Datasheet

13
LT1251/LT1256
APPLICATIONS INFORMATION
WUU
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In low gain applications, R
1
and R
2
are small compared to
the feedback resistors and therefore we can simplify the
equation to:
V
KV
RR
RR
KV
RR
RR
sR C
R
K
R
K
R
O
GF
GF
GF
GF
OL
OL F F
=
()()
+
+
−
()
()()
+
+
++
−
()
1
11
11
2
22
22
12
1
1
1
Note that the denominator causes a gain error due to the
open-loop gain (typically 0.1% for frequencies below
20kHz) and for mismatches in R
F1
and R
F2
. A 1% mis-
match in the feedback resistors results in a 0.25% error at
K = 0.5.
If we set R
F1
= R
F2
and assume R
OL
>> R
F1
(a 0.1% error
at low frequencies) the above equation simplifies to:
and
VKVA KVA
where A
R
R
A
R
R
OV V
V
F
G
V
F
G
=+−
()
=+ =+
11 22
1
1
1
2
2
2
1
11
This shows that the output fades linearly from input 2,
times its gain, to input 1, times its gain, as K goes from
0 to 1.
If only one input is used (for example, V
1
) and Pin 14 is
grounded, then the gain is proportional to K.
V
V
KA
O
V
1
1
=
Similarly for the inverting case where the noninverting
inputs are grounded and the input voltages V
1
and V
2
drive
the normally grounded ends of R
G1
and R
G2
, we get:
General Equation for the Inverting Amplifier Case
V
KV
RR
R
R
KV
RR
R
R
sR C
R
K
RR
R
R
K
RR
R
R
O
G
G
F
G
G
F
OL
OL
F
F
G
F
F
G
=−
++






+
−
()
++






+
+
++






+
−
()
++






1
11
1
1
2
22
2
2
11
1
1
22
2
2
1
1
1
1
1
1
1
Note that the denominator is the same as the noninverting
case. In low gain applications, R
1
and R
2
are small
compared to the feedback resistors and therefore we can
simplify the equation to:
V
KV
R
KV
R
sR C
R
K
R
K
R
O
GG
OL
OL F F
=−
+
−
()
+
++
−
()
1
1
2
2
12
1
1
1
Again, if we set R
F1
= R
F2
and assume R
OL
>> R
F1
(a 0.1%
error at low frequencies) the above equation simplifies to:
and
VKVA KVA
where A
R
R
A
R
R
OV V
V
F
G
V
F
G
=− + −
()
[]
==
11 22
1
1
1
2
2
2
1
The 4-resistor difference amplifier yields the same result
as the inverting amplifier case, and the common mode
rejection is independent of K.