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.