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Designers of motion systems often face challenges when selecting or developing electronics using PWM (Pulse Width Modulation) to drive brushless DC motors. It is useful to keep in mind some basic physical phenomena to avoid unexpected performance issues. This document provides general guidelines when using a PWM driver with a Portescap brushless DC motor.

COMMUTATION OF A BRUSHLESS DC MOTOR
Unlike brush DC motors (for which the commutation is made mechanically by brushes), brushless DC motors are electronically commutated. This means the phases of the motors are energized and unenergized in sequence according to the relative position of the rotor vs. the stator. For a 3-phase brushless DC motor, the driver is composed of 6 electronic switches (typically transistors), usually called a 3 phase H-bridge (see Figure 1). This configuration will allow 3 bidirectional outputs to energize the 3 phases of the motor.

Opening and closing the transistors in a specific sequence energizes the phases of the motor to maintain the optimal orientation of the magnetic field induced by the stator vs. rotor magnet (see Figure 2, Figure 3 & Figure 4).

The motor can be driven in a 6-step trapezoidal commutation which is broadly used (see Figure 3), or it can be operated to achieve a more advanced vector control also called as Field Oriented Control (FOC), depending on the sophistication of the electronics (see Figure 4).

PWM CONTROL

Whether for a brush (see Figure 5) or a brushless DC motor (see Figure 6), the working point (speed and torque) of an application can vary. The role of the amplifier is to vary the supply voltage or the current, or both, to achieve the desired motion output.

There are typically two different ways to vary the voltage or the current:

• Linear drivers (or linear amplifiers)
• Chopper drivers (or chopper amplifiers)
Linear amplifiers adapt the power delivered to the motor by linearly changing the voltage or current. It dissipates the power which is not delivered to the motor (lost power – see Figure 6). As a result, it requires a large heat sink to dissipate the power, increasing the amplifier size and making it more difficult to integrate in the application.

A chopper amplifier modulates the voltage (and current) by switching on and off the power transistors. The primary advantage is that it saves power when the transistor is off. This helps save on the battery life of the application, causes less heating from the electronic and allows a smaller size of the electronics. Most of the time, chopper amplifiers are using a PWM method.

The PWM method consists of varying the duty cycle at a fixed frequency (see Figure 7) to adjust the voltage or current within the desired target value.

Note that one advantage of the PWM technique to chop the current vs. others is that the switching frequency is a fixed parameter. It will make it easy for electronic designers to filter acoustic and electromagnetic noise generated.

When the transistor of the PWM is open 100% of the time, the voltage applied to the motor is the full bus voltage. When the transistor is open 50% of the time, the average voltage applied to the motor is half the bus voltage. When the transistor is closed 100% of the time, no voltage is applied to the motor.

INDUCTANCE EFFECT
A DC motor is characterized by an inductance L, a resistance R and a back electromotive force (back-EMF) E in series. The back-EMF is a voltage caused by the magnetic induction (Faraday-Lenz law of induction) that opposes the applied voltage and is proportional to the motor speed. See Figure 8 showing the motor when the PWM is ON, and when the PWM is OFF.

For now, to keep things simple, let's not consider the back EMF.

When applying voltage or switching off voltage to a RL circuit, the inductor will oppose to the change of the current. Applying a voltage U to the RL circuit, the current will follow a first-order exponential rise, whose dynamic depends on the electric time constant τ equal to the ratio L / R (see Figure 9). It will asymptotically reach the steady state value, i.e. 99.3% of U / R, after 5 times the time constant.

The same exponential behavior will be observed when the RL circuit will discharge. See Figure 10.

In practice, brushless DC amplifiers have a rather high PWM frequency and do not allow the current to reach steady state. This frequency is generally above 50 kHz so that the current can be modulated properly with enough cycles occurring during each commutation step. For a PWM frequency of 50kHz, the cycle time to close and open a transistor is equal to 20 μs. Considering a 6-step commutation, the time for one commutation, 1-pole pair motor running at 40,000 rpm (667Hz), would take 250 μs. This would allow at least 250/20 = 12.5 cycles of the PWM during one step of the commutation.

Portescap brushless DC motors have an electrical time constant τ of a few hundred microseconds, therefore the current will have the time to react during each PWM


 


Designers of motion systems often face challenges when selecting or developing electronics using PWM (Pulse Width Modulation) to drive brushless DC motors. It is useful to keep in mind some basic physical phenomena to avoid unexpected performance issues. This document provides general guidelines when using a PWM driver with a Portescap brushless DC motor.

COMMUTATION OF A BRUSHLESS DC MOTOR
Unlike brush DC motors (for which the commutation is made mechanically by brushes), brushless DC motors are electronically commutated. This means the phases of the motors are energized and unenergized in sequence according to the relative position of the rotor vs. the stator. For a 3-phase brushless DC motor, the driver is composed of 6 electronic switches (typically transistors), usually called a 3 phase H-bridge (see Figure 1). This configuration will allow 3 bidirectional outputs to energize the 3 phases of the motor.

Opening and closing the transistors in a specific sequence energizes the phases of the motor to maintain the optimal orientation of the magnetic field induced by the stator vs. rotor magnet (see Figure 2, Figure 3 & Figure 4).

The motor can be driven in a 6-step trapezoidal commutation which is broadly used (see Figure 3), or it can be operated to achieve a more advanced vector control also called as Field Oriented Control (FOC), depending on the sophistication of the electronics (see Figure 4).

PWM CONTROL

Whether for a brush (see Figure 5) or a brushless DC motor (see Figure 6), the working point (speed and torque) of an application can vary. The role of the amplifier is to vary the supply voltage or the current, or both, to achieve the desired motion output.

There are typically two different ways to vary the voltage or the current:

• Linear drivers (or linear amplifiers)
• Chopper drivers (or chopper amplifiers)
Linear amplifiers adapt the power delivered to the motor by linearly changing the voltage or current. It dissipates the power which is not delivered to the motor (lost power – see Figure 6). As a result, it requires a large heat sink to dissipate the power, increasing the amplifier size and making it more difficult to integrate in the application.

A chopper amplifier modulates the voltage (and current) by switching on and off the power transistors. The primary advantage is that it saves power when the transistor is off. This helps save on the battery life of the application, causes less heating from the electronic and allows a smaller size of the electronics. Most of the time, chopper amplifiers are using a PWM method.

The PWM method consists of varying the duty cycle at a fixed frequency (see Figure 7) to adjust the voltage or current within the desired target value.

Note that one advantage of the PWM technique to chop the current vs. others is that the switching frequency is a fixed parameter. It will make it easy for electronic designers to filter acoustic and electromagnetic noise generated.

When the transistor of the PWM is open 100% of the time, the voltage applied to the motor is the full bus voltage. When the transistor is open 50% of the time, the average voltage applied to the motor is half the bus voltage. When the transistor is closed 100% of the time, no voltage is applied to the motor.

INDUCTANCE EFFECT
A DC motor is characterized by an inductance L, a resistance R and a back electromotive force (back-EMF) E in series. The back-EMF is a voltage caused by the magnetic induction (Faraday-Lenz law of induction) that opposes the applied voltage and is proportional to the motor speed. See Figure 8 showing the motor when the PWM is ON, and when the PWM is OFF.

For now, to keep things simple, let's not consider the back EMF.

When applying voltage or switching off voltage to a RL circuit, the inductor will oppose to the change of the current. Applying a voltage U to the RL circuit, the current will follow a first-order exponential rise, whose dynamic depends on the electric time constant τ equal to the ratio L / R (see Figure 9). It will asymptotically reach the steady state value, i.e. 99.3% of U / R, after 5 times the time constant.

The same exponential behavior will be observed when the RL circuit will discharge. See Figure 10.

In practice, brushless DC amplifiers have a rather high PWM frequency and do not allow the current to reach steady state. This frequency is generally above 50 kHz so that the current can be modulated properly with enough cycles occurring during each commutation step. For a PWM frequency of 50kHz, the cycle time to close and open a transistor is equal to 20 μs. Considering a 6-step commutation, the time for one commutation, 1-pole pair motor running at 40,000 rpm (667Hz), would take 250 μs. This would allow at least 250/20 = 12.5 cycles of the PWM during one step of the commutation.

Portescap brushless DC motors have an electrical time constant τ of a few hundred microseconds, therefore the current will have the time to react during each PWM


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