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

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

“…The accuracy of the presented numerical algorithm has been validated by comparing the computation of per-unit-length internal impedance to the authors' closed-form expressions of a twolayer conductor [7]. Furthermore, comparison of per-unit-length internal impedance has also been made with the model based on a cascade of two-port networks presented in [11] where good agreement was found. Also, in this paper, the formula for computing the per-unit-length internal impedance is given, which is derived from the electric field on the surface of the multilayer conductor.…”

“…Equations (10)- (11) are valid for both the cases of a solid and tubular multilayer cylindrical conductor.…”

“…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.…”

“…The number of equations is always the double of the number of layers in the multilayer conductors which is significantly less than in the case of models based on a cascade of two-port networks. Furthermore, in the presented model, when the unknowns are computed, one can then compute electric and magnetic fields in any observation point directly, which is not the case in for example [11].…”