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

where R e is the wire resistance. The total noise seen at sink si starting at some upstream node v is
∑
Noise(v − si) = R v I T(v) + Noise(e) (16)
e∈path(v−si)
where R v = 0 if there is no gate at node v. The path from v to si has no intermediate buffers.
Each node v has a predetermined noise margin NM(v). If the circuit is to have no electrical
faults, the total noise propagated from each driver/buffer to each its sink si must be less than the
noise margin for si. We define the noise slack for every node v as
NS(v) =
min NM(si) − Noise(v − si) (17)
si∈SI T(v)
where SI T(v) is the set of sink nodes for the subtree rooted at node v. Observe that NS(si) =
NM(si) for each sink si.
4.6.2 Algorithm of buffer insertion with noise avoidance
We begin with the simplest case of a single wire with uniform width and neighboring coupling
capacitance. Let us consider a wire e = (u,v). First, we need to ensure NS(v) ≥ R b I T(v) where
R b is the buffer output resistance. If this condition is not satisfied, inserting a buffer even at node
v cannot satisfy the constraint of noise margin, i.e., buffer insertion is needed within subtree T(v).
If NS(v) ≥ R b I T(v) , we next search for the maximum wirelength l e,max of e such that inserting a
buffer at u always satisfies noise constraints. The value of l e,max tells us the maximum unbuffered
length or the minimum buffer usage for satisfying noise constraints. Let R = R e /l e be the wire
resistance per unit length and I = I e /l e be the current per unit length. According to [27], this value
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