4.2 Delay estimation by ⅞-∏θrm minimization
The signal propagation delays of a number of sensitizable paths are measured.
Linear equations are constructed with the scaling factors of gate delays (defined
in Section 4.1.1) as the unknown parameters. Finally, solving these equations,
we estimate the scaling factors and, therefore, the gate variations. In Section
4.3, we utilize the variations in spatial correlations to improve the scaling factor
estimations.
An example of path delay analysis is shown in Figure 4.2. Lines labeled by α,
b, c, and d are the circuit’s primary inputs and the line n is the circuit’s primary
output. We want to sensitize the delay of the highlighted path, Pi : (a-<71-z-e-<73-
f^ff4^s-5'6-k^S'7-n). We need to find an input vector that guarantees a transition in
input a that would propagate through the path. Let us assume a rising transition
in a (input a transits from 0 to 1). To allow propagation through the gate g1,
we need to set b to be equal to 0. Then, there would be a falling (1 → 0) and
a rising (0 → 1) transition in lines e and f, respectively. If g is equal to 1 and
m is equal to 0, then the rising transition propagates in the lines s, к and n. To
guarantee that g is equal to 1 and m is equal to 0, we just need to set the input
c = 0.
The input assignments above allow the transition in input a to propagate
through the path Pi m-g1-z-e-g3-f-<74-s-g⅛-k-g7-n. Using the delay bounding
method introduced in [64], one can measure the total delay of the underlying
41
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