Pelgrom's Law

Pelgrom's law is the device mismatch scaling relation stating that local threshold mismatch decreases with the inverse square root of transistor area - it provides a practical design rule linking precision to silicon area cost.

What Is Pelgrom's Law?

• Definition: Sigma(DeltaVth) = Avt / sqrt(W x L) for matched devices under local random mismatch assumptions.
• Interpretation: Doubling device area does not halve mismatch; improvement follows square-root behavior.
• Design Consequence: Precision analog blocks need significant area to reduce offset and gain error.
• Scope: Most applicable to local random mismatch, not global systematic shifts.

Why Pelgrom's Law Matters

• Area-Precision Tradeoff: Quantifies silicon cost of matching improvement.
• Analog Scaling Limit: Explains why analog blocks shrink much slower than digital logic.
• SRAM Stability: Helps estimate mismatch impact on cell read/write margins.
• Early Sizing Rule: Provides first-order sizing guidance before full simulation.
• Technology Comparison: Avt constants benchmark mismatch quality across process nodes.

How It Is Used in Practice

• Device Sizing: Choose W and L to meet mismatch sigma targets.
• Monte Carlo Calibration: Fit Avt from silicon data and update PDK statistics.
• Layout Strategy: Combine area sizing with matching layout techniques for best results.

Pelgrom's law is the fundamental mismatch economics rule in analog and memory design - it makes clear that precision is purchased with area, and the exchange rate follows square-root physics.