Datasheet

|A
CL
|(min) = G
min
A = - = 1 -
CL
R
F
R
1
1
F
A = 1 + =
CL
R
F
R
1
1
F
= 1 +
R
F
R
1
1
F
F =
V
A
- V
B
V
OUT
-
+
R
F
V
OUT
R
1
-
+
R
F
V
OUT
R
1
V
IN
V
IN
V
A
V
A
V
B
V
B
LMP7707, LMP7708, LMP7709
www.ti.com SNOSAW5B –JUNE 2007–REVISED MARCH 2013
EXTERNAL COMPENSATION FOR GAINS LOWER THAN G
MIN.
This section explains how decompensated amplifiers can be used in configurations requiring a gain lower than
G
MIN
. In the next sections the concept of the feedback factor is introduced. Subsequently, an explanation is given
how stability can be determined using the frequency response curve of the op amp together with the feedback
factor. Using the circuit theory, it will be explained how decompensated amplifiers can be stabilized at lower
gains.
FEEDBACK THEORY
Stability issues can be analyzed by verifying the loop gain function GF, where G is the open loop gain of the
amplifier and F is the feedback factor of the feedback circuit.
The feedback function (F) of arbitrary electronic circuits, as shown in Figure 52, is defined as the ratio of the
input and output signal of the same circuit.
Figure 52. Op Amp with Resistive Feedback. (a) Non-inverting (b) Inverting
The feedback function for a three-terminal op amp as shown in Figure 52 is the feedback voltage V
A
– V
B
across
the op amp input terminals relative to the op amp output voltage, V
OUT
. That is
(3)
GRAPHICAL EXPLANATION OF STABILITY ANALYSIS
Stability issues can be observed by verifying the closed loop gain function GF. In the frequencies of interest, the
open loop gain (G) of the amplifier is a number larger than 1 and therefore positive in dB. The feedback factor (F)
of the feedback circuit is an attenuation and therefore negative in dB. For calculating the closed loop gain GF in
dB we can add the values of G and F (both in dB).
One practical approach to stabilizing the system, is to assign a value to the feedback factor F such that the
remaining loop gain GF equals one (unity gain) at the frequency of G
MIN
. This realizes a phase margin of 45° or
greater. This results in the following requirement for stability: 1/F > G
MIN
. The inverse feedback factor 1/F is
constant over frequency and should intercept the open loop gain at a value in dB that is greater than or equal to
G
MIN
.
The inverse feedback factor for both configurations shown in Figure 52, is given by:
(4)
The closed loop gain for the non-inverting configuration (a) is:
(5)
The closed loop gain for the inverting configuration (b) is:
(6)
For stable operation the phase margin must be equal to or greater than 45°. The corresponding closed loop gain
G
MIN
, for a non-inverting configuration, is
(7)
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