Datasheet

+
¨
©
§
¨
©
§
-1
2C
IN
P
1,2
=
1
R
1
1
R
2
r
1
R
1
1
R
2
+
2
-
4 A
0
C
IN
R
2
-R
2
/R
1
1 +
s
¨
©
§
¨
©
§
+
s
2
A
0
C
IN
R
2
¨
©
§
¨
©
§
V
OUT
V
IN
(s) =
A
0
R
1
R
1
+ R
2
C
IN
R
1
R
2
V
OUT
+
-
+
-
V
IN
+
-
V
OUT
V
IN
R
2
R
1
A
V
=
-
=
-
C
F
LMV791, LMV792
www.ti.com SNOSAG6F –SEPTEMBER 2005–REVISED MARCH 2013
Figure 50. Isolation of C
L
to Improve Stability
INPUT CAPACITANCE AND FEEDBACK CIRCUIT ELEMENTS
The LMV791 family has a very low input bias current (100 fA) and a low 1/f noise corner frequency (400 Hz),
which makes it ideal for sensor applications. However, to obtain this performance a large CMOS input stage is
used, which adds to the input capacitance of the op-amp, C
IN
. Though this does not affect the DC and low
frequency performance, at higher frequencies the input capacitance interacts with the input and the feedback
impedances to create a pole, which results in lower phase margin and gain peaking. This can be controlled by
being selective in the use of feedback resistors, as well as by using a feedback capacitance, C
F
. For example, in
the inverting amplifier shown in Figure 51, if C
IN
and C
F
are ignored and the open loop gain of the op amp is
considered infinite then the gain of the circuit is −R
2
/R
1
. An op amp, however, usually has a dominant pole, which
causes its gain to drop with frequency. Hence, this gain is only valid for DC and low frequency. To understand
the effect of the input capacitance coupled with the non-ideal gain of the op amp, the circuit needs to be
analyzed in the frequency domain using a Laplace transform.
Figure 51. Inverting Amplifier
For simplicity, the op amp is modelled as an ideal integrator with a unity gain frequency of A
0
. Hence, its transfer
function (or gain) in the frequency domain is A
0
/s. Solving the circuit equations in the frequency domain, ignoring
C
F
for the moment, results in an expression for the gain shown in Equation 1.
(1)
It can be inferred from the denominator of the transfer function that it has two poles, whose expressions can be
obtained by solving for the roots of the denominator and are shown in Equation 2.
(2)
Equation 2 shows that as the values of R
1
and R
2
are increased, the magnitude of the poles, and hence the
bandwidth of the amplifier, is reduced. This theory is verified by using different values of R
1
and R
2
in the circuit
shown in Figure 50 and by comparing their frequency responses. In Figure 52 the frequency responses for three
different values of R
1
and R
2
are shown. When both R
1
and R
2
are 1 kΩ, the response is flattest and widest;
whereas, it narrows and peaks significantly when both their values are changed to 10 kΩ or 30 kΩ. So it is
advisable to use lower values of R
1
and R
2
to obtain a wider and flatter response. Lower resistances also help in
high sensitivity circuits since they add less noise.
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