Parallel, Optimized, Error Maxima-Agnostic, Pole Residue Equivalent System Solver

Abstract

Fitting of sampled frequency response data to a rational function is often required for macromodeling of advanced microelectronic packages. The pole residue equivalent system solver (PRESS) method was recently proposed, as a novel fitting method that builds the global fit from local fits, computed from at most three data points at an error peak. To increase the fitting accuracy of PRESS, the error-maxima agnostic PRESS (EMPRESS) was proposed, but it is computationally intensive as the central processing unit needs to sequentially perform the local fits at all the frequency sample points before choosing the best among them. In this paper, we propose the parallel optimized EMPRESS (POEMPRESS) to reduce the computational complexity of EMPRESS while improving the fitting performance. POEMPRESS optimizes both the EMPRESS algorithm and its implementation through: 1) simplified local fit types, enabling the algorithm to rely on at most two data points only, and 2) an algorithm that can be implemented on graphics processing units for rapid parallel computation and evaluation of local fits at all the frequency points. The proposed algorithm is demonstrated on the interconnects of a microelectronic package. The results show that POEMPRESS is effective in fast macromodeling of complex interconnects for signal and power integrity simulations.