Derivative control in shaping antenna patterns

An antenna pattern synthesis method is presented that permits the approximation of desired patterns with arbitrarily prescribed error criteria. Thus smoothness, linearity, or curvature may be specified for any part of the pattern. If desired, an equal ripple approximation may also be very closely approached. The techniques developed are applicable to arrays with real excitation coefficients and to those capable of complex excitations. For the latter type of array the desired far field magnitude fit may be optimized by full use of both the magnitude and phase of the excitation. The method is semi-numerical in nature and may involve several perturbations depending on how closely one desires to approach the optimum. Several numerical examples are worked out in detail, and an experimental verification is also provided.