Pulse Width Modulation

But before we start looking at the in’s and out’s of “Pulse Width Modulation” we need to understand a little more about how a DC motor works.

Next to stepper motors, the Permanent Magnet DC Motor (PMDC) is the most commonly used type of small direct current motor available producing a continuous rotational speed that can be easily controlled. Small DC motors ideal for use in applications where speed control is required such as in small toys, models, robots and other such electronics circuits.

A DC motor consist basically of two parts, the stationary body of the motor called the “Stator” and the inner part which rotates producing the movement called the “Rotor”. For D.C. machines the rotor is commonly termed the “Armature”.

Generally in small light duty DC motors the stator consists of a pair of fixed permanent magnets producing a uniform and stationary magnetic flux inside the motor giving these types of motors their name of “permanent-magnet direct-current” (PMDC) motors.

The motors armature consists of individual electrical coils connected together in a circular configuration around its metallic body producing a North-Pole then a South-Pole then a North-Pole etc, type of field system configuration.

The current flowing within these rotor coils producing the necessary electromagnetic field. The circular magnetic field produced by the armatures windings produces both north and south poles around the armature which are repelled or attracted by the stator’s permanent magnets producing a rotational movement around the motors central axis as shown.

2-Pole Permanent Magnet Motor

As the armature rotates electrical current is passed from the motors terminals to the next set of armature windings via carbon brushes located around the commutator producing another magnetic field and each time the armature rotates a new set of armature windings are energised forcing the armature to rotate more and more and so on.

So the rotational speed of a DC motor depends upon the interaction between two magnetic fields, one set up by the stator’s stationary permanent magnets and the other by the armatures rotating electromagnets and by controlling this interaction we can control the speed of rotation.

The magnetic field produced by the stator’s permanent magnets is fixed and therefore can not be changed but if we change the strength of the armatures electromagnetic field by controlling the current flowing through the windings more or less magnetic flux will be produced resulting in a stronger or weaker interaction and therefore a faster or slower speed.

Then the rotational speed of a DC motor (N) is proportional to the back emf (V_b) of the motor divided by the magnetic flux (which for a permanent magnet is a constant) times an electromechanical constant depending upon the nature of the armatures windings (K_e) giving us the equation of: N ∝ V/K_eΦ.

So how do we control the flow of current through the motor. Well many people attempt to control the speed of a DC motor using a large variable resistor (Rheostat) in series with the motor as shown.

While this may work, as it does with Scalextric slot car racing, it generates a lot of heat and wasted power in the resistance. One simple and easy way to control the speed of a motor is to regulate the amount of voltage across its terminals and this can be achieved using “Pulse Width Modulation” or PWM.

As its name suggests, pulse width modulation speed control works by driving the motor with a series of “ON-OFF” pulses and varying the duty cycle, the fraction of time that the output voltage is “ON” compared to when it is “OFF”, of the pulses while keeping the frequency constant.

The power applied to the motor can be controlled by varying the width of these applied pulses and thereby varying the average DC voltage applied to the motors terminals. By changing or modulating the timing of these pulses the speed of the motor can be controlled, ie, the longer the pulse is “ON”, the faster the motor will rotate and likewise, the shorter the pulse is “ON” the slower the motor will rotate.

In other words, the wider the pulse width, the more average voltage applied to the motor terminals, the stronger the magnetic flux inside the armature windings and the faster the motor will rotate and this is shown below.

Pulse Width Modulated Waveform

The use of pulse width modulation to control a small motor has the advantage in that the power loss in the switching transistor is small because the transistor is either fully “ON” or fully “OFF”. As a result the switching transistor has a much reduced power dissipation giving it a linear type of control which results in better speed stability.

Also the amplitude of the motor voltage remains constant so the motor is always at full strength. The result is that the motor can be rotated much more slowly without it stalling. So how can we produce a pulse width modulation signal to control the motor. Easy, use an Astable 555 Oscillator circuit as shown below.

This simple circuit based around the familiar NE555 or 7555 timer chip is used to produced the required pulse width modulation signal at a fixed frequency output. The timing capacitor C is charged and discharged by current flowing through the timing networks R_A and R_B as we looked at in the 555 Timer tutorial.

The output signal at pin 3 of the 555 is equal to the supply voltage switching the transistors fully “ON”. The time taken for C to charge or discharge depends upon the values of R_A, R_B.

The capacitor charges up through the network R_A but is diverted around the resistive network R_B and through diode D₁. As soon as the capacitor is charged, it is immediately discharged through diode D₂ and network R_B into pin 7. During the discharging process the output at pin 3 is at 0 V and the transistor is switched “OFF”.

Then the time taken for capacitor, C to go through one complete charge-discharge cycle depends on the values of R_A, R_B and C with the time T for one complete cycle being given as:

The time, T_H, for which the output is “ON” is: T_H = 0.693(R_A).C

The time, T_L, for which the output is “OFF” is: T_L = 0.693(R_B).C

Total “ON”-“OFF” cycle time given as:  T = T_H + T_L  with the output frequency being ƒ = 1/T

With the component values shown, the duty cycle of the waveform can be adjusted from about 8.3% (0.5V) to about 91.7% (5.5V) using a 6.0V power supply. The Astable frequency is constant at about 256 Hz and the motor is switched “ON” and “OFF” at this rate.

Resistor R₁ plus the “top” part of the potentiometer, VR₁ represent the resistive network of R_A. While the “bottom” part of the potentiometer plus R₂ represent the resistive network of R_B above.

These values can be changed to suite different applications and DC motors but providing that the 555 Astable circuit runs fast enough at a few hundred Hertz minimum, there should be no jerkiness in the rotation of the motor.

Diode D₃ is our old favourite the flywheel diode used to protect the electronic circuit from the inductive loading of the motor. Also if the motor load is high put a heatsink on the switching transistor or MOSFET.

Pulse width modulation is a great method of controlling the amount of power delivered to a load without dissipating any wasted power. The above circuit can also be used to control the speed of a fan or to dim the brightness of DC lamps or LED’s. If you need to control it, then use Pulse Width Modulation to do it.

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