Capturing Crosstalk-Induced Waveform for Accurate Static Timing Analysis

Capturing Crosstalk-Induced Waveform for Accurate Static Timing Analysis

Masanori Hashimoto, Yuji Yamada,Hidetoshi Onodera

Kyoto University

How cope with crosstalk-induced waveform?

Never provideaccurate waveforms

Problems of Conventional Methods

Conventionally crossing-point approach Calculate crossing timing of reference voltage

e.g. 50% delay, 20-70% transition time, etc.

Estimate large delay difference in error

almost the samewaveforms

Gate Waveform Calculation

Table look-up model Huge characterization cost Difficult to increase #parameter of

waveform

Characterization has to assume a typical waveform.

Related Works

Sasaki, ASIC/SoC Conf., 1999 Estimate delay change vs transition timing at

receiver output by circuit simulation Simulation is necessary for every instance

Sirichotiyakul, DAC, 2001 Estimate delay change at receiver output by lo

ok-up tables Library extension and characterization increas

e

Proposed Equivalent Waveform Approach

Propose equivalent waveform propagation that makes output waveforms equal Adjust both arrival time and slew

Characterization usestypical waveforms.

Derivation of Equivalent Waveform

Fitting waveforms using least square method Approximate entire outline

dttt

tgtf 2

1

)}()({2

Work well? NO!!

Problem of LSM Uniform fitting weight even for unnecessary

region misleads equivalent waveform.

Adaptive fitting for critical region is necessary.

Transition finishesbefore noise injection.

Proposed Method Improved LSM with weight coefficient

To consider output behavior

dttt dVin

dVout tgtf )()(2

2

1

slope

Noiseless waveforms Vout vs Vin curve

High gainsensitive to input

Critical Region

Higher weight

Strength of Proposed Method

No library extension No additional characterization No additional calculation except

fitting

Implemented easily with conventional STA tools

Experimental Conditions

True delay change is evaluated at Gate3 output. Conventional Method: delay change is evaluated at Gate2

input 100nm process, semi-global wire, 1mm coupled

Experimental Result （ Crosstalk ）

Agg., vic. drivers 4x, 4x, load(C1,C2)=100fF

Accurate delay variation curve is obtained.

Equivalent and Actual Waveforms

Proposed method is not misled by meaningless noise.

Cross 0.5Vdd

Conventional methodshifts waveformin error.

Agg.=vic. =4x, C1=C2=10fF

Agg.=vic. =8x, C1=C2=100fF Agg.=vic. =8x, C1=C2=10fF

Proposed method estimatesmore accurate curves thanconventional methods.

Worst case in our experiments.

Experimental Result (Crosstalk, two aggressors)

Proposed method works even when multiple aggressors.

Computational Cost

Numerical integration is necessary. #segments: accuracy vs CPU time CPU time increase is evaluated.

Path delay calculation of inverter chain File I/O and RC reduction are excluded.

3-20 #segments is accurate enough.

#segments

5 10 20 40

CPU time 1.17 1.27 1.48 1.71conventional method: 1.00

Conclusion

Propose equivalent waveform propagation scheme Cope with non-monotonic waveforms Familiar with conventional STA tools

Experimentally verify our method improves much accuracy just with 30% CPU time increase.