An inverse scattering procedure to design microwave filters

A novel analytical approach for the design of microwave planar filters is presented. The method is based on the solution of an inverse scattering problem in order to reconstruct the impedance profile corresponding to the dimensions of the appropriate filter for achieving the specified frequency response. The overall procedure requires the re-formulation of the famous Riccati differential equation in terms of the desired spectral domain reflection coefficient data and the corresponding impedance profile. The re-formulated Riccati equation is then solved using the recently proposed renormalization technique, which helps in obtaining a closed form solution of the required impedance profile in terms of the inverse Fourier transform of the desired frequency response. The impedance profile is finally transformed into geometry of the planar filter, which is then fabricated for any particular application. The applicability of the overall procedure is shown by designing and fabricating a number of microstrip filters of various types, and validating the response of these filters against both simulated and experimental data.