Closed-Form <emphasis>RC</emphasis> and <emphasis>RLC</emphasis> Delay Models Considering Input Rise Time

Abstract

The Elmore delay model is the most popular and efficient delay model used for analytical delay estimation. Closed-form delay formulas are useful for circuit design, timing-driven physical design, synthesis, and optimization. As signal rise time becomes faster and the line resistance becomes smaller from copper technology, the significance of inductance increases. Both RC and RLC delays are a strong function of signal rise time. We propose a novel and efficient delay modeling method based on nondimensionalization to consider finite input rise time as an improvement over the Elmore's approach. To further improve the accuracy of the delay model, a new correction method, effective distance correction factor (EDCF), is proposed to consider resistive shielding of downstream capacitance. EDCF can be used to correct the delays for both RC and RLC tree structures. The proposed delay modeling method was applied to a number of nets selected from an integrated circuit (IC) design, and the delay estimation results were compared with HSPICE simulations. The new delay model retains the efficiency and simplicity of the Elmore delay model with significantly improved accuracy.