Why MOSFET Power Loss Scales With the Square of Current
An H-bridge motor driver's power dissipation during normal (non-switching) conduction follows P = I² x RdsOn — current squared, multiplied by the MOSFET's on-resistance — which means power loss doesn't scale linearly with current draw, it scales with the square of it. Doubling motor current doesn't double the driver's heat output, it quadruples it — a nonlinear relationship that's easy to underestimate when sizing heatsinking or predicting thermal behavior at higher current loads than initially tested.
This squared relationship is exactly why a motor driver that runs comfortably cool at low current can overheat dramatically once current draw increases even moderately — the thermal margin doesn't shrink proportionally with current increases, it shrinks much faster, which is a common and genuinely dangerous surprise when scaling up a motor control design from a low-current prototype to a higher-current production load.
RdsOn itself isn't a fixed constant either — it typically increases with temperature, meaning a MOSFET that's already running hot has higher resistance (and therefore even more power dissipation) than its cold-state datasheet value would suggest, a positive feedback effect that can compound thermal problems if not accounted for with adequate margin from the start.