Brushless DC (BLDC) motors

Reference notes

A brushless DC (BLDC) motor is an "inverted" brushed DC machine — windings move to the stator, magnets to the rotor, and the mechanical commutator is replaced by an electronic inverter. Use Next → to walk through construction, the trapezoidal back-EMF that defines a BLDC (vs sinusoidal PMSM), six-step commutation via Hall sensors, the torque equation, and where BLDC fits among neighboring machine types.

BLDC = inverted brushed DC

• Brushed DC: rotor carries the windings; brushes + mechanical commutator switch polarity as the rotor turns.
• BLDC: stator carries 3-φ windings; rotor carries permanent magnets. An electronic inverter switches the stator current sequentially based on rotor position (sensed via Hall sensors, encoder, or back-EMF sensorless estimation).
• Benefits: no brush wear, sealed operation, ~5–10 % higher efficiency than equivalent induction motors, longer life (20 000 + hours), higher power density.

Construction

• Stator — laminated iron with slots holding 3-phase concentrated windings (each coil wound around a single tooth → short end-turns, high copper fill, cheap to wind). Star or delta connection.
• Rotor — solid steel core with high-energy NdFeB (neodymium-iron-boron) surface-mounted permanent magnets. Typical pole counts: 2, 4, 6, 8 (higher for low-speed direct drives).
• Outer-rotor variant — magnets on the outside, windings on a stationary inside hub. Common in computer fans, drone propellers, gimbals.

Trapezoidal back-EMF — the defining waveform

The fingerprint of a BLDC is its trapezoidal back-EMF: each stator phase sees a back-EMF e(θ) that is flat-topped for ~120 electrical degrees per half-cycle. This is engineered via magnet pole-arc shaping and concentrated stator winding placement. Compare to a PMSM (permanent-magnet synchronous motor), physically very similar but designed with distributed windings and shaped magnets to produce a perfectly sinusoidal back-EMF.

The trapezoidal shape is what permits simple six-step (square-wave) commutation while keeping torque ripple manageable.

Six-step commutation

• Three Hall-effect sensors are spaced 120 electrical degrees apart inside the stator. They sense rotor magnetic position.
• The 3 Hall outputs combine into a 3-bit code that takes 6 unique values per electrical revolution → 6 angular sectors of 60° each.
• For each sector, the inverter energizes exactly TWO of the 3 phases with a defined polarity (one to V_DC, one to ground); the third phase floats and contributes only back-EMF.
• Switching from sector N to sector N+1 — the "commutation event" — happens at the Hall transition. Six commutation events per electrical revolution, hence the name.

Torque equation

Because trapezoidal e(θ) × square i(θ) ≈ constant instantaneous power during the flat region, BLDC torque follows the same simple linear law as a brushed DC motor:

In SI units, k_t and k_e are numerically equal (consequence of energy conservation). Steady-state speed at terminal voltage V:

Speed control is therefore voltage control, same as brushed DC, but without the brushes-and-commutator maintenance penalty.

BLDC vs neighbors

• vs brushed DC — same torque law, no brushes, sealed, longer life, slightly higher efficiency. The brushless replacement of brushed DC in nearly every application.
• vs PMSM — BLDC simpler drive (6-step inverter, Halls only, simple PWM duty control); PMSM smoother torque via field-oriented control with continuous sinusoidal PWM currents and a high-resolution encoder. PMSM more common in high-performance EVs and CNC servos; BLDC dominates drones, computer fans, hard drives, power tools.
• vs induction motor — BLDC has no rotor slip (synchronous operation), so no rotor I²R loss → 5–10 % higher efficiency, higher power density. Induction depends on slip to produce torque and has slip-proportional rotor losses. Trade-off: BLDC needs rare-earth magnets (cost, supply-chain risk). Induction still favored for very large frames (multi-MW).

Field weakening

Above base speed, advancing the commutation angle relative to the rotor position effectively weakens the air-gap flux — same principle as separately-excited DC motor field weakening. Allows constant-power operation above base speed at reduced torque. Used in EV traction inverters and high-speed spindle drives.

Sensorless BLDC

The 3 Hall sensors can be eliminated for cost-sensitive applications. The inverter monitors the back-EMF in the currently-floating phase and uses zero-crossings of e(θ) to infer rotor position. Works well above ~10 % rated speed; below that, special starting algorithms are needed (open-loop ramping, high-frequency injection, or short-pulse inductance sensing). Used in nearly all hard drives and many drone ESCs.

Keyboard shortcuts

• The motor diagram cycles through 6 commutation sectors automatically; back-EMF panel compares trapezoidal (BLDC) and sinusoidal (PMSM) waveforms during step 6.