An electromagnetics-based circuit simulator of linear complexity, linear speedup, minimal order, and unconditional stability.

摘要

Guided by electromagnetics-based first principles, we develop a circuit simulator that allows for the simulation of an integrated circuit including both nonlinear devices and the layout of the linear network in linear (optimal) complexity. Furthermore, it permits an almost embarrassingly parallel implementation on a many-core computing platform, and hence enabling linear speedup. Moreover, it bypasses the step of circuit extraction, producing an RLC (resistor-inductor-capacitor) representation of the linear network without any numerical computation. In addition, it possesses electromagnetics first-principles based accuracy. Application to die-package co-simulation as well as very large-scale on-chip circuits has demonstrated the superior performance of the proposed electromagnetics-based circuit simulator.;The efficiency of a circuit simulator is determined not only by the computational cost at each time step, but also by the total number of time steps required to finish one simulation. In this work, we create the first explicit time-domain method that is unconditionally stable, which allows the time step in an explicit method to be solely determined by accuracy irrespective of space step, and meanwhile preserving the strength of an explicit time-domain method in avoiding a matrix solution. This method is further accelerated by a fast DC mode extraction algorithm. This algorithm is capable of decomposing the original large-scale problem rigorously into small problems that are fully decoupled, and then synthesizing the DC solution of the original large-scale problem from the nullspace of the small problems. The aforementioned work has significantly reduced the total number of time steps required to finish one simulation by the proposed electromagnetics-based linear-complexity circuit simulator by many orders of magnitude.;Last but not the least, guided by electromagnetic physics, we find a minimal order model of the linear network for a prescribed accuracy. This model is applicable to general circuits irrespective of whether the circuits are dominated by RC-, RLC-, or full-wave physics. For circuits dominated by RC physics, the size of the proposed minimal order model is only 2 regardless of the circuit size. As a result, the proposed electromagnetics-based circuit simulation can be performed on the proposed minimal order model, the size of which is orders of magnitude smaller than the size of the original physical layout, and therefore further speeding up the proposed circuit simulator.