Embedded Copper Resistor / Heater
Make a resistor or a heater from a copper trace — sheet resistance, squares and temperature.
Copper as a component
A length of PCB copper is a resistor — sometimes by accident, sometimes on purpose (a shunt, a calibration trace, or a deliberate heater). Its resistance is set by the copper's sheet resistance and the trace's aspect ratio:
The key idea is the square: a piece of copper L long and W wide has
L/W squares in series, and resistance is just sheet resistance times that count —
width and length only matter through their ratio. For 1 oz copper (35 µm) the sheet resistance
is about 0.49 mΩ/□, so 100 squares is ~49 mΩ.
Copper's resistance rises with temperature at about +0.39 %/°C, which both
shifts a precision shunt and — for a heater — gives it a built-in positive temperature
coefficient. In heater mode the dissipated power is V²/R (or
I²R); the self-heating estimate uses the same IPC-2221 relation as trace
current-capacity, run backwards from the current.