Timing analysis for full-custom circuits using symbolic DC formulations

摘要

Successful analysis of high-speed integrated circuits requires accurate delay computation. A number of delay models have been developed; however, none can claim to be truly robust in the face of large channel-connected regions (CCRs) with input "exclusivity" constraints. A good circuit-level delay model should: 1) consider input exclusivity constraints; 2) handle a wide range of circuit structures; and 3) have a robust underlying framework that can be applied independent of the actual device model. We present a symbolic timing analysis tool that aims to address these three goals. It uses algebraic decision diagrams (ADDs) to estimate delay within a CCR as a function of its inputs while easily handling Boolean input constraints. It starts with a simple linear resistor model for transistors and from there apply various heuristics to improve the delay estimation without altering the symbolic algorithms. It analyzes delay with simple series-parallel reduction when possible and use symbolic matrix techniques to handle more complex circuit structures. The effectiveness of our approach is demonstrated on circuits from industry used in the Alpha 21264 and 21364 instead of the usual International Symposium on Circuits and Systems (ISCAS) or Microelectronics Center of North Carolina (MCNC) benchmarks. Our delay estimates are within 10% of simulation program with integrated circuits emphasis (SPICE) for over 90% of the circuits we simulated. This difference can translate into significant savings in manpower by avoiding the need to verify many unrealizable worst case conditions with other, more costly, simulation techniques.