An efficient synthesis technique of tapered transmission line with loss and dispersion

A synthesis technique of lossy and dispersive tapered transmission line is presented that extends lossless cases suggested by Klopfenstein and others. A special optimization process based on the Fourier transform pair and generalized Taylor's procedure is performed to extract the exact null points of lobe-like frequency response in terms of the input reflection coefficient of lossy-tapered line in which the loss may be frequency dependent and distance dependent. The theory is verified by evaluation of a synthesized microstrip taper profile in the lossy case and is expected to be helpful for design of tapered line in the high-frequency microwave integrated circuits (MICs) with loss.