Synthesis of a closed plane antenna according to a prescribed amplitude pattern

A synthesis method for closed plane antennas is proposed which uses rms difference with a current norm (with a free weight coefficient) as the criterion for the closeness between the prescribed and synthesized patterns. The problem involves the solution of a nonlinear integral equation, and the applicability of the successive-approximation method to this equation is demonstrated. A modified conjugate-gradient method is proposed for direct functional minimization, and numerical results are presented for circular and elliptical antennas with different eccentricities. The possibility of using a weight function in the criterion for the generation of troughs in the prescribed radiation patterns is examined.