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After re-sizing gates by factor 'k i ' the final delay D f comes out to be:
C i 1 k i 1
C i k i
i 1
D f g i
P (10)
C i 1
C i
D i g i
(11)
Therefore,
k i 1
k i
N
i 1
D f D i
P (12)
We get the delay increase rate (d inc ) due to re-sizing of the gates as;
D i k i 1
k i
i 1
P D 0
d inc
(13)
D 0
Energy-Delay-Gain is the parameter used to optimize the power consumption of the
circuit.
It is defined as follows;
E 0 E f
E 0
D f D 0
D 0
EDG
(14)
Where,
Energy gain E 0 E f
E 0
Delay gain D f D 0
D 0
5
Optimization Technique
In order to do optimization we formulated an Objective function using equation 8 and
is given by;
N
k g AF h g k C
(15)
f k ,k ,k ,,k N KAF
To get the Constraint goal we use (13) which will give
N
d D D P k
D
(16)
1
f k ,k ,k N
k
(15) and (16) forms the optimization problem, which we will solve using geometric
programming problem technique. Geometric programming is an optimization
technique applicable to non-linear programming problems involving mathematical
functions called posynomials. This technique involves the use arithmetic mean-
geometric mean inequality for any number of non-negative numbers.
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