With the advantages of high efficiency, high power density and low maintenance cost, brushless motors have gradually replaced the traditional brush DC motors and become the core power source of industrial automation, electric vehicles and precision instruments in the field of modern electromechanical energy conversion.
The performance of brushless motor system depends not only on the electromagnetic design of the motor body, but also on the control strategy of the electronic commutator (driver).
In this paper, we will elaborate the technical connotation of two mainstream drive modulation technologies, “square wave drive” and “sine wave drive”, and deeply analyze the matching relationship between them and the back-EMF waveforms of brushless DC motor (BLDC) and permanent magnet synchronous motor (PMSM) respectively.
Electromagnetic Basis and Classification of Permanent Magnet Brushless Motor
In order to understand the difference of driving mode, we must first analyze the electromagnetic characteristics of the motor body in depth. Although BLDC and PMSM are often used interchangeably in commercial terms, in a strict electrical engineering definition, they represent two motor architectures based on different back-EMF waveform designs.
Basic working principle of permanent magnet motor
A stator of the permanent magnet brushless motor is provided with a three-phase winding, and a permanent magnet is attached to the surface or the inside of a rotor. When current is applied to the stator winding, a rotating magnetic field is generated, which interacts with the magnetic field of the rotor permanent magnet to generate a tangential force according to the Lorentz force law, thereby driving the rotor to rotate.
In this process, the rotor magnetic field cuts through the stator windings, inducing a voltage in the windings called the back-electromotive Force (back-EMF). The direction of the back EMF is always an attempt to impede the change in current (Lenz’s law). The shape of the back EMF waveform is the most central feature that distinguishes BLDC from PMSM.
Electromagnetic Characteristics of Brushless DC Motor
The BLDC motor was originally designed to mimic the mechanical characteristics of a DC motor, but with the mechanical brushes removed.
- Stator winding structure:BLDC usually adopts Concentrated Winding. In this configuration, that coil is tightly wound around each stator tooth without span multiple slots. This type of winding makes the flux linkage more concentrated.
- Air gap magnetic flux density:The rotor magnetic steel of BLDC is usually designed to be tile or rectangular, and the magnetizing mode is close to radial magnetizing, so that the magnetic flux density distribution in the air gap presents a flat-topped waveform close to trapezoidal or rectangular.
- Back-EMF waveform:Due to the superposition effect of concentrated winding and trapezoidal flux distribution, the back-EMF waveform generated by BLDC motor during rotation is Trapezoidal Back-EMF. It is characterized by a flat top region (typically lasting 120 electrical degrees) in which the magnitude of the back EMF remains constant.
Electromagnetic Characteristics of Permanent Magnet Synchronous Motor (PMSM)
The PMSM motor is closer to the traditional AC synchronous motor.
- Stator winding structure:PMSM usually adopts Distributed Winding. The coils span multiple stator slots and are distributed sinusoidally in space (or higher harmonics are attenuated by short, distributed effects). This structure can effectively filter out the high-order harmonic components in the air-gap magnetic field.
- Air gap magnetic flux density:The magnetic steel of PMSM may be modified (such as bread shape), or sinusoidal magnetization is used during magnetization, so that the air gap magnetic flux density is distributed in a sinusoidal manner in space.
- Back-EMF waveform:The combination of the distributed winding and the sinusoidal magnetic field makes the back-EMF output by the PMSM a standard Sinusoidal back-EMF. The voltage varies continuously with the rotor position as a sine function, and there is no flat-top area.
Detailed explanation of Square Wave Drive technology
Square wave drive, which is often called “trapezoidal wave control” or “Six-Step Commutation” in academia, is the most classical control method of BLDC motor.
3.1 Control principle: 120 degree conduction mode
The core feature of the square wave drive is the 120-degree conduction mode. In an electrical cycle (360 electrical angles), the six switches (MOSFETs or IGBTs) of the three-phase Inverter are turned on according to a specific timing sequence, so that at any time, only two phases of the winding have current flowing through, and the third phase is in a “suspended” or “off” state.
The specific commutation process is as follows:
- Current flows in one phase (Source) and out the other (Sink).
- Commutation occurs every 60 electrical degrees, and the current path changes.
- The six switch States are cycled once to complete an electrical cycle.
Because the current switching in the winding is transient, the current waveform ideally appears as a rectangular or square wave, hence the name “square wave drive”.
Hardware architecture and sensor feedback
The square wave drive system has a low requirement for the computing power of the hardware, and its control logic mainly depends on the discrete signal of the rotor position.
- Position Sensors:Three Hall Sensors are typically used, mounted on the stator at 120 degrees (or 60 degrees) apart. The Hall sensor directly outputs a high/low level signal, indicating the position sector of the rotor pole.
- Control logic:The controller reads the three-bit binary combination of the Hall signal (such as 100, 110, 010, etc.), and directly drives the power tube of the inverter through the look-up table method. This control method is simple and robust, and does not need complex coordinate transformation.
Analysis of performance characteristics
- Advantag:
- High torque density:The square wave drive makes full use of the DC bus voltage and injects constant current into the flat-top area of the trapezoidal back EMF, which can theoretically produce the maximum torque output.
- Low switching loss:Because each phase switch is off for 1/3 of the time in a cycle, the switching loss is lower than that of the full-time modulation driven by sine wave.
- Low cost:The algorithm is simple and can be implemented by a low-cost 8-bit microcontroller without high-precision current sampling and expensive encoders.
- Weaknesses:
- Torque Ripple: At the commutation point of every 60 degrees, because the current cannot change suddenly instantaneously (affected by the winding inductance), there will be a significant torque drop or spike. This pulsation causes mechanical vibration and noise.
- Acoustic noise: The square wave current contains abundant higher harmonics, which easily excite the structural resonance of the stator and produce the characteristic “hum” sound.
Sine-wave drive technology (Sine Wave Drive) detailed explanation
Sine wave drive, especially the advanced form combined with Field Oriented Control (FOC), is the mainstream scheme of modern high performance servo system and electric vehicle drive.
4.1 Control principle: 180-degree conduction and vector control
Unlike the square-wave drive, the sine-wave drive uses a 180-degree conduction mode. The three-phase inverter is in the modulation state at any time, so that current flows through the three-phase windings.
- SPWM and SVPWM: The controller uses sinusoidal pulse width modulation (SPWM) or space vector pulse width modulation (SVPWM) to apply a voltage that varies sinusoidally with time to the stator windings, thereby generating a sinusoidal current in the windings.
- FOC algorithm: In order to achieve accurate control, the FOC algorithm is usually used. The algorithm transforms the AC current in the three-phase stationary coordinate system (ABC) into two DC components in the synchronous rotating coordinate system (DQ) through Clark transformation and Park transformation:
- (direct axis current): generates magnetic flux, usually controlled to 0 to maximize efficiency (for surface-mounted permanent magnet motors).
- (quadrature axis current): produces torque.
Through independent control and sine wave drive, the decoupling control similar to the DC motor can be realized, so that the stator magnetic field is always 90 degrees perpendicular to the rotor magnetic field, thus producing the maximum torque.
Hardware architecture and sensor feedback
Sine wave drive requires high hardware.
- Position sensor:In order to generate a sine wave that is strictly synchronized with the rotor position, high-resolution position feedback is required, usually using a photoelectric encoder or a resolver, or even a high-precision sensorless observer algorithm. The low resolution of the Hall sensor (60 degree resolution) is usually not sufficient to support a high performance FOC, although it can be barely achieved with an interpolation algorithm.
- Controller:High-performance DSP or ARM chips are required to perform complex mathematical operations (trigonometric functions, matrix transformations, PID adjustments).
Analysis of performance characteristics
- Advantag:
- Ultra-low torque ripple:The ideal sine wave drive produces constant electromagnetic torque, which is theoretically ripple-free and extremely smooth.
- Quiet operation:The current waveform is smooth without high frequency harmonics, which significantly reduces the electromagnetic noise.
- High speed efficiency:With Field Weakening, the FOC allows the motor to operate above base speed and maintain high efficiency over a wide speed range.
- Weaknesses:
- Control complexity and high cost:the cost of algorithms and sensors increases significantly.
- Switching loss:The inverter needs to operate continuously at high frequency (such as 10 kHz-20 kHz), resulting in high switching loss and heating.
Analysis of matching between driving and back electromotive force
Our core question: Which drive waveform matches which BEMF waveform?
The formula for the generation of electromagnetic torque is:
Where is the counter electromotive force of each phase and is the current of each phase.
In order to obtain a constant torque, the current waveform must match the back EMF waveform in shape.
Perfect match one: square wave drive + BLDC (trapezoidal wave back EMF)
This is the most economical and classic combination.
- Matching mechanism:The back EMF of the BLDC motor is constant in the flat-top region of 120 degrees. The square-wave drive injects a constant current over the same 120 degree interval.
- Result:The product is constant, so the resulting torque is also constant.
- Engineering status:Due to manufacturing tolerances and edge effects, the actual back EMF is not perfectly trapezoidal, resulting in torque ripple at the commutation point. However, this is the standard configuration in areas such as power tools and fans that are not sensitive to noise.
Perfect match 2: Sine wave drive + PMSM (sine wave back EMF)
This is a standard combination for high performance servos.
- Matching mechanism:The back EMF of PMSM is a sinusoidal function. The driver injects a sinusoidal current.
- Results:According to the trigonometric function identity, the sum of three-phase power is a constant independent of time. This means that the torque output is completely smooth and non-pulsating.
- Engineering status:Widely used in robot joints, precision CNC machine tools and electric vehicle main drive motor.
Mismatch-Driven: Engineering Tradeoffs for Cross-Application
In practical engineering applications, “mismatched driving” often occurs, that is, driving BLDC with a sine wave or driving PMSM with a square wave. There are profound engineering considerations behind this “mismatch”.
Sine wave drive BLDC motor (Mismatch Type A)
This is a very popular “silent” scheme commonly found in electric bicycles and household fans.
- Motivation:The BLDC motor is low cost (simple structure), but the square wave drive is noisy. To reduce noise, a FOC/sine wave controller is used to drive the BLDC motor.
- Theoretical flaw:In a motor that injects a sinusoidal current into a trapezoidal back EMF, mathematically, the product of is no longer a constant. The theoretical calculation shows that this will produce a theoretical torque ripple of about 13% to 14%.
- Actual performance:Interestingly, the actual effect is often better than theoretical prediction. Due to the existence of motor inductance and manufacturing process, the back EMF of BLDC is actually difficult to achieve the standard trapezoidal, but between trapezoidal and sinusoidal (quasi-sinusoidal). Therefore, the use of sine-wave driving is more suitable for the actual back EMF waveform than square-wave driving.
- Conclusion:Driving the BLDC with a sine wave is feasible and beneficial, sacrificing a small amount of peak torque for significant silence and smoothness.
Square wave drive PMSM motor (Mismatch Type B)
This is often the case when legacy systems are upgraded or when they are extremely cost-sensitive.
- Performance:a square wave current containing a large number of higher harmonics (5th, 7th, etc.) is injected into a PMSM motor designed as a sine wave.
- Consequences:
- Harmonic loss:higher harmonic current can not produce effective average torque, but only cause heating of stator core (increase of core loss) and torque ripple.
- Vibration and noise:Due to the serious mismatch between the current waveform and the back EMF waveform, a huge torque ripple will be generated at 6 times the fundamental frequency, resulting in rough operation of the motor and great noise.
- Conclusion:This is generally considered a performance degradation and should be avoided except for the very low cost of turning with an existing PMSM motor.
Performance dimension depth comparison
In order to show the difference between the two driving modes more intuitively, the following table is used for comparison.
| Compare dimensions | Square Wave Drive (Square Wave) | Sine Wave (FOC) |
| Typical matching motor | BLDC (trapezoidal back EMF) | PMSM (Sinusoidal Back EMF) |
| Current waveform characteristics | Rectangular/blocky waves | Sine wave |
| Conduction mode | 120 ° conduction (two phases connected, one phase suspended) | 180-degree conduction (three-phase full-time modulation) |
| Torque smoothness | Moderate, commutation torque ripple present | Extremely high, no pulsation in theory |
| Acoustic noise | Higher (electromagnetic hum) | Very low (silent operation) |
| Low speed performance | The starting torque is large, but the low-speed jitter is obvious. | Low speed is stable, and zero speed servo can be realized |
| High speed performance | Limited by the back electromotive force, it is difficult to weaken the magnetic field | Excellent, FOC easy to achieve weak magnetic speed |
| System efficiency | High efficiency at rated point, but high harmonic loss | Higher overall efficiency across full speed range |
| Controller cost | Low (simple MCU, Hall sensor) | High (high performance DSP, encoder/high precision algorithm) |
| Dynamic response | Fast response, “Punchy” acceleration | The response is smooth and linear, and the controllability is stronger. |
Deep insight into efficiency and thermal distribution
The debate over efficiency is particularly fierce in the electric car community.
- Square-wave drive:Due to the low switching frequency (switching only at the commutation point), the controller itself has less switching losses and the MOSFETs generate less heat. However, due to the rich current harmonics inside the motor, the iron loss is large, resulting in relatively serious heating of the motor.
- Sine wave drive:In order to reconstruct the sine wave, the inverter must be modulated by high-frequency PWM, resulting in increased switching losses of the controller and relatively large heating of the controller. However, the current on the motor side is pure, the iron loss is very low, and the motor runs colder.
- Combined efficiency:Sine wave drive (FOC) typically provides 10% -15% better range under frequent start-stop and variable load conditions, because it distributes current more precisely, and the control strategy ensures that every milliamp of current is used to generate torque.
Industry application trends and case studies
E-bikes & Scooters
This is the most intense market for square wave and sine wave. Early electric bicycles commonly used square-wave controllers ( “savage” controllers) because they were powerful and cheap to start. However, with the increasing comfort requirements of consumers, sine wave controllers (often referred to as “vector controllers” or “silent controllers”) are rapidly becoming the mainstream of high-end models.
- User feedback:users generally reflect that the square wave controller starts very fast ( “rush”), but the noise is loud; the sine wave controller starts softly, the extreme speed is higher, and the motor generates less heat when climbing.
Industrial Servo and Robot
In this field, PMSM with sine wave drive (servo drive) is the absolute ruler. Robot joints need extremely high positioning accuracy and low-speed stability, and the torque ripple of square wave drive will lead to end shaking, which is unacceptable.
Automotive Electronics and Fans
Automotive cooling fans, oil pumps, and other accessories are often driven by sensorless BLDC square waves because they are cost sensitive and have a certain tolerance for noise. However, the main drive motor adopts PMSM with high-voltage sine wave drive without exception to ensure NVH (noise, vibration and acoustic roughness) performance and energy efficiency.
Conclusion
To sum up, “square wave drive” and “sine wave drive” are not only the choice of two waveforms, but also two completely different control philosophies.
- Define and match:
- Square Wave Drive:Generates a rectangular current with 120 degree conduction logic to match the trapezoidal back EMF of the BLDC motor. It is a pragmatic compromise between cost and performance.
- Sine wave drive:SVPWM and FOC algorithms generate sinusoidal current to match the sinusoidal back EMF of the PMSM motor. It is an idealistic solution that seeks the ultimate in smoothness and efficiency.
2.Engineering proposal:
- If the application scenario is extremely cost-sensitive and does not mind noise (such as electric drills, low-end fans), choose BLDC motor + square wave drive.
- If the application scenario pursues silence, high efficiency and precision control (such as electric vehicle, cooperative robots, high-end household appliances), PMSM motor + sine wave drive must be selected.
With the development of semiconductor technology, the computing power of control chips is constantly improving, and the cost threshold of sine wave drive (FOC) is rapidly decreasing. In the future, sine wave drive is expected to penetrate downward, gradually replace square wave drive, and become the general standard of brushless motor control.
