PWM Motor Effective Voltage

Formula

Description

PWM (pulse width modulation) is the standard method for controlling DC motor speed. By rapidly switching the supply voltage on and off, the motor sees an average (effective) voltage proportional to the duty cycle. At 50% duty cycle, the motor receives half the supply voltage and runs at approximately half speed (for an unloaded motor). The motor inductance acts as a natural low-pass filter, smoothing the pulsed voltage into a nearly constant current. PWM is far more efficient than linear voltage regulation because the switching transistor is either fully on (low Vds) or fully off (zero current), minimizing power loss in the driver.

Variables

• V_eff — Effective (average) voltage seen by the motor (V)
• V_cc — Supply voltage (V)
• D — PWM duty cycle (ratio 0 to 1)

Practical Notes

The PWM frequency must be high enough that the motor inductance smooths the current ripple. Typical PWM frequencies: small DC motors 20-50 kHz (above audible range), large motors 5-20 kHz, RC servos use 50 Hz with 1-2 ms pulse width. At very low duty cycles, the motor may not produce enough torque to start rotating (cogging). The actual motor speed is not perfectly proportional to duty cycle due to back-EMF, friction, and load variations.