An algorithm for wideband matching using Wiener-Lee transforms

An arbitrary passive load to be matched by a lossless equalizer to a resistive source so that system response approximates any desired gain shape over a prescribed band, e.g., rectangular, is considered. A least-squares optimization procedure is described that determines the equalizer design. The method stems from the real frequency technique and uses trigonometric basis functions (Wiener-Lee transforms) for expanding the real and imaginary parts of the unknown equalizer immittances. The algorithm is relatively simple and efficient since it is implemented using the fast Fourier transform. It also incorporates physical realizability considerations. The procedure is such that a large number of variables (Fourier coefficients) can be employed. This permits a determination of the limiting value of flat gain (a useful design yardstick) as the number of equalizer elements becomes infinite