TETA: Transistor-level waveform evaluation for timing analysis

Abstract

Static timing analysis breaks down the longest path problem into waveform analysis of paths of logic stages that are comprised of nonlinear transistors and complex RLC loads. Run-time efficiency is of the utmost importance; however, the waveform evaluation of these logic stages cannot be accelerated via timing simulation algorithms that attempt to exploit temporal or spatial latency since the simulation problem is already a partitioned one. TETA was developed as a general purpose transistor-level waveform evaluation engine for providing accuracy-efficiency tradeoffs for these logic-stage waveform evaluation problems that are encountered during timing analysis. Of particular emphasis are the large RC(L) coupled logic stages which present the bottleneck for waveform evaluation along multiple stages of a digital circuit path. TETA applies a novel compaction scheme for the logic-stage transistor clusters and employs a novel nonlinear algebraic solution method to analyze the circuit. Importantly, stability of the waveform evaluation with TETA requires only stable single-input multi-output N-port interconnect models that are not necessarily passive. Waveform evaluators that use general transistor and piecewise linear device models require provably passive multi-input multi-output interconnect models that can be extremely inefficient for large coupled N-port problems. Furthermore, the methodology in TETA brings extra efficiency by avoiding extra matrix factorizations and enabling the use of device model tables without any loss of accuracy. Complex logic gates and nonlinear capacitors are handled without loss of generality.