Antenna Synthesis by Levin’s Method using Reproducing Kernel Functions

An antenna synthesis application is presented by solving a highly oscillatory Fourier integral using a stable and accurate Levin’s algorithm. In antenna synthesis, the current distribution is obtained by the inverse Fourier integral of the antenna radiation pattern. Since this integral is highly oscillatory, the Levin method can be used for its solution. However, when the number of nodes or the frequency increases, the Levin method becomes unstable and ineffective due to the large condition number of the interpolation matrix. Thus, an improved scheme of the method is used in an antenna synthesis application in which reproducing kernel functions are used as the basis of the approximation function. The accuracy of the new method is verified by a log-periodic antenna example. The error and stability analysis results show that the new method is more stable and accurate than other well-known kernels, especially for a large number of nodes.