.THEORY.
I!)
~~~c L
,
APPLICATIONS.
CIRCUITS
FIRST EDITION
(Sixth
Printing)
HANDBOOK
OF
OPERATIONAL
AMPLIFIER
APPLICATIONS
This handboak has been compi led by
the Applications Engineering Section
of
Burr-Brown Research Corporation .
This section wi II welcome the opportunity
of offering its technical assistance in
the application of operational amplifiers.
BURR-BROWN
RESEARCH
Copyright 1963
Printed in U. $. A.
P. 0.
BOX
TUCSON.
CORPORATION
11400
ARI ZONA.
85706
Copyright
1963
by
Burr-Brown
Circuit
typical
diagrams in this handbook are included
operational
constructural
in preparing
Research Corporation
amplifier
information.
this handbook,
applications
Although
reasonable care has been taken
no responsibil ity is assumed for inaccuracies
or consequences of using information
information
to illustrate
and are not intended as
presented.
Furthermore,
does not convey to the purchaser of the amplifiers
such
described
any I icense under the patent rights of Burr-Brown Research Corporation
or others.
ii
PREFACE
The purpose of this handbook is to provide a single source of information
covering
the proper design of circuits
employing
be helpful
the versatile
amplifier.
This manual will
amplifiers,
as well as the new user, in extending
to the experienced
modern operational
user of operational
the range of potential
applica-
tions in which these devices can be used to advantage.
It is assumed that the reader will
but no particular
The operational
certain
have a basic knowledge of electronics,
knowlege of operational
amplifiers
ampl ifier is treated as a circuit
rules of operation.
is needed to use this handbook.
component inherently
The design of the operational
amplifiers
subject to
themselves is
considered only when necessary to describe their less evident properties.
Readers with a working
refer directly
inspection
to the circuit
knowlege of operational
collection.
ceed directly
will want to
Those concerned with evaluation
should refer to the section on testing.
not previously
amplifiers
Readers whose job functions have
brought them in contact with operational
through the handbook until
and
amplifiers
will
want to pro-
the desired degree of familiarity
is
obtained.
Refinements are continuously
operational
amplifiers,
being made in the design and application
yet the basic principles
of application
of
remain the same.
Please do not hesitate to contact Burr-Brown at any time with questions or comments
arising from the use of this handbook.
It is, after all,
-~
~
Thomas
iii
intended for you, the user.
I? L".
R.
Brown,
Jr.,
9.President
--
TABLE OF CONTENTS
Preface
iii
SECTION
1-
Operational
Amplifier
Theory
Introduction
Computat ion-Contro
I-I nstrumentat
The Feedback
Technique
Notation
1
and Terminology
Input
2
2
3
3
3
4
4
5
Terminals
Output
Terminals
Chopper
Power
Stabilized
Amplifier
Notation
Connections
Summary
of Notation
Electrical
Circuit
Circuit
Models
Notation
The Ideal
Operational
Defining
the
A Summing
Circuits
ion
Amplifier
Ideal
Point
Operational
Restraint
and Analyses
The Desirability
Two Important
Voltage
5
6
6
Amplifier
Using
the
Ideal
Operational
Amplifier
6
7
7
8
10
12
12
14
14
15
15
15
17
17
17
19
21
of Feedback
Feedback
Circuits
Follower
Non-lnverting
Inverting
Ampl ifier
Ampl ifier
Intuitive
Analysis
Current
Techniques
Output
Reactive
Elements
Integrator
Differentiator
Voltage
Adder
Scaling
Summer
Combining
Circuit
Functions
Differential
Input
Ampl ifier
Balanced
Ideal-Real
Amplifier
Comparison
iv
~ ~OV-O8v
(v ~~)
:XV'd
S~te-OSt
(t ..~)
:eUO1ld
v
Page
Characteristics of Practical Operational
Open Loop Characteristics
Open Loop Transfer Curve
Ampl ifiers
Open Loop Operation
Output Limiting
Frequency Dependent Properties
Introduction
Open Loop Gain and the Bode Plot
Bode Plot Construction
Closed Loop Gain
Stabil ity
Compensation
Compensation Changes
Bandwidth
Loop Gain
The Significance of Loop Gain
How Much Loop Gain?
Bode Plots and Basic Practical Circuitry
Voltage Follower
Inverter
X1OOO Amplifier
Differentiator
Integrator
Other Important Properties of Operational
Summing Point Restraints
Closed Loop Impedance Levels
Amplifiers
Output Impedance
Input Impedance
Increasing Input Impedance
Differential
Inputs and Common Mode Rejection
The Common Mode Voltage Limit
Offset
Drift
Capacitive
Loading
SECTION II -Circuit
Collection
Voltoge Detectors and Comparators
Buffers and Isolation Amp! ifiers
Voltage and Current References
Integrators
Differentiotors
DC Amplifiers
Differential
Ampl ifiers
Summing and Averaging Amplifiers
AC Amplifiers
Current Output Devices
Oscillators and Mu!tivibrators
Phase Lead and Lag Networks
Additional
Circuits
23
24
24
24
25
26
26
26
26
27
27
28
29
31
32
33
33
33
33
33
33
36
38
38
38
39
40
40
41
42
42
42
43
43
45
45
47
49
50
53
54
57
59
61
63
65
67
69
vi
Page
SECTION 111- How to Test Operotional
Standard Test Circuits
Test Procedures
SECTION
IV-
Selecting
Focus on Limiting
Avoid
Closed
Selection
Specifications
Mechanical
Reactance
Data
Chart
Operational
Open
Loop Confusion
List
Avai lable
APPENDIX
Proper
Specifications
Loop vs.
Check
Assistance
the
Amplifiers
from
Burr-Brown
Amplifier
74
75
77
80
80
81
81
82
83
83
85
87
SECTION I
OPERATIONAL
AMPLIFIER
THEORY
I NTRODUCTION
The operotional
Its applications
conditioning,
tation,
amplifier
is an extremely
span the broad electronic
characterized
-Control
Originally,
utilizing
device.
requirements for signal
analog compu-
operational
amplifiers
are
and precision.
-Instrumentation
the term, "Operational
ing field to describe amplifiers
of negative
would produce a circuit
only on the feedback
used.
operational
circuits
Amplifier,"
was used in the comput-
that performed various mathematical
It was found that the application
amplifier
and versatile
analog instrumentation,
Circuits
by the analog assets of simplicity
Computation
amplifier
industry filling
special transfer functions,
and special systems design.
efficient
operations.
feedback around a high gain DC
with a precise gain characteristic
By the proper selection
that depended
of feedback components,
could be used to add, subtract,
average,
integrate,
and differentiate.
As practical
operational
ampl ifier techniques became more widely
known,
it was apparent that these feedback techniques could be useful in many control and
instrumentation
applications.
Today, the general use of operational
been extended to include such applications
Comparators,
Oscillators,
Servo Valve Drivers,
AC to DC Converters,
What the operational
and ingenuity
the user will
of the user.
as DC Amplifiers,
Deflection
Yoke Drivers,
Multivibrators,
has
AC Amplifiers,
Low Distortion
and a host of others.
ampl ifier can do is I imited only by the imagination
With a good working
be able to exploit
amplifiers
more fully
knowledge of their characteristics,
the useful properties of operational
ampl ifiers.
The Feedback
Technique
The precision
of the use of negative
and flexibility
feedback.
of the operational
Generally
1
speaking,
amplifier
amplifiers
is a direct
employing
resul
2
Ro
RJ
feedback will
characteristics
EinputT-
O
'>-0
r--v
~E
With
have superiar aperating
at
enough
a
sacrifice
of
feedback,
the
gain.
closed
loop
output
amplifier
E t t
ou pu
=E input
F'
O
R
I
.
O
1
Ig.
R
I
.peratlona
amp
characteristics
become
a func-
-=-
tion of the feedback element~. In the
typical feedback circuit, Fig. I, the
I . f '
I
ler
feedback
with feedback.
elements
are
two
resistors.
The
precisian of the "closed loop" gain is set
by the ratio of the two resistors and is
practically
independent
of the "open loop" amplifier.
almost any degree of precision
AND
amplifier
Since there is no real standardization,
cuits may be discussed.
(shown in Fig. 2) will
Only input
and output terminals
TERMINOLOGY
symbols are presently employed in industry.
symbology must be agreed upon before cir-
The symbols employed by Burr-Brown Research Corporation
be used here.
a)
b)
~I
~
A
are commonly shown.
In Fig. 2, there are
to
can be achieved wit~ ease.
NOTATION
Various operational
Thus, amplification
c)
A
:4
2
d)
:&:
A
2
e)
4
5
f)
either one or two input
and output terminals
?I
G>
A
A
o-t"-v
~
'""'
depending on the
amplifier
type.
The
number appearing at
Fig.2.
Burr-Brown standard symbols: a) single ended, b)
differential
input, c) differential
output, d) chopper stabilized, e) symbol without terminals shown, f) special purpose
each terminal
is the
amplifier.
identification
used on Burr-Brown's
popular encapsulated
units and is used here
for convenience
in specifying
of each terminal
connection.
the significance
Input Terminals
In Fig. 2a, 2b, 2c, and 2d, pin (1) is the
"inverting
Fig. 3.
Encapsulated Modules
input"
or "summing point,"
meaning a
positive voltage
at (I) produces a negative
voltage
When only one input or output
at (4).
3
terminal
exists, its voltage
the familiar
is measured with respect to ground,
ground symbol, .:;:. .This
is a popular ambiguity
is indicated
not to explain
often denoted by
by the term, "single ended."
if a circuit,
earth,
It
or chassis ground is meant
by this, so the use of a common line is preferred with the ground symbol used to
indicate
which line is the common.
When there is a pin (2), such as in
may be measured with respect to pin (2).
difference
In use, such on amplifier
between the voltages at pins (I) and (2), i.e.,
In many circuits,
pin (2) is connected
the high gain of operational
amplifiers,
at pin (I) and pin (I) is virtually
analysis,
Fig. 2b and 2c, the voltage
Output
Terminals
exists,
its voltage
The relation
"virtual
Chopper Stabilized
Amplifier
If pin (3)
to the voltage at
When pins (3) and (4) are used as
ground reference,
they are known as "differential
outputs."
Notation
ampl ifier .The
the extra attached symbol.
ground."
(2), and (4) was stated above.
Fig. 2d is a "chopper stabilized"
performance operational
Due to
then appears
For purposes of circuit
equal and opposite in polarity
pin (4), each measured with respect to ground.
the output terminals without
input."
to ground or may not exist.
at ground potential.
between pins (I),
is approximately
responds to the
a "differential
only a very small input voltage
it can be assumed to be ground--a
at pin (I )
amplifier
which is a more stable,
extra circuitry
high
in these units is denoted by
Both the input and output of this type are single ended,
or referred to ground .
To summarize this information,
amplifier
symbol.
Fig. 2e represents the basic operational
Complete symbols will
one or two output terminals,
with perhaps a chopper stabilizer
Fig. 2f is not a true operational
ampl ifier with internal
include one or two input terminals and
amplifier.
feedback permanently
added.
It represents a "committed"
connected .
Power Connections
Power is suppl ied to each of these units at
connections
is implied
as shown in Fig. 4.
in all operational
Such a connection
amplifier
circuits.
The
dual supply presents the same absolute value of voltage to ground from either side, while
the center
Fig.4.
supply
Power
connections.
4
connection
ultimately
defines the common line and ground potential.
tions to this are AC amplifier
is accomplished
by creating
circuits
The excep-
which may use a single power supply.
a floating
AC ground with DC blocking
This
capacitors.
Summary af Notation
~
If it is understood that pin (2)
and/or
pin (3) may not be present,
~
+
~
Fig.
"direction"
-,
The arrows denote the
of the polarity
e-T
at each
terminal.
Electrical
4
+
5 is a concise summary of the notation
introduced.
A
Circuit
Fig.5.
Summary
notation
introduced.
of
Models
The simplified
shown in Fig. 6 and 7.
models of the differential
As indicated
input operational
in Fig. 6, the operational
amplifiers
amplifier
are
can be
represented by an ideal voltage source whose value depends on the input voltage
appearing across pins (1) and (2) plus the effects of finite
ances.
The value,
operational
input and output imped-
A, is known as the open loop (without
feedback) gain of the
amplifier.
The simplified
-@
(!)+
model
EO=-A
~~~i
~@-
E.
I
£
Fig. 6.
Circuit
model of the operationol
amplifier.
-l:out
-@
ential
output
(Fig.
rate
approximation
only
under
conditions
lin
~~~
special
of feed-
back
(see page
Fig.
6 represents
when
output
single
device,
simply
Fig.7.
Circuit
output
operational
model
of the differential
ampl ifier
.
the
type
it is used as a
ended
output
@-
~
21).
of the differ-
ential
Eo ;-2AEI
type
7) is an accu-
model
~
~<D--
of the differ-
ignored.
pin
being
(3)
5
Circuit
Notation
A circuit
amplifier
circuits
which will
become very familiar
as we progress into practical
and the notation we will use are shown in Fig. 8.
Resistors RI and
R are replaced by complex impedances Z , and Z in some appl ications of this
o
o
circuit.
THE
IDEAL
OPERATIONAL
In order to introduce
model of the operotionol
gain expressions, etc.,
basis, it will
omplifier
and finally
omplifier
to simplify
for the circuits
be convenient
in later sections,
operotionol
AMPLIFIER
circuitry,
we will
the mothemotics
presented.
use on ideol
involved
in deriving
With this understanding
as a
to describe the properties of the real devices themselves
to investigate
circuits
utilizing
practical
operational
amplifiers.
To begin
the presentation
of operational
amplifier
circuitry,
necessary first of all to define the properties of a mythical
ampl ifier .The
model of an ideal operational
<D+
Ej
@-
ampl ifier
"perfect"
then,
operational
is shown in Fig. 9.
~
Eo=-AEj
2
=
rin =00
rout=O
A=OO
Eo=O When Ej=O
Fig.9.
it is
Equivalent circuit of the ideal operational amplifier.
6
Defining
~
the Ideal Operational
-The
better.
primary function
Amplifier
of an ampl ifier is to ampl ify , so the more gain the
It can always be reduced with external
circuitry
so we assume gain to be
infinite.
Input Impedance -Input
impedance is assumed to be infinite.
source won't be affected
by power being drawn by the ideal operational
Output
output impedance of the ideal operational
Impedance -The
assumed to be zero.
This is so the driving
amplifier.
amplifier
is
It then can supply as much current as necessary to the load
being driven.
Response Time -The
output must occur at the same time as the input so the response
time is assumed to be zero.
input).
Frequency response will
simply a rapidly varying
~
Phase shift will
-The
amplifier
be 1800 (input pin (I) is the inverting
be flat and bandwidth
infinite
because AC will
be
DC level to the ideal ampl ifier .
output will
be zero when a zero signal appears between the
two inputs, pins (1) and (2).
A Summing Point Restraint
An important by-product
amplifier
fier.
of these properties of the ideal operational
is that the summing point,
This property
will
is to become an important
for it gives us an inherent
Later on, it will
pin (I),
conduct no current to the ampli-
tool for circuit
restraint on our circuit--a
analysis and design,
place to begin analysis.
also be shown that pins (1) and (2) must remain at the same voltage,
giving us a second powerful
tool for analysis as we progress into the circuits
of the
next section.
CIRCUITS
IDEAL
A description
last section,
AND
ANALYSES
OPERATIONAL
of the ideal operational
and the introduction
amplifier
of complete circuits
ideal model may seem a bit remote from reality--with
etc.,--it
derived
should be realized
in this section ~
THE
model was presented in the
may now begin.
infinite
gain,
Though the
bandwidth,
that the closed loop gain relations which will
directly
tenths of a percent in most cases.
example (page21).
USING
AMPLIFIER
applicable
We will
to real circuits--to
within
be
a few
show this later with a convincing
7
Rs
~
ES
~
I
A
:4;
f'
.I
source!
I
Load
The Desirability
10.
Open Loop Operation
of Feedback
Consider the open loop amplifier
used in the circuit
that no current flows from the source into the input,
restraint derived in the previous section--hence,
and E appears across the amplifier
s
E takes
s
RL
i.
,.J
Fig.
r+
I
on any non-zero
value,
input.
.the output
of Fig. 10.
pin (l),--the
summing point
there is no voltage
When E is zero,
s
voltage
Note
drop across R ,
s
If
the output is zero.
increases
to saturation,
and the
ampl ifier acts as a switch.
The open loop amplifier
a)
RI
may be employed in a limited
Ro
~.
-'.I\J'v---
greatest utility,
El
b)
is obtained
when negative
feedback
is employed.
Eo
Two
Feedback
Circuits
':"
Fig. 11 shows the connections and
the gain equations for two basic feedback
Ro
Important
The application
amplifier
.)-Q
r;;O
Eo =-
g
D"
Ro+ R1
of negative
feedback around the ideal operational
R.
Ig.
however,
Its
.~
circuits.
F"
number of applica-
tions such as voltage comparis0n.
E2.
results in another important
summing point restraint:
The voltage
Eo
appearing between the differential
:2
=
fier inputs, pins (1) and (2), approaches
"
zero when the feedback loop IS closed.
R1
II
B
.aslc
a) Inverting.
.
A
I "f "
mpller
(
b)Non-inverting.
"
"
Ircults:
(onsidereitherofthetwocircuits
shown
in Fig.
11.
Ifasmallvoltage,
ampl i-
8
measured at pin (1) with respect to pin (2), is assumed to exist,
put voltage
at pin (4) will
(with infinite
be of opposite polarity
output available)
infinitesimally
small.
output voltage will
until the voltage
When the amplifier
the amplifier
out-
and can always increase in value
between pins (1) and (2) becomes
output is fed back to input pin (I),
the
always take on the value required to drive the signal between
pins (1) and (2) toward zero.
The two summing point restraints are so important
that they are repeated
here:
I.
No
current
flows
into
either
input
terminal
of the ideal
operational
ampl ifier .
2.
When negative
ampl ifier , the differential
These two statements will
feedback
is appl ied around the ideal aperational
input vol tage approaches zero.
be used repeatedly
in the analysis of the feedback circuits
to be presented in the rest of this section.
Voltage Follower
The circuit
how the addition
in Fig. 12 demonstrates
of a simple feedback
to the open loop amplifier
{~'I-Q
loop
~~
converts it from a
Eo
O
..-~2
EO=Ez
':-
device of I imited usefulness to one with many
practical
Fig.
appl ications.
Analyzing
this circuit,
12.
Voltoge
follower.
we see that the voltage at pin (2) is E2' the volt-
age at pin (I) approaches the voltage at pin (2), and pin (4) is at the same voltage
as pin (I).
Hence,
Eo = E2' and our analysis is complete.
analysis is evidence of the power and utility
derived and have at our disposal.
The simplicity
of our
of the summing point restraints we
Our result also may be verified
by mathematical
analysis very simply (see page 9).
Since no current flows at pin (2), the
Ro
input impedance of the voltage
follower
is
t}--l'
infinite.
~
E2
Eo
O
2
The output impedance is just that of
the ideal operational
zero.
the feedback
Fig.
added
13.
ta
Feedback
the
voltage
resistar
follower.
amplifier
itself,
i.e.
Note also that no current flows through
loop, so any arbitrary
(but finite)
resistance may be placed in the feedback
without
loop
changing the properties of the ideal
9
THE
VOLTAGE
FOLLOWER
Ej \ ~.,I-Q
~
Eo
EC
Let the voltage
By Kirchoff's
at pin
voltoge
~
(I)
with
respect
to pin
I
by
I
low:
E2 + E. = E
But
(2) be E
O
definition:
E =-AE.;
o
I
where A is the gain of the
operational
amplifier.
Then:
-E
E .=
I
--.?.
A
And substituting:
E
E2-i=E
0
E
Letting A go to infinity , i approaches zero, and:
E =E
o
2
10
circuit,
shown
would
in Fig.
appear
across
13.
No voltage
the feedback
and the same mathematical
Ro
'vV\,-.,
element
analysis
R"
would
hold.
Unity
gain
circuits
electrical
buffers
vices
from
one another
sired
interaction.
are used as
to isolate
circuits
power
amplifier,
this
a heavy
loop
gain)
is unity
loop
(open
loop
will
allow
of the voltage
.The
gain)
a source
gain
follower
of the
is infinity,
Such a severe
R1
-'V\I\,
with
sacrifice
with
ideal
Thus,
)-0
gain
Eo
-:::-
voltage
follower.
Often
it is drawn
voltage
follower
is simply
a special
Since
no current
flows
The same voltage
From the voltage
RI
Eo'
I
while
give
without
any
f
onalysis
as in Fig.
next
inverting
15 which
makes
pin
(I),
Ro and RI form
at pins
(I)
it evident
that
voltage
and (2).
El = E2i
,
-@,
Eo
-<D
.E
\
;',
pin
of the nonis infinite
(2) .Output
since
analyzed
16.
for
to the
formula:
R1
circuit
loop
through
14 was chosen
a simple
o .
impedance
'
.
circuits
the
amplifier.
RI + R
into
I
closed
of its relation
case of the non-inverting
Fig.
flows
'
control
in Fig.
R
amplifier
not necessary
h
d
t e I ea
maintaining
because
"E:2=RI
Input
by adding
(finite)
0,
o
a feedback
Amplifier
o
E
(closed
for control
e rest o
The circuit
must appear
and
will
closed
to unity--is
Th
Non-lnverting
into
division
gain
infinity
desired
loop
So that
no current
to
feedback.
Non-inverting
amplifier
to ~how similarity
to the
follower.
El =R+R
amplifier
capabilities
ampl ifier
traded
,
,
,
In most circuits.
Q--~.
E2
16).
low current
operational
we have
to be studied
Fig.15.
redrawn
voltage
Non-inverting
the feedback
of gain--from
Ro
.v'V\r-
0:!:-
(Fig.
14.
following
load.
The gain
feedback.
circuit
Eo
undeFig.
drive
;)-Q
--
or de-
and prevent
As a voltage
(
>-'
~2
Non-inverting
as
a
voltage
amplifier
divider.
divider
11
Let the vol tage
gain
at pin
of the operational
The voltage
must equal
at pin
(I)
with
respect
amplifier
(1) is then
the current
to pin
be A (ideally,
E2+ Ei and,
(2) be E. and the
I
A = 00).
since
the current
inRI
in R :
o
E. + E2
E
I
-(E.
o
I
+ E2 )
but:
E
= -AE.
o
I
-E
E
=
o
iA
Letting
A go to infinity
, E. approaches
I
zero
and the first
becomes:
E2 -Eo
-E2
Rj-~
Solving:
E2 (Ro+ RI) = EoRI
E
o
"!2=~
R
0
+ R
,
equation
12
impedance is zero since output voltage
Closed loop gain is ~,
Such circuits
inverting
is ideally
independent
of output current .
hence can be any desired value above unity.
are widely
used in control
and instrumentation
where non-
gain is required .
INVERTING
The inverting
variations
AMPLIFIER
ampl ifier appears in Fig. 17.
folTn the bulk of commonly used operational
This circuit
amplifier
and its many
circuitry.
Single
ended input and output versions were first used, and they became the basis of analog
computation.
amplifier
Today's modem differential
input ampl ifier is used as an inverting
by grounding pin (2) and applying
the input signal to the inverting
input
telTninal.
Since the amplifier
draws no
input current and the input voltage
approaches zero when the feedback
loop
is closed (the two summing point restraints),
we may write
El + R
Eo = 0.
R
I
o
Hence
E
° -O
e;--"R-:
R
.
Fig.
Input impedance to this circuit
Pin (I) is at ground potential
impedance.
Output
gain of this circuit
Intuitive
17.
is not infinite
so the driving
Inverting
as in the two previous circuits.
source effectively
"sees" RI as the input
impedance is zero as in the two previous circuits.
Closed loop
is-?
.
I
Analysis Techniques
The popularity
of the inverting
control and instrumentation
applications,
omplifier
has been mentioned already.
its practical
ments of the associated circuitry.
Its utility
devices which are commonly used to simplify
If we draw the summing point,
amplifier
In
value lies in the eose with
which desired input impedance and gain values can be tailored
inverting
amplifier.
is reflected
to fit the require-
in the variety
of intuitive
its analysis.
pin (I) and output terminal,
pin (4), of the
as in Fig. IBa, the dotted line serves os a reminder that pin (I)
13
THE INVERTING AMPLIFIER
Let the voltage
amplifier
at pin
(I)
be E. and the open
J
gain be A (ideally,
A = 00
loop
).
Since equal currents flow in Ro and RI:
E
l
-E.
E
I
-E.
O
~+-y-=O
I
I
o
But by definition:
E
=
-AE.
o
Ei =
Letting
A go to infinity,
I
-~
E. approaches
I
El
zero
Eo
Rj"+~=O
or:
E
o
~=-~
R
o
and:
operational
]4
is at ground
potential
to ground.
Pin (4) can supply
current,
and analysis
Anothersuch
using
Current
pin
becomes
uses the anolog
(1) as the fulcrum
R,
~
El
rote.
of a lever
suppylng
we have
wide
Th'
evlce.
placing
19
considered
:t
°
voltage
,
pin
-=-
l '
h
Fig.
d
b
Q-'VI/'.
J
1
RL
"N\t-
loop as in
into
I,
pin
of RL.
~
~'-
ampl ifier
Intuitive
of
circuits
devices
based
for
on
the
,
I 'f '
Inverting amp I lero a)A current
device.
b) A voltage "Lever"
y
(1) ,
d
.
IS groun
potentia
18.
analysis
,
device,
the current
0
Eo
18b).
Islsaccomplse
RI
El
I
b)
as a current
.
the load in the feedback
SO
.Ince
I
I
ampl ifier , but
application
'
d
I
O
which
(Fig.
Ro
El
of the inverting
finds
I .
Ig.
ony needed
the vol tage relations
So far,
F'
a)
no current
Output
as the output
it also
quickly
device
to show as vectors
exist
but conducts
through
(1),
El
RI is Rj' .No
so IL =-i1
which
In simi lar configurations,
can serve
or deflection
as a I inear
coi I driver.
Input
current
flows
is independent
the
meter
inverting
ampl ifier
impedance
is RI
as before.
El
Reactive
Elements
IL=-~
Though only resistances have been used
Fig. 19.
Inverting
amplifier
as a. linear current output
device.
in the input and feedback
loop of the amplifiers
presented so far, the general form of the inverting amplifier
are complex impedances in general.
o
The gain relation may be verified in the
is shown in Fig. 20, where Zl and
Z
0--12!
~
same manner as for the resistive case by
summing currents using complex notation.
El
.--0
.~.
There is an area of control appl ication utilizing
this general form of the
O
~
inverting
ampl ifier .Many
=
-io
times it is necEl
i:,
essary to construct a network with some
specifically
designated
transfer
function.
Eo
O
Fig. 20.
Genera I f orm of
the inverting
amplifier.
f
15
By reducing
ratio
this transfer
function
of two polynomials,
consulted
for suitable
passive
be used in the inverting
Other
are found
ator
integrator
which
may be
networks
to
amplifier.
uses of reactive
in the
circuits
to the
a table
elements
and differenti-
follow.
Integrator
If a capacitor
is used as the feedback element in the inverting
Fig. 21, the result is an integrator.
An intuitive
be obtained from the statement under the section,
through the feedback
loop charges the capacitor
from pin (4) to ground.
This is a voltage
amplifier,
grasp of the integrator
"Current
action may
Output ," that current
and is stored there as a voltage
input current integrator.
Differentiator
Using a capacitor
CI
~
as the input element to the inverting
Ro
(
amplifier,
yields a differentiator
-Nv-
circuit .
Consideration
Fig. 23 will
~,~
~
entiator
Eo
of the device in
give a feeling
circuit.
Fig. 22,
for the differ-
Since pin (I) is at
ground potential:
-
'c = CI~del ' and Ic -IR = 0,
so that
Fig.
22.
Differentiator
Circuit
dEl
C,dt+R
Eo
=
O
o
It should
all
the circuits
be mentioned
presented
the differentiator
is the one which
least
with
successfully
that
of
E
in this section,
real
will
=
C dEl
-R
I ~
o
o
at
operate
components.
The
CI
capacitive
to random
discussed
Voltoge
input
noise
later
makes
it particularly
and special
for remedying
susceptible
techniques
this
effect
will
be
.
o-I~
E, - I
Ro
I
-I
c
O
I
Eo
R
:to
Adder
Fig.23.
In a greot
many
practical
applications,
ture
An intuitive
of the differentiator
pic.
.
16
THE INTEGRATOR AND THE DIFFERENTIATOR
Assume
the validity
Inverting
Amplifier:
of the
ideal
gain
expression
for the generalized
-z
E
=~
o
The operational
E
Zl
I
form of capacitive
Z
C
--Cp
impedance is:
I
where the symbol, p, is the operator,
compl ex frequency,
j21f f .
For the integrator;
Zo
1
= -Cp'
i,
or for AC analysis is the
Zl = RI
-z
-E
Eo = -z--o El = Rc- I
I
loP
eo = ~-Zo
el
= -Roclpel
T -"RC1
I o
) Eldt
= -RoCI-at"del
17
the input to the inverting
amplifier
more than one voltage.
of multiple
is
The simplestform
input is shown in Fig. 24.
Current in the feedback
loop is the alge-
braic sum of the current due to each input.
Each source,
El' E2' etc. , contributes
the total current, and no interaction
between them.
to
occurs
All inputs "see" RI as the
input impedance,
while gain is ~
Direct voltage addition
.
may be obtained
Fig.24.
with Ro = RI.
Scaling
Valtage
allows
tion
E3~
R2
E2.~
Ro
R1
~
E,~
scaling
(Fig.
O
1- --2
(EI E
..,g+-+..
E3
EO=-RO
R;+R2
input
"sees"
25.
Scaling
in fact,
to the reader include:
summer
a variable
in the summing amplifier;
Its operation
Functions
The basic
inverting
is very
that
inverting
ond non-inverting
amplifier,
Each
resistor
amplifier
flexible--so
it would
flexible,
be difficult
its usefulness.
Additional
to overappli-
of the
for RI or Ro or
E:§: :J
RI
Ro
A
2
RI
.,}-Q
Ro
Eo
.:J:,
Ro
can be appreciated
it a combination
is obvi-
circuit.
input
Circuit
~
'-"' -1El =
Input Amplifier
best by considering
addi-
resistance.
Fig. 26 shows a circuit utilizing
both inputs to the differential
operational
amplifier.
above
gain ampl ifier using a potentiometer
and many others.
Differential
of adder
before
ca t .Ions w h .ICh a Irea d y may h ave occurre d
circuit.
both; a summing integratorbyusingafeedback capacitor
The adder
case of this
configuration
=
R3
form
input
its respective
input
Combining
estimate
Fig.
25).
a special
Eo
general
of each
ously
as the
-f)-Q
circuit.
Summer
A more
,
,
R3
adding
EO=~
Fig.26.
fier
circuit
(E2-EI)
Differential
.
input
ampli-
18
THE VOLTAGE SUMMER
-:!:-
Assume
the
ideal
summing
point
1 .pin
(I)
2.
The current,
I,
0
restraints:
is at ground
potential
-10+11+12+13+...=0.
is given
by:
-Eo
=-=-+-+-+
Ro
El
E2
E3
RI
R2
R3
So that:
E
o
Thus, each input,
.n
summlnq.
=
-R
o
El
( -+
RI
En' is multiplied
E2
-+
R2
E3
-+
R3
by a factor,
...)
-R
r,
before
19
where the input voltage
divider
is tapped from the
Ro
"IVY-
E2.o-
formed by the lower Ro and RI (Fig.
RI
1
RI;
27).
Hence, the output due to E2 is
R+R
E =~(~)
o
R1
With
R
=...5!.. E
R1+ R~
RI
2
E2 grounded,
the circuit
inverting
ampl ifier
through
a resistance
with
an
(2) grounded
Fig.
conducts
input
no
27.
Analyzing
amplifier
inverting
current)
.Hence,
the output
El
so the total
-R
Eo = ~
Eo
Rn'
is simply
pin
(which
.1-0
!:::G>--'
ER
the differential
circuit
ampl ifier
as a non-
.
due to El is
output
is
E
R
o
= -(E
o
RI
-E
I
The input pins (I) and (2) reside at the voltage
which moy have a detrimentol
E R
~I
level
effect on a real operational
section on common mode voltage
)
2
however,
ampl ifier .(See
the
limit.)
Since
the action
-@
of
the voltage
a)
~
I
~
divider
<Dd~lly
Eo=
El
-2AEj
R
@-
rin
=00
~
formed
by the bottom
and
R
I
is
o
-
0
independent
z;out-
-@
A = 00
of the remainder of the
b)
circuit,
Ro
R1
El
~
E2
cj
D-I\N\i
common
independent
(1)-=-
voltage
to pins
of El"
"sees"
Ro + RI'
itself"
Output
(1) and (2) is
The source
the voltage
impedance
the
of E2
divider
is zero,
as
.NI.rRI
Ro
before"
Ro
Eo=R
I
(E2-EI)
Fig. 28. The differential output operational ampl ifier .a)
Ideal equivalent
circuit.
b) Balanced output amplifier.
Balanced
Amplifier
The differential
of operational
ampl ifier
output
type
is redrawn
20
THE DIFFERENTIALINPUT AMPLIFIER
Assume the ideal input restraints:
Solving
I.
pins (I) and (2) reside at the
2.
la=I11
common mode voltage,
Efo
12=13
for Eo:
Eo
Due to current
= Ef ( I + ~
.!:2.. E1
R] .
in the bottom
-R3
Ef -R2
Substituting:
Eo =
(
leg,
E
+ R3
R3
R2 and
R3 act as a simple
voltage
divider:
2
)(I
R2 + R3
Rl
Ro
+ -E2
RI
)
--El Ro
RI
Or:
{Ground reference point does not motter.
Input moy be "floating"
if desired.)
21
with
its ideal
!
-@)
<D-equivalent
280.
in Fig.
Any
~
of the
previoussingle
ended
output
moy
circuits
Eo
~
.
d 'ff
use t e I erentla
~
.2
I
@-
I
h
Ej
Fig. 29.
output type since the relation
Equivalent
circuit
between pins (I),
of a real operational
(2), and (4) is fixed.
the input terminals may even be reversed by applying
(2) instead of pins (4) and (I).
ignored.
(A finite)
-=-
ampl ifier .
The roles of
feedback between pins (3) and
In either case, the unused output terminal
may be
A single feedback path only determines the voltage of the output terminal
from which the feedback is taken.
To form a differential
or balanced output amplifier,
take feedback from both output terminals as in Fig. 28b.
form of the inverting
ideally
amplifier
output amplifier
gain is ~
servo motors, push-pull
amplifier
Ideal-Real
Throughout
ampl ifier
progressing
characteristics,
been
.ou
either signal input,
stages, and symmetrical
Connecting
%1= R
ro
the
into
ideal ized
the next
are
indeed
circuit
valid
of a real
it as in Fig.
real
operational
.--0
Eo
-=-
Fig. 30. Amplifier circuit using
a real aperational ampl ifier .
that
amplifier
gain,
impedance
real
used
operational
the gain
expressions
case.
a X10 amplifier
of finite
&./1/1,,--
by example
in the
30 gives
= IOR
ampl ifi er has been
concerning
input
are taken
characteristics
El
Such devices as
transmission lines may be
operationol
section
it wi II be demonstrated
derived
The equivalent
o--vv...
t is
output ampl ifier ,
this section,
Before
have
Fig.29.
Z
Camparison
as a model.
which
is a differential
is grounded.
may be used to convert a single ended voltage
into a pair of balanced voltages by grounding
driven by the differential
it is necessary to
This circuit
since neither output terminal
zero, and closed loop (differential)
A differential
then,
might
circuit.
appear
When
impedance,
into
are given
account,
by:
E
Z
1
~=-~(-)
[;1
ZJ
1 + 1.1
as in
the effect
and output
the gain
22
THE DIFFERENTIAL(BALANCED) OUTPUTAMPLIFIER
Assume
the ideal
1.
pins
2.
Current
input
restraints:
(1) and (2) reside
voltage,
Ef
II = 12'
13 = 14
I
in the top leg is give~by-,
/""
El -EfEf
1 =1
Current
at the same common
i n the
-(Eo
R
I
;
i,
bottom
1eg
o
.
~
/ /
by:
Ef -E
=-=~
3
Subtracting
R
is g iv~n
E2 -Ef
I
+
=,
,-,"\-"
E )
p
mode
these
RI
Ro
two
equations:
E -E
I
2-
-E
o
~-R;;
Or:
R
Eo =i
(E2-
El)
(Ground reference is not critical.
Input may be "floating"
Note that the values of Ef and Ep are not uniquely
above equations.
In practice,
if desired. )
determined by the
value determined by the internal
this means that E will reside at some
p
circuitry of the operational amplifier
itself
However,
plus the effects
fixed by the differential
of drift.
E will
o
gain equation above .
remain
accurately
23
z
0+
out
-z
fJ =
where
z
+
z-
o
z
z
o
(I + -+
Zl
out
load
r
0
In
(A -~)
0
This may be expanded
as
E
o
-Z
-=El
and, where fJ«I,
o
(I
,)
to
(I -fJ)
Zl
the open loop parameters take on the following
though conservatively
values which are typical,
estimated,
A
Z.
Zln
out
Solving,
3+
as is usually the case, simplifies
[:1
letting
-fJ
Zl
E
-Z
~ = --3-
Now,
2
-fJ+fJ
=10,000
= 50K
= 100
Zl
Z
ZO
load
=10K
= 100K
= 10K
we get fl = 0.0013 {which justifies our assumption above) and the real
closed loop gain is
E
r o = -10.000
I
+ 0.013 = -9.987
instead of -10 which would be ideally
The gain of this circuit
expected.
is accurate to within
0.13% of the idealized
This entire error may be considered as a "calibration"
cancelled
by a slight adjustment of the feedback
made, the gain accuracy of the circuit
gain of the amplifier
amplifier.
were
Practical
derived
Substituting
variation
from
ideal
Once such an adjustment
operational
feedback
for an ideal
operation
amplifier
circuits
employing
section
using
operational
which
OF PRACTICA
AMPLIFIERS
is a solid
the
high
gain,
DC voltage
it are based on the circuits
amplifier
is negligibly
state,
ideal
operational
will
small
is
less than 0.02% should the
change by 10"!0.
in the preceeding
a real
error and completely
resistor.
would be affected
CHARACTERISTICS
OPERATIONAL
The modern
value.
result
in many
amplifier
which
model.
in some predictable
applications.
This
24
section
with
is intended
to acquaint
the characteristics
so that
they
possible
may be utilized
extent
the
of the real
reader
devices
to the fullest
in practical
circuits.
Open Loop Characteristics
!
In the case of the ideal operational
~
.,.
amplifier,
circuit
operation
dependent entirely
was seen to be
on the feedback used.
is possible to use the real operationol
problems are encountered
amplifier
Random noise from the input circuit
unit become noticeable
Open loop operational
as they do~
due to this effect,
"typical"
of a circuit
it.
make it impossible for a manufacturer
Slight variations
circuits
"open loop" or "closed loop, " and the character
have a relatively
to campletely
can begin.
remote
specify closed loop
before the intelligent
must be qualified
by the information
of the feedback should be specified
loop" information.
Loop Transfer
The open
loop
operational
transfer
amplifier.
relation
loop
input-output
relationship
"well-behaved"
practical
31 .Input-output
Curve
for a rather
fier
Fig.
ampli-
Any statements which are
Open
open
in the
is, in essence, a special case, it is nec-
amplifiers
amplifier
ampli-
hence open loop specifica-
essary to understand both open and closed loop characteristics
to be made about operational
the operational
The sheer numbers of useful operational
Since each closed loop circuit
using operational
at DC).
since they do not as much ~e
fier circuits
for "closed
Modules
and stability
values.
operation.
design of circuitry
Series
due to temperature change
by open loop gain.
ampl ifier specifications
to closed loop operation
operation
/16
and noise generated within
tions are sometimes given conservative
circuit
and
in ampl ifier characteristics
or aging components are all multiplied
connection
/26
open loop, but control
due to the high open loop gain (X J00, 000 typically
fier itself plus any variations
manufactured
:1
It
operational
is shown
ampli-
in Fig.
31.
gain,
A,
The open
loop
measured
by the slope
is
the curve
So it can be seen
of
for the
25
that
the operatianal
ampl ifier
The slope of the amplifying
only
ampl ifys between
quency of the input voltage while
relation
the saturation
values
of E .
o
portion of the transfer curve is dependent on the frethe saturation
voltages remain constant.
This
between input and output holds regardless of the feedback configuration
used as long as the amplifier
The "well
is not in overload.
behaved"
aspect of this operational
transfer curve goes through the origin.
~,
a fault which effectively
plicate
matters further,
In practice,
amplifier
is the fact that its
all operational
amplifiers
shifts the transfer curve from the origin.
this offset value will
wander,
producing ~.
phenomena are of the same order of magnitude as the input voltage
drive the open loop amplifier
of circuit
into saturation
design is to minimize
(a few millivolts)
exhibi
To comBoth of these
necessary to
and a necessary part
their effect .
Open Loop Operation
As an example of open loop operation,
used as an open loop DC amplifier.
occurs at :f:10volts.
~
Hence, for linear operation,
= :f: 67 microvolts.
Output
circuits
output
power
output
specifications
rating
slightly
supply
and voltage
useful for linear operation,
comparison applications.
voltage
available
greater
to a load
full
output
circuit
the rated
unless
the autput
voltage
above
operational
amplifier
rated
voltage
output
may be saturated
Output
value
Though
Output
a voltage
saturation
when
voltages
will
output
the current
anly
voltage
after
speci-
supply
for an indefinite
higher
and a
the nominally
amplifiers
current
slightly
be attempted
low.
give
operational
voltages,
should
is extremely
the saturation
current.
conditions.
current
amplifiers
output
Burr-Brown
lower
exceeding
circuit
the rated
drawing
for
up to the short
short
than
is used.
ative,
and outputs
for operational
plus output
voltage
In addition,
time.
is not generally
Limiting
are commonly
fied
cannot exceed
is also subject to the full effect
using the high open loop gain of the modern operational
in sensitive null detection
Burr-Brown
current
3003/15 might be
any of which may be greater than 67 microvolts .
While the open loop amplifier
there are practical
the inputvoltage
The open loop amplifier
,
of random noise, offset, and drift,
amplifier
the Burr-BrownModel
DC open loop gain is 160,000 and output saturation
period.
current
ratings
full
is
are conserv-
some calculation,
is self-limiting,
will
not occur.
The output
without
damage
for an indefinite
however,
stage
of the
period
of
26
FREQUENCY DEPENDENTPROPERTIES
Introduction
The AC response characteristics
important
considerations
successfully
able variation
affected
in circuit
at audio,
of the operational
design.
ultrasonic,
ampl ifier are very
DC operational
amplifiers
and low radio frequencies
from DC operation.
Circuits
with
will
operate
some predict-
designed to operate at DC are also
by the AC response since random noise and varying
DC levels contain AC
components.
9pen
Loop Gain and the Bode Plot
The frequency
iently
response curve of operational
represented by the Bode plot.
in db (the hybrid but popular "decibel"
circuitry
is conven-
The absolute value of voltage gain is plotted
E
defined by db = 20 109 ~
so that a gain of
10 is 20db, a gain of 100 is 40db, etc.)
frequency scale.
amplifier
versus the orthodox decade logarithmic
The Bode plot of a typical
Model
3003/15.
open loop gain is shown in Fig. 32 along with a convenient
Operational
Amplifier's
linear approximation
to
the actual curve .
Bode
Plot
Construction
The shape
Burr-Brown
loop
of the Bode plot
operational
Bode plot
the particular
amplifiers.
may be approximated
shown
in Fig.
32 is characteristic
It is so characteristic,
rapidly
from
only
in fact,
two
of all
that
standard
any open
bits of information
about
operational
120
amplifier:
.
gain,
1) DC open
an
loop
d 2) h
..100
t e unity gain
crossover frequenc,
loop bandwidth).
(open
Igainl
As an
(db)
example, Model 3003/15 has
DC open loop gain of 110db
and open loop bandwidth
2.0Mc;
80
60
.40
of
both values are
10
given in the specification
sheet.
We can sketch the
Bode plot as indicated
in
loo
lK
Frequency
Fig. 32.
10K
Bode plot of an operational
and its linear approximation.
100K
lM
(cps)
amplifier
27
Fig.
33.
Brown
Fig.33.
Sketching
the Bode plot
from
information
Comparing this sketch with the typical
gain bandwidth
the typical
in Burr-
response of Fig. 32, the constant
product sketch is observed to be a conservative
response.
some points,
given
specifications.
Since the typical
gain falloff
there may be slight peaking at intermediate
peaks do not indicate
a condition
approximation
to
exceeds 6db per octave at
closed loop gains.
Such
of instability.
Closed Loop Gain
When feedback
is used around an operational
ampl ifier , the closed loop
gain of the circuit
is determined by a ratio involving
impedances used.
If the closed loop gain called for by the feedback configuration
is greater than the open loop gain available
particular
frequency,
closed loop gain will
the input and feedback
from the operational
be limited
amplifier
for any
to the open loop gain value.
Thus a plot of the closed loop gain of a X100 (4Odb) amplifier
using the Model
3003/15 would appear as in Fig. 34.
Stabil ity
As indicated
gain than is available
abave,
the closed loop amplifier
from the operatbnal
amplifier
circuit
itself,
cannot supply more
so at high frequencies,
the closed loop Bode plot intersects and follows the open loop gain e:urve.
intersection
The
point between the closed and open loop curves is important because
the angle between the two curves--or,
the curves aren't actually
straight
more precisely,
lines--determines
the "rate of closure" since
whether the closed loop
28
F-Fig.
34.
using
amplifier,
Closed
Model
loop
gain
of a X] 00 (40db)
inverting
ampl ifier
3003/]5,
differentiator,
etc.,
being designed will
be stable.
Principle:
If the
rate of closure between the open and closed loop sections of the Bode plot is
greater than 12db per octave (40db per decade) the system is likely
Bode plots may be varied almost at will
made frequency
to insure stability
response characteristic
to be unstable.
or to provide some tailor-
.
Compensation
The open loop gain of standard Burr-Brown operatipnal
tailored
or "compensated"
/Breakpoint
of RC phase compensation
100
network
,
" '
Roll-off due
effected in
to operational
amplifier withorder that the
out compensation majority of
60
40
roll-off
/
popular
due to
circuits
phase compensation
20
"
utilizing
~
I
I
I
I
I
I
p
10
100
IK
10K
100K
IM
Fig.
35.
tions (Fig. 35).
sation is
80
/
is
combina-
Phase compen-
~
Compensated
amplifiers
with one or more simple resistor and capacitor
The effect
of internol
phase
compensation
operational
amplifiers
will be
~
29
inherently
stable,
even under conditions
internal
compensation,
relative
impunity.
of 100% feedback.
As a consequence of
the user may connect feedback around the amplifier
We must hasten to add, though,
is, in essence, a special case.
that each feedback condition
Superior results may be obtainable
internal
compensation or by adding external
stability
criteria
and the Bode plot will
with
components.
by changing the
A knowledge of the
be adequate in all but the most unorthodox
circuits.
If compensation were not provided,
unstable under normal operating
or change of slope principle.
conditions
certain amplifier
according
circuits
would be
to the above "rate of closure"
The effect of compensation on closed loop stability
can be seen from the Bode plots of Fig. 36, showing several different
amplifiers
utilizing
Compensation
the same operational
phase compensation
operational
amplifiers
simply
capacitor.
These two
components
The purpose
in doing
the amplifier
of broadbanding
this
circuit
is shown
Broadbanding
which
shifts
with and without
closed loop
compensation.
Changes
The internal
band"
amplifiers
may be changed
by replacing
are mounted
is to increase
by changing
in Fig.
physically
the flatness
in many
resistor
for ease of replacement.
of the response
the 3db break
Burr-Brown
and
point
cuIVe
or "broad-
frequency.
The effect
37.
is accomplished
the 3db breakpoint
easily
the compensating
simply
to the desired
by choosing
a compensating
frequency.
The resistor
New
breakpoint
compensation
Open Loop
--
100
-
capacitor
is
of phase
network
,
80
v""'Uncompensoted
'\
\
60
40
6db/oct
(stable )
20
A10.01
0:1
10
100
lK
10K
lOOK
lM
F -Fig. 37.
The effect of broodbanding
by changing the internal
phase compensation.
30
~
Q)
::0
~
.?:0
~
-c
u
0
0".;:
""-0.Q-o
-oC
N
0
Q)
::0
c
:!i!..
~
Q)
""~~
t
o
~
t
,0
..a+"0
0)
--
~
-0
.0
::0
o
"'
C
:s
c
0)
Z:0§
~
°
:::.::8
Q)
::c
C
::f!-
..?.
,
~
~
o
0
c
O
\
.~
>..c
=8.
o E
u 0
.ii u
>..-!:
-~ .~
"
-0
Q)
"'6
~
Q)
Q.
E
o
u
"'
0
-O
u
-
...u
O
O
~
0
~
~
.!d>u
"
Q)
>
~
~
~
0~
u.
Q)~
--0
~-o
o
o
Q;
I;:
""ii
E
o
o
8
ox
o
o
O
00
~
0)
(;:
Qj
t;:
-0:.
E
c
o
o
o
01
'-=
-0..
E
c
"Q.
E
o
O
0
X
X
X
6
"I"
6
.0
T
o
""
I:~
.-.D
E;:g.
Fig. 36.
Composite Bode plots showing stability
provided by proper phase compensation.
31
t
IAI
Fig.
38.
Stability
used at goins
ather
effects
than
occurring
the designed
when
then selected to break with the new capacitor
and tailor
the high frequency
ful in selecting
response.
o broadbonded
amplifier
is
level.
at some frequency
above the 3db point
The reactance chart (page 86) will
The broadbanded ampl ifier may be used for any gain level ~
originally
be help-
component values.
the
designed gain value (by changing feedback components) but it may not
be used for lower gains without
readjusting
the compensation.
Instability
will
result
since the rate of closure may be toa large at low gain values (Fig. 38).
Bandwidth
The open loop bandwidth
explicitly
in the Bode plot.
of the modern operational
amplifier
The plot has only two distinguishing
being the unity gain crossover frequency
is shown
frequencies,
and the second being the 3db point.
of these two can be considered the bandwidth
of the open loop amplifier
one
Either
and used
in open loop specifications.
The unity gain crossover frequency may be from 0.1 to 60Mcps or higher .
An important aspect of bandwidth--besides
amplifier
circuits
practical--is
The loss of high frequency
control signals,
distortion
making high frequency operational
to improve the precision of signal amplification.
components of non-sinusoidal
vol tages such as pulses,
DC steps, or even speech patterns may result in undesirable
and phase shift .
32
The ultimate
purpose of wide bandwidth
at the lower signal frequencies.
operational
amplifier
may be to maintain.high
It may, for example,
with open loop bandwidth
loop gail
be necessary to use an
of 2Mc to provide a loop gain of
IOOdb at 100 cps.
Loop
Gain
As indicated
and closed
in Fig.
loop gain.
gain
and closed
lent
to division.
loop
34,
In actuality,
gain
since
loop gain
the
is the gain
loop gain
subtracting
L oop gain.open
=
on the
00
loop
0
"difference"
between
is the ratio
between
logarithmic
gain
open
scdle
open
loop
is equiva-
gain.
closea lOOp gain
In a practical
circuit,
loop gain is the increase in gain that is observed
when the feedback path is opened, but with all circuit
effects of finite
input and output impedance,
components, will
ing configuration,
feedback resistors.
lead to reduced loop gain.
Loading
feedback
For example,
6db is lost due to the voltage divider
in a unity gain invert-
effect of the input and
Since the 3db point and roll off rate of the frequency
is fixed by the phase compensation
bandwidth.
loads intact.
as well as the external
An inspection
network,
of Fig. 39 will
response
the reduced gain effectively
clarify
lowers the
this effect.
100
80
60
IAI
40
Resulting
20
loss
of bandwidth
F-
Fig. 39. Loss of high frequency
is used (low closed loop gain).
response when heavy feedback
33
The Significance
of Loop Gain
Just as local degeneration
to certain
amplifier
around a transistor can reduce circuit
parameter changes in that transistor,
will
phase shift,
reduce sensitivity
input impedance,
power supply voltage,
and gain accuracy,
basic stability,
sensitivity
feedback around an operational
to open loop parameter changes.
Open loop gain,
and output impedance may vary with temperature,
and time.
Loop gain is the payment made for circuit
stability
and it is a direct measure of the improvement obtained.
however,
The
must be designed into the open loop amplifier.
How Much Loop Gain?
While the amount of loop gain required is a function
selected and the desired performance,
point.
Suppose a 1% gain stability
temperature
l%;oC
range.
The Model
or lOO/0/10°C.
a sample calculation
of the amplifier
will
demonstrate the
is desired using the Model 3003/15 over a :!:100C
3003/15
has open loop gain stability
Thus, the closed loop gain stability
better than the open loop gain stability
available
of .ldb/OC
or
desired is 10 times
and at least 20db of loop gain is
required.
Noise,
are essentially
ond offset will
not be affected
by loop gain.
input functions which,
drift,
like the signal,
will
closed loop gain maintaining
Loop gain will
constant "signal
to noise ratio"
improve closed loop gain stability,
These parameters
be increased by the
independent
phase shift,
of gain.
input impedance,
and output impedance.
BODE PLOTS AND BASIC PRACTICAL CIRCUITRY
Voltage
Follower
The unity
there
gain
gain
is no feedback
line
to the open
follower
impedance
loop
unity
and
its Bode plot
loading,
gain
is shown
the closed
crossover
loop
before
in Fig.
plot
rolling
traces
40.
Since
out the unity
off.
Inverter
A unity gain inverting
ampl ifier is shown in Fig. 4 J .The
decreased by one octave (50"/0) from that of the voltage
division
follower
bandwidth
is
due to the voltage
effect of the input and feedback resistors mentioned above.
X1OOO~mplifier
Fig. 42 shows the Bode plot for either the inverting
amplifiet
with a gain of X1OOO (60db).
Negligible
bandwidth
or non-inverting
is last due to the
34
t
IAI
F-
F=ig.40.
JJO+
J07+-,
JOO- ,, ,
"',"'
80-
Voltage
follower
R
,
, ,
, ,
"
t 60IAI
f>-0
/15 f
,"',
"'
"
4020- ;
1
circuit
I~
l~";';;':~P~
l~:~~~IOSed
gain' loop'
10
100
lK
fo=fl
, ,, ,
", ,
,
10K
100K
, ,
,
'
Voltage
Closed
gain
F-
Fig. 41.
=
inverter
circuit
loop
0
35
a)
999R
R:
0
3003/15
0--
Eo
~2
O
~
Ro+RI
Eo = R;-
El
=IOOOEZ
b>
c)
10
100
IK
10K
160K
IM
F-
d)
t
IAI
Fig.42.
a) and b)60dbamplifier
circuits.
d) Bode plot of 6Odb amplifiers "broadbanded"
c) Bode plot of 60dbamplifiers.
by changing phase compensation.
36
vol tage divider
effect but is sti II very much reduced by the normal roll off of the
open loop curve.
This bandwidth
may be partly restored by broadbanding
as shown
in Fig. 42d.
Differentiator
The Bode plot of the differentiotor
{Fig. 43) is slightly
construct since the Zl value is dependent on frequency.
more trouble to
It is evident that the curve
must intersect the unity gain axis at the frequency where X
= R {conveniently
c
a
For DC, the capacitor represents
found from the reactance chart on page 86).
infinite
impedance,
hence gain is zero.
gain increases, which is approximated
At higher frequencies,
closely by a straight
Since highest gain is encountered
susceptible
to random noise.
drops and the
c
line rising at 6db/octave.
at high frequencies,
Even more important,
however,
X
this circuit
is very
is the fact that the
rate of closure is about 12db/octave,
making the simple differentiator
unstable in operation.
method of reducing nQise and preventing
instability
One practical
is shown in Fig. 44.
operates as an amplifier
quency at which
f =~
inherently
At high frequencies,
with resistive feedback.
.Note
X is negligible and the circuit
c
The transition "point" is the fre-
that a capacitor,
t
AI
Fig. 43.
Differentiator
circuit
Co' in parallel
with Ro'
Fig.44.
Differentiatorwith
"stop."
would have produced the same results with the significant
f=21TR
1
C
frequency given by
.
o o
Both techniques may be combined to give even better noise rejection
45).
With Ro and Co set to break at the same frequency
slope change will
6db/octave
as RI and CI' the total
be twice that of a single RC combination,
hence a roll off of
is introduced .
Fig. 45.
Differentiator
with "double stop."
(Fig.
38
t
IAI
FFig.46.
Integrator
circuit
Integrator
The discussion
{Fig.
46).
Unity
is a negative
above
gain
should
crossover
6db/octove
make
occurs
and gain
the Bode plot
for an integrator
at the frequency
would
ideally
where
go to infinity
XCo
= RI.
simple
to deduce
The slope
at DC .
OTHER IMPORTANT PROPERTIES
OF OPERATIONAL AMPLIFIERS
Summing Point Restraints
In the case of the ideal operational
amplifier,
circuit
analysis was simpli-
fied by the ideal summing point restraints of zero voltage and zero current
summing junction,
pin (I ).
close to this, as will
A typical
Amplifier
Op-
has a
fl=O.IV
o---w'
Ig=
R
IOOR
..vI\I\.
.2na
open loop in-
put impedance of 500K, and
a saturation
comes
Burr-
DC open loop gain of IIOdb
or 300,000,
ampl ifier summing junction
be shown in an example.
Brown Model 3003/15
erational
The real operational
"at" the
~
Eg= .1 rrw-
>c
voltage of more
EO=IOV
than :!:10 volts.
For the circuit
shown i n Fig. 47 to have
a full output of 10 volts,
,~
(,
Fig. 47.
DC summing point conditions.
39
the voltage at pin (I) must be
10
=
O.033mv
Eg
The current flowing
to pin (1) is the voltage
at pin (1) divided
pin (2) which is Z. open loop and available
In
by the impedance to
from the specification
sheet .
0.033 mv
10
= 0-{'7 xon 10nmos of= the
.067
na
Note that these calculations
Ig =
500K
do not depend
the volues
feedback
and input
elements.
In fact,
they don't depend on the nature of the closed loop circuit
so long as the operational
ampl ifier is not operating
Since the. dynamic voltage
junction
of a real operational
are considered zero--as
noted,
however,
amplifier.
voltage
current variations
amplifier
At high frequencies,
at all
condition.
which appear at the summing
in a closed loop circuit
in the ideal case--for
that this effect
in an overload
circuit
are so small,
analysis purposes.
they
It must be
is due to the high open loop gain of the operational
the open loop gain falls off and the summing point
and current increases accordingly
for the same output.
Also,
the static
effects of input voltage and current offset as well as drift must be taken into account.
These will
be discussed more fully
later.
Closed Loop Impedance Levels
Open loop output impedances are given in the specifications
from 3 ohms to 5000 ohms, with the majority
or 200 ohm open loop output impedance.
usually will
vary from 1Kohm to lMegohm,
of operational
this may represent a rather poor approxiHowever,
lent closed loop output impedance is typically
seems a very poor approximation
Practically,
inverting
this is of little
amplifier
the equivalent
as we shall see, the equiva-
less than an ohm.
Open loop input impedances are also specified
Compared to the typical
having a loo
Since the input and feedback resistors
mation of the ideal zero output impedance.
to 5 Megohms.
amplifiers
and range
and run from 0.1 Megohm
feedback impedance levels,
of the ideally
infinite,
this also
open loop input impedance.
importance since the closed loop input impedance of the
is determined
by the input resistor.
input impedance of the non-inverting
thousands of Megohms, closed loop.
Calculations
amplifier
will
show that
may be hundreds or
40
Output
Impedance
Using
3003/15asa
the Model
voltage
follower
ej
IL
-
~out
(I
,)-Q
in the circuit
of Fig.
"0
48,
E2
we can
readily
the effective
output
closed
impedance.
ing this circuit
incremental
l\
IL'
forces
-=
loop
Load-
with
output
an
Fig.48.
the amplifier
this
Voltage
follower.
current,
output,
11 eo =
To maintain
E;--r:CLOUt
determine
11 eo'
eo,
I1IL lout
to increase
by:
.
the voltage
across
pins (1) and (2) must change
by:
11eo
A
Since pin (1) is tied to the output and the input voltage,
Eo must decrease by ~ ei.
The effective
!! E
o
=
output impedance is then seen to be:
!! eo
(-
by the DC gain of 300,000
)
A
{}.IL
Thus, for the Model 3003/15,
E2' is applied to pin (2),
the open loop output impedance of5000ohms
to an effective.
is decreased
017 ohm at the output plus any lead
impedance between the feedback point ond the load.
More general calculations
by the loop gain.
The voltage
equal to the open loop gain.
would show thot the output impedance is reduced
follower
is a limiting
Thus, the Model
case in which the loop goin is
3003/15 will
exhibit
less than one ohm
of closed loop output impedance so long as loop gain is greater than 67db.
Input Impedance
Closed loop input impedance is also increased by loop gain in non-inverting
closed loop applications.
summing junction
In the inverting
is a virtual
or summing closed loop configuration,
ground and the input impedance is almost exactly
value of the summing impedance,
ZI.
the
the
41
In Fig.
Model
49,
3003/15
in the voltage
circuit
with
input
the
isagain
shown
11---
follower
the open
impedance,
indicated.
Z.
In
"Q
ej
I,n
-
loop
,
r
E2
Eo
O
2
For any change
in output
voltage,
the voltage
lCL
6 E ,
o
across
pins
(I )
Fig.49.
and (2) must change
6E
o
divided
Voltage
follower.
by
by the open
loop
gain,
6 Eo
A:
6 E2
6ei=~=~
The change
a current,
of voltage,
61.
In
6 e.,
I
across
,equalto6e.dividedbyZ.
I
-6
61
In
ej
Z.
6
in input
current,
In
, demands
.
this is a limiting
is the chonge in input voltage,
~ E2'
AZ.
= 6E 2 ( ~)= In
AZ.
61:-2
In
In
.
case in which the loop gain is equal to the open
In the more general case, the effective
input impedance is equal to the
open loop input impedance multipl ied by the loop gain.
currents,
Z.
~ I. .
In
6E 2
Again,
impedance,
In
ZCL in'
Z CL .=--:-0In
61.
loop gain.
input
E2
AZ.
In
The closed loop input impedonce,
by the change
loop
--=in
divided
the open
the input impedance of the Model 3003/15
long as loop gain is greater than 40db.
Thus, assuming zero offset
is greater than 50 Megohms as
Current leakage paths associated with the
input stage tend to limit the input impedance to be achieved
in this manner to about
50 Megohms.
Increasing Input Impedance
The input impedance of many operational
by a technique
input voltage
known as "bootstrapping.
(as from the non-inverting
amplifier
" Output voltage
amplifier
circuits
may be increased
of the same polarity
or two inverting
amplifiers
as the
in
tandem) is used to inject a current into the input which is equal to the current drawn
from the driving
source.
When this is done, the source no longer has to supply any
42
current,
vary
and input
with
circuits
impedance
the type
of circuit
at the end of this
Differential
is effectively
used.
infinite.
Examples
Techniques
of bootstrapping
for bootstrapping
will
be found
in the
handbook.
Inputs and Common Mode Rejection
The input to most Burr-Brown Operotional
neither of which is connected
are termed differential
transistor amplifiers.
inputs.
Ideally,
produce no net result,
difference
to ground.
Amplifiers
Each input connection
amplifier
input connections
drives separate,
the same voltage connected
hence the operational
in the two input voltages.
is a poir of leads,
Such a pair of "floating"
balanced
to each input would
would only detect the
The voltage which both inputs experience
is
known as the common mode voltage.
In practice,
the voltages on each input are amplified
to component variations,
rejection"
never perfectly
property of a differential
configuration
balance out to zero.
Limit
within
the operational
the voltages appearing at the two inputs separately.
the input transistor(s).
negligible
Restraints"),
The "common mode
input ampl ifier also depends on the feedback
As stated above, the circuitry
onlya
and, due
of the closed loop application.
The Common Mode Voltoge
saturating
separately
difference
amplifier
responds to
Either input can be overdriven,
Since under normal feedback conditions
there is
in voltage between the two inputs (see "Summing Point
the input saturation
voltage
is known as the common mode voltage
limit and appears in Burr-Brown specifications.
For the inverting
mode inputvoltage
ampl ifier, one input terminal is grounded; hence, the common
is zero.
In the non-inverting
configuration,
however, an equal
voltage appears at both input terminals and the common mode limit must be observed.
Offset
It was mentioned earlier
the operational
amplifier
bias current and voltage
circuit.
that a certain
input voltage
This input voltage
inherently
is necessary to balance
is needed because of a small
required by the operational
:!!!.;..=.:.: When these two bias components are not externally
amplifier,
supplied,
drawn from the input and feedback networks causing an output voltage
In many applications,
ance,
there are built-in
this small error is negligible.
called
they are
error .
For highest perform-
controls on many Burr-Brown operational
amplifiers,
or
43
simple biasing circuits
externally.
(f)
may be used
As an example,
'\N'y
the current
R1
components of input offset may be corrected
by a simple bias current injector
e
!
Ro
--'VV\r--
~
1-',3>-.
as shown
rJ--O
in Fig. 50.
Drift
The bias values
mentioned
will...Fig.50.
vary with temperature,
power
supply
output
error
taken
into
voltage,
Again,
account
time,
producing
or drift.
in critical
-1-=-
above
and
Inverting
.
WI th curren
t
a variable
this
effect
is negligible
in many
method is to readjust the internal
controls mentioned above at intervals
compatible
with the accuracy
may mean twice a day, or before each precision measurement.
Ampl ifiers,
desired.
This
Environmental
caused by external
are made
Thus, variations
in base
changes, i.e.
temperature,
tend to cause both input transistors to vary in the same direction.
Since the
base currents must flaw to ground through the external
can be minimized
be
or external
input connections
to the bases of a matched pair of input transistors.
current and emitter to base voltage
will
but it should
is used in some cases to reduce drift .
In some Burr-Brown Operational
directly
cases,
applications.
The most straightforward
temperature control
omplifier
o ff se t con t ro I .
by:
feedback network,
drift effects
(I) using the lowest resistance levels consistent with input
impedance requirements and output current capability;
and (2) balancing
ances from the two inputs to ground.
shown in Fig. 51, this latter
consideration
equivalent
is satisfied by connecting
fl
C
Ro
&-N\1"-
I
J
1
.1-0
RoRI
Eo
O
-::!:Drift
inverting
stabilizing
amplifier.
of capacitive
shunting the load of an operationol
may lead to peaking and finally
high frequencies.
.R2=~
Fig.51.
00 L d .
apacltlve oa Ing
The addition
:G>-'
the
a resistor from pin (2) to ground equal to the
resistance from pin (I) to ground.
R1
Q-JV\I'v
0
For the amplifier
the resist-
The capacitive
reactance
amplifier
instabil ity at
load tends
to break with the output impedance of the
ampl ifier causing the slope of the open loop
response to increase.
As the rate of closure
44
100
80
---,
,,
Increasing'
,
" r
C loading""
Effect
af increased
C
on closed
loop
A!Oading
gain
t
IAI
60
40
c
loading
loop
20
..,
100
lOK
lOOK
on
open
gain
lM
FFig.52.
approaches 12db/octave
Gain peaking caused by capacitive
(see "Stability"
peak and possibly oscillate
and at high frequencies.
(Fig. 52).
above),
loading.
the closed loop response begins to
This problem is most severe at low gain levels
SECTION II
CIRCUIT COLLECTION
A search of literature
year collection
in this section.
ordered within
in the field and Burr-Brown's seven-
of application
notes turned up the circuits
They have been grouped by general function
each group by increasing
that one of these will
trigger
nature,
controlled
conditions.
a specific
circuit
complexity.
and
It is our hope
the idea that develops into your circuit.
Please do not interpret
for your requirement.
specialized
presented
anyone
circuit
as our recommendation
Some of them, due to their simplicity
may perform only over limited
or
ranges and under
We would welcome the opportunity
to suggest
for you, given the details of your application.
45
VOLTAGE DETECTORSAND COMPARATORS
Inputs
nected
to separate
and cannot
fier.
are af two
input
exceed
inverting
input
and
both
input
and input
limit
may be connected
voltage
limited
may be conthreshold
voltage
for the operational
through
voltage
is set by scaling
may be saturation
voltages
case Eref is the actual
voltage
Eref to be any convenient
Threshold
Outputs
in which
mode
input
allowing
voltage.
The reference
terminals
the common
The reference
the signal
types.
input
resistors
opposite
the
input
or may be clamped
amplito the
in polarity
to
resistors.
to the desired
value
In all
equal
cases,
to the output
ampl ifier
the
input
voltage
must swing
divided
past the threshald
by the open
loop
gain
voltage
.
Saturation-Saturation
-simple,
but relatively
Eo =
+ saturation
(+lOv),
El < Et
Eo =
-saturation
(-IOv),
El > Et
Et =
Ethreshold
=
slow
response
El
Eref
~
Eref
El and Eref may be reversed
to change
polarity
of output
2
Eo =
+ saturation,
El < 1.5v
Eo =
-saturation,
El >
Et
-Eref
=
!:J.
R2
Single-Swing
-simple
Eo =
+ saturation,
Eo =
0,
output
clamping
El < 1 .5v
El > 1.5v
diode
gives
0,
-saturation
output
30O9/15C
o
-=-
Reversing
by an amount
of the operational
=
+
1.5v
1.5v
46
Hysteresis
-output
stability
or
decrease
in
sensitivity.
Eo =
+ saturation,
El <
Eref-
Eo =
-saturation,
El >
Eref + A
Potentiometer
Half
Swing
-single
output
A
or fixed resistors may be used.
clamping.
Eo = + saturation, El <
.5
Eo = -5, El > 1.5
Clamped
output
=
-EbRb
=
-5
Ra
Reversing
~
Voltage
Comparator
Eo =
-10,
Eo =
3,
El
El
<
-fully
>
1.5
1.5
clamped
give
diode
+5,
and
-saturation
E polarity
swing
volts
47
BUFFERS AND
The standard
isolation
due to their
circuits
are designed
Voltage
ISOLATION
inverting
and non-inverting
inherently
low equivalent
principally
for i6olation
AMPLIFIERS
ampl ifier
output
c ircuits
provide
impedance.
impedance
The following
and not for providing
gain.
Follower -precision
voltage source isolation, maximum common mode
voltages must be limited to specified valueso
~ISV
E =E
o
1
N,sv
e--:-J
Inverting
E
Buffer
-adjustable
Model
DC Gain
~jn
@
3003/15
0099999
> 50
1552/15
0.9999
>
I volt
Meg.n.
1011
ohms
gain.
=-E
o
z.
I
=
10K
In
Z
=
1-1\.
out
Potentiometer
trimming
resistor
in feedback
to compensate
values
1 Kohm external
(3OMc
allows
gain
for tolerance
with
resistors)
1560/25
in
and
.
-1-
Balanced Output -for driving balanced
reference is critical.
loads or push-pull
stages when ground
E' = El
E=
-E
I
E
0
By using E' terminal
at the reference,
a p-p swing of 4Ej is obtainable
usable swing of 40 volts p-p with a:!: 15 volt power supply.
= E -E'
= -2E,
at E, i.e.
a
48
Differential
Output
-similar
R,
to above
but provided
in a single
module.
Ro
Ro
E3 = -(El
-E2)
2RI
E4 = ~
(El -E2)
2RI
,
IOK
~!!pUt
E3-4 =-~
(El -EV
RI
IOK
Impedance
-DC
-Zin
falls
with
frequency
giving
equivalent
as above
with
input
and by-pass
improved
high
frequency
shunt
input
capacitance.
3003/15 > 1000 Meg .n., lOpf
High
Input
Impedance
-AC
-same
give
C1
IJJf
0-11
operation.
I
R1
200K~
~h
~1'jI5VI
'~~1<~
C2OOK,\"
Wide
Band -high
1'0
E0,
0
"'~~,...
I~OO~f
speed.
30Mc
response
at unity
gain.
capacitors
to
49
VOLTAGE
AND
CURRENT
REFERENCES
The high input impedance and low output impedance levels which can be
obtained with the precision
and stability
reference supplies practical.
diodes with isolator and multiplying
technique
circuitry
make
added.
Others use the "bootstrap"
values
infinity.
Isolated Standard Cell -Prevent
I~"
Constant
circuits
amplifier
are merely reference cells or zener
to raise the impedance level seen by the reference to theoretical
approaching
STD
CELL
E ref
of operational
Some circuits
0
~
T
Current
Generator
damage to standard cells induced by drawing
current from them with low
~
impedance {20K/volt) mea-115 v suring devices.
See section
~
on Buffers and Isolators for
~
15v gain error. Offset adjustE ref
e-:=--J
ments should not be made
,..,
-with
standard ce11 connected
~
-convenient
current
reference
up
-RI
E -E
o
to
20ma
+ Ro
R
ref
I
50
Reference
Voltage
Supply
-Positive
and negative
output
with
very
high
input
impedance.
R.
90K
R,
IOK
E ref
Ro
IOOK
R3
IOK
-:::--~-~
-C~~ ' ~
7
R2
IOK
~I
(
3003/15
~
""'3003/15
+Eo
-Eo
E
o
R
= -R o E
I
f = 10 E f
re
R4 = Ro -RI
Add 1520/15
for
10<Xna output
.
re
for "infinite
input
impedance."
Should
be trimmed
for best results.
INTEGRATORS
Simple
integrator
circuits
the feedback
capacitor
causing
drift
stabilized
amplifier
chopper
operate
output
successfully
voltage
and/or
error.
current
but current
biasing
Simple Integrators -
E =
o
Close
-s
E,dt
RICo
switches
= -10(" E dt
~ I
to reset
offset
This is corrected
to zero.
networks.
is stored
with
low
in
51
Model
Eo max.
1543/15
:!:2Ov
1552/15
:!:1Ov
This circuit
reduces current
" Bal" contrors.
With zero
autput
Regeneratian
-may
drift
offset in operational
amplifiers
without
input and switch open, set R3 for zera
.
be used to increase
open
loop
DC gain
to infinity.
52
Summing
Integrator
-one
d
amplifier
replaces
Eo = *
Co o---
E2 3f
E
circuits.
5 (El + E2 + E3) dt
= -10S<E,
+ E2 + E3) dt
Any number of inputs moy be used.
IOOK
3
>--0
,
~.
Eo
Zero control and regeneration
O added as in the above circuit.
O
may be
-L
Double
o
and integrator
'OOK
IOOK
R,
I~
=
summer
R,
El
c
separate
Integratar-
c
integrates
Differential
with
one
amplifier.
R
R = I
o 2
I
2
E --4
0 -~J)
twice
((
Eldt=
Integrator-
-15
integrates
Eldt
difference
between
two
signals.
Eo = ~
5 (El -E2) dt
= lOS(E2 -EI)dt
53
AC
Integrator
-integrates
AC
component
only.
/-':
Eo = ~
Augmenting
-R
E
o
=~
Integrator
-sums
E
RI
the
input
CoRI
and its time
R,
5 EdtI
--.!.--
signal
5 Eldt = -10005
Eldt
integral.
Ro
Go
~~
J
El
~
-'OE,-5E,dt
---0
-~
O
Eo
.0
l
DIFFERENTIATORS
The ideal
differentiator
It is susceptible
to high
output.
should
With
Design
"Stop"
-input
frequency
include
resistor
circuit
noise
high
is not generally
which
frequency
sets high
response
frequency
usable
may be greater
in its simple
than
form.
the derivative
limiting.
cutoff.
E = -R C ~dEl
a
a I at
-1
=TOO
.6kc
low frequency
cutoff
F = ~
I
dEl
F
= 16cps
11 Rn C)
54
Low
Noise
-double
high
frequency
cutoff
R,C) = RoCo
drift
compensating
resistor
Augmented
E
=o
Differentiator
-RoEI
-R
R,
Eo = -El
C
o
I
-sums
input
and
its
derivative
dEl
~
at
1 dEl
-TO'O" dt
DC AMPLIFIERS
There are two basic circuits,
entia! output form.
inverting
For a fixed or specific
may be increased by a simple modification
and non-inverting,
plus the differ-
minimum gain application,
of the operational
bandwidth
amplifier.
(See Phase
Compensation.)
Simple
Inverting
-sign
changing
amplifier
-R
o E = -lOOE
E =o
RI
I
I
~
e-:-J
nl5V
.Ro
reslstor=-
RI
15v
RI+Ro
z.
= R
In
=
I
1K
=
lK
55
Chopper
Stabilized
-improved
drift
and
stability.
E
= -100E
o
Simple
Unity
Gain
gain
Control
with
-wide
R centered
range
or
I
attenuation.
and increases
to left .
Gain
Z.
In
not
linear
drops as gain
with
R setting.
is increased.
Linear Gain Control
Variable
E
n
z.
fram
=Oto-10E
= R
In
I
= IOK
I
0 ta 10
56
Power
Booster
addition
stituted
-output
of a power
directly
current
booster.
of any of the above
The operational
for the original
operational
circuits
may be increased
amplifier-booster
combination
Model
Output
-for
driving
floating
is sub-
amplifier.
3016/25
Differential
by the
~
:!: lOv @ 200ma
load.
R
o
Eo=R;El = IOEI
Gain
Control
by a single
-equivalent
to replacing
both
resistors
in the non-inverting
amplifier
potentiometer.
Eo = (1 to infinity)
El
Z. = 50Meg
In
Observe common mode voltage
I-nverting
Gain
Eo = (-I
z.
= lOK
In
~on!~1
to -infinity)
-convenient
El
gain
technique
limit.
57
Buffer
-1011
R
.I\.
input
impedance
circuit
.
+ R
Eo = RIo
I
El = lOEI
-::!:-
DIFFERENTIAL AMPLIFIERS
In differential
ential
trast
inputs
amplifiers,
af the aperational
to the summing
Subtractor-
direct
separate
amplifier.
amplifier
which
subtraction
of
two
input
signals
The result
are applied
is direct
ta the differ-
subtraction
in con-
adds algebraically.
inputs.
Eo = E2 -El
Q!!!erence
Amplifier
-subtractor
with
-R
E
o
= --.!:..
R,
(E
-E
I
) =
2
100
(E
-E
2
amplification.
R1
Ro
IK
IOOK
)
I
J---Q
Eo
~
58
Common Mode Rejection
-subtroction
by inverting
common mode voltage.
and summing to el iminate
-R
Eo = RJ o (E,-
E2)= IO(E2 -EV
R2 + R3 = RI
R3 -common
mode adjustment
set for Zero
E, = E.,.
Differential
Input-Output
Ro
E = -(E
o
RI
Input
-E
2
-for
) = J O (E
I
may be floating
use
-E
2
source .
)
I
in
driving
floating
loads.
output
when
59
SUMMING
AND AVERAGING
Voltages ore summed by applying
amplifier.
Amplifying,
scaling.
averaging,
Inputs are effectively
etc.,
AMPLIFIERS
the signals to the same input of the
may be accomplished
isolated from each other.
by input resistor
Any number of inputs
may be used in each of these circuits.
~
-output
is inverted
algebraic
sum of inputs.
Eo = -(El + E2+ E3)
z.
= lOK for each
In
Scaling
Adder
-each
input
is multiplied
output.
Eo = -(
=-
z.
R
o
Rj"EI
R
R
o E2 + R3o E3)
+ "R2"
(IOOE, + IOE2+ E3)
= 1 K for E
l
In
= lOK
= lOOK
for
for
E2
E3
by a constant
before
summing-inverting
.
Input
60
Direct
Addition
-non-inverting
output.
Eo = El + E2
Zin
=~R2
= 15K for eoch
input
R = 2R
o
I
Adder Subtractor or Floating
Eo = -El
-E2
Input Combiner -as an adder-subtracter,
should be grounded.
unused inputs
+ E3 + E4
R and R) not necessari
Iy equal
Two or more "floating"
inputs may .be
combined by connecting them across
E3 to El and E4 to E2°
-=
Averager-
output is inverted average of input signals.
preserve scale.
E
Ground unused inputs to
= -R o
0
~
E+E
E
(EI+E2+E3>=--'-P
Ro = R) divided
by number of inputs
61
Weighted
Average
-each
input
is multipl
ied by aweighting
factorb~fore
For El = E2 = E3'
Then,
Ro +R~
-(R
E =
0
averaging.
set R~ so Eo = El
= RI" RZ" R3
+R')E
0000
,
R,-
(R + R')E 2
R2
-(16.4E,
(R +R')E
00
-~
+ 8.2E2 + 5.4E3)
30
=
AC AMPLIFIERS
DC Ampl ifiers with Blocking Capacitors
AC operational
amplifier
circuits
are below the range of more conventianal
blocking
still
is present.
High-gain
will
are equivalent
Simple Amplifier
R
E
=--
o
o
R
,
l
Low frequency
c,
0-1
1
= 16cps
=
In
lOK
R,
IMf IOK
f-"N
.'IIVI,---
amplifier
Ro
IOOK
~--0
-'~5C
Eo
O
z.
DC and AC operational
Onlya
begins
EI
=~
is practical.
DC
RC roll off at low frequency.
I
rolloff
signals which
at higher frequencies.
-simple
E =-10E
low frequency
open loop operation
single ended supply is required in one circuit.
circuits
amplify
ampl ifiers {0.1 cps to 20cps) while
O~
~
~15V
-.1
~
15v
3
62
Single
Supply
-equivalent
to above
with
the supply
"floated"
above
C2 -AC
ground.
bypass
-'-
High
Gain
-AC
Low frequency
{where
Xc
-p
open
rolloff
loop
operation
beginsat
1 Kc
+ R
= open
loop
gain)
CI
E = Ro +
o
RI
~=
IOE
I
Low frequency
I
rolloff
begins
Ro
90K
1
=~
= O.16cps
63
Double
Rolloff
-
-similar
to
above.
Ro
9OK
"\Nv--
c,
IOO)4f.r
R2
IOOK.
CJRI = C2R2
.R1
:IOK
"baatstrapped"
.-0
1-11--E
C2
I
IO~f
Eo Z.
~
input
increases
Z.
I
~ IOMeg maximum
In
-=
AC Preamplifier
E
0-
R + R
°
I
tj"-
~=500
R4-
Fine
Law
gain
-completely
developed AC amplifier
rolloff rate and gain trim.
with high Z. and double
In
adjust
frequency
rolloff
1
= 21fR.C.
begins
= 1.6cps
I
I
R,CI = R2C2
=
CURRENTOUTPUT DEVICES
These amplifiers
to the
input
Feedback
will
supply
output
current
to a lood
in linear
voltage.
Loop
R
IK
El
I = T = El ma
,
RL
~.
0-
~E,
,
~I
~
rl'5V
3~15
~'5V
z.
= R
In
=
I
1K
correspondence
64
Simple
Meter
Amplifier
-linear
current
meter
reads AC
I
Meter
Amplifier
-fully
developed
average
reading
meter
input
-El
-~
voltage.
El
= 3"0" ma
meter
-El
'meter
-~
(average)
=
O.9EI
~
(rms)
m
4
R5 -gain
control,
5
calibrate
-=
65
Linear
Current
Source
When RL«
~I
R2
= "RIR3
~
1 ma
=VOTt"""
E,
Co added
Deflection
for high
frequency
Coil Driver-
stabi I ity
load must be "floating,"
i.e.
ungrounded.
-R
I =
o
=
-1
OOma/volt
E;""""R1R3
OSCILLATORS
Oscillators
fixed
Simple
voltage
level
Oscillator
give
a continuous
or square
-double
wave
integrator
AND MULTIVIBRATORS
sine wave
similar
output.
to flip-flop
circuit
with
Multivibrator
output
ii
output.
regenerative
feedback.
I
f = "2""11RC
Components R, C, and 2C should be
very low tolerance
Trim
R/2 until
oscillation
is barely
sustained
=
66
Wien
Bridge
Oscillator
-high
purity
sine
wave
generotion.
1
f = 1"7fRC
100
r-:D
n
Ll
-6,
+T-El
:
Eo
00Ocps
:
Eo
~
Frequency
Manastable
set by C2 and ~
Multivibratar
-astable
R2 -triggering
multivibrator
with
diode
to prevent
reverse direction
or reset action.
phase compensation
removed .
>--0
Eo
R3
IOK
-y~EI
triggering
Use Mode13018/15with
I,
Eo
~-Lr
R4
-1-
level
-output
duration
in
67
PHASE
LEAD
AND
LAG
These networks are used to stabilize
shift as desired.
NETWORKS
servo systems by introducing
Transient and steady state responses may be tailored
phase
semi-
independently.
Log
Element
-integroting
type
R1
Ro
IOK
IOK
'M
,
~
n--W.
phose
log.
-R
to
lOw
E
R,
0
E,
I
1 + R C p
o o
-JOE
=TO"+l5
Eo
O
I
~
0-0
e---l
n'5V
15 V
~
Adjustable
Constant
Lag
-non-integrating
inverting
Maximum
where
E
o
=-
O ~
unity
lag for
6
E = , , , .."
1 + \ 60
~
gain
R, centered
1 is the
-El
6
type.
-)
for
6
= i
log setting.
-40 E
n~n -I
RCP -4Q":j:"""p"
=
Lag value
linear
Non-inverting
For
E
=
R setting
low distortion
= maximum
-o -1
P
with
El
+ ~
operator,
lOE)
RCP
dt
d
-TO""+""P
or
.
IW
68
Adjustable
Lead -putting
path
Lead-Lag
-composite
input
gives
lead
network
from
lead element
.
and
Jog
adjustable
lag
networks.
2
1+(61-61)RC,P
1+(62-62)RC2P
-.2
E=o
R
R
10K
10K
I
I
,
-.~.Rof-
~A,R
C
C2
O.IJJ.f
I
0.1
f
El
=-
circuit
in feedback
69
Time
Delay
-unity
gain
phase
or
time
shift
.
[;:;:::=
I
,
-RC
,
,
. r\I:::='
I
,
EI
Eo
1
,
,
-I.IRC,
,
-=-
ADDITIONAL
The following
CIRCUITS
are various circuits
which do not fall into one of the cater
I,
gories of the previous sections.
+El
follower
circuit
-El
inverter
circuit
En = IE1I
~
rll5V
Reverse
diodes
E
e-l15V
-=Null
Detector-
wide
sensitivity
range.
Non-1 ineor resistance, R , increases as
El decreases giving maxi~um gain near
El = O for precise null indication.
Thyrite varistor
GE 839683961
to give
= -IE
o
I
I
70
Peak Follower
-peak
value
memory.
Use low
leakoge
capacitor.
Eo = El maximum
Common
mode
input
voltage
must
be observed.
Precision Rectifier
-half wave with amplification
if desired.
Placing rectifiers
feedback loop decreases non-linearity
to very small value.
-R
Ea peak
= Rj
a
El peak
:1 -5EI
peak
?'" .!;: ~v p A.
J
AC to DC Converter
-
-precision
conversion for measurement or control
M-~
in
71
Go-
Rate
No
Go
-amplitude
discriminator
Limiter
-R
o
E
o
=-E=-E
R,
Rate limit =
I
I
= 7.5v/sec
72
Time
Delay
-time
operated
relay.
Deloy = ~RICo
Where
K is setting
RI'
Open
switch
close
Selective
Amplifier
Frequency
peak
-Twin
= 21rR
T
I
a
Set
C,
z.
,;
In
So that
R
=
I
IOK
CIRI
O <
K<
to
of
1
reset,
to being
timing.
= 33
,!, 3Odb
feedback.
R
C
=
1000cps
Gain
at
peak'!'
R,
a
> 2CaRa
-2.
and
RI <
100K
z
< 200
out
ohms
73
Full
Wave
Rectifier
-precisian
absolute
value
R1
2K
I
R4
IK
R3
IK
..NI.
Q--W.
~.
IK
Ro
2K
R2
IK
.M--
El
~
circuit
,
'7.
~
Eo
-=
SECTION III
HOW TO TESTOPERATIONAL AMPLIFIERS
The ultimate
application.
ever,
would
sections
test af an operational
Adequate
require
prediction
measurement
are presented.
operational
The tests are shown
input
Chopper
in your
application,
discussed
circuits
shown.
howin preceding
Differential
Alternatively,
output
and other
substituting
input,
single
the equivalent
Test circuits
the outputs
Power
amplifiers
for the other
and measuring
test circuits
for any differential
used by Burr-Brown
D and E below
single
ended
ended
input
inverting
output
amplifiers
circuits
da not apply
for
to single
ampl ifiers.
rechecked
amplifier
and test procedures
stabilized
the same circuits
non-inverting
back
of the parameters
the test circuits
amplifier.
use essentially
then
of many
is its performance
in a given
.
In this section,
ended
ampl ifier
of performance
and the pair
can be checked
(pin
amplifiers
should
procedures
in the circuits
the
simultaneously
between
used as a single
and standard
3) reversing
can be checked
the difference
booster
ampl ifiers--operational
output
amplifier
are intended
74
using
(pins
shown
and
1 and 2).
symmetrical
feed-
outputs.
be tested
ampl ifiers.
inputs
with
a suitable
in the standard
only
operational
test circuits.
for a distinct
class
The
of
~
75
BURR-BROWNSTANDARD TESTCIRCUITS
Standard
Test Circuit
A
Measuring AC open loop choracteristics
problems normally
encountered
el iminates DC drift and offset
in open loop measurements.
The gain called for by
the feedback at lOcps is
Ro
IOM
R + X
o
c = 116dB
X
c
so that measured gain is determined by
open loop gain in all but the highest
I
gain operational amplifiers.
Amplifier
response is flat to 1OOcps so low frequency
measurements are valid
Standard
Test Circuit
and convenient
for measurement with standard instruments.
B
This X 1000amplifier
is used
for the measurement of very small
voltage
drift and offset values.
These
are measured at the output and are
referred to the input by dividing
1000.
the output and must be included
load calculations
Standard
through
across
rent
Test Circuit
c
In this
gain
unity
the feedback
the feedback
is calculated.
loop.
resistor
amplifier,
current
The resulting
from
The isolating
which
due to offset
output
the
the operational ampl ifier make it possible to
measure the voltage across a lOMeg resistor
with any low impedance voltmeter .
voltage
of
in
.
and drift
is equol
cur-
properties
by
Note that Ro presents a load to
circulates
to the voltoge
Ro
IOM
~
I
I'
~
O~2f
A
. 1-0
Eo
76
Standard Test Circuit
Circuit
D
operation
Standard Test Circuit
C.
is identical
to
For perfectly
anced and matched differential
bal-
input stages,
current drift due to temperature should be
identical,
and their effects should cancel
completely.
Output voltage
of the difference
Standard
is a measure
in current drift.
Test Circuit
E
This is a unity
circuit.
most severe
and high
frequency
response
of this circuit
to Standard
Test Circuit
Standard
Test Circuit
Operation
~
R1
IK
the
compensation
stabi lity .Frequency
is I imited
amplifier
Test Circuit
itself
only
by
in contrast
F.
F
G
is identical
with
Standard
Ro
IK
IWv,
Test Circuit
level
Eo
0
The low
unity
was chosen
problem
of stray
at high
frequencies
Burr-Brown
amplifiers.
-=-
F.
used in this
amplifier
0
,~'
non-inverting
represents
test of phase
the operational
Standard
gain
1000/0 feedback
wide
resistance
gain
inverting
to eliminate
feedback
the
capacitance
for measurements
bandwidth
operational
on
77
c
Q)
0
>
.3
CT
Q)
«
1-
~
;:!;
~
O
-0
-u
+
0
0II
C
.0
rn
9
o
"'t"
('")
""
:I:
1
V1
W
~
=>
C
W
U
O
~
0-
~
VI
~
W
L1:
:;
Q.
~
-'
<
Z
O
1~
W
Q.
O
~
Z
i=
VI
W
1-
I:C
O
('")
.D
-c
c
"5
a.
"5
o
1V1
W
1-
0:
:I:
I
Q)
Q.
O
U
~
~
:)
c
Q)
~
.U
O
"E
"
c
>
.5
0"
0
~
£
:I:
Q
1U
w
z
z
o
u
0
~
"
c
"
~
c
c
OJ
In
IV)
::;
1Z
w
~
:)
a
w
:;5
.g
.g
N-
~
O
.= ~
0O>-H
a--U
0 0>
O .;:
-°
C >
0> 0>
"'
0.
°
"U
"
;1:
0 °
a-o>
-U~
C.-O
u.
>
-0>
;)
Oc
>
~c
:):)
o "'
>~
Q)
~ Q)
"'
:)
0
"' Q)
0 ~
Q)
<
<-a.
"
~
.--
Q) Q.
..0
;)
..;)
","UO
O
.-I:
~
"
Q)
-u
."'
~
:)
.."5
-NO
@!
@J
0
~
"§:
e
§,;g
.-00
V)
,
Q
C
I
~O
U...:.
C
U
--"
~> :>
="'6
:!} 'Qj
a.
~o E
V) "
.= 10 .
<-' ~
"'
~
<I>
~ -U
;) Q)
CI:"O
"'
~-UNO
~
-"
O-C
c:"t)0>0
.-CX)
U')
,
:3"
Q
>~
~a
1-'
..,..""'
0..
u
O
O
0-.
u
0
0
@!
@j
5
e >
.-=
:B
"
,-
::1.
~
~~
-c..D
c;:J
c>°
0- co
VI
.
>o-a.
~
0.
VI
:0
CVl
.-:0
O
.0.
,I\
"'
V
>
o
~
M
"""
N
~
-
C
::J'
2.
N
~
0.
~
0
""'
'+-:I
Q)
"'
C
0
...
"'
'-0..
u
I:
--U
0
'-
0)
a.
o
u
V)
~
1~
..0
""0
0
M
I
@J
'5
2
0)
Qj :1.
CO
QjO
~~
c
0)
O
CoD
c-U
0>0
.-00
""
,
c
>
c
E
0>0
;;; ""
-u
c
c
-'
~
C
-o
Q) ..;:
Q.:>
O U ..;:
V) "'
0)
co
0)0
u
"'
" "5
>- 0..
u "5
I: O
Q)~
>c .c
~
I
.D
x
:>
O
"'.D
-J
'6
c:oc:
<1>00
~~..;:
M
-I
..;:
I:
Q)
0 "' "'u
'- .-C
u
...Q)
0
I:
'- -<: -Q)
-2.<==
3: ii:
.-0
..5c
-N
> .~
>
...
E
E
C
"
...E
Q)
"
.-u
o..-g8e
.~ ...E
..."
~ I:
0 ~ ~
-"'
Q.
;)
-'
Q.
O ~
Q) .-C
"'-"U
CJ
.-c
e
.0
C)~..0
-'-U
0 0
"
on
~
-x
o
-0
~>-C
<I> :L
>
5I;g
.-0"'
.
::;0
~-.
@~
~ c:
o o
W ~
cO
wO
O~
-,
C-C
c
01
(1.
0-
o.~
0
~
Q) >
C :1.
Q)(V)
~(V)
-O.D
..<3
~~
<l:
~
a.
u
E
O
''+-
"
...O
.->
0..
;)
Q.
-
Q)~E~.:E
~'-'6
'+-
.~
-0
C
C
n
"5
o
"'- "
x
a.OO
O ..;: -0
u :1
VI .-=
a.
u
It)
N
-:ij
II
o
c
a.
2
-0
~
9
0£
.~
II
-'
"5
NO
C
>-.
""ii
aa
O
"
'0
0)
0.
°
..2
"
>
~
II
:0
o
J:;
~-' 10-
~-.
0-
~
.-:?:
c..
u
Il)
N
-a:
o
w
0"'
II
~
~
>
1=>
~
z
z
o
~
«
u
u:
u
!~
II
-"I;;
V)
z
t
~
<J~
Q)
a.
o
u
V)
1=>
~
1=>
0
x
c
E
~u
0)
u
00
'()
~
o
U
00
~
1>
C
Q)
0
>
.3
CT
Q)
~
::J'
.9.
-"
QJ
'2
-0
.:0
>~
~
"'
~ QJ
.3
O
~~u
u.O
c~
QJ
~
.:i
-0
0;
O
"'
""
78
og
l
~0
"0
5..~
x
c
.5
~
O
u "'Q;
<
1-
<t,
~g
lC»
~
'+a
6 ~
-==
>
-<3
II
I~
00
44-
.:::
$
-u
-!0
oU
o
V}
UJ
0.:
:J
c
UJ
u
O
0.:
"-
"5
"
>
~
"
c
.,
:2:
"i!.
::::;,I!
O o
cO
.-O
LL-l("I
~
~
;:)
o
-!:
~
N
~
0
"tt:
O
Q)~
0
8'-H
=.--0
O
Q)
> 0-0
"
>
@-Q)0)
0-
--o.E
c:0O
L1- '>
"'
g-
u
V1
VI
Z
O
f-
~o
~
E
-;:)C)
;:) E
0.-
'-0
>
"U
C
O
x-!:
~ U
O "U "'cii
U
C
"
.-"C!U-O
~
oU
o
"'
m
2
a
>
Q) "'
"' Q.
.0
u
c~
~o
"5
0.
"5
o
u
Q
::1Q.
~'+::1 0
O ~
Q) ::1
~
Q.
::1 ~
"'
::1
c
o
Q) ~
~
~
"
~
"'
~
"
«I
-5
200~
o
.Sl
"
II
~
'+-
.:::
-5
.-
c
c
"'=
E,+~ "'
, c
> Q.
E
"
C)
o
0
>
;:)
Q.
C
.-
a;
~
O
u
~
!1..
,"7,
1:J
"1-
::S
~
a
"'0;
~
"'Q;
~ ,0
a
O~
"'
m
2.
O
>
"5
Q.
"5
o
u
c
c
~~
t-u
::>
U
~
::>
~
:)
u
"5
0..
.-Q)
0
>
~
"
~
"'
:5
@:Q)
.-0!
-u.2
C.-0
U, ..
.=
-oU
cO
.-O
LL.",
~
Q.«1
O ~
u~'-=
-"'
01
CL
O
~8>~
1-0
>~
,~
"
o
E
E
0
u
U
W
Z
Z
O
(I
E
c
t
QJ
"
"
0
lJ
~
..I:
V)
4
~~
00
0.
c
~
.
"'
.,.
"5
N
-5
c Q) E
t: Q)
:> Q.
u
E
-Q)
:>1Q. .
c "'
->
,.t
c
~
3
u
~
Q
c
~2:" 0.
uo. "
-V")
"
0.
c
->
1'1
~
.
c
]~C
::§
c
w
~
Q)
"-
Q
E
U
Go
c
...
~
.
"'
-:;
"
I
0
~(/)
O
0)
>
E
...i=
:1
1:
Q)
t:
:>
u
~
.0
Z
0-
n-
"
0>
.E
~
~2O 0.
>0.
0.
c
->
"ii,
::::
O
:;
0
0)
c
Q)
0)
~
"5
a.
c
.:::
a
w
w 5
01...
0 e
=
W
O CL
>
E
...w
:>1CL .
C "'
->
:>-
~
~
.-I:
~
~
0
0)
0)
E
u~
V)
z
0
i=
«
u
;1:
u
w
~
V)
"
0
~
u
.,
"
"
0
u
0
z
~
:J
0
0
Q.
"
-0
w
.$!
'+o
-oU
"5
4-
2
-:E
~
>
~
"
0.
.=
~
.-
IV}
UJ
'-
>~
a.
~
a
Q)
0)
.E
O
~ 0)
0
"
II
-0
c
c
~;)
~ o
c:~
-:-
~
>
<1
44-o
o
I:
~
-Q)~
"5
79
x
c
E
u.
II
.,
~
O
(1.
~
<
~
<
'"'
"5
Q.
"5
0'0
II.,
~ .§ ~
.~
:I
x
O
E
U
I
0>
C
z..,g-:U
., .~ .-0
.~ '- .,
'- I >
'0
.P.
.-
.,
.,
E
...~
-~
Q. .,
E
"'
O .-CT
'-
Q)
-0
"
>0
""
w
~
=>
Q
w
v
O
~
~
(.) Q)
~ .-E
E
-..:
c
-"U
-Q)
..:
>(.)
c
Q)
"
0-
f""
w
"Uc
0
a.X
Q)
Q)
...~
"
a.
"
0
-Q)
4--C
Q)"U
~(')
Q) "'
...a.
(.)0.:P,"U
C
...
-"U
...
0"
Q) ~
.-
,
'o
:I
.u
o
Q.
O
O C
0
C
~
3
c~
8
>. 0U~U
C
.-
C
",-"C:=
,-C-~..a
C
QJ
QJ
~
'-'-"'
QJ
~
:;)
"'
tI
QJ
~
.-=
-2
c
..c
~..=:
o
c.D
c-U
ClO
.-M
"'
z
o
~
<
u
u:
O
w
a.
.~
Q)
m
c
~
~
>
c
.,
c
~
w
~
.5
!:!
u
I
~ a.
Q) I
>a.
C ~
3:>
Q) E
..0
Co
::)C-
"' "'6
~
~
00
I
GJ
Q.
O
u
I/)
..0
"
Q)
~
+.3
~
.u
+~
>00
u
c
Q)
;)
Q)
..
"E
o
-u
c
o
t;
Q)
"'
0
Q)
..
5!
:J
.
o~
-0c
.2
e
.,
c
.,
O
a
"'
QI
QI ..
c QI
QI "'
c
Q)
<-'
~-!:x
.-=
o3:..C
C..cC
C>
o
c
0)
;;;
.--c
V)O-0-
o
Q)
~
o
Q.
QJ
~
'Q;
3:
N~
~
W
...0. ~ :1
I:
'- .
UO
>c
o
~
Qj
;;:
c
0>
;;;
O
.-
01
""8
:?:
I:
O
E
E
o
U
0:1U
x
o
@J
@Ja
.."'
o
2
Q)
~
~
u
8
8.~
~..c
0-
~
0
"-
-0
Q) ':;:.
a."
0
...
"'U:;: ..
"'
I
Q.:J
U -0-
0
0.
0
u
c
~
o
.~
-0
O
"'.-.0
~
C
~
1>
0)
c
"0
o
O
-'
Q)
E
i=
C>-
Q)
~.:;:.
>2
1- .>~
Q)
.~
'u
Qj
-U
c
o
.-
.~
Q)
2
Q) >
cE
Q) o
~M
-~
~
cQ.~ y
.-Q)
-.0:u
Q) .-c
Vlu-
C
0
1:J
~
z
QJ
"'
tI
QJ
~
u
.-~
I
«>
0.
0
u
",
0'
Q.c>oE
o
0-'+-0
;)
>
>0~"'
..0 x
::1 O
"'..0
U
C
~ 0
~
>
Q)
-0.;)
-"'
=
~"E
:;):;)
0 a. E
~'&J-U
.2
~ C
:=
>.:;:
U
C)
"'C-U~
0
QJ
E
;)
E
.-tx
o
E
~
0
'+-
B..
E
--0
~
:;)
2:;)
o
QJ E
E
"=,,
cE
QJ QJ .~
"'
x
'c
c
~
0
-g
0
,
0
-0
't')
~
N-
..t:
0> I
~='o a.,t; E -u
QJ c
>
x
c
E
u.
II
Q)
~
o
a.
~
0II
U
~Q)
Q) E
Q)
0.
O
"
VI
1:J
~
1:J
O
V)
z
0
i=
u
w
z
z
o
u
Q)
"'
....
.,
>
3:
"'
't')
N
't')
~
:>u..
~
~
.
u~
I
"'
W
1O
Z
1O
O
"--
a.
E
o
-Qj
.D I
.E
"'
:)
'"C"
?
C
o
~C
::::.
SECTION
IV
SELECTING THE PROPER OPERATIONAL
Now, with the theory , circuits,
are ready to select an amplifier.
in the Appendix,
fraction
and test procedures ot our commond, we
A glance at the representative
shows the variety
of the operational
of ratings available.
amplifiers
available
presents several approaches to selecting
wide range of available
Focus on Limiting
tively.
however,
from Burr-Brown alone.
the proper operational
amplifier
correctly,
be uneconomical
With so many specifications
This section
amplifier
from the
none of its ratings should be
to apply the device too conserva-
and so many ampl ifiers,
the secret is to focus
specification.
In the majority
Drift
given
Specifications
It would,
on the limiting
specifications,
These represent only a small
units.
To apply the operational
exceeded.
AMPLIFIER
in operational
of DC appl ications,
amplifiers
is primarily
the )imiting
factor will
due to temperature
transistors causing base voltages and base currents to vary.
be DC drift .
effects on the input
The input current offset
(base current) must flow to ground through the external
feedback network and through
the source.
resistance to ground gives a
voltoge
The input current drift times the effective
effect which may add to or subtract from the input voltage
drift.
If the
resistance to ground is the same for both inputs, the input current variations
cancel as indicated
of the input stal:ility
temperature
accuracy
by the specification,
"differential
tend to
current drift. " A comparison
(combined effects of voltage and current drifts over your
range) with your input signal will
give a quick indication
of the
you can expect.
Specifications
fier are bandwidth,
gain-bandwidth
other than drift which can help you focus on the proper ampli-
output capability,
and packaging.
The requirement
for a high
product may narrow the field to a few high speed amplifiers.
80
High
81
power
units.
output
requirements
A packaging
While
application,
~void
preference
anyone
familiarity
the critical
Open
the smaller
rule
out
or more
operational
In your
vs~
out
will
of thirty
with
parameter
Clos~~~~p
may rule
packages
comparable
units
specifications
amplifiers
and more
in other
could
will
economical
configurations.
be limiting
enable
you
in your
to spot quickly
case .
Loop
Confusion
While an ampl ifier is rarely used open loop, open loop specifications
are
required to provide the information
needed for all possible closed loop applications.
As we have seen in the preceeding
sections,
difference
between open loop and closed loop characteristics
output impedance,
pletely
there may be a vast, but predictable,
and bandwidth.
The amplifier
for your application
described with either closed loop specifications
but the relationship
Selection
such as input impedance,
may be com-
or open loop specifications,
between the two should be clearly
understood.
Check List
The following
is a check list of the information
proper ampl ifier for your needs.
required to select the
Be sure you have enough information .
1.
The Source:
What type of source do you have?
2.
The Load:
What type of load do you have?
3.
Performance:
Voltage
level ?
Impedance?
required?
Voltage
level
Impedance?
In the closed loop, what is the required gain?
Band-
width?
Accuracy?
Linearity?
Input Impedance?
Output
Impedance?
DC drift?
Noise?
In the open loop, what standard Burr-Brown amplifier
will
do this?
4.
Environment:
Where will
5.
Power Supply:
Available
6.
Package:
Anyexceptions?
the amplifier
Other requirements?
per supply?
be used?
Temperature range?
Formal specifications?
in system/instrument?
Number of amplifiers
Current drain ?
Type of mounting?
Controls?
Connectors?
82
7. Availabi lity:
Quantity?
Future potential?
Delivery
requirements?
Price?
The above information
Assistance
Avai lable
The following
fram
will define your requirement
Burr-Brown
services ore availoble
The latest specifications
improved.
an amplifier
will
to you for the asking.
-Operational
Be sure your information
Applications
list,
amplifiers
assistance -Given
the information
in the preceeding
be recommended with an appropriate
purpose use, both price and performance
tai lored for a specific
Special packaging
are continually
being
is up to date .
Custom designs -Whi le the catalog amplifiers
amplifier
fully.
check
circuit.
are optimized
can be improved frequently
for general
with an
application.
-Ask
for a quotation
on an amplifier
packaged to fit
your configuration.
Availabilityinstallation
you need for on-schedule
at minimum cost .
Contact
services.
Get all the information
Burr-Brown or your nearest representative
for any or all of these
APPENDIX B
Typical
Burr-Brown
Operational
Amplifiers
The spec;Hcations shown m Table 1 and TabJe 2 (an the follawmg page) a,e md;cat;ve of:
(I) the complexUy of
ope,at;onal ampl;f;e",
(2) the state of the a't m ope,atianal ampl;He,s as of the publ;shmg date of th;s handboak, and (3) the
extens;ve Ime of ope,at;onal ampJ;He,s manufactu,ed by Bu,,-B,awn Resea,ch Co'pa,at;on, Camplete spec;Hcat;ons a'e ava;lable
on ,equest,
TABLE 1
Pe,fo,mance at 25°C w;th 'ated supply,
I 3003
3018
3019
umts
10
.10
"
10
20
.20
"
20
v
mA
3009
3010
3013
.10
" 10
" 20
"
"
.5
90
10
0.6
.3
.10
.20
160
92
112
100
dB
15
10
B,oodband
1.5
MH%
1000
500
60
30
" 10
"0.2
"0.5
.0.02
.0.0005
.0.001
120
"1.0
"1.5
I
Note
.0.5
.10
.15
.0.05
7
.10
.15
0.5
.15
V/f"
"0.5
" 10
I15
"0.5
" 5
" 10
mY
.0.1
"
nA
Note
J
Note
3
Note
J
Note
3
1011~
1011~
lOllA
lOllA
.10
"
!0
.15
"
!5
5
"0.2
"0.5
(8)
I'Y/OC
Note 8
0.5
50
" 10
" 15
f'V,rm.
M~
M~
v
v
k~
-40
+ 85
-40
+ 85
-40
+ 85
-40
+ 85
"c
"C
" 15
" 10
" 15
.8
.15
.5
"
15
Vdc
"
5
mA
125
Note,:
(I)
(2)
(3)
(4)
(5)
(6)
(7)
I'Y;Oc
n.VOC
nA/oC
0.5
-40
+ 85
kH%
1.2
10
0.5
50
20
/15
/15
/15
Specificotion, wbject to chonge without notice.
Externol'y odju,toble to zero. Alternote /13, /16, ond /26 moduie. feoture internol voltoge off.., odju.tment.
Either input.
Input current double, eve'Y IO'C r;...
Ronge: .3 volt. of typ;col for .15 ond .26 volt wppl;e,; .5 volt, of typicol for .60 ond .120 volt wppl;e,.
Totol current opprox;motely equol to qu;e,cent pM output current.
See mechon;col doto for olternote module type,.
Through oppropriote ..Iect;on of pho.. compe",ot;on, the u..r con ochieve goin-bondw;dth product, 0. h;gh 0' 100 MHz,
full-power re'po",e to 100 kHz, ond .!ewing rote. to 10 V/f"'
Typ;colly le" thon I f'V ,rm. no;.e, Complete noi.e ,pecificot;o", ovoiloble upon reque,t ,
83
APPENDIX
B (continued)
TABLE
2
Pe'!a'mance
at 2SOC with
,ated
rupply.
1514
1540
1542
1552
1560
"
20
10
"
10
10
.100
.10
"
"
"
20
"
30
106
110
1.5
10
1.2
1.8
.0.3
.5
.10
.0.5
.10
.25
.10
.0.3
.0.5
" 10
"0.5
"1.0
"0.5
"
5
"
15
120
0.6
"0.5
" 10
,,25
"0.5
"
5
mY
"
f'Y!"C
.0.1
Note
3
3
Note
3
Notes,
(I)
Spec;f;cot;ons
subject
Extemolly
odiustoble
to chonge w;thout
to ,eco.
Altemote
not;ce .
/13,
/16,
(2)
(3)
(4)
Elthec ;nput.
Input cuccent doubles eve'Y
Ronge,
.3 volts of typ;col
.20
.10
.120
.15
(5)
Totol
(6)
(7)
See mechon;col
doto foc oltemote
module types.
Thcough oppcopc;ote
select;on
of pho.. compe",ation,
(8)
full-powe,
Typ;colly
cu,cent
oppcox;motely
cespon..
les, than
I(1'C c;...
foc .15 ond .26
equol
volt
to quiescent
suppl;es;
.5
the u..c
TA8LE
Output
mA
~
" 10
.200
DC Gam
O.L.
typ
dB
3016/25
of typ;col
nA
nA/"C
nA/"C
0.5
50
M~
M~
-40
+ 85
°c
°c:
.15
.5
.15
.20
/25
Vdc
mA
117
;ntemol
voltoge
off..t
foc .60
ond .120
voft
odjustment.
suppl;es.
cuccent.
con ach;eve
to 100 kH"
ond slew;ng cote, to 10 V/..s.
I..V,cms
no;...
Complete
no;.. ,pec;f;cot;ons
MODEL
Rated
volts
f'Y!"C
k~
/15
feotuce
V/f'S
v
v
.15
.8
module,
kHz
..V,.m.
IOllA
40
85
/25
plus output
% 10
%0.5
%1.0
0.5
.120
.10
ond /26
15
10
-40
+ 85
/15
MHz
3
1011~
1011~
dB
10
Note
10
.26
"
5
100
.0.05
Note
0.5
100
40
85
v
mA
2000
10
" 15
" 26
" 10
" 10
30
100
100
Un;ts
90
106
0.4
0.5
1706
ovailoble
gom-bondwidth
upon
pcoducts
os h;gh
cequest.
3
Powe,
8o0stec
Ope,a';ng
Tempe'atu,e
Range
max
,~C
-40
84
+85
'area
I typ
I valt,-
~
max
~
.15
os 100 MHz,
MECHANICAL DATA
Typical Mounting
Connector Burndy EC 4205-P5
Applies to /13 Package and /]6 Package
/25
PACKAGE
0.3"GRIO
/15
PACKAGE
OJ"GRIO
c
i
,
1.80"
, ,,
,
-&~!-0!-~--~
,
,
,
, A
'
1 <t.-- --0-~--r' ,
2K~--- --~--(::\
,
,--I
,
~,
o
' 2,
'
,
'
'
~J
'
OPYlONAL
040.m
-7-z
'I
'
--G--i--y
-,
:
,
:
1 fo--
,
18"
<t.
,
0'
n
n
'
,
4
MAL
:-r
~ UD"
..,
o --,
'
,
1-'
,
'
'
,
, yAPPEO440,09"0E£P,
n
TOJ9"0E£P,2HOLES
I
-n
<t.-
,-,
I TAPPEO 440,.09"OEEP,
1
~
~.04°"TYP.
SCREW ClEARANCE
.1
TO.19"OEEP,2NOlES
~-n
n
n
n--.
SCREW CLEARANCE
~
.18'
.GO"
MAL
~
--1-
60"
,.,
--L
IlBD"
r
~
I
.,'
,
85
2.40"
MIX
-J
MECHANICAL DATA IcontinuedJ
/17 PACKAGE
01"GRIO
Ct.
~",,~
-coo"
.,'
-I
,
140 PACKAGE
/29 PACKAGE
01"GRID
'i.
'00"
."
'00"
.,'
86
,
REACTANCE CHART
IOM '/X'I-I/X"'
I/'X"I
I/'X"~ r/y"'
l/y"l
I/V'I
~X~~~X~X~X~X~X
M--1
~,
x
x
~X~X~X~X~><~><~X
0<
x
x
~
V< ~
~,OOO-
~
~~A
A
X
x
x
X
x
x
~
~
x
x
A
~
x
x
~
IOOK
A
x
x
x
x
Ax~
x
10K
";n'
E
..r:
.2w
~
IK
U
Z
<
IV)
V)
w
~
~
9
XI
~x~~x~x~
~
x
x
~~
:~:~x~
~
IX'
)<!
x
x
X'
XI
><
100
*
~X~~X~~A
~X~X~X~
~
XI
IXI
IX,
~
""
x
.x
~X~
Xi
IXI
10
,'
",j1
"~ ~
~
XI
~
.x
~~
x
x
x
Xi~
~
IX
IX
X~
~;,"'...
0.1
x
xxx
'x Ax
~~~~~~
10
~
100
IK
10 K
FREQUENCY, Hz
87
100 K
IM
IOM
-DOMESTIC
ENGINEERING
ALABAMA
ILliNOIS
"H;;;;;;:ijj;
BCS-;0..,.,",.
c;;;;;L~"FG",".Au=;"",
,(205)'34-1..8
REPRESENTATIVES
Now
-
Ho,,10td
JAReo00"Compo"y.,"'
PhoM,(31')732-377'
PhoM'(3'2)2
824
..."',..,
LOUISIANA
J
~
~
-";,
W;";,m.
BCSA,~;0..,.
PhoM
('04)
-;0..'.
Pho""
I~.
(6021
,",.
..8-22..
2S4--
Reogo"
C,mpo"y,
(716)
473-211'
NORTH
CAROliNA
BCS ..W';ot,..
T~w"
m;;-;1;;;;;g
"",-8,ow"Re~""hC..,po'",;0"
-(60l)
294-'431
QEDEI",,0";,..,",.
"',""
(30')
ARKANSAS
MASSACHUSETTS
Do"m)
"',",
S..-8',.
SIio,Jdo"
M.m."mom
".
PhoM'
IM"...m
Spo,;0I;".,
PhoM'
(2'3)
Eq.;pmom
(611)
c...,
I~
24'-4870
Spo,;0I;".,
PhoM,
(4081244-"05
,",.
(2'6)
~
Doy...
0."",
"",;da"-;
S"',;do"A",,;0...,I~
IM"...m
PhoM
76'-5432
Sho,;da"-;0...,I~
PhoM'
So""CI,ro
,~.
("3)
CI,~I."'
I~.
665-"8'
273-"18
-;0..',
-,
~
,",
('1')
~
C'~,MQ..
-Wo",;,ld
lo
I~.
G",",bo,o
MARYLAND
(s.,
A
PhoM'
237-',4'
,I~.
PhoM'("3)m-8"'
(313)
3'.-3333
~
(s.,
Do1lml
MINNESOTA
~
Do WM.;'W
~
L~,"
"'",;,
."
A"o"Crowlo"'...=;0...
PhoM'
(4'61
F
.PENNSYLVANIA
'
G","
p t.~'8
c
h
PhoM,(6121781-1611
S"',;do"A.w,;0...,,"'.
636-4"0
pho",
(4121
243-665'
MISSOURI
Mom".I,
A"o"
P
Q.
Crowl~d
PhoM'
s;:-G;;;..-;"".
(S'41
73'-.776
C'ow'.,d
Au=;"".
(613)
nS-1288
Pho""
..~;'.."
"',~
O."WO,""";'
A"o"
",;lod,lph;o
S"',;do"
(3141
QEDEI"",";,.,
..C.
..~;"".
,",
(21'1
Pho""
"'0""
(3031
388-43"
('0'1
,",.
,
436
Binghom""
J A
Reo00"
M'.
,",
42'-2764
C..mpo""
("8)
Pho~,
FLORIDA
=-- ,
~,"',
.CS ...=;
Pho~,
(305)
2"-1638
Re,go"
PhoM
c..,
C..mpo",;
(607)
OVERSEAS
A;...ARGfNTINA
45-582~
,",.
(B°')
8709
,",
VIR
'
~ "~".' 1
,",
( s.,Mo'yo"'l
I
WASHtNGTn...
723--,
s."'tl,
IM".m,mSpo".I;,".,",.
Pho~
(2061
767-4260
V.m'"
QED El.",,";,..
Pho~,
('14)
"";.G"'~'.IEHli~S.A.
"""1-..",'.24
774-2'68
~
S,"
lo',
CI!,
W"'iam.-;",.,.
Albo"y
J A
M.m."mom
Eq.;pmom
Pho~;
(203)
874-'222
I~.
(7131
,",
~
CONNECTICUT
E,.,Ha,,'.,d
I~.
A "'0
II
PhoM'
W;";~.A..,,;0
,",
A..=;0...,
(21413'7-.."
Hou..."
.,-
AI,"q."q~
~
0."."
W"';om.Au=;,...,
N".",
PhoM'
92'-8711
~
(6041 291-7'61
N.J.)
~
Do"m
c..md,"
"'o~'
""""
C..mdo",
'24-4800
~
Vo",~.".
A"~
C'-'0"'
(s.,
,",.
,",.
968-2200
WASHINGTON.
D.C.
(s.,
REPRESENTATIVES
-
"";...S.E.P.T.A.
13.,~d,T;q~""~
H.OOR;w
A/S
C..tlGro"'oh"V.,'
7'-Po,;,2.,F"'Na
",0~,236-37-~
P.O..,8T~."
O.I08.NORWAY
","",,;rn-;o-
K.~I.,,
49 E.~,
.,..
y.L'd.
W~.ti.Y.
VI,,~;..
""""M.lbo.K",277~
Syd,.y
s.,";,.
A-I~oW;".
Cap;.'ro,-3
V;."~.
"'0~"~
,.
S
c..,.,..,;,"
-maM"ro.M"
2",
M.";,h.GERMANY
","""
001T7!T69m
,"",",..'.'.p.O..,502'
Ka,=h;-2.
PAKISTAN
FI-.
Dod.
Cho...n
G",.
EI.ctro";,.C...po",L"'.
6. K,;."".
S",.,
TELECT"'
...Rod,;OO
A""M.
L;
","",,223m--
, Mo,,"'";
,"'
2
232703
'",.
Salm
A,"TRALIA
3'8243
Ad.I,;",
D;pl
D;pl.I",E-F.y
8 M."",,"
..,.,
134.
GREECE
Do F-~.
M'
~
A;,-Po",,"..,~,;,~INV
Do";dPo"='("'""d
EI,ctro";,.Dopo"mom
17M.".S,
149.--,
PO...,31"8
Ry.wy.
( ZH"HOlLAND
"-,(070)~
JoIoonM...',.
",,~,n4-.27.
,"",-"",,~
...m;.Alo
'-'.C;o.L
C.'~ro 7 No. ...'9
Apo,'oda ..~O 6287
"""",.D.E.~
..,omEI""-;,,c..
"d.
74.-da,BI...
p O ..170
T;t-A";":~SRAEL
44 "!f«:
2' 07 'J
~ ..:
2' 77 20
~'"".~po"mom
DISTESA
v;,;"".'2
Mod,;d-10, SPA'N
","",,223~
-,"7806
4' "
StNmo"",.,~
I"'~",o.
V;o..ld:"""
".60
I,
E
",,~,
02/
, '.0
3uo:w
46
V.H";M
129,
;03
1, PORTUGAL
","",,62'46.-
AUSTRIA
--0
q.'pmo"
2'
d T .."
..;:.~..~."..L';;~
,..,
N,i
2600 GI~,,",.
,,-,
(O')96~
12-419
T..,
'..'
SW£OEN
","",,18293.-182939
Ky"'""...';K.;.ho.l..
Now0..-h;.,d,
,EI",,-;,AG
Ge~,hl'
Ch;yoda-K,
".-2'
;;.D; z~,l":
-,Q51-2'~
SW'TZER"'ND
Pho~,~;
-TEL£.C..
;M"-m.
Glo""...,"..;",E."..
H."",",.,
GI-,
T.I
4. 2-Cho..,
",,-h;.
To'yo.
JAPAN
c..1"R,m;,hoo082'..27,ECUADOl
Pho~,
43.
OEN-.
T",";,m
L
G~yaq,;1
Ge~,,1
T.'
P.O..,43070
S,=.ho1m
"'""'3761'8'-
7thFI-.
Som;";",~
..,2'9-44'2.
~I,".."
SOUTHAfRICA
,;
Nybol
,."'56
go 0"'"'
2""Mtlo~.ITALY
S'
",.
,.
ENGLAND
E"ct'o"~;-.'"..-;'~I...
L".~
N,m.
S.A.
S8
,"';-,;"""'...
P.O.
..,376
MEXICO..D.F.
=-41-0l
Karo.,y,TURKEY
~,4'~
W.KM",0"",d.
..'.'0"'.
PO.
103-1Q5
..,3097
F.I,,"NEWMot"'w
ZEAlANDA~"~
V;b",;"P,;,""l;m;..d
4,
--77,~
..,10""'.ti.I
Ph-,'86-000
"-,",
""~,GI,"",,..671'.N"..
F,b;~;".oN
...,,;",; .CO10, FINLAN,,:
OY
32
~I~.o
Mo,yl",,)
'
E
A.
IMPORTANT NOTICE
Texas Instruments Incorporated and its subsidiaries (TI) reserve the right to make corrections, modifications,
enhancements, improvements, and other changes to its products and services at any time and to discontinue
any product or service without notice. Customers should obtain the latest relevant information before placing
orders and should verify that such information is current and complete. All products are sold subject to TI’s terms
and conditions of sale supplied at the time of order acknowledgment.
TI warrants performance of its hardware products to the specifications applicable at the time of sale in
accordance with TI’s standard warranty. Testing and other quality control techniques are used to the extent TI
deems necessary to support this warranty. Except where mandated by government requirements, testing of all
parameters of each product is not necessarily performed.
TI assumes no liability for applications assistance or customer product design. Customers are responsible for
their products and applications using TI components. To minimize the risks associated with customer products
and applications, customers should provide adequate design and operating safeguards.
TI does not warrant or represent that any license, either express or implied, is granted under any TI patent right,
copyright, mask work right, or other TI intellectual property right relating to any combination, machine, or process
in which TI products or services are used. Information published by TI regarding third–party products or services
does not constitute a license from TI to use such products or services or a warranty or endorsement thereof.
Use of such information may require a license from a third party under the patents or other intellectual property
of the third party, or a license from TI under the patents or other intellectual property of TI.
Reproduction of information in TI data books or data sheets is permissible only if reproduction is without
alteration and is accompanied by all associated warranties, conditions, limitations, and notices. Reproduction
of this information with alteration is an unfair and deceptive business practice. TI is not responsible or liable for
such altered documentation.
Resale of TI products or services with statements different from or beyond the parameters stated by TI for that
product or service voids all express and any implied warranties for the associated TI product or service and
is an unfair and deceptive business practice. TI is not responsible or liable for any such statements.
Mailing Address:
Texas Instruments
Post Office Box 655303
Dallas, Texas 75265
Copyright  2001, Texas Instruments Incorporated