<s>
A	O
resistor	O
–	O
inductor	O
circuit	O
(	O
RL	B-Algorithm
circuit	I-Algorithm
)	O
,	O
or	O
RL	B-Algorithm
filter	I-Algorithm
or	O
RL	B-Algorithm
network	I-Algorithm
,	O
is	O
an	O
electric	O
circuit	O
composed	O
of	O
resistors	O
and	O
inductors	O
driven	O
by	O
a	O
voltage	O
or	O
current	O
source	O
.	O
</s>
<s>
A	O
first-order	O
RL	B-Algorithm
circuit	I-Algorithm
is	O
composed	O
of	O
one	O
resistor	O
and	O
one	O
inductor	O
,	O
either	O
in	O
series	O
driven	O
by	O
a	O
voltage	O
source	O
or	O
in	O
parallel	O
driven	O
by	O
a	O
current	O
source	O
.	O
</s>
<s>
It	O
is	O
one	O
of	O
the	O
simplest	O
analogue	O
infinite	O
impulse	O
response	O
electronic	B-Architecture
filters	I-Architecture
.	O
</s>
<s>
These	O
circuit	O
elements	O
can	O
be	O
combined	O
to	O
form	O
an	O
electrical	O
circuit	O
in	O
four	O
distinct	O
ways	O
:	O
the	O
RC	B-Algorithm
circuit	I-Algorithm
,	O
the	O
RL	B-Algorithm
circuit	I-Algorithm
,	O
the	O
LC	O
circuit	O
and	O
the	O
RLC	B-Algorithm
circuit	I-Algorithm
,	O
with	O
the	O
abbreviations	O
indicating	O
which	O
components	O
are	O
used	O
.	O
</s>
<s>
In	O
practice	O
,	O
however	O
,	O
capacitors	O
(	O
and	O
RC	B-Algorithm
circuits	I-Algorithm
)	O
are	O
usually	O
preferred	O
to	O
inductors	O
since	O
they	O
can	O
be	O
more	O
easily	O
manufactured	O
and	O
are	O
generally	O
physically	O
smaller	O
,	O
particularly	O
for	O
higher	O
values	O
of	O
components	O
.	O
</s>
<s>
Both	O
RC	O
and	O
RL	B-Algorithm
circuits	I-Algorithm
form	O
a	O
single-pole	O
filter	O
.	O
</s>
<s>
Depending	O
on	O
whether	O
the	O
reactive	O
element	O
(	O
C	O
or	O
L	O
)	O
is	O
in	O
series	O
with	O
the	O
load	O
,	O
or	O
parallel	O
with	O
the	O
load	O
will	O
dictate	O
whether	O
the	O
filter	O
is	O
low-pass	B-Algorithm
or	O
high-pass	O
.	O
</s>
<s>
Frequently	O
RL	B-Algorithm
circuits	I-Algorithm
are	O
used	O
as	O
DC	O
power	O
supplies	O
for	O
RF	O
amplifiers	O
,	O
where	O
the	O
inductor	O
is	O
used	O
to	O
pass	O
DC	O
bias	O
current	O
and	O
block	O
the	O
RF	O
getting	O
back	O
into	O
the	O
power	O
supply	O
.	O
</s>
<s>
The	O
complex-valued	O
eigenfunctions	O
of	O
any	O
linear	O
time-invariant	B-Algorithm
(	O
LTI	O
)	O
system	O
are	O
of	O
the	O
following	O
forms	O
:	O
</s>
<s>
These	O
expressions	O
together	O
may	O
be	O
substituted	O
into	O
the	O
usual	O
expression	O
for	O
the	O
phasor	B-Application
representing	O
the	O
output	O
:	O
</s>
<s>
The	O
zero-input	O
response	O
(	O
ZIR	O
)	O
,	O
also	O
called	O
the	O
natural	O
response	O
,	O
of	O
an	O
RL	B-Algorithm
circuit	I-Algorithm
describes	O
the	O
behavior	O
of	O
the	O
circuit	O
after	O
it	O
has	O
reached	O
constant	O
voltages	O
and	O
currents	O
and	O
is	O
disconnected	O
from	O
any	O
power	O
source	O
.	O
</s>
<s>
The	O
ZIR	O
of	O
an	O
RL	B-Algorithm
circuit	I-Algorithm
is	O
:	O
</s>
<s>
In	O
this	O
configuration	O
,	O
the	O
circuit	O
behaves	O
as	O
a	O
low-pass	B-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
Compare	O
this	O
with	O
the	O
behaviour	O
of	O
the	O
resistor	O
output	O
in	O
an	O
RC	B-Algorithm
circuit	I-Algorithm
,	O
where	O
the	O
reverse	O
is	O
the	O
case	O
.	O
</s>
<s>
The	O
range	O
of	O
frequencies	O
that	O
the	O
filter	O
passes	O
is	O
called	O
its	O
bandwidth	B-Algorithm
.	O
</s>
<s>
These	O
equations	O
show	O
that	O
a	O
series	O
RL	B-Algorithm
circuit	I-Algorithm
has	O
a	O
time	O
constant	O
,	O
usually	O
denoted	O
being	O
the	O
time	O
it	O
takes	O
the	O
voltage	O
across	O
the	O
component	O
to	O
either	O
fall	O
(	O
across	O
the	O
inductor	O
)	O
or	O
rise	O
(	O
across	O
the	O
resistor	O
)	O
to	O
within	O
of	O
its	O
final	O
value	O
.	O
</s>
<s>
When	O
the	O
voltage	O
source	O
is	O
then	O
replaced	O
with	O
a	O
short	B-Application
circuit	I-Application
,	O
the	O
voltage	O
across	O
the	O
resistor	O
drops	O
exponentially	O
with	O
from	O
towards	O
0	O
.	O
</s>
<s>
For	O
short	B-Application
circuit	I-Application
evaluation	O
,	O
RL	B-Algorithm
circuit	I-Algorithm
is	O
considered	O
.	O
</s>
<s>
The	O
parallel	O
RL	B-Algorithm
circuit	I-Algorithm
is	O
generally	O
of	O
less	O
interest	O
than	O
the	O
series	O
circuit	O
unless	O
fed	O
by	O
a	O
current	O
source	O
.	O
</s>
