Impedance Transformation Equations for Exponential, Cosine-Sqaared, and Parabolic Tapered Transmission Lines

Closed-form equations that give the value of an arbitrary complex impedance transformed through a length of dissipationless, nonuniform transmission line with exponential cosine-squared, and parabolic taper are presented. These equations are obtained by a second order nonlinear differential (Riccati) equation relating impedance, the nonuniform line impedance and the line length. The results presented should be useful in solving impedance matching problems.