Back-EMF Voltage

Vemf = Ke × ω

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Formula

Vemf = Ke × ω

Description

A spinning motor generates a voltage (back-EMF) proportional to its rotational speed due to Faraday's law of electromagnetic induction. The back-EMF constant Ke has the same numerical value as the torque constant Kt when both are expressed in SI units (V/(rad/s) and N·m/A respectively). Back-EMF opposes the applied voltage and limits the motor current at speed. At no load, the motor spins at a speed where back-EMF nearly equals the supply voltage. Back-EMF detection is used in sensorless BLDC motor control to determine rotor position without Hall sensors.

Variables

  • Vemf — Back-EMF voltage (V)
  • Ke — Back-EMF constant (V/(rad/s))
  • ω — Angular velocity (rad/s)

Practical Notes

Back-EMF can be used as a tachometer for speed measurement. During regenerative braking, the motor acts as a generator and the back-EMF drives current back to the source. BLDC sensorless control algorithms detect back-EMF zero-crossings on the undriven phase to commutate the motor. Ke is often specified in V/kRPM in datasheets; convert by dividing by 1000 × 2π/60.

Related Formulas

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