The skin effect of single and coupled conductor strips of finite thickness is analyzed using the dyadic Green's function and integral equation formulation. Galerkin's method is used to solve the integral equation for the dispersion characteristics. The effects of the geometrical and the electrical parameters on the conductor loss are investigated. Results are compared with literature, and shown to be in good agreement. This approach is very useful for analyzing the electrical properties of interconnects in high performance computer circuitries.
INTRODUCTIONTo calculate the conductor loss of microstrip lines, a perturbation method has usually been used. The surface currents for the lossless case are obtained first by either a quasi-TEM approximation [1]-[3] or a full-wave approach [4]. Then, the conductor loss is evaluated by using the surface resistance and the surface current. By using the surface resistance approximation, it is assumed that the strip thickness is much larger than the skin depth.In [5], the equivalent surface impedance is used in the boundary condition from which an integral equation is derived. The conductor loss is then obtained by solving this integral equation. Similar to [4], it is assumed that the thickness of the strip is at least several skin depths, and is much smaller than the width of the strip. In [6}, a complex resistive boundary condition is applied to solve for the propagation constant of thin superconducting striplines. It is assumed that the strip is thin compared to the superconducting penetration depth.In [7] and [8], a skin loss expression is derived based on the incremental inductance rule which was first proposed by Wheeler [9]. In this technique, the thickness of the conductors exposed to the electric field should be greater than several skin depths. [12] have been used to calculate the conductor loss. These approaches are based on either an electrostatic scalar potential[3] or a magnetic vector potential[10]- [12]. In the magnetic vector potential approach, only the longitudinal current component is considered. In [10], the ac resistance is derived from the power loss calculated from the current distribution in the cross section. In [11], the thickness of the strip is assumed to be much smaller than the skin depth, and only surface current is considered.
Finite element methods[3], [10]-In [13], a finite element method is used to calculate the attenuation constant of a copper microstrip at 77° K. The results are compared with the closed form solution obtained by neglecting the effect of fringing fields[14]. In [15], a phenomenological equivalence method is proposed for characterizing a planar quasi-TEM transmission line with a thin normal conductor or superconductor strip. This method is based on various empirical formulas valid under different conditions. In [16], a perturbation series and coupled integral equation approach is used to calculate the frequency-dependent resistance and inductance for quasi-TEM transmission lines with conductor strip of arbitrary cro...