A Statistically-Enhanced Analytical Method for PCB Traces Impedance Extraction

One of the most important electrical parameters of printed circuit board traces is the characteristical impedance, and various methods for impedance extraction are widely used in modern CAE-CAD applications for signal integrity analysis. The method proposed in this paper, further named "Statistically-Enhanced Analytical" (SEA), combine the precision of numerical field-solvers with the speed of analytical approximations to provide an impedance extraction algorithm that is both fast and accurate. Using an analytical approximation as an initial solution for a given impedance extraction problem, a numerical field-solver to precisely calculate the solution for a reduced number of reference points and a low-degree polynomial for Lagrange interpolation in the Chebyshev nodes as a mean for relative error estimation, out method can provide results with less then 0.3 % error as compared with the field-solver solutions. The main advantage of SEA is that the on-line calculus complexity overhead, as compared with the least calculus-intensive method currently used in the impedance extraction process, is just that of a 3^rd degree polynomial, while the errors are reduced with almost an order of magnitude.