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Motor

PWM Duty Cycle to Motor Voltage

Convert PWM duty cycle to effective motor voltage, calculate no-load speed and stall current for DC motor PWM control.

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Formula

Veff=Vs×D,n0=Veff×KvV_eff = V_s × D, n₀ = V_eff × Kv
D— Duty cycle (0–1)
Kv— Motor speed constant (RPM/V)

How It Works

This calculator determines PWM duty cycle, average voltage, and timing parameters for DC motor speed control. Embedded systems engineers, robotics programmers, and motor control designers use it to configure microcontroller timers for precise speed regulation. PWM enables efficient speed control—linear voltage regulators waste 30-60% of power as heat, while PWM switching achieves 90-98% efficiency.

Per motor control fundamentals (Krishnan, 'Electric Motor Drives'), duty cycle D represents the fraction of time the supply is connected: V_avg = D × V_supply. For a given load, motor speed is approximately proportional to average voltage within the linear operating region. The PWM frequency must balance two constraints: high enough to exceed audible range (>18-20 kHz per human hearing limits) and low enough to limit switching losses (<50 kHz for typical motor drivers).

Current ripple depends on motor inductance and PWM frequency: ΔI = V × D × (1-D) / (L × f). Per Texas Instruments motor control guidelines, current ripple should be <20% of DC current to minimize additional copper losses. A 24V motor with 2 mH inductance at 20 kHz and 50% duty exhibits ΔI = 24×0.5×0.5/(0.002×20000) = 0.15A ripple—acceptable for a 1A+ motor. Lower frequencies or lower inductances require LC filtering or acceptance of higher ripple losses.

Worked Example

Configure PWM for a 36V DC motor that must run at 40% of maximum speed. Motor inductance is 5 mH, rated current 8A. Target current ripple <10%.

Step 1 — Calculate required duty cycle: For 40% speed: D = 0.40 (assuming linear V-speed relationship) V_avg = 0.40 × 36V = 14.4V

Step 2 — Determine minimum PWM frequency for ripple target: ΔI_target = 10% × 8A = 0.8A From ΔI = V × D × (1-D) / (L × f): f_min = V × D × (1-D) / (L × ΔI) f_min = 36 × 0.4 × 0.6 / (0.005 × 0.8) = 8.64 / 0.004 = 2160 Hz

Step 3 — Select practical PWM frequency: Minimum for ripple: 2.16 kHz Minimum for inaudible: 20 kHz Select 20 kHz for noise-free operation

Step 4 — Calculate actual current ripple at 20 kHz: ΔI = 36 × 0.4 × 0.6 / (0.005 × 20000) = 8.64 / 100 = 0.086A Ripple = 0.086 / 8 × 100 = 1.1% (well under 10% target)

Step 5 — Calculate timer parameters for 72 MHz MCU: Period = 72 MHz / 20 kHz = 3600 counts On-time = 0.40 × 3600 = 1440 counts Pulse width = 1440 / 72 MHz = 20 µs ON, 30 µs OFF

Result: Configure timer for 20 kHz (3600-count period at 72 MHz) with 40% duty cycle (1440-count compare value). Current ripple is only 1.1%, ensuring minimal efficiency loss from ripple heating.

Practical Tips

  • ✓Per EMC guidelines, select PWM frequency above 20 kHz for noise-free operation; many 3D printer and CNC controllers use 25 kHz as a standard that balances audible noise elimination with acceptable switching losses
  • ✓For high-side MOSFET driving, use bootstrap gate drivers (IR2104, IR2184) that generate V_gate = V_supply + 10-15V for full enhancement—logic-level MOSFETs require V_gs > V_supply for saturation
  • ✓Per thermal management guidelines, monitor motor temperature during extended low-duty-cycle operation: reduced speed means reduced self-cooling from shaft-mounted fans, potentially causing 30-50% higher temperature rise

Common Mistakes

  • ✗Using PWM frequency below 1 kHz: Per motor control practice, frequencies <1 kHz cause audible whining at 80-100 dB and current ripple >50% that increases copper losses by 25%+ and accelerates brush wear in brushed motors
  • ✗Ignoring minimum duty cycle threshold: Per motor physics, below 10-20% duty cycle, average voltage may be insufficient to overcome static friction—motor draws stall current without rotating, wasting power as heat
  • ✗Driving MOSFET gates directly from GPIO: Per gate driver requirements, PWM transitions require 1-10A peak gate current for fast switching; GPIO pins rated 10-25 mA cause slow transitions (100-500 ns vs. 10-50 ns), increasing switching losses 5-10×

Frequently Asked Questions

Per vibration analysis fundamentals: Motor mechanical resonance (typically 50-200 Hz) can couple with PWM fundamental or harmonics. The motor acts as a speaker, converting electrical pulses to acoustic vibration. Solutions: (1) Operate above 18-20 kHz where harmonics exceed audible range; (2) Use spread-spectrum PWM that distributes energy across frequencies; (3) Add LC filtering to smooth current waveform. Most complaints occur at 1-5 kHz where the fundamental is loudest.
Yes—two competing effects per power electronics analysis: (1) Higher frequency reduces current ripple, decreasing I²R losses by 2-10% at typical operating points; (2) Higher frequency increases MOSFET switching losses proportionally (P_sw ∝ f). Optimal frequency depends on motor inductance and driver characteristics—typically 15-25 kHz for brushed motors, 10-20 kHz for BLDC. Above 30 kHz, switching losses dominate for most drivers, reducing system efficiency.
Per motor fundamentals: Relationship is approximately linear for light-to-moderate loads but deviates significantly under heavy load due to I×R_a voltage drop. At 50% duty cycle with 10% armature resistance ratio, actual speed may be 45% of no-load. For precise speed control, implement closed-loop feedback using encoder or back-EMF sensing—PID controllers typically achieve ±0.5-2% speed regulation versus ±10-20% for open-loop PWM.

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