<s>
An	O
RLC	B-Algorithm
circuit	I-Algorithm
is	O
an	O
electrical	O
circuit	O
consisting	O
of	O
a	O
resistor	O
(	O
R	O
)	O
,	O
an	O
inductor	O
(	O
L	O
)	O
,	O
and	O
a	O
capacitor	O
(	O
C	O
)	O
,	O
connected	O
in	O
series	O
or	O
in	O
parallel	O
.	O
</s>
<s>
The	O
circuit	O
forms	O
a	O
harmonic	O
oscillator	O
for	O
current	O
,	O
and	O
resonates	B-Application
in	O
a	O
manner	O
similar	O
to	O
an	O
LC	O
circuit	O
.	O
</s>
<s>
RLC	B-Algorithm
circuits	I-Algorithm
have	O
many	O
applications	O
as	O
oscillator	O
circuits	O
.	O
</s>
<s>
Radio	O
receivers	B-Device
and	O
television	O
sets	O
use	O
them	O
for	O
tuning	B-Device
to	O
select	O
a	O
narrow	O
frequency	O
range	O
from	O
ambient	O
radio	O
waves	O
.	O
</s>
<s>
An	O
RLC	B-Algorithm
circuit	I-Algorithm
can	O
be	O
used	O
as	O
a	O
band-pass	O
filter	O
,	O
band-stop	O
filter	O
,	O
low-pass	B-Algorithm
filter	I-Algorithm
or	O
high-pass	O
filter	O
.	O
</s>
<s>
The	O
tuning	B-Device
application	O
,	O
for	O
instance	O
,	O
is	O
an	O
example	O
of	O
band-pass	O
filtering	O
.	O
</s>
<s>
The	O
RLC	B-Algorithm
filter	I-Algorithm
is	O
described	O
as	O
a	O
second-order	O
circuit	O
,	O
meaning	O
that	O
any	O
voltage	O
or	O
current	O
in	O
the	O
circuit	O
can	O
be	O
described	O
by	O
a	O
second-order	O
differential	O
equation	O
in	O
circuit	O
analysis	O
.	O
</s>
<s>
An	O
important	O
property	O
of	O
this	O
circuit	O
is	O
its	O
ability	O
to	O
resonate	O
at	O
a	O
specific	O
frequency	O
,	O
the	O
resonance	B-Application
frequency	O
,	O
.	O
</s>
<s>
Resonance	B-Application
occurs	O
because	O
energy	O
for	O
this	O
situation	O
is	O
stored	O
in	O
two	O
different	O
ways	O
:	O
in	O
an	O
electric	O
field	O
as	O
the	O
capacitor	O
is	O
charged	O
and	O
in	O
a	O
magnetic	O
field	O
as	O
current	O
flows	O
through	O
the	O
inductor	O
.	O
</s>
<s>
This	O
is	O
no	O
passing	O
metaphor	O
;	O
a	O
weight	O
on	O
a	O
spring	O
is	O
described	O
by	O
exactly	O
the	O
same	O
second	O
order	O
differential	O
equation	O
as	O
an	O
RLC	B-Algorithm
circuit	I-Algorithm
and	O
for	O
all	O
the	O
properties	O
of	O
the	O
one	O
system	O
there	O
will	O
be	O
found	O
an	O
analogous	O
property	O
of	O
the	O
other	O
.	O
</s>
<s>
Likewise	O
,	O
the	O
resistance	O
in	O
an	O
RLC	B-Algorithm
circuit	I-Algorithm
will	O
"	O
damp	O
"	O
the	O
oscillation	O
,	O
diminishing	O
it	O
with	O
time	O
if	O
there	O
is	O
no	O
driving	O
AC	O
power	O
source	O
in	O
the	O
circuit	O
.	O
</s>
<s>
The	O
resonance	B-Application
frequency	O
is	O
defined	O
in	O
terms	O
of	O
the	O
impedance	O
presented	O
to	O
a	O
driving	O
source	O
.	O
</s>
<s>
This	O
is	O
similar	O
to	O
the	O
way	O
that	O
a	O
tuning	B-Device
fork	O
will	O
carry	O
on	O
ringing	O
after	O
it	O
has	O
been	O
struck	O
,	O
and	O
the	O
effect	O
is	O
often	O
called	O
ringing	O
.	O
</s>
<s>
This	O
effect	O
is	O
the	O
peak	O
natural	O
resonance	B-Application
frequency	O
of	O
the	O
circuit	O
and	O
in	O
general	O
is	O
not	O
exactly	O
the	O
same	O
as	O
the	O
driven	O
resonance	B-Application
frequency	O
,	O
although	O
the	O
two	O
will	O
usually	O
be	O
quite	O
close	O
to	O
each	O
other	O
.	O
</s>
<s>
Various	O
terms	O
are	O
used	O
by	O
different	O
authors	O
to	O
distinguish	O
the	O
two	O
,	O
but	O
resonance	B-Application
frequency	O
unqualified	O
usually	O
means	O
the	O
driven	O
resonance	B-Application
frequency	O
.	O
</s>
<s>
The	O
driven	O
frequency	O
may	O
be	O
called	O
the	O
undamped	O
resonance	B-Application
frequency	O
or	O
undamped	O
natural	O
frequency	O
and	O
the	O
peak	O
frequency	O
may	O
be	O
called	O
the	O
damped	O
resonance	B-Application
frequency	O
or	O
the	O
damped	O
natural	O
frequency	O
.	O
</s>
<s>
The	O
reason	O
for	O
this	O
terminology	O
is	O
that	O
the	O
driven	O
resonance	B-Application
frequency	O
in	O
a	O
series	O
or	O
parallel	O
resonant	O
circuit	O
has	O
the	O
value	O
.	O
</s>
<s>
This	O
is	O
exactly	O
the	O
same	O
as	O
the	O
resonance	B-Application
frequency	O
of	O
a	O
lossless	O
LC	O
circuit	O
–	O
that	O
is	O
,	O
one	O
with	O
no	O
resistor	O
present	O
.	O
</s>
<s>
The	O
resonant	O
frequency	O
for	O
a	O
driven	O
RLC	B-Algorithm
circuit	I-Algorithm
is	O
the	O
same	O
as	O
a	O
circuit	O
in	O
which	O
there	O
is	O
no	O
damping	O
,	O
hence	O
undamped	O
resonant	O
frequency	O
.	O
</s>
<s>
Circuits	O
with	O
topologies	O
more	O
complex	O
than	O
straightforward	O
series	O
or	O
parallel	O
(	O
some	O
examples	O
described	O
later	O
in	O
the	O
article	O
)	O
have	O
a	O
driven	O
resonance	B-Application
frequency	O
that	O
deviates	O
from	O
,	O
and	O
for	O
those	O
the	O
undamped	O
resonance	B-Application
frequency	O
,	O
damped	O
resonance	B-Application
frequency	O
and	O
driven	O
resonance	B-Application
frequency	O
can	O
all	O
be	O
different	O
.	O
</s>
<s>
The	O
resonance	B-Application
effect	O
can	O
be	O
used	O
for	O
filtering	O
,	O
the	O
rapid	O
change	O
in	O
impedance	O
near	O
resonance	B-Application
can	O
be	O
used	O
to	O
pass	O
or	O
block	O
signals	O
close	O
to	O
the	O
resonance	B-Application
frequency	O
.	O
</s>
<s>
A	O
key	O
parameter	O
in	O
filter	O
design	O
is	O
bandwidth	B-Algorithm
.	O
</s>
<s>
The	O
bandwidth	B-Algorithm
is	O
measured	O
between	O
the	O
cutoff	O
frequencies	O
,	O
most	O
frequently	O
defined	O
as	O
the	O
frequencies	O
at	O
which	O
the	O
power	O
passed	O
through	O
the	O
circuit	O
has	O
fallen	O
to	O
half	O
the	O
value	O
passed	O
at	O
resonance	B-Application
.	O
</s>
<s>
where	O
is	O
the	O
bandwidth	B-Algorithm
,	O
is	O
the	O
lower	O
half-power	O
frequency	O
and	O
is	O
the	O
upper	O
half-power	O
frequency	O
.	O
</s>
<s>
The	O
fractional	O
bandwidth	B-Algorithm
is	O
also	O
often	O
stated	O
as	O
a	O
percentage	O
.	O
</s>
<s>
The	O
damping	O
of	O
filter	O
circuits	O
is	O
adjusted	O
to	O
result	O
in	O
the	O
required	O
bandwidth	B-Algorithm
.	O
</s>
<s>
It	O
is	O
defined	O
as	O
the	O
peak	O
energy	O
stored	O
in	O
the	O
circuit	O
divided	O
by	O
the	O
average	O
energy	O
dissipated	O
in	O
it	O
per	O
radian	O
at	O
resonance	B-Application
.	O
</s>
<s>
is	O
related	O
to	O
bandwidth	B-Algorithm
;	O
low	O
-	O
circuits	O
are	O
wide-band	O
and	O
high	O
-	O
circuits	O
are	O
narrow-band	O
.	O
</s>
<s>
factor	O
is	O
directly	O
proportional	O
to	O
selectivity	O
,	O
as	O
the	O
factor	O
depends	O
inversely	O
on	O
bandwidth	B-Algorithm
.	O
</s>
<s>
The	O
article	O
next	O
gives	O
the	O
analysis	O
for	O
the	O
series	O
RLC	B-Algorithm
circuit	I-Algorithm
in	O
detail	O
.	O
</s>
<s>
is	O
the	O
angular	O
resonance	B-Application
frequency	O
.	O
</s>
<s>
For	O
the	O
case	O
of	O
the	O
series	O
RLC	B-Algorithm
circuit	I-Algorithm
these	O
two	O
parameters	O
are	O
given	O
by	O
:	O
</s>
<s>
This	O
is	O
called	O
the	O
damped	O
resonance	B-Application
frequency	O
or	O
the	O
damped	O
natural	O
frequency	O
.	O
</s>
<s>
The	O
resonance	B-Application
frequency	O
,	O
,	O
which	O
is	O
the	O
frequency	O
at	O
which	O
the	O
circuit	O
will	O
resonate	O
when	O
driven	O
by	O
an	O
external	O
oscillation	O
,	O
may	O
often	O
be	O
referred	O
to	O
as	O
the	O
undamped	O
resonance	B-Application
frequency	O
to	O
distinguish	O
it	O
.	O
</s>
<s>
The	O
value	O
of	O
at	O
this	O
peak	O
is	O
,	O
in	O
this	O
particular	O
case	O
,	O
equal	O
to	O
the	O
undamped	O
natural	O
resonance	B-Application
frequency	O
:	O
.	O
</s>
<s>
The	O
properties	O
of	O
the	O
parallel	O
RLC	B-Algorithm
circuit	I-Algorithm
can	O
be	O
obtained	O
from	O
the	O
duality	O
relationship	O
of	O
electrical	O
circuits	O
and	O
considering	O
that	O
the	O
parallel	O
RLC	O
is	O
the	O
dual	O
impedance	O
of	O
a	O
series	O
RLC	O
.	O
</s>
<s>
Likewise	O
,	O
the	O
other	O
scaled	O
parameters	O
,	O
fractional	O
bandwidth	B-Algorithm
and	O
are	O
also	O
reciprocals	O
of	O
each	O
other	O
.	O
</s>
<s>
The	O
change	O
from	O
a	O
series	O
arrangement	O
to	O
a	O
parallel	O
arrangement	O
results	O
in	O
the	O
circuit	O
having	O
a	O
peak	O
in	O
impedance	O
at	O
resonance	B-Application
rather	O
than	O
a	O
minimum	O
,	O
so	O
the	O
circuit	O
is	O
an	O
anti-resonator	O
.	O
</s>
<s>
The	O
graph	O
opposite	O
shows	O
that	O
there	O
is	O
a	O
minimum	O
in	O
the	O
frequency	O
response	O
of	O
the	O
current	O
at	O
the	O
resonance	B-Application
frequency	O
when	O
the	O
circuit	O
is	O
driven	O
by	O
a	O
constant	O
voltage	O
.	O
</s>
<s>
The	O
first	O
example	O
of	O
an	O
electrical	O
resonance	B-Application
curve	O
was	O
published	O
in	O
1887	O
by	O
German	O
physicist	O
Heinrich	O
Hertz	O
in	O
his	O
pioneering	O
paper	O
on	O
the	O
discovery	O
of	O
radio	O
waves	O
,	O
showing	O
the	O
length	O
of	O
spark	O
obtainable	O
from	O
his	O
spark-gap	O
LC	O
resonator	O
detectors	O
as	O
a	O
function	O
of	O
frequency	O
.	O
</s>
<s>
One	O
of	O
the	O
first	O
demonstrations	O
of	O
resonance	B-Application
between	O
tuned	O
circuits	O
was	O
Lodge	O
's	O
"	O
syntonic	O
jars	O
"	O
experiment	O
around	O
1889	O
He	O
placed	O
two	O
resonant	O
circuits	O
next	O
to	O
each	O
other	O
,	O
each	O
consisting	O
of	O
a	O
Leyden	O
jar	O
connected	O
to	O
an	O
adjustable	O
one-turn	O
coil	O
with	O
a	O
spark	O
gap	O
.	O
</s>
<s>
When	O
a	O
high	O
voltage	O
from	O
an	O
induction	O
coil	O
was	O
applied	O
to	O
one	O
tuned	O
circuit	O
,	O
creating	O
sparks	O
and	O
thus	O
oscillating	O
currents	O
,	O
sparks	O
were	O
excited	O
in	O
the	O
other	O
tuned	O
circuit	O
only	O
when	O
the	O
inductors	O
were	O
adjusted	O
to	O
resonance	B-Application
.	O
</s>
<s>
Lodge	O
and	O
some	O
English	O
scientists	O
preferred	O
the	O
term	O
"	O
syntony	O
"	O
for	O
this	O
effect	O
,	O
but	O
the	O
term	O
"	O
resonance	B-Application
"	O
eventually	O
stuck	O
.	O
</s>
<s>
The	O
first	O
practical	O
use	O
for	O
RLC	B-Algorithm
circuits	I-Algorithm
was	O
in	O
the	O
1890s	O
in	O
spark-gap	O
radio	O
transmitters	O
to	O
allow	O
the	O
receiver	B-Device
to	O
be	O
tuned	O
to	O
the	O
transmitter	O
.	O
</s>
<s>
The	O
first	O
patent	O
for	O
a	O
radio	O
system	O
that	O
allowed	O
tuning	B-Device
was	O
filed	O
by	O
Lodge	O
in	O
1897	O
,	O
although	O
the	O
first	O
practical	O
systems	O
were	O
invented	O
in	O
1900	O
by	O
Anglo	O
Italian	O
radio	O
pioneer	O
Guglielmo	O
Marconi	O
.	O
</s>
<s>
A	O
very	O
frequent	O
use	O
of	O
these	O
circuits	O
is	O
in	O
the	O
tuning	B-Device
circuits	O
of	O
analogue	O
radios	O
.	O
</s>
<s>
Adjustable	O
tuning	B-Device
is	O
commonly	O
achieved	O
with	O
a	O
parallel	O
plate	O
variable	O
capacitor	O
which	O
allows	O
the	O
value	O
of	O
to	O
be	O
changed	O
and	O
tune	O
to	O
stations	O
on	O
different	O
frequencies	O
.	O
</s>
<s>
For	O
the	O
IF	O
stage	O
in	O
the	O
radio	O
where	O
the	O
tuning	B-Device
is	O
preset	O
in	O
the	O
factory	O
,	O
the	O
more	O
usual	O
solution	O
is	O
an	O
adjustable	O
core	O
in	O
the	O
inductor	O
to	O
adjust	O
.	O
</s>
<s>
RLC	B-Algorithm
circuit	I-Algorithm
as	O
a	O
low-pass	B-Algorithm
filterthumb|none|Figure	O
7	O
.	O
</s>
<s>
RLC	B-Algorithm
circuit	I-Algorithm
as	O
a	O
high-pass	O
filterthumb|none|Figure	O
8	O
.	O
</s>
<s>
RLC	B-Algorithm
circuit	I-Algorithm
as	O
a	O
series	O
band-pass	O
filter	O
in	O
series	O
with	O
the	O
linethumb|none|Figure	O
9	O
.	O
</s>
<s>
RLC	B-Algorithm
circuit	I-Algorithm
as	O
a	O
parallel	O
band-pass	O
filter	O
in	O
shunt	O
across	O
the	O
linethumb|none|Figure	O
10	O
.	O
</s>
<s>
RLC	B-Algorithm
circuit	I-Algorithm
as	O
a	O
series	O
band-stop	O
filter	O
in	O
shunt	O
across	O
the	O
linethumb|none|Figure	O
11	O
.	O
</s>
<s>
The	O
value	O
of	O
the	O
damping	O
factor	O
is	O
chosen	O
based	O
on	O
the	O
desired	O
bandwidth	B-Algorithm
of	O
the	O
filter	O
.	O
</s>
<s>
For	O
a	O
wider	O
bandwidth	B-Algorithm
,	O
a	O
larger	O
value	O
of	O
the	O
damping	O
factor	O
is	O
required	O
(	O
and	O
vice	O
versa	O
)	O
.	O
</s>
<s>
Two	O
of	O
these	O
are	O
required	O
to	O
set	O
the	O
bandwidth	B-Algorithm
and	O
resonant	O
frequency	O
.	O
</s>
<s>
An	O
RLC	B-Algorithm
circuit	I-Algorithm
can	O
be	O
used	O
as	O
a	O
low-pass	B-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
This	O
is	O
also	O
the	O
bandwidth	B-Algorithm
of	O
the	O
filter	O
.	O
</s>
<s>
The	O
corner	O
frequency	O
is	O
the	O
same	O
as	O
the	O
low-pass	B-Algorithm
filter	I-Algorithm
:	O
</s>
<s>
A	O
band-pass	O
filter	O
can	O
be	O
formed	O
with	O
an	O
RLC	B-Algorithm
circuit	I-Algorithm
by	O
either	O
placing	O
a	O
series	O
LC	O
circuit	O
in	O
series	O
with	O
the	O
load	O
resistor	O
or	O
else	O
by	O
placing	O
a	O
parallel	O
LC	O
circuit	O
in	O
parallel	O
with	O
the	O
load	O
resistor	O
.	O
</s>
<s>
The	O
first	O
case	O
requires	O
a	O
high	O
impedance	O
source	O
so	O
that	O
the	O
current	O
is	O
diverted	O
into	O
the	O
resonator	O
when	O
it	O
becomes	O
low	O
impedance	O
at	O
resonance	B-Application
.	O
</s>
<s>
The	O
second	O
case	O
requires	O
a	O
low	O
impedance	O
source	O
so	O
that	O
the	O
voltage	O
is	O
dropped	O
across	O
the	O
antiresonator	O
when	O
it	O
becomes	O
high	O
impedance	O
at	O
resonance	B-Application
.	O
</s>
<s>
In	O
either	O
case	O
,	O
the	O
RLC	B-Algorithm
circuit	I-Algorithm
becomes	O
a	O
good	O
approximation	O
to	O
an	O
ideal	O
LC	O
circuit	O
.	O
</s>
<s>
An	O
overdamped	O
series	O
RLC	B-Algorithm
circuit	I-Algorithm
can	O
be	O
used	O
as	O
a	O
pulse	O
discharge	O
circuit	O
.	O
</s>
