A Matrix Approach for the Evaluation of the Internal Impedance of Multilayered Cylindrical Structures

Abstract

Abstract-A matrix technique for the computation of the perunit-length internal impedance of radially inhomogeneous cylindrical structures is presented. The cylindrical structure is conceptually divided into a number of layers, each layer being characterized by its constitutive parameters, conductivity, permeability, and permittivity. Within this general framework, compound conductors, compound capacitors, compound magnetic cores, or any other compound structures resulting from a mix of the above, can be analyzed by using the very same tool. The developed software program, MLCS, which implements the mentioned matrix technique, also permits the evaluation of the electric and magnetic fields intensity at the layers' interfaces. The MLCS program is validated by using several application examples.

Computation of Electric and Magnetic Field Distribution Inside a Multilayer Cylindrical Conductor

“…To circumvent these problems, these kinds of algorithms must subdivide layers into a multitude of fictive sublayers to ensure that the quantity 1/ν i does not become too large or tend to infinity. The same problem exists in approach [10], but in this case this is not immediately visible because unscaled Bessel and modified Bessel functions are used which produces additional numerical instabilities at higher frequencies. The numerical algorithm presented in this paper has no need for fictive sublayers and it requires in all cases the computation of 2 • m unknown coefficients.…”

“…(8)- (9). However, algorithms based on a cascade of two-port networks [9][10][11] have significantly more unknowns, and electric and magnetic fields are computed only on the boundaries of fictive layers…”

“…In the available literature, most authors analyze homogeneous single-layer conductors [2][3][4][5][6], in some cases two-layer conductors [7,8], and some consider multilayer conductors [9][10][11]. In the case of cylindrical multilayer structures, the authors in [9][10][11] utilize a cascade of two-port networks to model a multilayer structure. The problem that occurs with this approach lies in the inherent numerical instability present in the transfer matrix of the system, where some elements of the matrix tend to infinity for high frequencies even for extra thin layers.…”

“…In this paper, a different approach to model multilayer structures will be presented, which is both numerically robust and highly accurate. In addition, the proposed algorithm features a smaller number of unknowns than those in [9][10][11]. In the numerical algorithm proposed in this paper, a multilayer cylindrical structure consisting of an arbitrary number of layers is considered.…”

Computation of per-unit-length internal impedance of a multilayer cylindrical conductor with possible dielectric layers

“…In order to obtain the distribution of electric and magnetic fields inside the multilayer structure, authors in the available literature mainly utilize a cascade of two-port networks [8][9][10]. This approach leads to certain numerical instabilities that are inherent to the transfer matrix of the system, where some elements of the matrix tend to infinity for high frequencies even for extra thin layers, which was demonstrated in [11].…”