Use of the FFT to Speed Analysis of Planar Symmetrical 3- and 5-Ports by the Integral Equation Method

In a recent paper, it was shown that, for planar two-dimensional problems with symmetry, linear eigenvalue-impedence matrix entry relations may be used to simplify the integral equation method of analysis. In this paper, it is pointed out that, in the case of planar circuits with N-fold rotational symmetry, these linear relations take the form of the discrete Fourier transform (DFT). Consequently, the fast Fourier transform (FFT) may be used in its place to give a further substantial improvement in computational speed.