path. We can measure the time difference between the transitions in line a and
in line n. Let us denote the total delay of the path Pi for the rising transition by
⅛(Fι)∙ 4
,o The total path delay is an additive composition of the delays of its elements.
For example, delay of the path P1 can be written as the summation of the delays
in line a, gate g1, line k, line e, gate g⅛, and so on. i.e.,
dr(Pι) — d(α) ÷ dr(<7ι) ÷ d(z) ÷ d(e ) ÷ df(g3)
+ d(J ) + ⅛¼) + d(s ) + df(g6) + d(k )
+ dr(g7) + d(n ), (4.2)
where d{x) is the delay of the line x, and dr(gi) and df(gi) are the rising and
falling delays of gate g⅛, respectively.
Here, we assume for presentation clarity that interconnect delays (line delays)
are zero. The proposed method can be easily extended to cases with non-zero
interconnect delays. Note that it maybe the case that variations in the inter-
connects have a separate statistical representation. In such scenarios, one may
consider compressed sensing methods that address the summation of two distinct
distributions in one framework [24]. Assuming zero interconnect delays, Equation
4.2 reduces to:
dr(Pι) = ⅛∙(<7ι) ÷ df{gs) + dr(g⅛) + df(gβ) + dr(g7). (4.3)
In Section 4.1, we illustrated that because of the process variation, delays of
42
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