Pulse-width Modulation

Pulse-width modulation (PWM) of a Signal or Power source involves the Modulation of its Duty Cycle , to either convey information over a communications channel or control the amount of power sent to a load.

PRINCIPLE

, showing the definitions of

y_{min}

y_{max}

and D.]]

Pulse-width modulation uses a Square Wave whose Duty Cycle is modulated resulting in the variation of the Average value of the waveform. If we consider a square waveform

f(t)

with a low value

y_{min}

, a high value

y_{max}

and a duty cycle D (see figure 1), the average value of the waveform is given by:

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

f(t)

is a square wave, its value is

y_{max}

for

0 and y_{min} for D\cdot T . The above expression then becomes:

\begin{matrix}
\bar y&=&rac{1}{T}\left(\int_0^{DT}y_{max}\,dt+\int_{DT}^T y_{min}\,dt
ight)\
&=&rac{D\cdot T\cdot y_{max}+ T\left(1-D
ight)y_{min}}{T}\
&=&D\cdot y_{max}+ \left(1-D
ight)y_{min}
\end{matrix}

This latter expression can be fairly simplified in many cases where

y_{min}=0

\bar y=D\cdot y_{max}

. From this, it is obvious that the average value of the signal (

\bar y

) is directly dependent on the duty cycle D.

TECHNIQUE

Generation

Intersective

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 green 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.

Delta

See Also: Delta modulation

The output signal is compared with limits, which correspond to a reference signal offset by a constant. Every time the output signal reaches one of the limits, the PWM signal changes state.

Sigma-Delta

See Also: Delta-sigma modulation

The output signal is subtracted from a reference signal to form an error signal. This error is integrated, and when the integral of the error exceeds the limits, the output changes state.

Digital

Many digital circuits can generate PWM signals (e.g many Microcontrollers have PWM outputs to control an Electrical Motor ). They normally use a Counter that increments periodically (it is connected directly or indirectly to the Clock of the circuit) and is reset at the end of every period of the PWM. When the counter value is more than the reference value, the PWM output changes state from high to low.

Types

Three types of pulse-width modulation (PWM) are possible.

#The pulse center may be fixed in the center of the time window and both edges of the pulse moved to compress or expand the width.
#The lead edge can be held at the lead edge of the window and the tail edge modulated.
#The tail edge can be fixed and the lead edge modulated.

Spectrum

The resulting Spectra (of the three cases) are similar, and each contains a Dc component, a base sideband containing the modulating signal and phase modulated Carrier s at each Harmonic of the frequency of the pulse. The amplitudes of the harmonic groups are restricted by a

\sin x / x

envelope ( Sinc Function ) and extend to infinity.

APPLICATIONS

Telecommunications

In Telecommunications , the widths of the pulses correspond to specific data values encoded at one end and decoded at the other.

Pulses of various lengths (the information itself) will be sent at regular intervals (the Carrier Frequency of the modulation).

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Pulse-width Modulation