Motor PWM Average Voltage Calculator
Calculate first-order motor PWM average applied voltage for unipolar drives, custom two-level drive states, and bipolar H-bridge references. MOT-007 also solves duty cycle, PWM timing, terminal RMS voltage reference, back-EMF headroom, and a steady-state average resistive current reference.
The calculator deliberately avoids treating duty cycle as motor speed, torque, or true PWM current. Real motor behavior depends on winding inductance, current ripple, back EMF, driver topology, freewheel path, load and control loop behavior.
Engineering tool
Motor PWM Average Voltage Calculator
Calculate motor PWM average applied voltage, duty cycle, H-bridge bipolar voltage, timing, back-EMF headroom, and first-order resistive current references.
Calculation mode
Parameter panel
Result console
- Average Applied Voltage
- 6V
- Terminal RMS Voltage Reference
- 8.48528V
- Duty Cycle
- 50%
- Duty Fraction
- 0.5
The familiar Vavg = D × Vbus applies only when the on level is Vbus and the off-state voltage is 0 V.
Reference table
| Effective On Level | 12 | V |
|---|
Motor PWM Average Voltage Formula Audit
| Drive Model | V1 uses a two-level motor terminal applied-voltage reference. |
|---|---|
| Duty Cycle Convention | Duty D is a fraction from 0 to 1, displayed as percent when requested. |
| General Two-Level Formula | Vavg = DVon + (1-D)Voff. |
| Unipolar Formula | If Von = Vbus and Voff = 0, Vavg = D × Vbus. |
| Bipolar Formula | If Von = +Vbus and Voff = -Vbus, Vavg = (2D - 1)Vbus. |
| Inverse Duty Formula | D = (Vavg - Voff)/(Von - Voff), requiring Von ≠ Voff and reachable target voltage. |
| On-State Voltage Definition | Von is the applied motor terminal voltage during the PWM on state. |
| Off-State Voltage Definition | Voff is the motor terminal voltage during off, decay, coast, brake or recirculation state. |
| Driver-Drop Model | Fixed driver drop is a simplified effective conduction-drop reference. |
| PWM Period Formula | T = 1/f. |
| On-Time Formula | ton = D × T. |
| Off-Time Formula | toff = (1-D) × T. |
| Average / RMS Voltage Boundary | Terminal RMS voltage is not winding current RMS and does not determine motor torque by itself. |
| Back-EMF Headroom Formula | Vheadroom = Vavg - E - Vfixed. |
| Resistive Current Reference | Ireference ≈ (Vavg - E - Vfixed)/R. |
| Inductance Boundary | Real motor current depends on R, L, back EMF, PWM frequency and freewheel path. |
| Current-Ripple Boundary | Higher PWM frequency often reduces ripple but can increase switching loss. |
| Coast / Brake Boundary | Coast and brake states can have similar average voltage but different current decay. |
| Current-Control Boundary | Current-regulated drivers dynamically adjust effective PWM behavior. |
| PWM / Speed Boundary | Duty cycle is not a direct motor-speed percentage. |
| PWM / Torque Boundary | Duty cycle is not a direct motor-torque percentage. |
| Generic PWM Scope Boundary | MOT-007 is motor-drive average voltage and headroom, not a generic PWM or timer calculator. |
Formula
Formula reference
Motor PWM average-voltage formulas
The general two-level average is the shared core formula. D×Vbus is only the common unipolar simplification.
Vavg = DVon + (1-D)VoffD = (Vavg - Voff)/(Von - Voff)Unipolar: Vavg = D × VbusBipolar: Vavg = (2D - 1)VbusT = 1/fton = D × Ttoff = (1-D) × TVrms = sqrt(DVon² + (1-D)Voff²)Vheadroom = Vavg - E - VfixedIreference ≈ Vheadroom / RVariable definitions
- D
- PWM duty fraction from 0 to 1
- Von
- motor terminal on-state voltage
- Voff
- motor terminal off-state voltage
- E
- motor back EMF
- R
- winding resistance
- Ireference
- steady-state average resistive current reference
Motor PWM Average Voltage Formula Audit
| Drive Model | Two-level motor terminal applied-voltage reference. |
|---|---|
| Duty Cycle Convention | D is internally 0 to 1. |
| General Two-Level Formula | Vavg = DVon + (1-D)Voff. |
| Unipolar Formula | Vavg = D × Vbus only when Von = Vbus and Voff = 0 V. |
| Bipolar Formula | Vavg = (2D - 1)Vbus for ideal symmetric ±Vbus switching. |
| Inverse Duty Formula | D = (Vavg - Voff)/(Von - Voff). |
| On-State Voltage Definition | Voltage across the motor terminal pair during the PWM on state. |
| Off-State Voltage Definition | Voltage across the motor terminal pair during the off, decay, coast, brake or recirculation state. |
| Driver-Drop Model | Fixed drop is a simplified effective voltage-drop reference. |
| PWM Period Formula | T = 1/f. |
| On-Time Formula | ton = D × T. |
| Off-Time Formula | toff = (1-D) × T. |
| Average / RMS Voltage Boundary | Average terminal voltage, terminal RMS voltage and winding current RMS are different quantities. |
| Back-EMF Headroom Formula | Vheadroom = Vavg - E - Vfixed. |
| Resistive Current Reference | Ireference ≈ (Vavg - E - Vfixed)/R. |
| Inductance Boundary | The real PWM current waveform depends on L di/dt. |
| Current-Ripple Boundary | PWM frequency changes ripple and switching behavior, not ideal average voltage. |
| Coast / Brake Boundary | Same average voltage can hide different decay paths. |
| Current-Control Boundary | Current-loop drivers can decouple command duty from effective voltage. |
| PWM / Speed Boundary | Duty is not speed percentage. |
| PWM / Torque Boundary | Duty is not torque percentage. |
| Generic PWM Scope Boundary | MOT-007 is motor-drive average voltage and back-EMF headroom, not a generic PWM tool. |
Worked Examples
| Example | Calculation | Result |
|---|---|---|
| Unipolar 12 V, 50% | Vavg = 0.5 × 12 | 6 V |
| Unipolar 12 V, 25% | Vavg = 0.25 × 12 | 3 V |
| Unipolar 12 V, 100% | Vavg = 1 × 12 | 12 V |
| Unipolar 12 V, 0% | Vavg = 0 × 12 | 0 V |
| General Von = 12 V, Voff = 2 V, 50% | 0.5×12 + 0.5×2 | 7 V |
| Target 6 V, levels 12/0 | D = (6 - 0)/(12 - 0) | 50% |
| Target 15 V, levels 12/0 | Target outside reachable range | Rejected |
| Bipolar 12 V, 50% | (2×0.5 - 1)×12 | 0 V |
| Bipolar 12 V, 75% | (2×0.75 - 1)×12 | +6 V |
| Bipolar 12 V, 25% | (2×0.25 - 1)×12 | -6 V |
| PWM f = 20 kHz | T = 1/20000 | 50 µs |
| 20 kHz, 25% | ton = 0.25×50 µs; toff = 0.75×50 µs | 12.5 µs / 37.5 µs |
| Vavg = 8 V, E = 6 V, R = 1 Ω | Iref = (8 - 6)/1 | 2 A |
| Vavg = 6 V, E = 6 V, R = 1 Ω | Iref = 0/1 | 0 A |
| Vavg = 4 V, E = 6 V, R = 1 Ω | Iref = -2/1 | -2 A |
| 10 kHz vs 20 kHz same levels | Same duty and voltage levels | Same ideal average voltage |
| Unipolar 12 V, 25% | Vrms = 12√0.25 | 6 V RMS, 3 V average |
| Unipolar 12 V, 50% | Vrms = 12√0.5 | 8.4853 V RMS, 6 V average |
| Bipolar ±12 V, 25% | Vrms = sqrt(0.25×12² + 0.75×12²) | 12 V RMS, -6 V average |
| Driver fixed drop 1 V | Effective on level = 12 - 1 | 5.5 V average at 50% |
| Duty fraction 0.5 | 0.5 × 100% | 50% |
| Forward duty round-trip | D → Vavg → D | Original duty recovered |
| 1 kHz timing | f = 1000 Hz | T = 1 ms |
| Invalid f = 0 | T = 1/0 | Rejected |
| Bipolar 0% | All negative state | -Vbus |
| Bipolar 100% | All positive state | +Vbus |
Engineering Notes
Motor PWM
PWM controls how long the motor terminal spends in selected voltage states.
Duty Cycle
Duty cycle is a time fraction, not a guaranteed speed, torque or current percentage.
Average Voltage
Average voltage is useful for first-order motor-drive references and back-EMF headroom.
H-Bridge
H-bridge operation can create unipolar, bipolar, coast, brake, fast-decay or slow-decay states.
Unipolar PWM
The common D×Vbus formula assumes switching between Vbus and 0 V.
Bipolar PWM
A symmetric ±Vbus drive has zero average voltage at 50% duty.
Back EMF
Back EMF reduces the voltage available to drive winding current.
Winding Resistance
Resistance sets the first-order current reference after subtracting back EMF and fixed drops.
Motor Inductance
Inductance controls current rise and decay during PWM cycles.
Current Ripple
Ripple depends on voltage, inductance, resistance, back EMF, frequency and freewheel path.
Freewheel
The off-state voltage is set by diode, synchronous rectification, recirculation and driver topology.
Coast
Coasting generally lets current decay through a different path than active braking.
Brake
Brake mode can short or clamp the motor terminals and change current decay.
PWM Frequency
Frequency affects audible noise, ripple, switching loss and control bandwidth.
RMS Voltage
Terminal RMS voltage is only a voltage waveform reference, not motor torque or winding-current RMS.
Current Control
Chopper and current-loop drivers can make duty a control output rather than a direct user command.
Common Mistakes
- Using D×Vbus for every PWM motor drive.
- Ignoring the off-state motor terminal voltage.
- Using D×Vbus for bipolar H-bridge PWM.
- Thinking 50% bipolar PWM means +50% voltage.
- Confusing average voltage with RMS terminal voltage.
- Assuming 50% duty means 50% motor speed.
- Assuming 50% duty means 50% motor torque.
- Dividing average voltage by resistance and calling it true PWM motor current.
- Ignoring back EMF.
- Ignoring motor winding inductance.
- Assuming the off state is always 0 V.
- Treating coast and brake as identical.
- Treating driver voltage drop as a universal constant.
- Assuming PWM frequency changes ideal average voltage at fixed duty and voltage levels.
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Open CalculatorFAQ
Support reference
FAQ
How do I calculate motor PWM average voltage?
Use the general two-level formula Vavg = DVon + (1-D)Voff, where D is duty fraction, Von is the on-state motor terminal voltage, and Voff is the off-state voltage.
What voltage does a motor receive at 50% PWM duty cycle?
In a 12 V unipolar Vbus-to-0 V drive, 50% duty gives 6 V average. In a symmetric bipolar ±12 V H-bridge, 50% duty gives 0 V average.
Is motor voltage simply duty cycle times supply voltage?
Only for the simplified unipolar case where the on level is Vbus and the off level is 0 V. Other driver topologies can have different off-state voltages.
What is the difference between unipolar and bipolar PWM?
Unipolar PWM commonly switches between Vbus and 0 V or another off-state level. Bipolar PWM switches between positive and negative motor terminal voltage.
How do I calculate bipolar H-bridge average voltage?
For ideal symmetric +Vbus and -Vbus switching, use Vavg = (2D - 1)Vbus.
Why can the PWM off-state voltage be different from zero?
The off state depends on driver topology, freewheel path, synchronous rectification, slow decay, fast decay, coast, brake, and diode conduction.
How do I calculate PWM on-time and off-time?
Calculate period with T = 1/f, then ton = D × T and toff = (1-D) × T.
Does PWM frequency affect average motor voltage?
Not in the ideal two-level average formula when duty cycle and voltage levels are fixed. Frequency affects ripple, audible noise, switching loss, and control bandwidth.
How does PWM frequency affect motor current ripple?
Higher PWM frequency usually reduces single-cycle current ripple for the same motor inductance and voltage, but it can increase driver switching loss.
Is PWM average voltage the same as RMS voltage?
No. For unipolar 0/12 V PWM at 25% duty, average voltage is 3 V while terminal RMS voltage is 6 V.
Does 50% duty cycle mean 50% motor speed?
No. Motor speed depends on back EMF, load torque, winding current, friction, supply voltage, driver behavior, and control loop.
Does 50% duty cycle mean 50% motor torque?
No. Torque is primarily related to current, not directly to duty cycle or terminal RMS voltage.
How does back EMF affect PWM motor current?
Back EMF subtracts from the average applied voltage available to push winding current in a first-order steady-state model.
How do I estimate current from PWM average voltage?
A first-order reference is I ≈ (Vavg - E - Vfixed)/R. This is not a true PWM waveform or ripple-current calculation.
Why does motor inductance matter with PWM?
The winding inductance controls current rise and decay during each PWM cycle, so the current waveform cannot be predicted from average voltage alone.
What is the difference between coast and brake in an H-bridge?
Coast and brake can produce different recirculation paths and current-decay behavior even when an average-voltage reference appears similar.
How does driver voltage drop affect effective motor voltage?
MOSFET, diode, wiring, or driver drops reduce the effective voltage applied to the motor. V1 models this only as a fixed simplified drop.
Why do current-controlled motor drivers behave differently from simple duty-cycle control?
A current-regulated driver changes PWM behavior dynamically to regulate winding current, so command duty and effective motor voltage are not a fixed one-to-one relationship.
Engineering Disclaimer
This calculator provides first-order PWM motor-drive voltage references. Production motor-drive design should verify current waveform, inductance, driver topology, current limits, switching losses, back EMF, load torque, thermal behavior, EMI and measured operation.