INFERRING TRIGGER NOISE FROM TRIGGER JITTER
We address the relationship between voltage noise at the input of a threshold comparator and random changes in the timing of the comparator output toggle timing (jitter). Models that go beyond the na¨ıve linear relationship are presented and shown to match experiment. They help reconcile predictions with verifiable device performance; more over, they allow an approximate measurement of the noise bandwidth without the help of high-frequency equipment. In the course our investigation, a PC/laptop toolset was constructed that lets a neophyte study noise via jitter. This toolset can also be used in education to teach the notion that a biased view of a random phenomenon can arise from triggering on the tails of its distribution.
M. Miller, White paper, Presented at DesignCon 2014, Santa Clara, CA, USA, 2014.
J. Res. Natl. Inst. Stand. Technol. 110, pp. 511–527, 2005.
E. W. Weisstein, “Uniform Distribution,” MathWorld–A Wolfram Web. [Online]. Available: http://mathworld.wolfram.com/UniformDistribution.html
A. Lenart, “The moments of the Gompertz distribution and maximum likelihood estimation of its parameters,” Scandinavian Actuarial Journal, no. 3, pp. 255–277, 2014; doi: 10.1080/03461238.2012.687697
N. M. Temme, “The asymptotic expansion of the incomplete Gamma functions,” SIAM Journal on Mathematical Analysis, vol. 10, no. 4, pp. 757–766, 1979.
D. L. Decker, “Computer evaluation of the complementary error function,” American Journal of Physics, vol. 43, issue 9, pp. 833–834, 1975; doi: 10.1119/1.9699
R. Kiely, “Understanding and Eliminating 1/f Noise,” Analog Dialogue. [Online]. Available: http://www.analog.com/en/analog-dialogue/articles/understanding-and-eliminating-1-f-noise.html
J. F. Stephany, “A theory of 1/f noise,” Journal of Applied Physics, vol. 83, no. 6, pp. 3139–3143, 1998; doi: 10.1063/1.367071
J. H. Lambert, “Observationes variae in mathesin puram,” Acta Helveticae physico-mathematico-anatomicobotanico-medica, vol. 3, pp. 128–168, 1758.
J. Kim, B. S. Leibowitz, J. Ren, and C. Madden, “Simulation and Analysis of Random decision Errors in Clocked Comparators,” IEEE transactions on Circuits and Systems – I: Regular Papers, vol. 56, no. 8, pp. 1844–1857, 2009; doi: 10.1109/TCSI.2009.2028449