Scalable trajectory methods for on-demand analog macromodel extraction

Model Order Reduction (MOR) methods have proved to be very successful for efficiently computing the response of linear systems. One of the most successful extensions of the idea for nonlinear dynamical systems is based on a strategy called trajectory based models. Trajectory methods sample the state trajectory of a circuit as it simulates in the time domain, and build macromodels by reducing and interpolating among the linearizations created at a suitably spaced subset of the time points visited during training simulations. Unfortunately, moving from simple to industrial circuits requires more extensive training, which creates models too large to interpolate efficiently. To make trajectory methods practical, this work describes a scalable interpolation architecture, and the first implementation of a complete trajectory "infrastructure" inside a full SPICE engine. The generated models are suitable for creating "on-demand" macromodels for predicting AC, DC and transient response of the circuit. The proposed methodology is generic and can easily be applied for generating simulation macromodels for a range of applications.;Our approach supports arbitrarily large training runs, automatically prunes redundant trajectory samples, supports limited hierarchy and enables incremental macromodel updates for generating efficient macromodels. We have also introduced: a new mechanism for capturing loading; a novel "self monitoring" capability that allows our models to deduce dynamically where accuracy may be compromised; and a new architecture for handling process variability in trajectory models. We present a range of analog circuit examples for demonstrating the usefulness of the macromodels including a folded cascode opamp circuit with common mode feedback stage, a sample and hold circuit used as a part of analog to digital converter, and a phase locked loop. We present several AC and transient simulation examples using these circuits from a working implementation of our methodology built on top of Berkeley SPICE3. The generated macromodels show speed-ups of up to 30X for transient and 200--300X for AC simulations with errors < 3%. Experimental results emphasize the attractiveness of trajectory methods for generating "on-demand" simulation macromodels for analog circuits.