MCP6271R Microchip Technology Inc., MCP6271R Datasheet - Page 21

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

The units of the y-axis of the phase plot in Figure 2 (bottom
plot) are degrees. You can convert degrees to radians with the
following formula:
Phase in degrees can be translated to phase delay or group delay
(seconds) with the following formula:
The same x-axis frequency scale aligns across both plots.
The phase response of an amplifier in this open-loop
configuration is also predictable. The phase shift or change
from the non-inverting input to the output of the amplifier is zero
degrees at DC. Conversely, the phase shift from the inverting
input terminal to the output is equal to -180 degrees at DC.
At one decade (1/10 f
relationship of non-inverting input to output has already started
to change, ~ -5.7 degrees. At the frequency where the first pole
appears in the open-loop gain curve (f
dropped to -45 degrees. The phase continues to drop for another
decade (10f
degrees. These phase-response changes are repeated for the
second pole, f
What is important to understand are the ramifications of changes
in this phase relationship with respect to the input and output of
the amplifier. One frequency decade past the second pole, the
phase shift of the non-inverting input to output is ~ -180 degrees.
At this same frequency, the phase shift of the inverting input to
output is zero or ~ -360 degrees. With this type of shift, V
actually inverting the sig nal to the output. In other words, the
roles of the two inputs have reversed. If the role of either of the
inputs changes like this, the amplifier will ring as the signal goes
from the input to the output in a closed-loop system. The only
thing stopping this condition from occurring with the stand-alone
amplifier is that the gain drops below 0 dB. If the open-loop gain
of the amplifier drops below 0 dB in a closed-loop system, the
feedback is essentially “turned OFF’.
Stability in Closed-Loop Amplifier Systems
Typically, op amps have a feed back network around them. This
reduces the variability of the open-loop gain response from part
to part. Figure 3 shows a block dia gram of this type of network.
Figure 3: A block diagram of an amplifier circuit, which includes
the amplifier-gain cell, A
Operational Amplifiers
Phase in radians = (Phase in degrees)*2π/360°
Phase delay = - (δphase/δf)/360°
V
IN
1
) where it is 5.7 degrees above its final value of -90
2
B
.
C
1
OL
) before the first pole, f
+
A
–
and the feedback network, B.
OL
β(jω)
(jω)
1
), the phase margin has
D
1
, the phase
A
V
OUT
IN
+ is
In Figure 3, β(jω) represents the feedback factor. Due to the
fact that the open-loop gain of the amplifier (A
large and the feedback factor is relatively small, a fraction of the
output voltage is fed back to the inverted input of the amplifier.
This configuration sends the output back to the inverting
terminal, creating a negative-feedback condition. If β were fed
back to the non-inverting terminal, this small fraction of the
output voltage would be added instead of sub tracted. In this
configuration, there would be positive feedback and the output
would eventually sat urate.
Closed-Loop Transfer Function
If you analyze the loop in Figure 3, you must assume an output
voltage exists. This makes the voltage at A equal to V
The signal passes through the feedback system, β(jω), so
that the voltage at B is equal to β(jω)V
input voltage, at C is added to the voltage at B; C is equal to
(V
cell, A
-β(jω)V
V
system is equal to:
By collecting the terms, the manipulated transfer func tion becomes:
This formula is essentially equal to the closed-loop gain of the
system, or A
This is a very important result. If the open-loop gain (A
the amplifier is allowed to approach infinity, the response of the
feedback factor can easily be evalu ated as: A
This formula allows an easy determination of the fre quency
stability of an amplifier’s closed-loop system.
Calculation of 1/β
The easiest technique to use when calculating 1/β is to place
a source directly on the non-inverting input of the amplifier and
ignore error contributions from the amplifier. You could argue
that this calculation does not give the appropriate circuit closed-
loop-gain equation for the actual signal, and this is true. But, if
you use this calculation, you can determine the level of circuit
stability.
The circuits in Figure 4 show how to calcu late 1/β.
Figure 4: The input signal in circuit a.) at DC is gained by (R
(R
-R
feedback fac tor, 1/ β .
OUT
IN
1
F
/R
+R
(jω) – b(jω)V
. The formula that describes this complete closed-loop
A = D or
V
V
IN
OUT
OUT
OL
2
OUT
)(1+R
. Neither of these gain equations match the DC gain of the
(jω), the voltage at point D is equal to A
(jω) = A
(jω)/V
(jω)). This voltage is equal to the original node, A, or
CL
F
Analog and Interface Guide – Volume 2
/R
(jω).
IN
(B)
(A)
OUT
IN
OL
(jω) = A
). The input signal in circuit b.) has a DC gain of
(jω)(V
(jω)). With the signal passing through the gain
V
IN
IN
OL
R
R
C
C
IN
(jω) -β(jω)V
IN
IN
(jω) /(1 + A
IN
V
IN
R
R
1
1
V
STABILITY
R
V
2
STABILITY
OUT
OL
OUT
+
–
+
–
(jω))
(jω) β (jω))
R
(jω). The voltage, or
R
C
C
F
F
F
F
CL
OL
OL
(jω) = 1/β(jω)
V
V
) is relatively
OUT
OUT
(jω)(V
OUT
OL
IN
(jω)) of
(jω)
(jω).
2
/
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