Improved Numerical Method for Computing Internal Impedance of a Rectangular Conductor and Discussions of Its High Frequency Behavior

Abstract

Abstract-An efficient numerical solution is been developed to compute the impedances of rectangular transmission lines. Method of moments is applied to integral equations for the current density, where the cross section is discretized, to improve the convergence, by a nonuniform grid that obeys the skin effect. Powerfulness of this approach up to rather high frequencies is verified by comparing with asymptotic formulas and other references. Detailed discussion is given for the current density distribution and its effect to the impedance, especially for a high frequency range.

Efficient Impedance Computation for Multiconductor Transmission Lines of Rectangular Cross Section

“…Note that, if the substrate is removed, (9) is reduced to the conventional form where the kernel is only log |r − r | [5,8,9,13]. This is understood by the fact that the small argument approximation L(i x ξ + i y η) ≈ log ξ 2 + η 2 + constant cancels the image kernel log |r −r |.…”

“…(4) of [13]). Let us deform (2) for y > 0 with paying attention to the denominators 2γ 0 and γ + γ 0 in the integrand.…”

“…In the process of the moment method [14], discretization of the cross section was performed according to the skin effect by using nonuniform grid, which remarkably saves the computational cost. As a straightforward extension of the procedure in [13], the present paper deals with more practical structures, i.e., the multiconductor transmission lines backed by a substrate. With retaining the merit of this solution, we will extend the geometry of the line with regard to the number of conductors and the existence of lossy semi-infinite substrate.…”

“…In view of the above, the present authors recently proposed an efficient numerical method for computing per-unit-length impedances of a free-standing single conductor line having rectangular cross section [13]. In the process of the moment method [14], discretization of the cross section was performed according to the skin effect by using nonuniform grid, which remarkably saves the computational cost.…”

Numerical Method of Computing Impedances in Shielded and Unshielded Three-Phase Rectangular Busbar Systems

“…In other types of rectangular busbars, analytical-numerical and numerical methods must be applied [1,4,6,14,17,18,[31][32][33][34][35][36][37][38][39][40]. These impedances can also be determined by experimental methods [41][42][43][44].…”