廬
APPLICATION BULLETIN
By Jerald G. Graeme (602) 746-7412
Mailing Address: PO Box 11400 鈥?Tucson, AZ 85734 鈥?Street Address: 6730 S. Tucson Blvd. 鈥?Tucson, AZ 85706
Tel: (602) 746-1111 鈥?Twx: 910-952-111 鈥?Telex: 066-6491 鈥?FAX (602) 889-1510 鈥?Immediate Product Info: (800) 548-6132
FEEDBACK PLOTS DEFINE OP AMP AC PERFORMANCE
(Originally published in EDN magazine as 鈥淔eedback Plots
Offer Insight into Operational Amplifiers鈥?and 鈥淏ode Plots
Enhance Feedback Analysis of Operational Amplifiers鈥?on
1/19/89 and 2/2/89, respectively.)
Feedback plots simplify the analysis of an op amp鈥檚 closed-
loop AC performance by showing bandwidth and stability
conditions as a function of the op amp鈥檚 gain and phase
response. These plots also provide insight into noise perfor-
mance and the special feedback requirements of circuits
such as integrating converters, photodiode amplifiers, com-
posite amplifiers and active feedback circuits.
Engineers routinely use Bode plots
(1)
to determine the
bandwidth and frequency stability of voltage-gain op amp
circuits. A Bode plot provides a visual representation of an
op amp鈥檚 transfer response and its potential stability. More-
over, such plots define the circuit鈥檚 pole and zero locations
at the intercepts of the response-curve extensions.
The Bode plot of Figure 1, for example, shows the interac-
tion of the magnitude response of the open-loop gain (|A|)
and the reciprocal of the feedback factor (1/尾). The fraction
of the output that feeds back to the input is
尾.
The voltage-
divider action of Figure 1鈥檚 feedback network determines
the value of
尾;
for moderate resistance values,
尾
= R
1
/(R
1
+ R
2
). For this noninverting example, the feed-
back equation, A
CL
= A/(1 + A尾), defines the closed-loop
voltage gain. A尾 is the loop gain, and where it is high:
A
CL
鈮?/div>
1/尾 = (R
1
+ R
2
)/R
1
A尾 represents the amplifier gain available to maintain the
ideal closed-loop response. At the point where the loop gain
no longer matches the feedback demand, the closed-loop
curve deviates from the ideal. The Bode plot graphically
defines this limit by plotting the 1/尾 curve with the gain-
magnitude response curve of the op amp. Because the 1/尾
line represents the feedback demand, closed-loop require-
ments will be satisfied as long as this line is below the
amplifier-gain curve. Where this condition is no longer true,
the actual response drops, following the amplifier鈥檚 open-
loop response downward. The rate of descent for the roll-off
is 鈥?0dB/decade (for most op amps) and is characteristic of
a single-pole response. In Figure 1, the heavier line on the
gain-magnitude plot depicts the resulting closed-loop curve.
INTERCEPT DEFINES BANDWIDTH
For a basic voltage-gain amplifier, the location of the f
p
pole
determines the closed-loop bandwidth. In this case, a single-
pole roll-off determines the point at which the gain magni-
tude goes below 3dB (equivalent to 0.707 of its low-fre-
漏
R
2
鈥?/div>
e
o
R
1
e
o
A
A
+
e
i
e
o
1/尾
A
CL
= e =
1 + 1/A尾
i
尾
=
R
1
R
1
+ R
2
LOG |A|
|A|
3dB BW
|A
CL
|
1/尾
鈥?0dB/DECADE
0
f
p
f
c
LOG f
蠁
A
0.1f
o
0擄
f
o
10f
o
LOG f
45擄
90擄
FIGURE 1. This feedback analysis provides a summary of
loop conditions in the 1/尾 curve and defines the
underlying poles, zeros, and phase shift.
quency level). To find this point relative to the Bode plots,
rewrite the closed-loop gain as
A
CL
= (1/尾)/(1/A尾 + 1)
The bandwidth-defining gain error is a result of the 1/A尾
term in the denominator. Because
尾
is constant for the circuit
in Figure 1, the amplifier gain (A) determines the frequency
dependence of the loop gain. For a typical op amp, the gain-
Printed in U.S.A. June, 1991
1991 Burr-Brown Corporation
AB-028A
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