and interior surfaces of the resonant antenna as well as the transparency distribution of its exterior surface when the desired directivity pattern (or its amplitude only) is given. Numerical and experimental results are presented.

I. P. Bolotova, N. N. Voitovich, A. I. Rovenchak, Yu. V. Semenyuk. Calculation of shape of inner surface of resonant antenna at given external surface and its transparency distribution. Radiotekhnika i Elektronika, v.32, No.9, 1987, p. 1848-1853. (In Russian).

Abstract. A numerical method for determing the interior field in the resonant antenna and the exterior metallic surface shape is proposed. It is assumed that the field on exterior surface as well as its transparency are known. The interior field is expressed in the form of a limited superposition of the functions satisfying the Helmholtz equation. Unknown coefficients in this superposition are found from satisfying the boundary conditions on exterior surface in the mean. Interior surface shape is calculated as one of the zero lines of interior field. Numerical results are presented.

N. N. Voitovich, B. Z. Katsenelenbaum, A. V. Kukushkin, V. E. Kunitcin, L. N. Litvinenko, A. N. Sivov, A. G. Kyurkchan. Inverse Problems (Proc. of IX All-Union Scool on Wave Diffraction and Propagation), Kazan,1988, 107 p. (In Russian).

N. N. Voitovich. Synthesis of two-dimensional antenna arrays by generalized variable separation method. Radiotekhnika i Elektronika, v. 33, No.12, 1988, p. 2637-2639 (In Russian).

Abstract. A method of the rectangular antenna arrays synthesis according to prescribed amplitude pattern, based on generalized separation of variables, is proposed. In the method, a functional having the form of sum of the mean square difference between the given and obtained amplitude patterns, and the weighted current norm, is minimized. A matrix of the current distribution is expressed in the form of the limited sum, every term in which is a product of two one-dimensional vectors. The terms are calculated in successions, from the requirement of the functional minimum. In every step of the method a set of nonlinear algebraic equations should be solved. The set is effective solved by an iterative procedure.

Abstract. A problem of constructive synthesis of open resonators with spherical external surface is considered. The problem is solved in two steps. The first step consists in calculation of a in-phase tangential electric field distribution on the external surface, which creates the directivity pattern close to the given one in amplitude distributions of their components or in their power distributions. The functional being the mean square difference betweenthe given and obtained patterns is minimized by an iterative method. In second step, the distribution of transparency components on external surface as well as the shape of inner surface and its impedance distribution are calculated. Numerical results regarding some concrete examples of given amplitude and power patterns are presented.

Abstract. An antenna being a semitransparent closed surface with known sources located inside its is considered (two-dimensional problem). An iterative method is proposed, which permits to calculate the transparency distribution from the condition of minimum of the mean square difference between the given and obtained amplitude patterns. Numerical results are presented and compared with asymptotic ones in order to determine the application range of these latter.

Abstract. The method of generalized separation of variable proposed before is applied with some modification to solving concrete synthesis problems according to prescribed amplitude pattern. The arrays having 5x5 and 9x9 elements were synthesed by the method. It turned out that the sufficient accuracy was obtained by 2-4 summands with separated variables in these cases.

Abstract. The paper is a short rewiev of publications on an antenna synthesis method according to prescribed magnitude pattern. The method's idea as well as some results obtained by it are described.

Abstract. It is proved that finite sums of field development in the series of expanding waves may be used for approximately (in the L2 space) determing the directivity pattern of the scattered field of sources placed inside a smooth nonresonant surface with variable transparency if directivity pattern of these sources in the free space is given. The proof is based on using the generalized eigen oscillation method. The proved fact permits to apply above development to calculate the directivity pattern also in the case when Rayleigh hypothesis is inusable. The numerical results regarding concrete antennas are presented.

Abstract. A two-dimensional problem about resonant antenna with plane semitransparent upper wall and variable heigh,t excited by a plane waveguide is solved. The methods of partial regions and cross-sections are used. Numerical results such as field distributions, directivity pattern, and front-to rear factor value in a frequency band are presented.

Abstract. The method of antenna synthesis according to predefined magnitude pattern is applied to the problems of synthesis of the conform antennas of two types: spherical antenna array and spherical resonant antenna. The mathematical formulation of the problems as well as numerical results are presented.

Abstract. In the review form, the method of antenna synthesis according to prescribed magnitude pattern and its applications are presented. There are discussed the results obtained for following types of antenna: linear antennas and arrays, conform antenna arrays, hybrydic antennas, quasioptical radiation systems, resonant antennas.

Abstract. The resonant antenna with plane semitransparent upper wall and variable height, excited by a plane waveguide is considered. Transparency distribution and resonator height as functions of the longitudinal coordinate, maximizing the value of front-to rear factor in a given frequency range, are found. The numerical algorithm is combined from the following methods: local variations, cross- sections, basic problems of excitation, opposite directions. Numerical results are presented.

Abstract. The linear antenna synthesis problem according to prescribed amplitude pattern is solved analytically with a limited numbers of complex parameters to be calculated. These parameters are found from a set of transcendental equations. Its solutions are nonunique. The optimal solution is chosen from the all obtained ones. A measure of the synthesis efficiency is offered. The case, when the given amplitude pattern is constant inside the limited angle, is considered in details and numerical results are presented.

Abstract. The problem of the least-square minimization of the difference between the prescribed and obtained amplitude patterns is solved for the linear antenna in the closed form with a limited number of complex parameters which are calculated from the set of transcendental equations. The number of parameters depends on the electrical length of antenna. Numerical results concerning two concrete problems are presented. The method is extended to the equidistant linear antenna arrays. The results may be applied to other problems described by the continuous or discrete Fourier transformation.

Abstract. The problem of optimization of the planar resonant and leaky-wave antennas with waveguide excitation are considered. The directivity factor in some frequency range or deviation of the amplitude pattern from the desired one is optimized. The algorithm consists of transforming the exterior problem to an interior one and using the following combined methods: local variations, cross-sections, opposite directions, and basic problems of excitations. Numerical results for the resonant antenna and the detailed algorithm description for the leaky-wave antenna are presented.

Abstract. The methods and algorithms of the amplitude distribution synthesis used for increasing the Wireless Power Transmission (WPT) efficiency are discussed. It is shown that WPT efficiency increases not only at the uniform or taper distribution but also when the field intensity is raised at the edges of the radiating apertures. In this case the receiving antenna (rectenna) is illuminated uniformly enough and the level of the near side lobes is essentially decreased. Peculiarities of requirements on the field are described. Some numerical results concerning the optimal field distributions on the antenna and in the rectenna plane are presented.

Abstract. Two criteria of antenna synthesis by the amplitude radiation pattern are compared. They use the reactive power and weighted current norm, respectively, both supplying the mean square difference between the desired and obtained amplitude patterns. The technique based on the generating polynomial concept is applied to nonlinear integral equations in both cases. Numerical results are presented.