Ultra wideband wave-based linear inversion in lossless ladder networks

A wave-based inversion algorithm for the recovery of deviation in the values of elements of discrete lossless inductance-capacitance and capacitance-inductance ladder networks from their nominal values is formulated. The algorithm uses ultra wideband source excitation over the frequency range where forward and backward voltage and current waves propagate along the network. Employing a weak type scattering formulation renders the voltage wave reflection coeffcient to be a Z transform of the sequence of perturbation in the value of the elements. Inversion of the reflected date from the transformed domain to the spatial domain by Fourier type integration yields the element's perturbations and consequently, the actual elements of the network. Demonstrations of the algorithm performance on several test cases show its effcacy as a non-destructive testing tool.