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FUNCTIONALS OF BROWNIAN BRIDGES ARISING IN THE CURRENT MISMATCH IN D/A CONVERTERS

Published online by Cambridge University Press:  13 November 2008

Markus Heydenreich ,
Remco van der Hofstad  and
Georgi Radulov
Markus Heydenreich
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands E-mail: m.o.heydenreich@tue.nl; r.w.v.d.hofstad@tue.nl
Remco van der Hofstad
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands E-mail: m.o.heydenreich@tue.nl; r.w.v.d.hofstad@tue.nl
Georgi Radulov
Affiliation:
Department of Electrical Engineering, Eindhoven University of Technology, EH 5.15, 5600 MB Eindhoven, The Netherlands E-mail: g.radulov@tue.nl
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Abstract

Digital-to-analog converters (DAC) transform signals from the abstract digital domain to the real analog world. In many applications, DACs play a crucial role. Due to variability in the production, various errors arise that influence the performance of the DAC. We focus on the current errors, which describe the fluctuations in the currents of the various unit current elements in the DAC. A key performance measure of the DAC is the Integrated Nonlinearity (INL), which we study in this article. There are several DAC architectures. The most widely used architectures are the thermometer and the binary and the segmented architectures. We study the two extreme architectures, namely the thermometer and the binary architectures. We assume that the current errors are independent and identically normally distributed and reformulate the INL as a functional of a Brownian bridge. We then proceed by investigating these functionals. For the thermometer case, the functional is the maximal absolute value of the Brownian bridge, which has been investigated in the literature. For the binary case, we investigate properties of the functional, such as its mean, variance, and density.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 23 , Issue 1 , January 2009 , pp. 149 - 172
Copyright
Copyright © Cambridge University Press 2009

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References

1.Bain, L.J. & Engelhardt, M. (1991). Introduction to probability and mathematical statistics, 2nd ed.Pacific Grove, CA: Duxbury.Google Scholar
2.Bastos, J. (1998). Characterization of MOS transistor mismatch for analog design. Ph.D. thesis, Katholieke Universiteit Leuven.Google Scholar
3.Billingsley, P. (1986). Convergence of probability measures. New York: Wiley.Google Scholar
4.Bosch, A.v.d., Steyaert, M. & Sansen, W. (2004). Static and dynamic performance limitations for high-speed D/A converters. Amsterdam: Kluwer Academic Publications.CrossRefGoogle Scholar
5.Conroy, C.S.G., Lane, W.A., Moran, M.A., Lakshmikumar, K.R., Copeland, M.A., & Hadaway, R.A. (1988). Comments, with reply, on “Characterization and modeling of mismatch in MOS transistors for precisision analog design.” IEEE Journal of Solid-State Circuits 23(1): 294–296.CrossRefGoogle Scholar
6.Fey-den Boer, A. (2006) Personal Communication.Google Scholar
7.Grimmett, G.R. & Stirzaker, D.R. (2001). Probability and random processes, 3rd ed.New York: Oxford University Press.CrossRefGoogle Scholar
8.Guillemin, F., Robert, P., & Zwart, B. (2004). AIMD algorithms and exponential functionals. The Annals of Applied Probability, 14(1): 90–117.CrossRefGoogle Scholar
9.Jesper, P.G.A. (2001). Integrated converters. Oxford: Oxford University Press.Google Scholar
10.Kendall, M. & Stuart, A. (1977). The advanced theory of statistics, Volume 1, 4th ed.London: Griffin.Google Scholar
11.Lakshmikumar, K., Hadaway, R., & Copeland, M. (1986). Characterization and modeling of mismatch in MOS transistors for precision analog design. IEEE Journal of Solid-State Circuits 21(6): 1057–1066.CrossRefGoogle Scholar
12.Litvak, N. & van Zwet, W.R. (2004). On the minimal travel time needed to collect n items on a circle. The Annals of Applied Probability, 14(2): 881–902.CrossRefGoogle Scholar
13.Ott, T.J., Kemperman, J.H.B., & Mathis, M. (1996). The stationary behavior of ideal TCP Congestion Avoidance. Available at http://www.teunisott.com/Papers.Google Scholar
14.Pelgrom, M.J.M., Duinmaijer, A.C.J., & Welbers, A.P.G. (1989). Matching properties of MOS transistors. IEEE Journal of Solid-State Circuits 24(5): 1433–1439.CrossRefGoogle Scholar
15.Radulov, G.I., Heydenreich, M., Hofstad, R.v.d., Hegt, J.A., & Roermund, A.H.M.v. (2007). Brownian bridge based statistical analysis of DAC INL caused by current mismatch. IEEE Transactions on Circuits and Systems II: Express Briefs 54(2): 146–150.Google Scholar
16.Radulov, G.I., Quinn, P.J., van Beek, P.C.W., Hegt, J.A., & van Roermund, A.H.M. (2006). A binary-to-thermometer decoder with built-in redundancy for improved DAC yield. In ISCAS, Kos, Greece.Google Scholar
17.Razavi, B. (2001). Design of analog CMOS integrated circuits. New York: McGraw-Hill.Google Scholar
18.Van de Plassche, R.J. (1994). Integrated analog-to-digital and digital-to-analog converters. Amsterdam: Kluwer Academic Publishers.CrossRefGoogle Scholar
19.Wikner, J.J. (2001). Studies on CMOS digital-to-analog converters. Ph.D. thesis, Department of Electrical Engineering, Linköping University.Google Scholar