PWM Motor Effective Voltage
Veff = Vcc × D
Quick answer
This calculator solves V_eff = V_cc × D for Effective Voltage. With Supply Voltage 26.4 V, Duty Cycle 50 %, the result is 13.2 V. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
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.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Veff | Effective Voltage | V | pV, nV, µV, mV, V, kV |
| Vcc | Supply Voltage | V | pV, nV, µV, mV, V, kV |
| D | Duty Cycle | — | —, % |
Step by step
- 1. What you know: Supply Voltage 26.4 V, Duty Cycle 50 %
- 2. The relation: V_eff = V_cc × D
- 3. Substitute: Vcc = 26.4 V, D = 50 %
- 4. Result: Effective Voltage = 13.2 V
Worked examples
Minimum range
Given: Supply Voltage 0.726 V, Duty Cycle 2.5 %
Result: Effective Voltage = 18.15 mV
Low range
Given: Supply Voltage 7.26 V, Duty Cycle 25 %
Result: Effective Voltage = 1.815 V
Typical
Given: Supply Voltage 26.4 V, Duty Cycle 50 %
Result: Effective Voltage = 13.2 V
High range
Given: Supply Voltage 0.506 kV, Duty Cycle 0.8
Result: Effective Voltage = 0.4048 kV
Maximum range
Given: Supply Voltage 5.06 kV, Duty Cycle 8
Result: Effective Voltage = 40.48 kV
Solving for each variable
Solve for Effective Voltage
Supply Voltage 0.726 V, Duty Cycle 2.5 % → 18.15 mV
Solve for Supply Voltage
Effective Voltage 0.33 V, Duty Cycle 2.5 % → 13.2 V
Solve for Duty Cycle
Effective Voltage 0.33 V, Supply Voltage 0.726 V → 45.45 %
How Effective Voltage changes with Supply Voltage
| Supply Voltage (input) | Effective Voltage (result) |
|---|---|
| 2.64 V | 1.32 V |
| 6.6 V | 3.3 V |
| 13.2 V | 6.6 V |
| 19.8 V | 9.9 V |
| 26.4 V | 13.2 V |
| 39.6 V | 19.8 V |
| 52.8 V | 26.4 V |
| 105.6 V | 52.8 V |
| 0.1848 kV | 92.4 V |
| 0.264 kV | 132 V |
The same result in other units
| Unit | Value |
|---|---|
| mV | 13200 |
| V | 13.2 |
| kV | 0.0132 |
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<p><a href="https://vbatpower.com/formulas/pwm-motor-voltage/">PWM Motor Effective Voltage</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate PWM Motor Effective Voltage?
Use V_eff = V_cc × D. With Supply Voltage 26.4 V, Duty Cycle 50 %, Effective Voltage works out to 13.2 V.
What is the formula for PWM Motor Effective Voltage?
The formula is V_eff = V_cc × D. PWM (pulse width modulation) is the standard method for controlling DC motor speed.
How do you find Supply Voltage when you know the other values?
Rearrange for Supply Voltage: with Effective Voltage 0.33 V, Duty Cycle 2.5 %, Supply Voltage is 13.2 V.
How do you find Duty Cycle when you know the other values?
Rearrange for Duty Cycle: with Effective Voltage 0.33 V, Supply Voltage 0.726 V, Duty Cycle is 45.45 %.
What units does PWM Motor Effective Voltage use?
Effective Voltage is shown in mV, V, kV. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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