Segregation by primary phase factors: a full-wave algorithm for model order reduction

Abstract

Existing Full-wave Model Order Reduction (FMOR) approaches are based on Expanded Taylor Series Approximations (ETAS) of the oscillatory full-wave system matrix. The accuracy of such approaches hinges on the worst case interaction distances, producing accurate models over a very narrow band of frequencies. In this paper we present Segregation by Primary Phase Factors (SPPF), a novel algorithm for FMOR enabling wideband interconnect impedance analysis. SPPF extracts exponential terms (primary phase factors) and then approximates the smoother remainder with an ETAS, thus resulting in good accuracies over a very wide band of frequencies. We also present a technique to improve conditioning for the required computation. Example results are given for simple interconnect structures modeled using a discretized mixed potential integral equation formulation.

Multipoint Full-Wave Model Order Reduction for Delayed PEEC Models With Large Delays

“…As in [26], the NDDE formulation is preserved. The multipoint expansion feature allows to reduce electrically large structures with large delays (2πfreq max τ max > 10) [25] that cannot be neglected or easily approximated by a single-point expansion and rational functions. The equivalent first-order system obtained after the singlepoint Taylor expansion of exponential terms has an order equal to qn u , where q is the order of the Taylor expansion and n u the order of the original NDDE system [26].…”

Multipoint model order reduction of delayed PEEC systems

“…, n r , q) systems becomes computationally expensive and sometimes not feasible, when large delays (2πf req max τ max > 10) [11] are involved, since exponential terms with large delays need many terms in the Taylor expansion to be accurately approximated. The multipoint feature [15] addresses this issue and is able to accurately reduce NDDE systems with large delays, since a small expansion Taylor order can be used for each expansion point and the accuracy of the reduced model is increased by adding new expansion points.…”

“…As in [9], the NDDE formulation is not preserved in the reduction process. In [11], some exponential terms (primary phase factors) are extracted and the smoother remainders are expanded into a linear form and then projected to obtain the reduced model. Hence, the extraction of primary phase factors and the segregation of the system into multiple remainder phase matrices are needed.…”

Reduced order modeling of delayed PEEC circuits

“…As in [12], the NDDE formulation is preserved. The multipoint feature allows to reduce electrically large structures with large delays (2πf req max τ max > 10) [11] that cannot be neglected or easily approximated by a single point expansion and rational functions. The equivalent first order system obtained after the single point Taylor expansion of exponential terms has an order equal to qn u , where q is the order of the Taylor expansion and n u the order of the original NDDE system [12].…”

“…As in [9], the NDDE formulation is not preserved in the reduction process. The approach in [11] extracts exponential terms (primary phase factors) and then the smoother remainders are expanded into a linear form and then projected to obtain the reduced model. Hence, the extraction of primary phase factors and the segregation of the system into multiple remainder phase matrices, each corresponding to a primary phase factor, are needed.…”