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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.
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Mohammad Jamil Ahmed (1981) studied this question.
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