BLDC motors and drivers

Why it matters

Brushless DC (BLDC) motors drive drones, e-bikes and electric scooters, computer fans, pumps, cordless tools and many small robot joints. They give the controllability of a DC motor without brushes to wear out, so knowing how they are commuted, how their speed and torque relate to voltage and current, and how a driver is built is basic mechatronics knowledge.

Key ideas

Construction. A BLDC motor is an "inside-out" DC motor. The permanent magnets are on the rotor and the three-phase winding (usually star-connected) is on the stator. Commutation, which a brushed motor does mechanically with a commutator, is done electronically by switching the stator phases in step with the rotor position. Inrunner motors have the rotor inside the stator (high speed, low inertia); outrunner motors have the magnet bell outside (more torque, higher inertia, used in drones and fans).

Trapezoidal back EMF and six-step commutation. A BLDC motor is wound so that each phase back EMF is trapezoidal (flat-topped). It is driven by six-step (120° block) commutation: at any instant two phases carry current (one connected to +V_dc, one to 0 V) and the third floats. Every 60 electrical degrees the driver changes which pair conducts, so there are six commutation states per electrical cycle. With the current timed to the flat part of the back EMF, torque is nearly constant, with a small ripple at each commutation.

BLDC versus PMSM. The permanent-magnet synchronous motor (the AC servo) has a sinusoidal back EMF and is driven with sinusoidal currents using field-oriented control. The hardware is similar; the difference lies in the back-EMF shape and the drive method. Many "BLDC" drives today use field-oriented control for smoother, quieter running.

Rotor position sensing.

• Hall sensors: three Hall sensors spaced 120° (or 60°) electrical give six valid codes per electrical cycle, one for each commutation step. Codes 000 and 111 are invalid and signal a sensor fault.
• Sensorless: the driver watches the back EMF of the floating phase and commutes 30° electrical after its zero crossing. It is cheap and robust, but there is no back EMF at standstill, so the motor is started open-loop (align, then ramp) before the observer locks on. Sensorless control therefore suits fans, pumps and propellers, not loads that must start under heavy torque or hold position.

Electrical versus mechanical angle. A motor with P poles (P/2 pole pairs) goes through P/2 electrical cycles per mechanical revolution. A 14-pole outrunner commutes 6 × 7 = 42 times per revolution.

The driver. A three-phase inverter bridge of six MOSFETs (or IGBTs at high voltage) with gate drivers (high-side bootstrap supply), dead time to prevent shoot-through, current sensing (shunt resistors), and a microcontroller or dedicated BLDC controller IC. Speed is controlled by PWM of the conducting switches: the effective voltage is D·V_dc. Current limiting protects the motor at start-up and stall, when only the winding resistance limits the current.

Steady-state behaviour. Seen from the DC link with six-step drive, a BLDC motor behaves like a brushed DC motor: the two conducting phases in series form the armature resistance, torque is proportional to current and back EMF to speed. The same linear torque–speed line, stall torque and no-load speed apply.

Formulas

f_e = (P/2) · n / 60

• f_e: electrical frequency (Hz); P: number of poles; n: speed (rpm). Electrical angle = (P/2) × mechanical angle.

Commutations per second = 6 · f_e

• Six-step drive changes state every 60° electrical.

K_e = 60 / (2π · K_V)

• K_e: back-EMF constant (V·s/rad); K_V: hobby-style speed constant (rpm per volt, no-load). For an ideal motor in SI units K_t ≈ K_e (N·m/A), using line-to-line values with six-step drive.

T = K_t · I

• T: torque (N·m); I: DC-link (phase) current during a conduction interval (A).

V_eff = D · V_dc = I · R_LL + K_e · ω

• D: PWM duty cycle (0–1); V_dc: DC bus voltage (V); R_LL: line-to-line resistance (Ω), equal to 2 × phase resistance for a star winding; ω: speed (rad/s). Steady state, inductance and switch drops neglected.

ω_0 = V_dc / K_e, T_stall = K_t · V_dc / R_LL

• No-load speed and stall torque at full duty; the stall current V_dc/R_LL is usually far above what the driver allows, so it is limited.

Worked examples

Example 1 (standard): commutation timing. Given: an 8-pole BLDC motor runs at 3000 rpm with Hall-sensor six-step commutation. Find the electrical frequency, commutation events per second, and the mechanical angle between commutations.

1. Pole pairs = P/2 = 4.
2. f_e = (P/2)·n/60 = 4 × 3000 / 60 = 200 Hz.
3. Commutations per second = 6 × f_e = 6 × 200 = 1200 per second (one every 0.833 ms).
4. One step = 60° electrical = 60°/4 mechanical = 15° mechanical; check: 360°/15° = 24 steps per revolution = 6 × 4.

Example 2 (GATE level): duty cycle for a loaded speed. Given: BLDC motor with K_V = 100 rpm/V, line-to-line resistance R_LL = 0.2 Ω, fed from a 48 V bus by a six-step PWM driver. Load torque 1.5 N·m. Find (a) the current, (b) the speed at 100 % duty, (c) the duty cycle for 3000 rpm, (d) the efficiency at 3000 rpm counting only copper loss.

1. K_e = 60/(2π·K_V) = 60 / (2π × 100) = 0.0955 V·s/rad, and K_t ≈ 0.0955 N·m/A.
2. Current: I = T/K_t = 1.5 / 0.0955 = 15.7 A.
3. At D = 1: ω = (V_dc − I·R_LL)/K_e = (48 − 15.7 × 0.2) / 0.0955 = 469.8 rad/s = 4486 rpm.
4. For 3000 rpm: ω = 3000 × 2π/60 = 314.2 rad/s. Required voltage V_eff = I·R_LL + K_e·ω = 15.7 × 0.2 + 0.0955 × 314.2 = 3.14 + 30.0 = 33.1 V.
5. Duty: D = V_eff/V_dc = 33.1 / 48 = 0.69 (69 %).
6. Output power = T·ω = 1.5 × 314.2 = 471 W; copper loss = I²·R_LL = 15.7² × 0.2 = 49.3 W; input ≈ 520 W. Efficiency ≈ 471/520 = 90.5 % (switching and iron losses would lower it).

Common mistakes

• Using mechanical frequency for commutation. Commutation follows electrical angle, which is (P/2) times the mechanical angle; P is poles, not pole pairs.
• Using the phase resistance in the DC-motor equation. With six-step drive two phases conduct in series, so use the line-to-line resistance (2 × phase for star).
• Treating K_V as an SI constant. Convert: K_e = 60/(2π·K_V) V·s/rad.
• Expecting a sensorless drive to start under full load or hold position. There is no back EMF at standstill.
• Omitting dead time in the bridge, which causes shoot-through of the high-side and low-side switches.
• Saying BLDC motors need no position information. They need it for commutation; it is either sensed (Hall, encoder) or estimated (sensorless).

For GATE ME

BLDC motors appear in mechatronics questions as an application of the DC-motor equations: speed from voltage and current, torque from current, no-load speed and stall torque, duty cycle for a required speed, and pole/frequency relations. Practise converting K_V to K_e, relating electrical and mechanical angles, and reasoning about Hall-sensor commutation sequences and the inverter bridge.

Quick check

1. How many commutation steps occur per electrical cycle in six-step drive?
2. A 14-pole motor turns at 6000 rpm. What is the electrical frequency?
3. Convert K_V = 1000 rpm/V to K_e in V·s/rad.
4. Why can a sensorless BLDC drive not use back-EMF sensing at standstill?
5. Which phases conduct at any instant in six-step drive?

Answers: 1. Six. 2. 700 Hz. 3. 0.00955 V·s/rad. 4. Back EMF is proportional to speed, so it is zero at standstill. 5. Two phases conduct (one high, one low) while the third floats.