Two approaches to solving the antenna synthesis problems according to the amplitude radiation pattern

A nonlinear synthesis problem according to given amplitude radiation pattern for plane aperture is considered in two ways. An analytical formula for the optimal current is obtained in the first approach. This current generates the amplitude radiation pattern which is close to the given one with the prescribed accuracy. The second approach consists of variational statement of synthesis problem. The numerical results illustrate that each method has advantages in the certain range of frequencies.