Highly Accurate and Numerically Stable Matrix Computations of the Internal Impedance of Multilayer Cylindrical Conductors

The inhomogeneous wires are composed of different metals to exploit the advantages of particular material. One of the most relevant electrical parameter used to describe the conductor is its internal impedance. This impedance has two components: resistance and inductance per-unit length. The currently existing methods of analytical calculation of the internal impedance are based upon the approximations to keep the numerical stability and are limited to two layers made of different materials. This study presents the matrix approach of calculating the per-unit-length parameters of the multilayer wire with high accuracy. Due to the implementation of the modified scaled Bessel functions and the division onto additional sub-layers, the presented method is numerically stable for relatively thick conducting layers, even at high frequencies. The time of computations done by the presented method of internal impedance and required memory is much lower than in the case of the finite-element models.