ELEC 5970-001/6970-001(Fall 2005) Special Topics in Electrical Engineering Low-Power Design of Electronic Circuits Power Analysis: Probability WaveformDigital Signal WaveformsTransient EventsProbability WaveformProbability SimulationPrimary Input Pattern AnalysisPI WaveformsSlide 8Slide 9Slide 10Power Consumption of a GateMethods Related to Probability WaveformReferencesPower Estimation by Prob. Waveform10/11/05 ELEC 5970-001/6970-001 Lecture 12 1ELEC 5970-001/6970-001(Fall 2005)Special Topics in Electrical EngineeringLow-Power Design of Electronic CircuitsPower Analysis: Probability WaveformVishwani D. AgrawalJames J. Danaher ProfessorDepartment of Electrical and Computer EngineeringAuburn Universityhttp://www.eng.auburn.edu/[email protected]/11/05 ELEC 5970-001/6970-001 Lecture 12 2Digital Signal WaveformstimeTransient regionClock periodPrimaryInputsGateOutputs10/11/05 ELEC 5970-001/6970-001 Lecture 12 3Transient Events2 4 611 353100022Path P1P2P310/11/05 ELEC 5970-001/6970-001 Lecture 12 4Probability WaveformInput vector appliedNext input vector appliedVector periodTransient interval0Steady stateSamples of signal, s(t)0Prob. waveform, P(t)1.0P(t)=0.25P(t)=0.250.25 0.50.250.50.50.250.250.5Transition probabilitiestimetime10/11/05 ELEC 5970-001/6970-001 Lecture 12 5Probability Simulation131200110011001100011100011101010101010110/11/05 ELEC 5970-001/6970-001 Lecture 12 6Primary Input Pattern AnalysisPI bit stream p1 p0 p01 p10010101010101… 0.5 0.5 0.50 0.50001100110011… 0.5 0.5 0.25 0.25000111000111… 0.5 0.5 0.167 0.16710/11/05 ELEC 5970-001/6970-001 Lecture 12 7PI Waveforms0 1 2 3 4 5 6 T time0.5time0.5time0.5PI 1PI 2PI 30 1 2 3 4 5 6 T 0 1 2 3 4 5 6 T10/11/05 ELEC 5970-001/6970-001 Lecture 12 8Probability Simulation2time0.5time0.50 1 2 3 4 5 6 T 0 1 2 3 4 5 6 T time0.750 1 2 3 4 5 6 T 0.20850.20850.250.250.1670.16710/11/05 ELEC 5970-001/6970-001 Lecture 12 9Probability Simulation1310 1 2 3 4 5 6 T 0.5PI 1time0.750 1 2 3 4 5 6 T 0.20850.20850.250 1 2 3 4 5 6 T 0.20850.20850.3750 1 2 3 4 5 6 T 0.3750.3750.104250.104250.50.510/11/05 ELEC 5970-001/6970-001 Lecture 12 10Probability Simulation10.250 1 2 3 4 5 6 T 0.20850.20850.3750 1 2 3 4 5 6 T 0.3750.3750.104250.104250.531250 1 2 3 4 5 6 T 0.281250.281250.07818750.07818750.13031250.130312510/11/05 ELEC 5970-001/6970-001 Lecture 12 11Power Consumption of a Gate•An input change can multiple transitions at the output of a gate.•Per vector power consumed by a gate = CV2 Σ p01(ti)ti ε [0,T]10/11/05 ELEC 5970-001/6970-001 Lecture 12 12Methods Related to Probability Waveform•Tagged probability simulation (TPS): Four waveforms corresponding to steady states, 00, 01,10 and 11, are explicitly simulated.•Dual-transition simulation (Dual-Trans): An improvement of TPS that considers pairs of consecutive transitions and gate delay to filter glitches.•Further improvement is possible with supergate analysis to account for signal correlation.10/11/05 ELEC 5970-001/6970-001 Lecture 12 13References•F. Najm, R. Burch, P. Yang and I. Hajj, “CREST – A Current Estimator for CMOS Circuits,” Proc. IEEE Int. Conf. on CAD, Nov. 1988, pp. 204-207.•C.-S. Ding, et al., “Gate-Level Power Estimation using Tagged Probabilistic Simulation,” IEEE Trans. on CAD, vol. 17, no. 11, pp. 1099-1107, Nov. 1998.•F. Hu and V. D. Agrawal, “Dual-Transition Glitch Filtering in Probabilistic Waveform Power Estimation,” Proc. IEEE Great Lakes Symp. VLSI, Apr. 2005, pp. 357-360.•F. Hu and V. D. Agrawal, “Enhanced Dual-Transition Probabilistic Power Estimation with Selective Supergate Analysis,” Proc. IEEE Int. Conf. Computer Design, Oct. 2005. pp. 366-369.10/11/05 ELEC 5970-001/6970-001 Lecture 12 14Power Estimation by Prob. WaveformCircuitTPS DualTrans Supergate methodEavgσEtotEavgσEtotEavgσEtotc17 2.3 2.6 0.1 2.3 2.6 0.1 2.3 2.6 0.1 c432 29.9 38.8 35.8 9.5 11.8 6.5 11.5 16.6 11.5c499 6.8 14.0 7.0 3.6 8.2 0.6 2.3 3.0 3.0 c880 8.3 15.3 1.6 8.0 15.7 5.2 4.8 9.0 0.0 c1355 24.2 31.6 32.9 5.8 11.2 5.4 5.0 9.5 0.5 c1908 15.0 23.1 4.1 17.7 27.9 11.2 7.0 16.3 2.0 c2670 16.6 29.8 7.2 16.7 28.3 9.9 13.2 23.6 6.2 c3540 13.8 26.3 9.8 10.3 25.6 2.4 10.5 26.4 3.7 c5315 11.8 24.4 2.3 13.4 31.5 10.1 11.3 27.0 3.4 c6288 27.4 27.5 32.1 15.7 18.8 4.1 12.7 15.4 0.2 c7552 14.5 27.5 3.2 14.8 31.4 7.8 14.1 27.6 1.3 Avg. 15.5 23.7 12.4 10.7 19.4 5.7 8.6 16.1