Plane Spreading Resistance

Formula

Description

When current enters a large ground or power plane through a via or pad of radius r, it spreads radially outward. The spreading resistance represents the concentrated resistance near the via where current density is highest. For a 1 oz copper plane (35 µm thick), the spreading resistance from a typical 0.2mm radius via pad is in the low milliohm range. This resistance is important in power distribution network analysis because it limits how effectively a plane can deliver transient current to a specific location. Multiple vias reduce the effective spreading resistance.

Variables

• Rspread — Spreading resistance (Ω)
• ρ — Sheet resistivity of the plane (Ω·m)
• r — Radius of the current injection point (m)

Practical Notes

This formula assumes a semi-infinite plane. For finite planes or near edges, the resistance increases. Copper sheet resistance for 1 oz (35µm): 0.5 mΩ/square. For PDN analysis, spreading resistance from capacitor mounting pads to IC power pins is a key contributor to the total impedance. Wider vias and via arrays reduce spreading resistance effectively.