Information Technology Reference
In-Depth Information
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.