<s>
Pulse-width	B-Algorithm
modulation	I-Algorithm
(	O
PWM	O
)	O
,	O
or	O
pulse-duration	B-Algorithm
modulation	I-Algorithm
(	O
PDM	O
)	O
,	O
is	O
a	O
method	O
of	O
controlling	O
the	O
average	O
power	O
delivered	O
by	O
an	O
electrical	O
signal	O
.	O
</s>
<s>
In	O
electronics	O
,	O
many	O
modern	O
microcontrollers	B-Architecture
(	O
MCUs	O
)	O
integrate	O
PWM	O
controllers	O
exposed	O
to	O
external	O
pins	O
as	O
peripheral	O
devices	O
under	O
firmware	B-Application
control	O
by	O
means	O
of	O
internal	O
programming	O
interfaces	O
.	O
</s>
<s>
It	O
used	O
pulse	B-Algorithm
width	I-Algorithm
modulation	I-Algorithm
to	O
control	O
the	O
intake	O
valve	O
of	O
a	O
steam	O
engine	O
cylinder	O
.	O
</s>
<s>
Pulse-width	B-Algorithm
modulation	I-Algorithm
uses	O
a	O
rectangular	O
pulse	O
wave	O
whose	O
pulse	O
width	O
is	O
modulated	O
resulting	O
in	O
the	O
variation	O
of	O
the	O
average	O
value	O
of	O
the	O
waveform	O
.	O
</s>
<s>
Many	O
digital	O
circuits	O
can	O
generate	O
PWM	O
signals	O
(	O
e.g.	O
,	O
many	O
microcontrollers	B-Architecture
have	O
PWM	O
outputs	O
)	O
.	O
</s>
<s>
Three	O
types	O
of	O
pulse-width	B-Algorithm
modulation	I-Algorithm
(	O
PWM	O
)	O
are	O
possible	O
:	O
</s>
<s>
The	O
amplitudes	O
of	O
the	O
harmonic	O
groups	O
are	O
restricted	O
by	O
a	O
envelope	O
(	O
sinc	B-Algorithm
function	I-Algorithm
)	O
and	O
extend	O
to	O
infinity	O
.	O
</s>
<s>
The	O
infinite	O
bandwidth	O
is	O
caused	O
by	O
the	O
nonlinear	O
operation	O
of	O
the	O
pulse-width	B-Algorithm
modulator	I-Algorithm
.	O
</s>
<s>
In	O
consequence	O
,	O
a	O
digital	O
PWM	O
suffers	O
from	O
aliasing	B-Error_Name
distortion	O
that	O
significantly	O
reduce	O
its	O
applicability	O
for	O
modern	O
communication	O
systems	O
.	O
</s>
<s>
By	O
limiting	O
the	O
bandwidth	O
of	O
the	O
PWM	O
kernel	O
,	O
aliasing	B-Error_Name
effects	O
can	O
be	O
avoided	O
.	O
</s>
<s>
The	O
theorem	O
states	O
that	O
"	O
Any	O
bandlimited	O
baseband	O
signal	O
within	O
±	O
0.637	O
can	O
be	O
represented	O
by	O
a	O
pulsewidth	B-Algorithm
modulation	I-Algorithm
(	O
PWM	O
)	O
waveform	O
with	O
unit	O
amplitude	O
.	O
</s>
<s>
PWM	O
is	O
used	O
to	O
control	O
servomechanisms	O
;	O
see	O
servo	B-Algorithm
control	I-Algorithm
.	O
</s>
<s>
However	O
,	O
the	O
load	O
may	O
be	O
inductive	O
,	O
and	O
with	O
a	O
sufficiently	O
high	O
frequency	O
and	O
when	O
necessary	O
using	O
additional	O
passive	O
electronic	B-Architecture
filters	I-Architecture
,	O
the	O
pulse	O
train	O
can	O
be	O
smoothed	O
and	O
average	O
analog	O
waveform	O
recovered	O
.	O
</s>
<s>
Modern	O
semiconductor	O
switches	O
such	O
as	O
MOSFETs	B-Architecture
or	O
insulated-gate	O
bipolar	O
transistors	O
(	O
IGBTs	O
)	O
are	O
well	O
suited	O
components	O
for	O
high-efficiency	O
controllers	O
.	O
</s>
<s>
Variable-speed	O
computer	O
fan	B-Device
controllers	I-Device
usually	O
use	O
PWM	O
,	O
as	O
it	O
is	O
far	O
more	O
efficient	O
when	O
compared	O
to	O
a	O
potentiometer	B-Device
or	O
rheostat	O
.	O
</s>
<s>
For	O
a	O
few	O
decades	O
,	O
industrial	O
and	O
military	O
PWM	O
amplifiers	O
have	O
been	O
in	O
common	O
use	O
,	O
often	O
for	O
driving	O
servo	B-Algorithm
motors	I-Algorithm
.	O
</s>
<s>
Field-gradient	O
coils	O
in	O
MRI	B-Algorithm
machines	O
are	O
driven	O
by	O
relatively	O
high-power	O
PWM	O
amplifiers	O
.	O
</s>
<s>
Historically	O
,	O
a	O
crude	O
form	O
of	O
PWM	O
has	O
been	O
used	O
to	O
play	O
back	O
PCM	B-Algorithm
digital	O
sound	O
on	O
the	O
PC	B-Device
speaker	I-Device
,	O
which	O
is	O
driven	O
by	O
only	O
two	O
voltage	O
levels	O
,	O
typically	O
0V	O
and	O
5V	O
.	O
</s>
<s>
it	O
was	O
possible	O
to	O
obtain	O
an	O
approximate	O
playback	O
of	O
mono	O
PCM	B-Algorithm
samples	O
,	O
although	O
at	O
a	O
very	O
low	O
quality	O
,	O
and	O
with	O
greatly	O
varying	O
results	O
between	O
implementations	O
.	O
</s>
<s>
In	O
more	O
recent	O
times	O
,	O
the	O
Direct	O
Stream	O
Digital	O
sound	O
encoding	O
method	O
was	O
introduced	O
,	O
which	O
uses	O
a	O
generalized	O
form	O
of	O
pulse-width	B-Algorithm
modulation	I-Algorithm
called	O
pulse-density	B-Algorithm
modulation	I-Algorithm
,	O
at	O
a	O
high	O
enough	O
sampling	O
rate	O
(	O
typically	O
in	O
the	O
order	O
of	O
MHz	O
)	O
to	O
cover	O
the	O
whole	O
acoustic	O
frequencies	O
range	O
with	O
sufficient	O
fidelity	O
.	O
</s>
<s>
SPWM	O
(	O
Sine	O
–	O
triangle	O
pulse	B-Algorithm
width	I-Algorithm
modulation	I-Algorithm
)	O
signals	O
are	O
used	O
in	O
micro-inverter	O
design	O
(	O
used	O
in	O
solar	O
and	O
wind	O
power	O
applications	O
)	O
.	O
</s>
<s>
These	O
switching	O
signals	O
are	O
fed	O
to	O
the	O
FETs	B-Application
that	O
are	O
used	O
in	O
the	O
device	O
.	O
</s>
<s>
The	O
indicator	O
lamp	O
on	O
the	O
Apple	B-Device
iBook	I-Device
G4	O
,	O
PowerBook	O
6	O
,	O
7	O
(	O
2005	O
)	O
was	O
of	O
this	O
type	O
.	O
</s>
