Frequency-dependent mutual resistance and inductance formulas for coupled IC interconnects on an Si-SiO\(_{2}\) substrate (Q2778430)

A highly accurate closed-form approximation of frequency-dependent mutual impedance per unit length of a lossy silicon substrate coplanar-strip IC interconnects is developed. The derivation is based on a quasi-stationary full-wave analysis and Fourier integral transformation. The derivation shows the mathematical approximations which are needed in obtaining the desired expressions. As a result, for the first time, we present a new simple, yet surprisingly accurate closed-form expression which yield accurate estimates of frequency-dependent mutual resistance and inductance per unit length of coupled interconnects for a wide range of geometrical and technological parameters. The developed formulas describe the mutual line impedance behaviour over the whole frequency range (i.e. also in the transition region between the skin effect, slow wave, and dielectric quasi-TEM modes). The results have been compared with the reported data obtained by the modified quasi-static spectral domain approach and new CAD-oriented equivalent-circuit model procedure.