**4. Conclusions**

In the process of solving the amplitude-phase synthesis problem, the influence of weight multiplier *t* on the synthesis results was investigated. It turned out that the mean-square deviation of the prescribed *F* and synthesized | *f* | amplitude RPs diminishes if *t* decreases. At the same time the norm ||*I*|| of current grows. This testify that one should take into account the above fact in order to receive the solution with smaller mean-square deviation of the RPs or with small norm of current. The elaborated iterative procedures guarantee convergence of the successive approximation methods for numerical solving the arising non-linear equations.

The proposed approach for solving the synthesis problems of resonant antennas is universal, and it provides the possibility to synthesize antennas with the arbitrary form of external boundary. The calculation time of the RP of antenna is small enough what it is very important in the process of solution of the synthesis problem. The used variational statement of the synthesis problem also allows to take into account restrictions on the field at the given points (areas) of a near zone.

The synthesis of the resonant antenna with waveguide excitation gives the possibility to take into account the various requirements to the FRF in the operating frequency range. The developed algorithms enable to optimize the values of FRF in the single range, as well as in the several frequency ranges. The values of the objective parameters *d* and *ρ*, which are received in the process of numerical calculations, are constructive characteristics of resonant antenna and they can be directly used in the antenna design.

The variational approach for solving the phase synthesis problem can be applied effectively for the plane, cylindrical and conical arrays. It allows to decrease the computational time, at the same time the accuracy of determination of the array characteristics is sufficient for practice. The branching solutions are investigated for the case of linear array. It is shown that one can receive the solutions with various properties starting the iterative process with different initial approximations.

The considered optimization problems of waveguide array give the possibility to take into account the requirements to the amplitude RP and amplitude-phase distribution of field in the aperture of exciting waveguides. The developed algorithms enable to achieve the minimal mean-square deviation *σ* of the prescribed and synthesized amplitude RPs, and to optimize simultaneously the restrictions on the phase or amplitude characteristics of the excited fields.
