Inverse Scattering for Coupled Nonuniform Lossless Transmission Lines Based on a State-Space Method and Nonuniform Frequency Sampling

This article presents an analytical method for reconstructing an arbitrary nonuniform multiconductor transmission line profile by measuring its scattering parameters. It is based on state space formulation and is generalized to tackle an arbitrary number of conductors with no limitations. The proposed technique benefits multiple frequency data to circumvent the nonlinearity raised in inverse problems and provides a unique solution. By rearranging the well-known Peano-Baker series, a nonuniform frequency sampling scheme based on Chebyshev polynomial expansion is proposed, which results in a well-posed stable system of equations that is rather robust to noise and interference. The state transition matrix is obtained from the measured S-parameters. Combining the obtained state transition matrix and the Peano-Baker series theorem results in an efficient inversion algorithm. The proposed methodology avoids solving the nonlinear integro-differential equation, which is mathematically cumbersome. The validity of the method is investigated by analyzing some examples of nonuniform coupled transmission lines, which are simulated and measured experimentally. It has been shown from the established results that the proposed method leads to an accurate and robust technique for solving the 1-D inverse scattering problem on nonuniform coupled transmission lines.