MCP6271R Microchip Technology Inc., MCP6271R Datasheet - Page 22

• Manufacturer Part Number: MCP6271R
• Description: 170 ?a, 2 Mhz Rail-to-rail Op Amp
• Manufacturer: Microchip Technology Inc.

In Figure 4A and 4B, V
to zero volts. It is used for the 1/β stability analysis. Note that
this source is not the actual application-input source.
Assuming that the open-loop gain of the amplifier is infi nite, the
transfer function of this circuit is equal to:
or
In the equation above, when ω is equal to zero:
As ω approaches infinity:
The transfer function has one zero and one pole. The zero is
located at:
The Bode plot of the 1/β(jω) transfer function of the cir cuit in
Figure 4A is shown in Figure 5.
Figure 5: These are the Bode plots of the inverse of the feedback
factor (1/ β ) for the circuit in Figure 4A. using V
source.
Once again, in Figure 4B the input source that is used for this
analysis is not the same as the input source for the actual
application circuit. However, the amplifier stability is determined
in the same manner. The closed-loop transfer function, using
V
or
Note that the transfer functions of 1/β between Figure 4A and
4B are identical.
20
Analog and Interface Guide – Volume 2
STABILITY
Operational Amplifiers
V
1/β = 1 + (R
(C1 = C
for Figure 4B)
1/β(jω) = (R
R
1/β(jω) = 1+ R
1/β(jω) = 1 + C
f
f
V
1/β = 1 + (R
1/β(jω) = (R
R
Z
P
OUT
OUT
IN
IN
=1 /(2πR
= 1/(2πR
((jω)R
((jω)R
, is equal to:
/V
/V
STABILITY
STABILITY
IN
F
F
C
C
+ C
F
F
IN
F
IN
IN
+ 1)
+ 1)
C
F
F
||R
CM
||C
||C
((jω)R
((jω)R
F
F
)
= 1/β
= 1/β
1
/R
- for Figure 4A and C
F
F
F
(C
)/(R
)/(R
/C
STABILITY
IN
1
F
F
F
+C
C
C
IN
IN
F
F
||C
||C
F
+ 1) + R
+ 1) + R
))
1
IN
is a fictitious voltage source equal
)
)
F
F
((jω)R
((jω)R
1
IN
IN
= C
C
C
1
1
STABILITY
IN
+ 1))/
+ 1))/
+ C
CM
as the input
- + C
DIFF
Determining System Stability
If you know the phase margin, you can determine the stability
of the closed-loop amplifier system. In this analysis, the
Bode stability-analysis technique is commonly used. With this
approach, the magnitude (in dB) and phase response of both the
open-loop response of the amplifier and circuit feedback factor
are included in a Bode plot.
The system closed-loop gain is equal to the lesser (in magnitude)
of the two gains. The phase response of the system is the equal
to the open-loop gain phase shift minus the inverted feedback
factor’s phase shift.
The stability of the system is defined at the frequency where the
open-loop gain of the amplifier intercepts the closed-loop gain
response. At this point, the theoretical phase shift of the system
should be greater than -180 degrees. In practice, the system
phase shift should be smaller than -135 degrees. This technique
is illus trated in Figures 6 through 9. The cases presented in
Figure 6 and 7 represent stable systems. The cases presented in
Figures 8 and 9 represent unstable systems.
In Figure 6, the open-loop gain of the amplifier (A
with a zero dB change in frequency and quickly changes to a
-20 dB/decade slope. At the frequency where the first pole
occurs, the phase shift is -45 degrees. At that frequency, one
decade above the first pole, the phase shift is approximately
-90 degrees. As the gain slope progresses with frequency, a
second pole is introduced, causing the open-loop-gain response
to change -40 dB/decade. Once again, this is accompanied with
a phase change. The third incident that occurs in this response
is where a zero is introduced and the open-loop gain response
returns back to a -20 dB/decade slope.
The 1/β curve in this same graph starts with a zero dB change
with frequency. This curve remains flat with increased frequency
until the very end of the curve, where a pole occurs and the curve
starts to attenuate -20 dB/decade.
Figure 6: This closed-loop system is stable with a phase shift of
-90 degrees at the intercept of the AOL and 1/ β curves.
OL
(jω)) starts