Fast on-chip inductance simulation using a precorrected-FFT method

In this paper, a precorrected-fast-Fourier-transform (FFT) approach for fast and highly accurate simulation of circuits with on-chip inductance is proposed. This work is motivated by the fact that circuit analysis and optimization methods based on the partial element equivalent circuit model require the solution of a subproblem in which a dense inductance matrix must be multiplied by a given vector, an operation with a high computational cost. The grid representation enables the use of the discrete FFT for fast magnetic vector potential calculation. The precorrected-FFT method has been applied to accurately simulate large industrial circuits with up to 121 000 inductors and over 7 billion mutual inductive couplings in about 20 min. Techniques for trading off CPU time with accuracy using different approximation orders and grid constructions are also illustrated. Comparisons with a block-diagonal sparsification method are used to illustrate the accuracy and effectiveness of this method. In terms of accuracy, memory, and speed, it is shown that the precorrected-FFT method is an excellent approach for simulating on-chip inductance in a large circuit.