<s>
The	O
Sallen	B-Algorithm
–	I-Algorithm
Key	I-Algorithm
topology	I-Algorithm
is	O
an	O
electronic	B-Algorithm
filter	I-Algorithm
topology	I-Algorithm
used	O
to	O
implement	O
second-order	O
active	O
filters	O
that	O
is	O
particularly	O
valued	O
for	O
its	O
simplicity	O
.	O
</s>
<s>
It	O
is	O
a	O
degenerate	O
form	O
of	O
a	O
voltage-controlled	O
voltage-source	O
(	O
VCVS	B-Algorithm
)	O
filter	O
topology	O
.	O
</s>
<s>
A	O
VCVS	B-Algorithm
filter	I-Algorithm
uses	O
a	O
voltage	O
amplifier	O
with	O
practically	O
infinite	O
input	O
impedance	O
and	O
zero	O
output	O
impedance	O
to	O
implement	O
a	O
2-pole	O
low-pass	B-Algorithm
,	O
high-pass	O
,	O
bandpass	O
,	O
bandstop	O
,	O
or	O
allpass	O
response	O
.	O
</s>
<s>
The	O
VCVS	B-Algorithm
filter	I-Algorithm
allows	O
high	O
Q	O
factor	O
and	O
passband	B-Algorithm
gain	O
without	O
the	O
use	O
of	O
inductors	O
.	O
</s>
<s>
A	O
VCVS	B-Algorithm
filter	I-Algorithm
also	O
has	O
the	O
advantage	O
of	O
independence	O
:	O
VCVS	B-Algorithm
filters	I-Algorithm
can	O
be	O
cascaded	O
without	O
the	O
stages	O
affecting	O
each	O
others	O
tuning	O
.	O
</s>
<s>
A	O
Sallen	B-Algorithm
–	I-Algorithm
Key	I-Algorithm
filter	I-Algorithm
is	O
a	O
variation	O
on	O
a	O
VCVS	B-Algorithm
filter	I-Algorithm
that	O
uses	O
a	O
unity-voltage-gain	O
amplifier	O
(	O
i.e.	O
,	O
a	O
pure	O
buffer	O
amplifier	O
)	O
.	O
</s>
<s>
Because	O
of	O
its	O
high	O
input	O
impedance	O
and	O
easily	O
selectable	O
gain	O
,	O
an	O
operational	O
amplifier	O
in	O
a	O
conventional	O
non-inverting	O
configuration	O
is	O
often	O
used	O
in	O
VCVS	B-Algorithm
implementations	O
.	O
</s>
<s>
Implementations	O
of	O
Sallen	B-Algorithm
–	I-Algorithm
Key	I-Algorithm
filters	I-Algorithm
often	O
use	O
an	O
op	O
amp	O
configured	O
as	O
a	O
voltage	O
follower	O
;	O
however	O
,	O
emitter	O
or	O
source	O
followers	O
are	O
other	O
common	O
choices	O
for	O
the	O
buffer	O
amplifier	O
.	O
</s>
<s>
VCVS	B-Algorithm
filters	I-Algorithm
are	O
relatively	O
resilient	O
to	O
component	O
tolerance	O
,	O
but	O
obtaining	O
high	O
Q	O
factor	O
may	O
require	O
extreme	O
component	O
value	O
spread	O
or	O
high	O
amplifier	O
gain	O
.	O
</s>
<s>
The	O
generic	O
unity-gain	O
Sallen	B-Algorithm
–	I-Algorithm
Key	I-Algorithm
filter	I-Algorithm
topology	I-Algorithm
implemented	O
with	O
a	O
unity-gain	O
operational	O
amplifier	O
is	O
shown	O
in	O
Figure1	O
.	O
</s>
<s>
This	O
interpretation	O
is	O
the	O
reason	O
why	O
Sallen	B-Algorithm
–	I-Algorithm
Key	I-Algorithm
filters	I-Algorithm
are	O
often	O
drawn	O
with	O
the	O
op	O
amp	O
's	O
non-inverting	O
input	O
below	O
the	O
inverting	O
input	O
,	O
thus	O
emphasizing	O
the	O
similarity	O
between	O
the	O
output	O
and	O
ground	O
.	O
</s>
<s>
By	O
choosing	O
different	O
passive	O
components	O
(	O
e.g.	O
,	O
resistors	O
and	O
capacitors	O
)	O
for	O
,	O
,	O
,	O
and	O
,	O
the	O
filter	O
can	O
be	O
made	O
with	O
low-pass	B-Algorithm
,	O
bandpass	O
,	O
and	O
high-pass	O
characteristics	O
.	O
</s>
<s>
An	O
example	O
of	O
a	O
unity-gain	O
low-pass	B-Algorithm
configuration	O
is	O
shown	O
in	O
Figure2	O
.	O
</s>
<s>
This	O
transfer	O
function	O
has	O
no	O
(	O
finite	O
)	O
zeros	O
and	O
two	O
poles	B-Algorithm
located	O
in	O
the	O
complex	O
s-plane	O
:	O
</s>
<s>
For	O
example	O
,	O
a	O
second-order	O
Butterworth	O
filter	O
,	O
which	O
has	O
maximally	O
flat	O
passband	B-Algorithm
frequency	O
response	O
,	O
has	O
a	O
of	O
.	O
</s>
<s>
By	O
comparison	O
,	O
a	O
value	O
of	O
corresponds	O
to	O
the	O
series	O
cascade	O
of	O
two	O
identical	O
simple	O
low-pass	B-Algorithm
filters	I-Algorithm
.	O
</s>
<s>
which	O
shows	O
how	O
every	O
combination	O
comes	O
with	O
some	O
combination	O
to	O
provide	O
the	O
same	O
and	O
for	O
the	O
low-pass	B-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
The	O
input	O
impedance	O
of	O
the	O
second-order	O
unity-gain	O
Sallen	O
–	O
Key	O
low-pass	B-Algorithm
filter	I-Algorithm
is	O
also	O
of	O
interest	O
to	O
designers	O
.	O
</s>
<s>
where	O
undamped	O
natural	O
frequency	O
and	O
factor	O
are	O
discussed	O
above	O
in	O
the	O
low-pass	B-Algorithm
filter	I-Algorithm
discussion	O
.	O
</s>
<s>
Follow	O
an	O
approach	O
similar	O
to	O
the	O
one	O
used	O
to	O
design	O
the	O
low-pass	B-Algorithm
filter	I-Algorithm
above	O
.	O
</s>
<s>
An	O
example	O
of	O
a	O
non-unity-gain	O
bandpass	O
filter	O
implemented	O
with	O
a	O
VCVS	B-Algorithm
filter	I-Algorithm
is	O
shown	O
in	O
Figure5	O
.	O
</s>
<s>
Although	O
it	O
uses	O
a	O
different	O
topology	O
and	O
an	O
operational	O
amplifier	O
configured	O
to	O
provide	O
non-unity-gain	O
,	O
it	O
can	O
be	O
analyzed	O
using	O
similar	O
methods	O
as	O
with	O
the	O
generic	O
Sallen	B-Algorithm
–	I-Algorithm
Key	I-Algorithm
topology	I-Algorithm
.	O
</s>
