Delay Model Estimation in RC-tree Circuits Based on the Power-lognormal Distribution

Subject Areas : Journal of Computer & Robotics

Farshad Safaei ¹

1 - Department of ECE, Shahid Beheshti University, Tehran, Iran

Received: 2008-12-12 Accepted : 2009-10-18 Published : 2012-06-11

Keywords:

References:

[1] W. C. Elmore, The transient response of damped linear network with
particular regard to wideband amplifiers, J. Appl. Phys., vol. 19, pp.
55–63, 1948.
[2] C. J. Alpert, F. Liu, C. Kashyap, and A. Devgan, Delay and slew
metrics using the lognormal distribution, Computer-Aided Design,
vol. 20, pp. 382–385, 2003.
[3] L.T. Pillage and R.A. Rohrer, Asymptotic waveform evaluation for
timing analysis, IEEE Trans. Computer-Aided Design, vol. 9, no. 4,
pp. 352-366, 1990.
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delay (ns)
Spice
Lognormal
WED
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D2M
Elmore
PowerLognormal
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F. Safaei /Delay Model Estimation in RC-tree Circuits Based on the Power-lognormal Distribution.
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[4] W on-Kwang Kal, and Seok-Y oon Kim, An analytical calculation method for delay time of RC-class interconnects, IEEE/ACM Conf., pp. 457–462, 2000. [5] C. J. Alpert, A. Devgan, and C. Kashyap, A two moment RC delay metric for performance optimization, Int. Symp. on Physical Design, pp. 69-74, 2000. [6] C. J. Alpert, A. Devgan, and C. V. Kashyap, RC delay metric for performance optimization, IEEE Trans. Computer-Aided Design, vol. 20, pp. 571–582, 2001. [7] L. T. Pileggi, Timing metrics for physical design of deep submicron technologies, in Proc. Int. Symp. Phys. Design, pp. 28–33, 1998. [8] R. Gupta, B. Tutuianu, and L. T. Pileggi, The Elmore delay as a bound for RC trees with generalized input signals, IEEE Trans. Computer- Aided Design, vol. 16, pp. 95–104, 1997. [9] A. B. Kahng and S. Muddu, A general methodology for response and delay computations in VLSI interconnects, Computer Science Department, University of California, Los Angeles, Tech. Rep. TR-940 015, 1994. [10] A.B. Kahng and S. Muddu, An analytic delay model for RLC interconnects, IEEE Trans. Computer-Aided Design, vol. 16, pp. 1507–1514, 1997. [11] J. Rubenstein, P. Penfield, Jr., and M. A. Horowitz, Signal delay in RC tree networks, IEEE Trans. on Computer- Aided Design, CAD-2, pp. 202-211, 1983. [12] F.Liu, C.Kashyap, C.J.Alpert, A Delay Metric for RC Circuits based on the Weibull Distribution, IEEE trans. on Computer-Aided Design of Integrated Circuits and Systems, vol. 23, pp. 443-447, 2004. [13] R. Kay and L. Pileggi, PRIMO: Probability interpretation of moments for delay calculation, in Proc. IEEE/ACM Design Automation Conf., pp. 463–468, 1998. [14] T. Lin, E. Acar, and L. Pileggi, H-gamma: An RC delay metric based on Gamma distribution approximation of the homogeneous response, in Proc. IEEE/ACM Int. Conf. Computer-Aided Design, pp. 19–25, 1998. [15] B. Tutuianu, F. Dartu, and L. Pileggi, An explicit RC-circuit delay approximation based on the first three moments of the impulse response, in Proc. IEEE/ACM Design Automation Conf., pp. 611–616, 1996. [16] A. B. Kahng And S. Muddu, Accurate Analytical Delay Models for VLSI Interconnects, University of California, Los Angeles, UCLA CS Dept. TR-950034, Sept. 1995. [17] http://www.matworld.wolfram.com
[18] http://www.itl.nist.gov