Design of tapered transmission lines with arbitrary reflection characteristics

The Fourier transform method for the design of tapered transmission lines with arbitrary reflection characteristics is extended by employing an iterative scheme. We derive an approximate spectral function which consists of an amplitude function and a phase function from a nonlinear Riccati equation and the spectral function improves numerically by iteration. We also resolve the problem of discontinuity that may occur at both ends of the taper section. This method enhances the degrees of freedom in designing tapered lines and numerical examples of microwave filters and impedance matching circuits are given to illustrate the validity of the present method.