Faster, parametric trajectory-based macromodels via localized linear reductions

Trajectory-based methods offer an attractive methodology for automated, on-demand generation of macromodels for custom circuits. These models are generated by sampling the state trajectory of a circuit as it simulates in the time domain, and building macromodels by reducing and interpolating among the linearizations created at a suitably spaced subset of the time points visited during training simulations. However, a weak point in conventional trajectory models is the reliance on a single, global reduction matrix for the state space. We develop a new, faster method that generates and weaves together a larger set of smaller localized linearizations for the trajectory samples. The method not only improves speedups to 30X over SPICE, but as a side benefit also provides a platform for parametric small-signal simulation of circuits with variational device/process parameters, at a speedup of roughly 200X over SPICE.