How do you derive rectangular core width and height from area and aspect ratio?
From PDVerse PnR Interview Handbook, part of the pdVerse Mentor Guide
Short Answer
This is one of the most basic but most-used floorplanning calculations — you know how much area your logic needs, and you've decided (for I/O, package, or routing reasons) what shape you want that area to take, and you need actual width/height numbers to build a floorplan from. 5 means twice as tall as wide.
Technical Explanation
- 5 means twice as tall as wide.
- Given total area
Aand your chosenAR, the two formulas fall right out of substitutingwidth = AR × heightintoA = width × height: - width = √(A × AR)
- height = √(A / AR)
- Sanity check with AR = 1 (a square): both formulas reduce to
width = height = √A— exactly what you'd expect, since a square with area A has side length √A. - Worked example: for A = 1,000,000 µm² and AR = 1 (square), width = √(1,000,000 × 1) = 1000 µm, and height = √(1,000,000 / 1) = 1000 µm — matching the reference example in the original answer.
- Keep your units consistent through every step (µm² for area, µm for dimensions) — mixing units here is a classic source of "why is my die 1000x too big" bugs.
- Don't stop at the raw math — after computing width/height, round to something that respects the manufacturing grid and lands on a legal row boundary (a whole number of standard-cell rows). A mathematically "correct" but non-grid-aligned dimension will just get silently snapped by the tool anyway, so it's better to round deliberately.
Visual Verification
Core Width = sqrt(Area / AR) and Core Height = sqrt(Area * AR). Calculated dimensions must snap to integer multiples of standard-cell row heights and site pitches.
Formula Or Decision Rule
Width [um] = sqrt(A [um^2] x AR); height [um] = sqrt(A [um^2] / AR).
What To Check
- Warning sign: Rounded dimensions change area or land off the manufacturing, site, or block grid.
- Inspect: choose one affected region, macro, row, pin, path, or net and trace the physical cause.
- Correct: Snap deliberately, recompute actual area and utilisation, and record the rounded values.
Command Checks & Actions
report_design-floorplan: reports the floorplan state understood by the tool
Run only the commands needed for this question. Save the report with the floorplan version and analysis context.
Healthy, Suspicious & Hard-stop Results
- Healthy: For area A and aspect ratio AR = width/height, width is sqrt(A x AR) and height is sqrt(A / AR). Keep units through every step.
- Hard stop: required legality or physical feasibility is missing or unexplained.
Common Mistake
The Trap: Do not hide the symptom with an arbitrary utilisation, halo, channel, blockage, pin move, or die-size change.
What The Interviewer Is Testing
” to measurable physical evidence and an owned correction.
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