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Chapter 4: Probability Power Analysis: 06-88-541: Low Power CMOS Design

This document discusses probabilistic power analysis techniques. It introduces static probability and transition density to characterize digital signals, which allows analyzing a circuit's power consumption. It describes how to calculate the static probability and expected frequency of each node by propagating probabilities through Boolean functions. Additionally, it covers transition density propagation and defines signal entropy. Finally, it presents an entropy-based power estimation method relating switching activity and circuit area to the entropy of input and output signals.

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Mrunal Salve
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247 views4 pages

Chapter 4: Probability Power Analysis: 06-88-541: Low Power CMOS Design

This document discusses probabilistic power analysis techniques. It introduces static probability and transition density to characterize digital signals, which allows analyzing a circuit's power consumption. It describes how to calculate the static probability and expected frequency of each node by propagating probabilities through Boolean functions. Additionally, it covers transition density propagation and defines signal entropy. Finally, it presents an entropy-based power estimation method relating switching activity and circuit area to the entropy of input and output signals.

Uploaded by

Mrunal Salve
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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06-88-541:

Low Power
CMOS Design

Chapter 4 : Probability Power


Analysis
Low Power

4. Probability power analysis

C. Chen

Probabilistic Based Analysis


Signals can be characterized by some quantities (e.g,
frequency) instead of full waveform.
This image cannot currently be display ed.

Same frequency (f )
--> Same power
dissipation (P=CV2f )

Such signal quantities allow us to characterize a large


number of different signals into a single class.
Low Power

4. Probability power analysis

C. Chen

Static Probability and Frequency


The static probability, p, of a digital signal is the ratio of
the time it spends in logic 1 to the total observation time.
Under temporal independence assumption, the probability
T that a transition occurs is:
T = 2 p(1 - p)

--- transition probability

and the expected frequency is f = T/2 = p(1 - p).


We need a propagation model for static probability in
order to derive the frequency of each node in a circuit for
power analysis.
Low Power

C. Chen

4. Probability power analysis

Propagation of Static Probability


Find out static probability propagation of a two-input
OR gate.
The general formula for the propagation of static
probability through an arbitrary Boolean function y = f (x1 ,
x2 , , xn) is given by

P ( y ) P ( x i f xi ) P ( x i f x )
i

P ( x i ) P ( f xi ) P ( x i ) P ( f x )
i

where P ( x i ) 1 P ( x i )
Low Power

4. Probability power analysis

C. Chen

Transition Density Model


In addition to static probability (p), we add another
parameter to characterize a logic signal -- transition density
(D) which denotes the number of transitions per unit time.
p = 0.4 , D = 4 per sec.

p = 0.4 , D = 6 per sec.

1.0 sec

Low Power

4. Probability power analysis

C. Chen

Propagation of Transition Density


The Boolean difference of y with respect to xi is
defined as
dy
f xi f x
i
dx i
Under zero-delay model and the uncorrelated
inputs assumption, the transition density of y is
given by
D( y)

i 1

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dy

P ( dx

) D ( xi )

4. Probability power analysis

C. Chen

Signal Entropy
For a discrete variable x which takes n different
values, its entropy is defined as
H ( x)

p
i 1

log 2

1
pi

( pi is the probability that x takes the ith value xi )


If x is a random Boolean variable with probability
p of being logic 1, we have
H ( x) p log 2
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1
1
(1 p) log 2
p
1 p
C. Chen

4. Probability power analysis

Entropy-Based Power Estimation


Recall the dynamic power
Power

CV
i 1

2
dd

i f

F C i FA
i 1

where F is the average switching activity on N


nodes, and A is proportional to the circuit area.
The following relation has been observed:
A 2 n H (Y )
F
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for small n (n 10) , or A

2n
H (Y )
n

for l arg e n.

2
[ H ( X ) 2 H (Y )]
3(m n)
4. Probability power analysis

C. Chen

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