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APPLICATION BULLETIN
OP AMP PERFORMANCE ANALYSIS
By Jerald Graeme (602) 746-7412
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Given the numerous specifications describing op amp per-
formance, the above title suggests an ambitious goal for one
bulletin. Yet, this bulletin reflects the analysis power gained
through knowledge of an op amp circuit鈥檚 feedback factor.
Feedback dictates the performance of an op amp both in
function and in quality. The major specifications of the
amplifier describe an open-loop device awaiting feedback
direction of the end circuit鈥檚 function. Just how well the
amplifier performs the function reflects through the feed-
back interaction with the open-loop error specifications.
Fortunately, most open-loop errors simply reflect to the
circuit output amplified by the reciprocal of the circuit鈥檚
feedback factor.
Amplifier bandwidth limits this simple relationship but the
feedback factor defines this limit as well. Above a certain
frequency, the amplifier lacks sufficient gain to continue
amplification of signal and errors alike. Graphical analysis
defines this frequency limit through plots representing avail-
able amplifier gain and the feedback demand for that gain.
This same analysis indicates frequency stability characteris-
tics for op amp circuits. Just the slopes of the plots indicate
the phase shift in the feedback loop. Thus, the feedback
factor of an op amp circuit is a powerful performance
indicator.
The determination of a circuit鈥檚 feedback factor depends
upon feedback modelling. The basic feedback model of an
op amp applies directly to the noninverting circuit configu-
ration. Using this configuration, this treatment demonstrates
the performance, feedback and stability concepts common to
all op amp configurations. A simple guideline extends feed-
back factor determination to most other op amp circuits. Just
knowing a circuit鈥檚 feedback factor extends the concepts and
conclusions of this bulletin to these other op amp configura-
tions.
FEEDBACK FACTOR DEFINES PERFORMANCE
More than any other parameter, the feedback factor of an op
amp application defines the circuit performance.
1
Feedback
factor sets the gain received by the input-referred errors of
the amplifier. These open-loop errors include offset voltage,
noise and the error signals generated by limitations in open-
loop gain, common-mode rejection and power-supply rejec-
tion. In addition, a circuit鈥檚 feedback factor determines
bandwidth and frequency stability.
For the noninverting op amp configuration, a convenient
relationship between closed-loop gain and feedback factor
simplifies performance analysis. There, the gain of the
application circuit itself sets the amplification of input-
漏
referred errors and determines the circuit bandwidth. Shown
in Figure 1 as a voltage amplifier, this noninverting circuit
produces the familiar, ideal closed-loop gain of A
CLi
= (R
1
+
R
2
)/R
1
. This gain amplifies both the input signal e
i
and the
differential input error e
id
of the op amp. Simply multiplying
e
id
by A
CLi
defines the resulting output error. Later examina-
tion adds frequency dependence to this simple relationship.
e
o
R
1
R
1
+ R
2
R
1
=
尾
e
o
= e
o
/A
CLi
R
2
鈥?/div>
e
id
+
e
i
e
o
= A
CLi
(e
i
鈥?e
id
)
FIGURE 1. Noninverting op amp connections amplify input
signal e
i
and error signal e
id
by a gain of A
CLi
=
1/尾.
The fundamental mechanism relating input and output errors
lies in the feedback factor. Feedback factor is the fraction of
the amplifier output signal fed back to the amplifier input. In
the figure, a feedback voltage divider defines this fraction
through the output to input transfer response
尾e
o
=
e
o
R
1
R
1
+
R
2
This defines
尾
as simply the voltage divider ratio, R
1
/(R
1
+
R
2
). Comparison of this result with A
CLi
shows that A
CLi
=
1/尾 for the noninverting case.
Other op amp circuit configurations produce different A
CLi
but
尾
remains the same. As a general guideline, the feedback
factor of an op amp circuit equals the voltage divider ratio
of the feedback network. This fact extends the results devel-
oped below with the noninverting circuit to almost all other
op amp circuits. Just determining this voltage divider ratio
for a circuit defines the
尾
term common to a broad range of
performance results. In rare cases, complex feedback defies
this simple guideline, requiring detailed feedback model-
ling.
1
AB-045
Printed in U.S.A. January, 1993
1993 Burr-Brown Corporation
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