Pulse-width Modulation - Principle

Principle

Pulse-width modulation uses a rectangular pulse wave whose pulse width is modulated resulting in the variation of the average value of the waveform. If we consider a pulse waveform with a low value, a high value and a duty cycle D (see figure 1), the average value of the waveform is given by:

\bar y=\frac{1}{T}\int^T_0f(t)\,dt.

As is a pulse wave, its value is for and for . The above expression then becomes:

\begin{align} \bar y &=\frac{1}{T}\left(\int_0^{DT}y_{max}\,dt+\int_{DT}^T y_{min}\,dt\right)\\ &= \frac{D\cdot T\cdot y_{max}+ T\left(1-D\right)y_{min}}{T}\\ &= D\cdot y_{max}+ \left(1-D\right)y_{min}. \end{align}

This latter expression can be fairly simplified in many cases where as . From this, it is obvious that the average value of the signal is directly dependent on the duty cycle D.

The simplest way to generate a PWM signal is the intersective method, which requires only a sawtooth or a triangle waveform (easily generated using a simple oscillator) and a comparator. When the value of the reference signal (the red sine wave in figure 2) is more than the modulation waveform (blue), the PWM signal (magenta) is in the high state, otherwise it is in the low state.

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