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Explicit Gate Delay Model for Timing Evaluation Muzhou Shao : University of Texas at Austin D.F.Wong : U. of Illinois at Urbana- Champaign Huijing Cao : Motorola, Inc. Youxin Gao : Synopsys, Inc., Li-Pen Yuan : Synopsys, Inc., Li-Da Huang : University of Texas at Austin Seokjin Lee : University of Texas at Austin

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One part of stage delay Crucial in timing synthesis/optimization Value of Gate Modeling

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Switch-resistor model k-factor functions Lookup table model Previous Gate Delay Model

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Previous Gate Delay Model – cont. k-factor functions Delay/transition are functions of input signal and gate load. Lookup table model Delay/transition is tabulated for each input, load pair.

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Previous Gate Delay Model – cont. Switch-resistor model Structure: step voltage source linear driver resistance Advantages: Simple Stage delay

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Trends in DSM The increasing of resistive shielding of interconnect. The output impedance of gate reduces relatively.

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Trends in DSM – cont. Step input --> piecewise C_eff is needed in gate modeling.

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Our New Approach Gate modeling work independent of its load. Can be easily integrated into timing analysis. Concise circuit structure.

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Based on a second-order circuit. Structure of Explicit Gate Model

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Parameters of Gate Model Totally 5 unknown parameters 4 unknown parameters in the model circuit. R 1, R 2, C 1, C 2 1 unknown parameters in the input signal.

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With two operating points, two poles are obtained. Parameters of Gate Model – cont.

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Another two operating points, another two poles. Parameters of Gate Model – cont.

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Obtain Operating Points There are four operating points of the gate output needed in the deduction. - Run SPICE twice to obtain the two groups of (v i, t i ). - Obtained from k-factor functions

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The gate intrinsic delay and signal regenerating ability. is defined as t p t r. Another Parameter

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Another Parameter – cont.

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Choose an operating point of 50% power supply as (50%V DD, t 50% ). Another Parameter – cont.

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Two Ways to Set up the Model Solving nonlinear equations. optimize function of transit analysis in HSPICE.

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Focus of the Experimental Results Can be pre-computed. The saving of runtime is obvious. The accuracy issue is focused on.

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36 gates of different types and technologies. The gate load is randomly generated. The input signal is also randomly chosen. 3,600 experimental results all together. MOS transistor model level is from 13 to 49. Experimental Results

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Statistic results of computation errors in gate delay model. Experimental Results– cont.

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Waveforms obtained from HSPICE simulations Waveform Comparisons (Driving Pin)

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Waveforms obtained at the fan-out point. Waveform Comparisons (Sink Pin)

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The test results on the clock tree of a commercial IC. Another Test Case

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Conclusion Independent of gate load. Can be pre-characterized. No effective capacitance iteration. Compatible with interconnect timing analysis.

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