Pulse Width Modulation

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Varying the on- and off-switch-time of a rectangular signal with fixed base frequency, is described as Pulse Width Modulation [short: PWM]. The ratio ton / (ton + toff) is called duty cycle.

Easy to perceive, what applies for the average value of the voltage:

Spannung-mittelwert.png

Uoff is usually 0V, Uon is the operating voltage, for instance 5V.

Examples

The following examples are showing PWM-signals with a duty cycle of 75% resp. 25%.

Example 1

Pwm-01.png Pwm-02.png Pwm-03.png Pwm-04.png

Pwm-05.png

Pwm-06.png

Example 2

Pwm-07.png Pwm-08.png Pwm-09.png Pwm-10.png

Pwm-11.png

Pwm-12.png

Wattage

If you send a pulse-width-modulated signal directly to an ohmic consumer (i.e. hot-wire), you have to pay attention to the calculation of the wattage. Don't try:

Pwm-13.png

Instead you have to consider the wattage while on- and off-switching seperately:

Pwm-14.png

Example:

Pwm-15.png Pwm-16.png Pwm-17.png Pwm-18.png Pwm-19.png

The average value of this voltage is:

Pwm-20.png

If you would calculate with this value of wattage, it would result in

Pwm-21.png

But the exact result is

Pwm-22.png

Use as DA-converter

If you average the voltage with a low pass filter, you can use the pulse width modulation to generate analog signals (digital-analog-converter). Because the PWM-signal only consists of two different voltages, sometimes it is also called 1-Bit-DA-converter, but this term is actually misleading, for it has nothing to do with the solution of the resulting analog signal.

The filter could be realised through a simple passive RC-combination for instance. It eliminates the high PWM base frequency and leaves over the analog signal. The critical frequency must be chosen in the way that the desired analog signal doesn't change. At the same time it has to be as low as possible to remove the upper waves of the PWM base frequency.

A filter is not neccessary to control a DC-motor, the signal can directly be sent to the [Motortreiber]. The inertia of the magnetic field inside the motor is smoothing the signal sufficiently.

Pulse width modulation is also used for generation of several output voltages of adjusters. Therefor a transistor with variable duty cycle will be controlled and by that the output voltage will be regulated.