Capture high-frequency partial inductance more accurately by gauss quadrature integration with skin-effect model

Simulating the current distribution is the key to extracting equivalent frequency-dependent partial inductance and resistance for a very large scale integration circuit by integral-equation-based numerical methods. However, it is very difficult to calculate the current distribution and the electromagnetic (EM) field induced by the current due to skin effect and proximity effect at high frequency. In this paper, we propose a skin-effect model and view the current distribution as two parts, i.e., the skin-effect part and the smooth part. We use the current density at certain Gaussian points to approximate the total current and the EM field induced by it. This approach can achieve the highest algebra accuracy for the smooth part of the current distribution function with the same number of current density points, and experiments show that our method is more efficient and accurate than traditional piecewise-constant or piecewise-linear methods to extract frequency-dependent partial inductance and resistance.