How does POCV combine per-arc sigma values, and how does that scale differently than flat derating as path length grows?

Short Answer

Parametric on-chip variation (POCV) gives each timing arc its own nominal delay and a standard deviation, or sigma, taken from the library's variation data — rather than one derate factor applied uniformly. Along a path, independent per-arc sigmas combine statistically, so total path variation grows with roughly the square root of the number of stages, not linearly with stage count the way flat derating effectively does. That makes flat derating increasingly over-conservative on long paths.

Technical Explanation

• Each library timing arc under POCV carries a nominal delay plus a sigma value, sourced from Liberty variation format (LVF) tables such as ocv_std_dev_cell_rise, describing how much that specific arc's delay is expected to vary due to random, uncorrelated process effects.
• timing_pocvm_enable_analysis (PT) turns POCV on; PrimeTime then folds these per-arc sigmas into graph-based timing automatically as part of update_timing (PT), rather than requiring a separate derating pass.
• A flat derate factor effectively assumes every stage's variation points the same direction and adds up linearly — N stages each contributing their full worst-case delta stack directly. Independent random variables do not behave this way: when uncorrelated, their variances add, so the combined standard deviation across a path grows with the square root of the number of stages, not with the stage count itself.
• This statistical combination means a long path's worst-case delay under POCV is nominal delay plus some chosen number of combined sigmas (timing_pocvm_corner_sigma, PT, default 3-sigma), and that combined-sigma term grows much more slowly than a flat multiplier would as more stages are added.
• Because the growth rate differs, flat OCV and POCV increasingly diverge as path length grows: a short path may see similar margin under either method, while a long, many-stage path sees POCV settle to noticeably less added margin than flat derating would apply.
• timing_pocvm_enable_extended_moments (PT) additionally enables moment-based POCV, which uses higher-order statistical moments from LVF data for even more accurate modeling on paths where a simple mean-and-sigma normal approximation is not accurate enough — this needs the library to actually contain moment-based LVF models.
• What breaks: applying flat derating on a design whose critical paths are long and multi-stage wastes real margin, exactly as with AOCV, but for a different underlying reason — flat derating models correlated worst-case stacking that mostly does not exist for independent random variation.

Follow-up Question & Model Response

"Two paths have the same nominal delay but different stage counts — a 4-stage path and a 16-stage path. Under POCV, which one has the larger sigma-driven margin added, in absolute terms, and why might that still be smaller than what flat OCV would have added to the 16-stage path?"

Candidate Model Response: In absolute terms the 16-stage path typically has the larger combined sigma, since it is summing more individual arc variances even though each is small, giving it a bigger combined-sigma margin than the 4-stage path in absolute picoseconds. But that combined-sigma margin still grows only with the square root of stage count, while a flat derate factor scales with the full nominal delay of all 16 stages linearly, so the flat-OCV margin on the 16-stage path is very likely still larger than what POCV's statistical combination actually adds — the more stages a path has, the wider that gap tends to become.