How does POCV combine per-arc sigma values, and how does that scale differently than flat derating as path length grows?
From PDVerse STA Mentor Guide · pdVerse Mentor Guide
Technical Explanation
POCV models variation statistically per timing arc rather than with derate factors: each arc carries a nominal delay and a standard deviation (sigma) from the library's variation data, and these sigmas are combined along a path in a root-sum-square (RSS) statistical sense rather than added linearly.
Timing-path Reasoning
Because per-stage variation is largely independent/random, summing sigmas in quadrature (RSS) reflects how uncorrelated random variables combine statistically, whereas flat OCV derating effectively adds variation linearly (as a fixed percent of the growing nominal sum). This means as path length N grows, RSS-based variation grows as sqrt(N) while linear derate-style variation grows as N — a widening gap that lets POCV avoid over-margining long paths.
Equation
POCV worked (5-stage path, nominal,sigma pairs): (40,1.2)(50,3.5)
(45,1.0)(55,2.0)(48,1.4); nominal sum=238ps; path sigma = sqrt(1.2^2
+ 3.5^2 + 1.0^2 + 2.0^2 + 1.4^2) = ~4.6 ps; 3-sigma ~14ps -> POCV
total 238+14=252ps vs flat OCV(+8%) 238x1.08=257ps -> +19ps blanket
margin. Scaling law: N equal stages, per-stage sigma=s: linear
(flat-OCV-style) variation = s*N; statistical RSS variation =
s*sqrt(N). N=4: linear 4s vs RSS 2s (2x less); N=16: 16s vs 4s (4x
less); N=64: 64s vs 8s (8x less).Expected Result
POCV signoff produces total delay estimates that are less pessimistic than flat OCV, with the gap between the two growing (in relative terms) the longer/deeper the path becomes, since flat-style variation scales with N while RSS scales with sqrt(N).
Failure Symptoms
Flat OCV on long paths reports a delay margin far exceeding what POCV's statistical combination would justify (e.g., 257ps vs 252ps in the 5-stage case, with the gap growing much larger for deeper paths per the N vs sqrt(N) scaling).
Root Cause
Flat derating implicitly assumes per-stage variations add up linearly (worst-case-aligned), which overstates risk since independent random variations actually combine via rootsum-square, growing only as the square root of stage count.
Mentor Note — Debugging Procedure
Verify that LVF-based sigma data is present for every arc in the path and that the RSS combination (not a linear sum) is being used to derive path-level sigma before applying the chosen sigma multiplier (e.g., 3-sigma) for signoff. POCV's RSS combination of per-arc sigmas means variation as a fraction of nominal delay shrinks as paths get longer (~s/sqrt(N) versus flat's ~s), which is exactly why deep paths benefit the most from moving off flat OCV.
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