Radiation pattern synthesis with sources located on a conical surface

This paper presents various methods of synthesizing sources placed on a conical surface to produce a prescribed radiation pattern. The sources considered are a series of electric dipoles placed in free space on the surface of the cone around a set of circumferences. These circumferences are equidistant from each other, and the dipoles are oriented in the circumferential direction with no circumferential variation in intensity and phase. A successive approximation method is employed to obtain the source function for those sources which are placed in a region where the circumferences measure approximately less than two wavelengths. For sources placed in the region where the circumference is less than approximately (4/3)\pi wavelengths, an expansion formula of the product of the Bessel and exponential functions is employed. When the sources are located far from the cone tip, a method utilizing the maximum points of the Bessel function is used to compute the source function. In considering the beamwidth and the sidelobe level, the Tchebycheff pattern with the tapering effect is employed. Numerical examples are given to illustrate the effectiveness of the methods.