Buffer Insertion Basics - Computer Engineering & Systems Group ...

admittance Y u (s) after merging them (Figure 9(b)).
y u,1 = y d1,1 + y d2,1 y u,2 = y d1,2 + y d2,2 y u,3 = y d1,3 + y d2,3 (20)
Y (s) d1
Y u(s)
R
Y (s) d
Y (s) u
Y (s) d2
(a)
(b)
Figure 9: Two scenarios of admittance propagation.
The third order approximation (y 1 ,y 2 ,y 3 ) of an admittance can be realized as an RC π−model
(C u ,R π ,C d ) (Figure 10)where
C u = y 1 − y2 2
y 3
R π = − y2 3
y 3 2
C d = y2 2
y 3
(21)
Y(s)
R π
C
u
C d
Figure 10: Illustration of π−model.
4.7.2 Higher order wire delay model
While the Elmore delay is equal to the first order moment of transfer function, the accuracy of
delay estimation can be remarkably improved by including higher order moments. For example,
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