<s>
A	O
resistor	B-Algorithm
–	I-Algorithm
capacitor	I-Algorithm
circuit	I-Algorithm
(	O
RC	B-Algorithm
circuit	I-Algorithm
)	O
,	O
or	O
RC	B-Algorithm
filter	I-Algorithm
or	O
RC	B-Algorithm
network	I-Algorithm
,	O
is	O
an	O
electric	O
circuit	O
composed	O
of	O
resistors	O
and	O
capacitors	O
.	O
</s>
<s>
A	O
first	O
order	O
RC	B-Algorithm
circuit	I-Algorithm
is	O
composed	O
of	O
one	O
resistor	O
and	O
one	O
capacitor	O
and	O
is	O
the	O
simplest	O
type	O
of	O
RC	B-Algorithm
circuit	I-Algorithm
.	O
</s>
<s>
RC	B-Algorithm
circuits	I-Algorithm
can	O
be	O
used	O
to	O
filter	O
a	O
signal	O
by	O
blocking	O
certain	O
frequencies	O
and	O
passing	O
others	O
.	O
</s>
<s>
The	O
two	O
most	O
common	O
RC	B-Algorithm
filters	I-Algorithm
are	O
the	O
high-pass	O
filters	O
and	O
low-pass	B-Algorithm
filters	I-Algorithm
;	O
band-pass	O
filters	O
and	O
band-stop	O
filters	O
usually	O
require	O
RLC	B-Algorithm
filters	I-Algorithm
,	O
though	O
crude	O
ones	O
can	O
be	O
made	O
with	O
RC	B-Algorithm
filters	I-Algorithm
.	O
</s>
<s>
These	O
may	O
be	O
combined	O
in	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
,	O
and	O
the	O
RLC	B-Algorithm
circuit	I-Algorithm
,	O
with	O
the	O
acronyms	O
indicating	O
which	O
components	O
are	O
used	O
.	O
</s>
<s>
This	O
article	O
considers	O
the	O
RC	B-Algorithm
circuit	I-Algorithm
,	O
in	O
both	O
series	O
and	O
parallel	O
forms	O
,	O
as	O
shown	O
in	O
the	O
diagrams	O
below	O
.	O
</s>
<s>
The	O
simplest	O
RC	B-Algorithm
circuit	I-Algorithm
consists	O
of	O
a	O
resistor	O
and	O
a	O
charged	O
capacitor	O
connected	O
to	O
one	O
another	O
in	O
a	O
single	O
loop	O
,	O
without	O
an	O
external	O
voltage	O
source	O
.	O
</s>
<s>
The	O
current	O
through	O
the	O
resistor	O
must	O
be	O
equal	O
in	O
magnitude	O
(	O
but	O
opposite	O
in	O
sign	O
)	O
to	O
the	O
time	O
derivative	B-Algorithm
of	O
the	O
accumulated	O
charge	O
on	O
the	O
capacitor	O
.	O
</s>
<s>
Thus	O
,	O
the	O
circuit	O
behaves	O
as	O
a	O
low-pass	B-Algorithm
filter	I-Algorithm
.	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
RC	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
rise	O
(	O
across	O
the	O
capacitor	O
)	O
or	O
fall	O
(	O
across	O
the	O
resistor	O
)	O
to	O
within	O
of	O
its	O
final	O
value	O
.	O
</s>
<s>
More	O
accurate	O
integration	O
and	O
differentiation	B-Algorithm
can	O
be	O
achieved	O
by	O
placing	O
resistors	O
and	O
capacitors	O
as	O
appropriate	O
on	O
the	O
input	O
and	O
feedback	O
loop	O
of	O
operational	O
amplifiers	O
(	O
see	O
operational	O
amplifier	O
integrator	O
and	O
operational	O
amplifier	O
differentiator	O
)	O
.	O
</s>
<s>
The	O
parallel	O
RC	B-Algorithm
circuit	I-Algorithm
is	O
generally	O
of	O
less	O
interest	O
than	O
the	O
series	O
circuit	O
.	O
</s>
<s>
When	O
fed	O
by	O
a	O
current	O
source	O
,	O
the	O
transfer	O
function	O
of	O
a	O
parallel	O
RC	B-Algorithm
circuit	I-Algorithm
is	O
:	O
</s>
<s>
It	O
is	O
sometimes	O
required	O
to	O
synthesise	O
an	O
RC	B-Algorithm
circuit	I-Algorithm
from	O
a	O
given	O
rational	O
function	O
in	O
s	O
.	O
For	O
synthesis	O
to	O
be	O
possible	O
in	O
passive	O
elements	O
,	O
the	O
function	O
must	O
be	O
a	O
positive-real	O
function	O
.	O
</s>
<s>
To	O
synthesise	O
as	O
an	O
RC	B-Algorithm
circuit	I-Algorithm
,	O
all	O
the	O
critical	O
frequencies	O
(	O
poles	O
and	O
zeroes	O
)	O
must	O
be	O
on	O
the	O
negative	O
real	O
axis	O
and	O
alternate	O
between	O
poles	O
and	O
zeroes	O
with	O
an	O
equal	O
number	O
of	O
each	O
.	O
</s>
