What does a sigma value in a POCV Liberty variation table actually represent?

Short Answer

Sigma is the standard deviation of a cell delay's expected spread around its mean value if you could measure that same cell many times across normal manufacturing variation. A larger sigma means the real delay is more likely to land far from the mean; the tool combines each arc's sigma with its neighbors statistically instead of assuming every arc's delay lands at its absolute worst value at once.

Technical Explanation

POCV treats each cell's delay as a distribution, not a single fixed number, and sigma is what describes the width of that distribution.

• Mean is the expected, most likely delay value. The library's ocv_std_dev_cell_rise (LIB) style table pairs a mean delay with a sigma for the same rising-transition arc, at a given input slew and output load.
• Sigma measures spread, not direction. A sigma of 5ps means most real instances of that arc's delay across the chip will land within a few multiples of 5ps of the mean, in either direction, following the normal-distribution assumption the tool uses.
• Combining sigmas is not the same as adding worst cases. If a path has ten arcs each with their own sigma, the tool statistically combines all ten sigmas into one path-level sigma, rather than assuming every arc hits its own worst extreme delay at the same time.
• The output is still a single number for signoff. The tool converts the combined mean and sigma into an effective delay at some number of sigmas out — for example, three sigmas — giving one concrete number a report can show, even though the underlying model is statistical.
• Sigma values can vary by transition and load. A more accurate library uses an LVF (Liberty variation format) table so sigma itself changes with input slew and output load, rather than one fixed sigma for every condition on that arc.
• Why the distinction matters: treating a sigma value as if it were just another fixed derate percentage misses the point that POCV's advantage comes specifically from combining many independent spreads statistically, not from a single conservative number.

Follow-up Question & Model Response

A path has ten arcs, each with a sigma of about 5ps. A colleague estimates the path's total variation at 50ps by adding them up. Is that right?

Candidate Model Response: Not for independent random variations — that estimate overstates the real spread. When ten independent sigma values combine statistically, the combined sigma grows roughly with the square root of the number of arcs rather than linearly, so ten arcs at 5ps each combine to something closer to 16ps, not 50ps. This is exactly the effect that makes POCV less pessimistic than adding up worst cases: independent variations partly cancel each other out rather than all pushing in the same direction at once. I would let the tool compute the combined sigma directly rather than approximating it by hand, since the exact combination depends on each arc's specific correlation assumptions.