MOTOR-10 — BLDC Motors

FACT — Brushless Direct Current (BLDC) motors were developed to eliminate the mechanical commutator and carbon brush wear of classical DC motors. They feature permanent magnets on the rotor and a three-phase stator winding. Despite the “DC” in their name, BLDC motors are intrinsically alternating current (square/trapezoidal AC) machines requiring a three-phase solid-state inverter for commutation.

In this lesson, we examine the workhorse of automotive auxiliary systems and light e-mobility:

1. Electromagnetic Topology & Trapezoidal Back-EMF
2. 120° Conduction & Six-Step Commutation
3. Position Sensing: Hall Sensors and Floating-Phase Zero-Crossing Detection (ZCD)
4. BLDC vs. PMSM Comparative Analysis (Theoretical Torque vs. Acoustic NVH)
5. Commutation Torque Ripple ($\Delta T$) Mechanics
6. Automotive Auxiliary Applications

---

1. Structure and Trapezoidal Back-EMF

Unlike sinusoidal AC machines with distributed windings, a typical BLDC stator features concentrated (tooth-wound) windings. The rotor permanent magnets are shaped to create a uniform, flat radial flux density across a broad electrical arc ($120^\circ - 150^\circ_e$).

When the rotor spins at angular speed $\omega_m$, Faraday’s law induces a trapezoidal Back-EMF waveform across each stator phase:

    E_phase
       +E_p  +----------------+
             /                \
            /                  \
           /                    \
    ------/                      \----------------+  0V
                                  \                /
                                   \              /
                                    +----------------+ -E_p
          |<-- 60° -->|<-- 120° -->|<-- 60° -->|

The flat-top plateau of the trapezoidal Back-EMF spans exactly $120^\circ$ electrical.

$E_p = 2 \cdot N_{turn} \cdot B_g \cdot L_{stator} \cdot R_{rotor} \cdot \omega_m = k_e \cdot \omega_m$

Where:

• $k_e$: Back-EMF constant ($\text{V}\cdot\text{s/rad}$ or $\text{V/krpm}$)
• $B_g$: Peak air-gap magnetic flux density ($\text{T}$)

If a rectangular flat-top current block ($I_{dc}$) is forced through the winding during this $120^\circ$ plateau, instantaneous electromagnetic power ($P_e$) and torque ($T_e$) remain constant in theory:

$P_e = e_a i_a + e_b i_b + e_c i_c = 2 \cdot E_p \cdot I_{dc}$

$T_e = \frac{P_e}{\omega_m} = 2 \cdot k_e \cdot I_{dc} = k_t \cdot I_{dc}$

FACT — In SI units ($\text{rad/s}$ and $\text{N}\cdot\text{m/A}$), the torque constant $k_t$ and the back-EMF constant $k_e$ are theoretically identical ($k_t = 2 \cdot k_e$).

---

2. 120° Conduction and Six-Step Commutation

The standard control strategy for BLDC machines is 120° conduction six-step commutation, implemented using a conventional 3-phase inverter (6 MOSFETs or IGBTs).

During each $60^\circ_e$ sector:

1. Two phases conduct current: One connected to the positive DC rail (High-Side switch) and one to ground (Low-Side switch).
2. One phase is floating (unexcited): Disconnected from both rails, carrying zero current.

3-Phase Bridge Inverter:
       +Vdc --------------------------+
             |         |         |
           [Q1]      [Q3]      [Q5]   (High-side switches)
             |-- U     |-- V     |-- W
           [Q2]      [Q4]      [Q6]   (Low-side switches)
             |         |         |
       GND ---------------------------+

Across one electrical cycle ($360^\circ_e$), six switching states execute in sequence:

Sector	Electrical Angle ($\theta_e$)	Conducting High Switch	Conducting Low Switch	Current Path	Floating Phase
1	$0^\circ - 60^\circ$	Q1 (Phase U)	Q4 (Phase V)	$U \to V$	Phase W
2	$60^\circ - 120^\circ$	Q1 (Phase U)	Q6 (Phase W)	$U \to W$	Phase V
3	$120^\circ - 180^\circ$	Q3 (Phase V)	Q6 (Phase W)	$V \to W$	Phase U
4	$180^\circ - 240^\circ$	Q3 (Phase V)	Q2 (Phase U)	$V \to U$	Phase W
5	$240^\circ - 300^\circ$	Q5 (Phase W)	Q2 (Phase U)	$W \to U$	Phase V
6	$300^\circ - 360^\circ$	Q5 (Phase W)	Q4 (Phase V)	$W \to V$	Phase U

Commutation frequency scales directly with rotor speed and pole-pair count:

$f_{comm} = 6 \cdot p \cdot \frac{n}{60} = \frac{p \cdot n}{10} \quad [\text{Hz}]$

---

3. Position Sensing Technologies

Precise commutation requires timely synchronization between the stator field and rotor magnetic axis.

A. Discrete Hall Effect Sensors

Three digital Hall effect ICs ($H_a, H_b, H_c$) spaced $120^\circ$ (or $60^\circ$) electrically along the stator detect the rotor magnetic poles.

• Output transitions to logic ‘1’ under North poles and logic ‘0’ under South poles.
• The 3-bit binary code ($001_2, 011_2, 010_2, 110_2, 100_2, 101_2$) directly indexes the next inverter switching state via hardware interrupt.

B. Sensorless Floating-Phase Zero-Crossing Detection (ZCD)

To cut BOM cost and eliminate failure-prone sensors in hot environments, the terminal voltage of the unexcited (floating) phase is measured:

• Since no current flows through the floating phase, its terminal voltage equals the induced Back-EMF plus the neutral voltage.
• The Back-EMF crosses the zero reference point (ZCP) exactly in the middle of each $60^\circ$ sector.
• Once ZCP is detected by an analog comparator, a timer delays the next commutation step by exactly $30^\circ$ electrical.

WARNING — Sensorless BLDC motors produce zero Back-EMF at standstill ($E = 0$). Start-up requires an open-loop alignment and frequency ramp (blind stepping) before transitioning to closed-loop ZCD tracking once sufficient speed is reached.

---

4. BLDC vs. PMSM Comparison

Both belong to the synchronous permanent magnet family, but their electromagnetic and control paradigms differ fundamentally:

Metric	BLDC Motor	PMSM (Sinusoidal Machine)
Back-EMF Profile	Trapezoidal (Flat top)	Sinusoidal
Phase Current	120° Block / Rectangular	Sinusoidal 3-phase AC
Winding Distribution	Concentrated (Tooth-wound)	Distributed or Hairpin
Control Architecture	6-Step Commutation (Scalar)	Field-Oriented Control (FOC / Vector)
Sensor Resolution	Low ($60^\circ_e$ steps, 3 Hall ICs)	High (12–16 bit Resolver / Absolute Encoder)
Torque Density	Theoretically $\approx 14\%$ higher peak	Higher continuous optimized torque
Torque Ripple	High ($\approx 15\% - 30\%$ during transitions)	Ultra-low ($< 2\% - 3\%$)
Acoustic NVH	High harmonic whine / buzz	Extremely quiet, smooth
High-Speed Field Weakening	Limited / Inefficient	Wide constant power speed ratio (CPSR)

---

5. Commutation Torque Ripple ($\Delta T$)

The primary barrier preventing BLDC use in passenger EV traction is commutation torque ripple.

During phase current handover (e.g. from Phase U to Phase V), finite stator phase inductance ($L_s$) limits the rate of current rise and fall:

$\frac{di}{dt} = \frac{V_{bus} - 2E_p}{2 L_s}$

1. At Low Speeds: Incoming current ramps faster than outgoing current decays, creating a positive torque spike.
2. At High Speeds: High Back-EMF ($E_p$) starves the incoming phase of driving voltage ($V_{bus} - 2E_p$), causing incoming current to rise slower than outgoing current collapse. This creates a severe torque dip.

This periodic $60^\circ$ disturbance induces high-frequency torsional oscillations in the driveline and loud cabin acoustic whine.

---

6. Automotive Auxiliary Applications

Thanks to robust brushless operation, compact packaging, and low silicon requirements, BLDC motors dominate 12V / 48V vehicle subsystems:

1. Electric Water Pumps (EWP): Cooling circuits for power electronics and battery packs ($50\text{ W} - 250\text{ W}$).
2. Cabin HVAC Blowers: High reliability, spark-free air distribution.
3. Electro-Hydraulic Brake Boosters (e-Booster): Fast-response pressure build-up for ADAS emergency braking.
4. Light Electric Vehicles (LEV): Hub motors for e-scooters and utility e-trikes.

---

7. Summary

• BLDC motors combine permanent magnet rotors with concentrated stator windings to produce trapezoidal Back-EMF.
• Six-step 120° commutation energizes two phases simultaneously while leaving the third floating.
• Position feedback relies on three cheap Hall sensors or sensorless back-EMF zero-crossing detection.
• High commutation torque ripple excludes BLDC from modern passenger car traction drives, but it remains the dominant, cost-effective solution for vehicle auxiliary systems.

Next Lesson

• MOTOR-11 — PMSM, SPMSM, and IPMSM: Sinusoidal permanent magnet machines, rotor saliency ($L_q > L_d$), and the interior magnet architecture powering modern EV traction drives.