lec11lp

# lec11lp - ELEC 5970-001/6970-001(Fall 2005) Special Topics...

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10/4-6/05 ELEC 5970-001/6970-001 Lecture 11 1 ELEC 5970-001/6970-001(Fall 2005) Special Topics in Electrical Engineering Low-Power Design of Electronic Circuits Power Analysis: Probabilistic Methods Vishwani D. Agrawal James J. Danaher Professor Department of Electrical and Computer Engineering Auburn University http://www.eng.auburn.edu/~vagrawal vagrawal@eng.auburn.edu

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10/4-6/05 ELEC 5970-001/6970-001 Lecture 11 2 Basic Idea View signals as a random processes Prob{s(t) = 1} = p 1 p 0 = 1 – p 1 C 0→1 transition probability = (1 – p 1) p 1 Power, P = (1 – p 1) p 1 CV 2 f ck
10/4-6/05 ELEC 5970-001/6970-001 Lecture 11 3 Source of Inaccuracy 1/ f ck p 1 = 0.5 P = 0.5 CV 2 f ck p 1 = 0.5 P = 0.33 CV 2 f ck p 1 = 0.5 P = 0.167 CV 2 f ck Observe that the formula, Power, P = (1 – p 1) p 1 CV 2 f ck , is not Correct.

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10/4-6/05 ELEC 5970-001/6970-001 Lecture 11 4 Switching Frequency Number of transitions per unit time: N(t) T = ─── t For a continuous signal: N(t) T = lim ─── t→∞ t T is defined as the transition density.
10/4-6/05 ELEC 5970-001/6970-001 Lecture 11 5 Static Signal Probabilities Observe signal for interval t 0 + t 1 Signal is 1 for duration t 1 Signal is 0 for duration t 0 Signal probabilities: p 1 = t 1/( t 0 + t 1) p 0 = t 0/( t 0 + t 1) = 1 – p 1

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10/4-6/05 ELEC 5970-001/6970-001 Lecture 11 6 Static Transition Probabilities Transition probabilities: T 01 = p 0 Prob{signal is 1 | signal was 0} = p 0 p 1 T 10 = p 1 Prob{signal is 0 | signal was 1} = p 1 p 0 T = T 01 + T 10 = 2 p 0 p 1 = 2 p 1 (1 – p 1) Transition density: T = 2 p 1 (1 – p 1) Transition frequency: f = T/ 2 Power = CV T/ 2 (correct formula)
10/4-6/05 ELEC 5970-001/6970-001 Lecture 11 7 Static Transition Frequency 0 0.25 0.5 0.75 1.0 0.25 0.2 0.1 0.0 p 1 f = p 1 ( – p )

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10/4-6/05 ELEC 5970-001/6970-001 Lecture 11 8 Inaccuracy in Transition Density 1/ f ck p 1 = 0.5 T = 1.0 p 1 = 0.5 T = 4/6 p 1 = 0.5 T = 1/6 Observe that the formula , T = 2 p 1 (1 – p 1), is not correct.
10/4-6/05 ELEC 5970-001/6970-001 Lecture 11 9 Cause for Error and Correction Probability of transition is not independent of the present state of the signal. Consider probability

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## lec11lp - ELEC 5970-001/6970-001(Fall 2005) Special Topics...

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