Application Report
SBOA092A –October 2001
HANDBOOK OF OPERATIONAL AMPLIFIER
APPLICATIONS
Bruce Carter and Thomas R. Brown
ABSTRACT
While in the process of reviewing Texas Instruments applications notes, including those
from Burr-Brown – I uncovered a couple of treasures, this handbook on op amp
applications and one on active RC networks. These old publications, from 1963 and
1966, respectively, are some of the finest works on op amp theory that I have ever seen.
Nevertheless, they contain some material that is hopelessly outdated. This includes
everything from the state of the art of amplifier technology, to the parts referenced in the
document – even to the symbol used for the op amp itself:
These numbers in the circles referred to pin numbers of old op amps, which were potted
modules instead of integrated circuits. Many references to these numbers were made in
the text, and these have been changed, of course.
In revising this document, I chose to take a minimal approach to the material out of
respect for the original author, – Thomas R. Brown, leaving as much of the original
material intact as possible while making the document relevant to present day designers.
There were some sections that were deleted or substantially changed:
•=
“Broadbanding” operational amplifier modules – replaced with discussion of uncompensated
operational amplifiers.
•=
Open loop applications and Comparators – Applications showing an operational amplifier
used open loop, as a comparator have been deleted. At the time of original publication,
there were no dedicated comparator components. Good design techniques now dictate
using a comparator instead of an operational amplifier. There are ways of safely using an
operational amplifier as a comparator – if the output stage is designed to be used that way as
in a voltage limiting operational amplifier – or if clamping is added externally that
prevents the output from saturating. These applications are shown.
•=
Testing Operational Amplifiers – a section that had become hopelessly outdated. Testing
techniques are now tailored to the individual amplifier, to test for parameters important to its
intended purpose or target end equipment.
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•=
Some other application circuits were eliminated – if they were deemed impractical in the
light of today’s technology.
This handbook has also been reorganized to eliminate some redundancy, and place all
application circuits in one location.
The reader is cautioned that proper decoupling techniques should be followed with
operational amplifiers. Decoupling components are omitted from applications schematics
in this document for clarity. Consult reference 2 for proper decoupling techniques.
I also cleaned up grammatical and spelling mistakes in the original.
--- Bruce Carter, Texas Instruments Applications
(Excerpts from) Thomas Brown’s original Preface:
The purpose of this handbook is to provide a single source of information covering the proper
design of circuits employing the versatile modem operational amplifier. This manual will be
helpful to the experienced user of operational amplifiers, as well as the new user, in extending
the range of potential applications in which these devices can be used to advantage.
It is assumed that the reader will have a basic knowledge of electronics, but no particular
knowledge of operational amplifiers is needed to use this handbook. The operational amplifier is
treated as a circuit component inherently subject to certain rules of operation. The design of the
operational amplifiers themselves is considered only when necessary to describe their less
evident properties.
Readers with a working knowledge of operational amplifiers will want to refer directly to the
circuit collection. Readers whose job functions have not previously brought them in contact with
operational amplifiers will want to proceed directly through the handbook until the desired degree
of familiarity is obtained.
Refinements are continuously being made in the design and application of operational
amplifiers, yet the basic principles of application remain the same. Please do not hesitate to
contact Texas Instruments at any time with questions or comments arising from the use of this
handbook. It is, after all, intended for you, the user.
---Thomas R. Brown, Jr.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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Contents
INTRODUCTION...................................................................................................................................7
Computation Control Instrumentation .............................................................................................7
The Feedback Technique...............................................................................................................7
Notation and Terminology...............................................................................................................8
Input Terminals..............................................................................................................................9
Output Terminals...........................................................................................................................9
Power Connections ......................................................................................................................10
Summary of Notation....................................................................................................................10
Electrical Circuit Models ...............................................................................................................10
Circuit Notation............................................................................................................................11
The Ideal Operational Amplifier ....................................................................................................12
Defining the Ideal Operational Amplifier........................................................................................12
A Summing Point Restraint...........................................................................................................13
CIRCUITS AND ANALYSES USING THE IDEAL OPERATIONAL AMPLIFIER.................................14
The Desirability of Feedback ........................................................................................................14
Two Important Feedback Circuits .................................................................................................15
Voltage Follower..........................................................................................................................15
Non-Inverting Amplifier.................................................................................................................17
INVERTING AMPLIFIER..............................................................................................................18
Intuitive Analysis Techniques........................................................................................................19
Current Output.............................................................................................................................20
Reactive Elements.......................................................................................................................20
Integrator.....................................................................................................................................21
Differentiator................................................................................................................................21
Voltage Adder..............................................................................................................................23
Scaling Summer..........................................................................................................................23
Combining Circuit Functions.........................................................................................................24
Differential Input Amplifier.............................................................................................................24
Balanced Amplifier.......................................................................................................................25
Ideal-Real Comparison.................................................................................................................27
CHARACTERISTICS OF PRACTICAL OPERATIONAL AMPLIFIERS...............................................29
Open Loop Characteristics ...........................................................................................................29
Open LoopOperation..................................................................................................................30
Output Limiting .............................................................................................................................30
FREQUENCY DEPENDENT PROPERTIES........................................................................................31
Introduction..................................................................................................................................31
Open LoopGain and the Bode Plot..............................................................................................31
Bode Plot Construction.................................................................................................................31
Closed Loop Gain.........................................................................................................................32
Stability........................................................................................................................................33
Compensation ..............................................................................................................................33
Compensation Changes...............................................................................................................34
Bandwidth....................................................................................................................................35
Loop Gain....................................................................................................................................35
The Significance of Loop Gain......................................................................................................36
BODE PLOTS AND BASIC PRACTICAL CIRCUITRY........................................................................37
Voltage Follower..........................................................................................................................37
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Inverter........................................................................................................................................ 37
X1000 Amplifier ............................................................................................................................ 38
Differentiator................................................................................................................................ 38
INTEGRATOR............................................................................................................................. 40
OTHER IMPORTANT PROPERTIES OF OPERATIONAL AMPLIFIERS............................................ 41
Summing Point Restraints ............................................................................................................ 41
Closed Loop Impedance Levels....................................................................................................42
Output Impedance.......................................................................................................................42
Input Impedance.......................................................................................................................... 43
Differential Inputs and Common Mode Rejection..........................................................................44
The Common Mode Voltage Limit ................................................................................................ 44
Offset........................................................................................................................................... 44
Drift 45
Capacitive Loading.......................................................................................................................45
VOLTAGE DETECTORS AND COMPARATORS ............................................................................... 46
Voltage Limiting Operational Amplifiers ........................................................................................ 46
THE VOLTAGE FOLLOWER .............................................................................................................. 49
BUFFERS AND ISOLATION AMPLIFIERS .................................................................................. 50
Inverting Buffer Adjustable Gain ................................................................................................... 50
Balanced Output.......................................................................................................................... 50
VOLTAGE AND CURRENT REFERENCES........................................................................................ 50
Isolated Standard Cell .................................................................................................................. 51
Constant Current Generator ......................................................................................................... 51
Buffer Variation............................................................................................................................ 52
Presettable Voltage Source .......................................................................................................... 52
Reference Voltage Supply............................................................................................................52
THE NON-INVERTING AMPLIFIER ....................................................................................................53
THE INVERTING AMPLIFIER ............................................................................................................. 54
INTEGRATORS.................................................................................................................................. 55
PRACTICAL INTEGRATORS.............................................................................................................. 55
Simple Integrators ........................................................................................................................ 56
Summing Integrator.....................................................................................................................58
Double Integrator......................................................................................................................... 58
Differential Integrator....................................................................................................................59
AC Integrator...............................................................................................................................59
Augmenting Integrator .................................................................................................................. 59
DIFFERENTIATORS........................................................................................................................... 61
With “Stop” .................................................................................................................................. 61
Low Noise ................................................................................................................................... 62
Augmented Differentiator.............................................................................................................. 62
THE VOLTAGE SUMMER...................................................................................................................63
SUMMING AND AVERAGING AMPLIFIERS................................................................................ 64
Adder........................................................................................................................................... 64
Scaling Adder..............................................................................................................................64
Direct Addition.............................................................................................................................65
Averager...................................................................................................................................... 65
Weighted Average........................................................................................................................66
THE DIFFERENTIAL INPUT AMPLIFIER............................................................................................ 67
Adder-Subtractor or Floating Input Combiner ............................................................................... 68
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THE DIFFERENTIAL (BALANCED) OUTPUT AMPLIFIER.................................................................69
DC AMPLIFIERS ................................................................................................................................70
Simple Inverting sign changing amplifier.......................................................................................70
Chopper Stabilized......................................................................................................................70
Simple Gain Control......................................................................................................................70
Linear Gain Control ......................................................................................................................71
Simple Non-Inverting....................................................................................................................71
Power Booster.............................................................................................................................71
Differential Output.........................................................................................................................73
Gain Control................................................................................................................................73
Inverting Gain Control...................................................................................................................73
DIFFERENTIAL AMPLIFIERS......................................................................................................74
Subtractor....................................................................................................................................74
Difference Amplifier......................................................................................................................74
Common Mode Rejection.............................................................................................................75
Differential Input-Output................................................................................................................75
AC AMPLIFIERS ................................................................................................................................76
DC Amplifiers with Blocking Capacitors ........................................................................................76
Simple Amplifier .....................................................................................................................................76
Single Supply .........................................................................................................................................76
Non-Inverting..........................................................................................................................................77
Double Rolloff.........................................................................................................................................77
AC Preamplifier ......................................................................................................................................78
CURRENT OUTPUT DEVICES............................................................................................................79
Feedback Loop............................................................................................................................79
Simple Meter Amplifier..................................................................................................................79
Meter Amplifier .............................................................................................................................80
Current Injector............................................................................................................................80
Linear Current Source ..................................................................................................................81
Deflection Coil Driver....................................................................................................................82
OSCILLATORS AND MULTI VIBRATORS .........................................................................................83
Simple Oscillator..........................................................................................................................83
Wien Bridge Oscillator ..................................................................................................................83
PHASE LEAD AND LAG NETWORKS ...............................................................................................84
Lag Element................................................................................................................................84
Adjustable Lag.............................................................................................................................84
Lag value linear with R setting......................................................................................................85
Adjustable Lead...........................................................................................................................85
Lead-Lag .....................................................................................................................................86
Time Delay..................................................................................................................................86
ADDITIONAL CIRCUITS .....................................................................................................................87
Absolute Value .............................................................................................................................87
Peak Follower..............................................................................................................................87
Precision Rectifier........................................................................................................................88
AC to DC Converter......................................................................................................................88
Full Wave Rectifier .......................................................................................................................89
Rate Limiter.................................................................................................................................89
Time Delay..................................................................................................................................90
Selective Amplifier.......................................................................................................................91
SECTION III: SELECTING THE PROPER OPERATIONAL AMPLIFIER ...........................................92
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Focus on Limiting Specifications................................................................................................... 92
Avoid Closed Loop vs. Open Loop Confusion............................................................................... 92
Selection Check List..................................................................................................................... 92
Assistance Available from Texas Instruments............................................................................... 93
References......................................................................................................................................... 93
Figures
Figure 1. Operational Amplifier withFeedback.............................................................................8
Figure 2. Texas Instruments Standard Symbols ........................................................................... 8
Figure 3. Op Amp Package Options...............................................................................................9
Figure 4. Power Supply Connections........................................................................................... 10
Figure 5. Summary of Notation Introduced.................................................................................. 10
Figure 6. Circuit Model of the Single Ended Operational Amplifier ........................................... 10
Figure 7. Circuit Model of the Differential Output Operational Amplifier................................... 11
Figure 8. Notation and Terms Used in Closed Loop Circuits ..................................................... 11
Figure 9. Equivalent Circuit of the Ideal Operational Amplifier .................................................. 12
Figure 10. Open Loop Operation .................................................................................................... 14
Figure 11. Basic Amplifier Circuits................................................................................................. 15
Figure 12. Voltage Follower ............................................................................................................ 15
Figure 13. Feedback Resistor Added to the Voltage Follower ..................................................... 16
Figure 14. Non-Inverting Amplifier ................................................................................................. 17
Figure 15. Non-Inverting Amplifier Re-Drawn to Show Similarity to the Voltage Follower......... 17
Figure 16. Non-Inverting Amplifier Analyzed as a Voltage Divider .............................................. 17
Figure 17. Inverting Amplifier ......................................................................................................... 18
Figure 18. Intuitive Devices for Analysis of Circuits Based on theInverting Amplifier..............19
Figure 19. Inverting Amplifier as a Linear Current Output Device ............................................... 20
Figure 20. General Form of the Inverting Amplifier....................................................................... 20
Figure 21. Integrator Circuit............................................................................................................21
Figure 22. Differentiator Circuit ...................................................................................................... 21
Figure 23. An Intuitive Picture of the Differentiator....................................................................... 22
Figure 24. Voltage Adding Circuit .................................................................................................. 23
Figure 25. Scaling Summer Circuit................................................................................................. 24
Figure 26. Differential Input Amplifier Circuit ................................................................................ 24
Figure 27. Analyzing the Differential Input Amplifier Circuit as Non-Inverting Amplifier ........... 25
Figure 28. The Differential Output Operational Amplifier ............................................................. 26
Figure 29. Equivalent Circuit of aRealOperationalAmplifier......................................................27
Figure 30. Amplifier Circuit Usinga RealOperationalAmplifier..................................................27
Figure 31. Input-Output Transfer Relation for the Open Loop Operational Amplifier................. 29
Figure 32. Bode Plot of anOperational Amplifier and its LinearApproximation........................31
Figure 33. Sketching the Bode Plot Approximation for Figure 32................................................ 32
Figure 34. Closed Loop Gain of a X100 (40 dB) Inverting Amplifier............................................. 32
Figure 35. The Effect of Internal Phase Compensation................................................................. 33
Figure 36. Composite Bode Plots Showing Stability Provided by Proper Phase Compensation34
Figure 37. The Effect of Internal Compensation for Gains Greater Than 1.................................. 34
Figure 38. Instability when an Uncompensated Amplifier is Used at Gains Lower Than the
Designated Level......................................................................................................... 35
Figure 39. Loss of High Frequency Response When Heavy Feedback is Used.......................... 36
Figure 40. Voltage Follower Circuit ................................................................................................ 37
Figure 41. Voltage Inverter Circuit.................................................................................................. 37
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Figure 42. 60 dB Amplifier Circuits.................................................................................................38
Figure 43. Differentiator Circuit ......................................................................................................38
Figure 44. Differentiator With “Stop” .............................................................................................39
Figure 45. Differentiator With “Double Stop”.................................................................................39
Figure 46. Integrator Circuit............................................................................................................40
Figure 47. DC Summing Point Conditions .....................................................................................41
Figure 48. Voltage Follower ............................................................................................................42
Figure 49. Voltage Follower ............................................................................................................43
Figure 50. Inverting Amplifier with Current Offset Control...........................................................44
Figure 51. Drift Stabilizing the Inverting Amplifier ........................................................................45
Figure 52. Gain Peaking Caused byCapacitive Loading..............................................................45
Figure 53. Voltage Limiting Operational Amplifiers ......................................................................46
Figure 54. Fully Clamped Voltage Comparator..............................................................................47
Tables
Table 1. Compound Amplifier,ResultingPerformance.............................................................72
Table 2. Current Source Scaling Resistors ................................................................................81
INTRODUCTION
The operational amplifier is an extremely efficient and versatile device. Its applications span the
broad electronic industry filling requirements for signal conditioning, special transfer functions,
analog instrumentation, analog computation, and special systems design. The analog assets of
simplicity and precision characterize circuits utilizing operational amplifiers.
Computation Control Instrumentation
Originally, the term, “Operational Amplifier,” was used in the computing field to describe
amplifiers that performed various mathematical operations. It was found that the application of
negative feedback around a high gain DC amplifier would produce a circuit with a precise gain
characteristic that depended only on the feedback used. By the proper selection of feedback
components, operational amplifier circuits could be used to add, subtract, average, integrate,
and differentiate.
As practical operational amplifier 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 amplifiers has been extended to include such applications
as DC Amplifiers, AC Amplifiers, Comparators, Servo Valve Drivers, Deflection Yoke Drivers,
Low Distortion Oscillators, AC to DC Converters, Multivibrators, and a host of others.
What the operational amplifier can do is limited only by the imagination and ingenuity of the user.
With a good working knowledge of their characteristics, the user will be able to exploit more fully
the useful properties of operational amplifiers.
The Feedback Technique
The precision and flexibility of the operational amplifier is a direct result of the use of negative
feedback. Generally speaking, amplifiers employing feedback will have superior operating
characteristics at a sacrifice of gain.
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RI RO
-
+
Eoutput
Einput
Eoutput R
=. O
ER
input I
Figure 1. Operational Amplifier with Feedback
With enough feedback, the closed loop amplifier characteristics become a function of the
feedback elements. In the typical feedback circuit, figure 1, the feedback elements are two
resistors. The precision of the “closed loop” gain is set by the ratio of the two resistors and is
practically independent of the “open loop” amplifier. Thus, amplification to almost any degree of
precision can be achieved with ease.
Notation and Terminology
Texas Instruments employs the industry standard operational amplifier symbols shown in figure
2. Power pins are often omitted from the schematic symbol when the power supply voltages are
explicit elsewhere in the schematic. Some op amp symbols also include offset nulling pins,
enable / disable pins, output voltage threshold inputs, and other specialized functions.
-
+
(c)
-
Vocm
+
(a) (b)
Figure 2. Texas Instruments Standard Symbols
•=
Symbol (a) is a buffer op amp
•=
Symbol (b) is a differential input, single ended output op amp. This symbol represents the
most common types of op amps, including voltage feedback, and current feedback. It is
often times pictured with the non-inverting input at the top and the inverting input at the
bottom.
•=
Symbol (c) is a differential input, differential output op amp. The outputs can be thought of
as “inverting” and “non-inverting”, and are shown across from the opposite polarity input for
easy completion of feedback loops on schematics.
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Figure 3. Op Amp Package Options
Figure 3 represents a small number of the many op amp package options offered by Texas
Instruments.
Input Terminals
In figures 2b and 2c, the “-“ pin is the “inverting input” or “summing point,” meaning a positive
voltage produces a negative voltage at the output on symbol (b), and the top (non-inverting)
output on symbol (c). When only one input or output terminal exists, its voltage is measured with
respect to ground. This is indicated by the term, “single ended.” It is a popular ambiguity not to
explain if a circuit, earth, 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 an inverting input, such as in figures 2b and 2c, the voltage at the inverting input
may be measured with respect to the non-inverting input. In use, such an amplifier responds to
the difference between the voltages at the inverting and non-inverting inputs, i.e., a “differential
input.
In many circuits, the non-inverting input is connected to ground. Due to the high gain of
operational amplifiers, only a very small input voltage then appears at the output and the output
is virtually at ground potential. For purposes of circuit analysis, it can be assumed to be ground a
“virtual ground.”
Output Terminals
The relation between the inverting and non-inverting inputs and the output was stated above.
For the symbol of (c) the second output voltage is approximately equal and opposite in polarity
to the other output voltage, each measured with respect to ground. When the two outputs are
used as the output terminals without ground reference, they are known as “differential outputs”.
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Power Connections
-
+
Figure 4. Power Supply Connections
Power is supplied to each of these units at connections as shown in figure 4. Such a connection
is implied in all operational amplifier circuits. The dual supply presents the same absolute value
of voltage to ground from either side, while the center connection ultimately defines the common
line and ground potential. The exceptions to this are AC amplifier circuits that may use a single
power supply. This is accomplished by creating a floating AC ground with DC blocking
capacitors. In such circuits, a source of “half-supply” creates a “virtual ground” exactly half way
between the positive supply and ground potentials.
Summary of Notation
If it is understood that the there may not be two inputs or two outputs, figure 5 is a concise
summary of the notation introduced. The arrows denote the “direction” of the polarity at each
pin.
-
Vocm
+
Figure 5. Summary of Notation Introduced
Electrical Circuit Models
The simplified models of the differential input operational amplifiers are shown in figures 6 and 7.
Figure 6. Circuit Model of the Single Ended Operational Amplifier
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As indicated in figure 6, the operational amplifier can be represented by an ideal voltage source
whose value depends on the input voltage appearing across the inverting and non-inverting
inputs plus the effects of finite input and output impedances. The value, A, is known as the open
loop (without feedback) gain of the operational amplifier.
Figure 7. Circuit Model of the Differential Output Operational Amplifier
The simplified model of the differential output operational amplifier (figure 7) is an accurate
approximation only under special conditions of feedback (see “Balanced Amplifier” later in this
handbook). Figure 6 represents the model of the differential output type when it is used as a
single ended output device; the inverting output simply being ignored.
Circuit Notation
RI RO
Input Resistor Feedback Resistor
Inputvoltage
Common line
Drift stabilizing
resistor -
optional
SummingPoint -
+
-
-
-
+
+
+
Ei
EO
Feedback
Loop
Outputvoltage
EI
Figure 8. Notation and Terms Used in Closed Loop Circuits
A circuit that will become very familiar as we progress into practical amplifier circuits and the
notation we will use are shown in figure 8. Resistors RI and RO are replaced by complex
impedances ZI and ZO in some applications of this circuit.
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The Ideal Operational Amplifier
In order to introduce operational amplifier circuitry, we will use an ideal model of the operational
amplifier to simplify the mathematics involved in deriving gain expressions, etc., for the circuits
presented. With this understanding as a basis, it will be convenient to describe the properties of
the real devices themselves in later sections, and finally to investigate circuits utilizing practical
operational amplifiers.
To begin the presentation of operational amplifier circuitry, then, it is necessary first of all to
define the properties of a mythical “perfect” operational amplifier. The model of an ideal
operational amplifier is shown in figure 9.
Figure 9. Equivalent Circuit of the Ideal Operational Amplifier
Defining the Ideal Operational Amplifier
•=
Gain: The primary function of an amplifier is to amplify, so the more gain the better. It can
always be reduced with external circuitry, so we assume gain to be infinite.
•=
Input Impedance: Input impedance is assumed to be infinite. This is so the driving source
won’t be affected by power being drawn by the ideal operational amplifier.
•=
Output Impedance: The output impedance of the ideal operational amplifier is assumed to
be zero. 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 inverting input so the
response time is assumed to be zero. Phase shift will be 180°. Frequency response will be
flat and bandwidth infinite because AC will be simply a rapidly varying DC level to the ideal
amplifier.
•=
Offset: The amplifier output will be zero when a zero signal appears between the inverting
and non-inverting inputs.
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A Summing Point Restraint
An important by-product of these properties of the ideal operational amplifier is that the summing
point, the inverting input, will conduct no current to the amplifier. This property is to become an
important tool for circuit analysis and design, for it gives us an inherent restraint on our circuit - a
place to begin analysis. Later on, it will also be shown that both the inverting and non-inverting
inputs must remain at the same voltage, giving us a second powerful tool for analysis as we
progress into the circuits of the next section.
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CIRCUITS AND ANALYSES USING THE IDEAL OPERATIONAL AMPLIFIER
A description of the ideal operational amplifier model was presented in the last section, and the
introduction of complete circuits may now begin. Though the ideal model may seem a bit remote
from reality - with infinite gain, bandwidth, etc., it should be realized that the closed loop gain
relations which will be derived in this section are directly applicable to real circuits -to within a
few tenths of a percent in most cases. We will show this later with a convincing example.
The Desirability of Feedback
Load ES
-
+
RS
RO
Source
Figure 10. Open Loop Operation
Consider the open loop amplifier used in the circuit of figure 10. Note that no current flows from
the source into the inverting input - the summing point restraint derived in the previous section hence,
there is no voltage drop across RS and ES appears across the amplifier input. When ES is
zero, the output is zero. If ES takes on any non-zero value, the output voltage increases to
saturation, and the amplifier acts as a switch.
The open loop amplifier is not practical - once an op amp is pushed to saturation, its behavior is
unpredictable. Recovery time from saturation is not specified for op amps (except voltage
limiting types). It may not recover at all; the output may latch up. The output structure of some
op amps, particularly rail-to-rail models, may draw a lot of current as the output stage attempts to
drive to one or the other rail. For more details on op amps in open loop operation, consult
reference 1.
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Two Important Feedback Circuits
(a) Inverting
(b) Non-Inverting
EO
-+
RORI
RI
-
+
EOEI
EI
RO
. R
.
R
E
= OE E = 1 + O .E
OI
O I
R
R
I
.
I
Figure 11. Basic Amplifier Circuits
Figure 11 shows the connections and the gain equations for two basic feedback circuits. The
application of negative feedback around the ideal operational amplifier results in another
important summing point restraint: The voltage appearing between the inverting and non-
inverting inputs approaches zero when the feedback loop is closed.
Consider either of the two circuits shown in figure 11. If a small voltage, measured at the
inverting input with respect to the non-inverting input, is assumed to exist, the amplifier output
voltage will be of opposite polarity and can always increase in value (with infinite output
available) until the voltage between the inputs becomes infinitesimally small. When the amplifier
output is fed back to the inverting input, the output voltage will always take on the value required
to drive the signal between the inputs toward zero.
The two summing point restraints are so important that they are repeated:
1.
No current flows into either input terminal of the ideal operational amplifier.
2.
When negative feedback is applied around the ideal operational amplifier, the differential
input voltage approaches zero.
These two statements will be used repeatedly in the analysis of the feedback circuits to be
presented in the rest of this section.
Voltage Follower
EO
EO = EI
EI
-
+
Figure 12. Voltage Follower
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The circuit in figure 12 demonstrates how the addition of a simple feedback loop to the open
loop amplifier converts it from a device of no usefulness to one with many practical applications.
Analyzing this circuit, we see that the voltage at the non-inverting input is EI, the voltage at the
inverting input approaches the voltage at the non-inverting input, and the output is at the same
voltage as the inverting input. Hence, EO = EI, and our analysis is complete. The simplicity of our
analysis is evidence of the power and utility of the summing point restraints we derived and have
at our disposal.
Our result also may be verified by mathematical analysis very simply. Since no current flows at
the non-inverting input, the input impedance of the voltage follower is infinite. The output
impedance is just that of the ideal operational amplifier itself, i.e. zero. Note also that no current
flows through the feedback loop, so any arbitrary (but finite) resistance may be placed in the
feedback loop without changing the properties of the ideal circuit, shown in figure 13. No voltage
would appear across the feedback element and the same mathematical analysis would hold.
-
+
EO = EI
EO
EI
RO
Figure 13. Feedback Resistor Added to the Voltage Follower
The feedback resistor is of particular importance if the op amp selected is a current-feedback
type. The stability of current-feedback op amps is dependent entirely on the value of feedback
resistor selected, and the designer should use the value recommended on the data sheet for the
device.
Unity gain circuits are used as electrical buffers to isolate circuits or devices from one another
and prevent undesired interaction. As a voltage following power amplifier, this circuit will allow a
source with low current capabilities to drive a heavy load.
The gain of the voltage follower with the feedback loop closed (closed loop gain) is unity. The
gain of the ideal operational amplifier without a feedback loop (open loop gain) is infinity. Thus,
we have traded gain for control by adding feedback. Such a severe sacrifice of gain -from
infinity to unity - is not necessary in most circuits. The rest of the ideal circuits to be studied will
give any (finite) closed loop gain desired while maintaining control through feedback.
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Non-Inverting Amplifier
RO
RI
EI EO
-
+
.
RO
EO =
1 + .
.EI
R
.
I
Figure 14. Non-Inverting Amplifier
The circuit in figure 14 was chosen for analysis next because of its relation to the voltage
follower. It is re-drawn as in figure 15, which makes it evident that the voltage follower is simply a
special case of the non-inverting amplifier.
-
+
RO EO RI
EI
Figure 15. Non-Inverting Amplifier Re-Drawn to Show Similarity to the Voltage Follower
Since no current flows into the inverting input, RO and RI form a simple voltage divider (figure
16).
RO
EO
RI
EI
Figure 16. Non-Inverting Amplifier Analyzed as a Voltage Divider
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The same voltage must appear at the inverting and non-inverting inputs, so that:
(E .)= (E +) = EI
From the voltage division formula:
RI
EI =.EO
RI + RO
ER + RR
OIO O
== 1 +
ER R
II I
The input impedance of the non-inverting amplifier circuit is infinite since no current flows into
the inverting input. Output impedance is zero since output voltage is ideally independent of
R
output current. Closed loop gain is 1 + O hence can be any desired value above unity.
RI
Such circuits are widely used in control and instrumentation where non-inverting gain is required.
INVERTING AMPLIFIER
RI
RO
EO
EI
-
+
OE = OR.
IE IR
Figure 17. Inverting Amplifier
The inverting amplifier appears in figure 17. This circuit and its many variations form the bulk of
commonly used operational amplifier circuitry. Single ended input and output versions were first
used, and they became the basis of analog computation. Today’s modern differential input
amplifier is used as an inverting amplifier by grounding the non-inverting input and applying the
input signal to the inverting input terminal.
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:
EI EO
== 0
RI RO
Hence:
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EO RO
=.
EI RI
Input impedance to this circuit is not infinite as in the two previous circuits, the inverting input is
at ground potential so the driving source effectively “sees” RI as the input impedance. Output
. RO
impedance is zero as in the two previous circuits. Closed loop gain of this circuit is .
RI
Intuitive Analysis Techniques
The popularity of the inverting amplifier has been mentioned already. In control and
instrumentation applications, its practical value lies in the ease with which desired input
impedance and gain values can be tailored to fit the requirements of the associated circuitry. Its
utility is reflected in the variety of intuitive devices that are commonly used to simplify its
analysis.
RI RO
I EOEI I
Figure 18. Intuitive Devices for Analysis of Circuits Based on the Inverting Amplifier
If we draw the summing point, the inverting input and output of the inverting amplifier as in figure
18, the dotted line serves as a reminder that the inverting input is at ground potential but
conducts no current to ground. The output can supply any needed current, and analysis quickly
becomes rote. Another such device uses the action of a lever to show as vectors the voltage
relations that exist using the inverting input as the fulcrum.
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Current Output
-
+
IL
RI RL
EI
EI
IL =.
RI
Figure 19. Inverting Amplifier as a Linear Current Output Device
So far, we have considered voltage as the output of the inverting amplifier, but it also finds wide
application as a current supplying device. This is accomplished by placing the load in the
feedback loop as in figure 19. Since the inverting input is ground potential, the current through
EI . EI
RI is . No current flows into the inverting input, so IL = , which is independent of RL. In
RI RI
similar configurations, the inverting amplifier can serve as a linear meter amplifier or deflection
coil driver. Input impedance is RI as before.
Reactive Elements
Though only resistances hove been used in the input and feedback loop of the amplifiers
presented so far, the general form of the inverting amplifier is shown in figure 20, where ZO and
ZI are complex impedances in general.
EI
EO
ZO
-
+
ZI
OE =
. OZ
IE IZ
Figure 20. General Form of the Inverting Amplifier
The gain relation may be verified in the same manner as for the resistive case by summing
currents using complex notation. There is an area of control application utilizing this general form
of the inverting amplifier. Many times it is necessary to construct a network with some
specifically designated transfer function.
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By reducing this transfer function to the ratio of two polynomials, a table may be consulted for
suitable passive networks to be used in the inverting amplifier.
Other uses of reactive elements are found in the integrator and differentiator circuits that follow.
Integrator
EO
-
+
CO
EI
RI
.1
E = E dt
ORC I
IO
Figure 21. Integrator Circuit
If a capacitor is used as the feedback element in the inverting amplifier, shown in figure 21, the
result is an integrator. An intuitive grasp of the integrator action may be obtained from the
statement under the section, “Current Output,” that current through the feedback loop charges
the capacitor and is stored there as a voltage from the output to ground. This is a voltage input
current integrator.
Differentiator
CI
RO
EO
EI -
+
dE
E =.RC 1
O OI
dt
Figure 22. Differentiator Circuit
Using a capacitor as the input element to the inverting amplifier, figure 22, yields a differentiator
circuit. Consideration of the device in figure 23 will give a feeling for the differentiator circuit.
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EO
RO
EI IC IR
CI
Figure 23. An Intuitive Picture of the Differentiator
Since the inverting input is at ground potential:
dE
I = C I,andI . I = 0
CI CR
dt
so that:
dE ECI
I + O = 0
dt RO
dE
E =.RC I
O OI
dt
It should be mentioned that of all the circuits presented in this section, the differentiator is the
one that will operate least successfully with real components. The capacitive input makes it
particularly susceptible to random noise and special techniques will be discussed later for
remedying this effect.
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Voltage Adder
In a great many practical applications the input to the inverting amplifier is more than one
voltage. The simplest form of multiple inputs is shown in figure 24.
-
+
E1
E2
RI
RORI
EO
RI
E3
O
E =
.
RRI
(E + E + E + ...)
O 123
Figure 24. Voltage Adding Circuit
Current in the feedback loop is the algebraic sum of the current due to each input. Each source,
E1, E2, etc., contributes to the total current, and no interaction occurs between them. All inputs
. RO
“see” RI as the input impedance, while gain is . Direct voltage addition may be obtained
RI
with RO = RI.
Scaling Summer
A more general form of adder allows scaling of each input before addition (figure 25).
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RO
E3
EO
E1
R2
-
+
E2
R1
R3
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RO
E3
EO
E1
R2
-
+
E2
R1
R3
.
EE E
123
EO =.RO
.
+++ ...
RR R
.
123
Figure 25. Scaling Summer Circuit
The adder above is obviously a special case of this circuit. Each input “sees” its respective input
resistor as the input resistance.
Combining Circuit Functions
The basic inverting amplifier configuration is very flexible - so flexible, in fact, that it would be
difficult to overestimate its usefulness. Additional applications that already may have occurred to
the reader include: a variable gain amplifier using a potentiometer for RI or RO or both; a
summing integrator by using a feedback capacitor in the summing amplifier; and many others.
Differential Input Amplifier
RI RO
RI
E2 EO
RO
E1
-
+
RO
EO =(E2 . E1 )
RI
Figure 26. Differential Input Amplifier Circuit
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Figure 26 shows a circuit utilizing both inputs to the differential operational amplifier. Its
operation can be appreciated best by considering it a combination of the inverting and non-
inverting amplifier, where the input voltage is tapped from the divider formed by the lower RO and
RI (figure 27).
RI RO
E2
RO
RI
EO
-
+
Figure 27. Analyzing the Differential Input Amplifier Circuit as Non-Inverting Amplifier
Hence, the output due to E2 is:
R + R .
ER .
R
OI 2 OO
E = .
= E
O 2
RR + RR
I .
IO I
With E2 grounded, the circuit is simply an inverting amplifier with the non-inverting input
grounded through a resistance (which conducts no current). Hence, the output due to E1 is
. RO
E = E1
O RI
so the total output is:
RO
EO =
RI
(E2 . E1 )
ER
The input pins reside at the voltage level 2 O , however, which may have a detrimental
RI + RO
effect on a real operational amplifier. (See the section on common mode voltage limit.)
Since the action of the voltage divider formed by the bottom RO and RI is independent of the
remainder of the circuit, the voltage common to the input pins is independent of EI. The source of
E2 “sees” RO + RI, the voltage divider itself. Output impedance is zero, as before.
Balanced Amplifier
The differential output type of operational amplifier is redrawn with its ideal equivalent in figure
28.
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RI RO
-
+
EO
E2
E1
RI RO
RO
EO =(E2 . E1 )
RI
Figure 28. The Differential Output Operational Amplifier
Any of the previous single ended output circuits may use the differential output type since the
relation between the inputs and non-inverting output is fixed. The roles of the input terminals
may even be reversed by applying feedback across the bottom feedback pathway (inverting
output to non-inverting input) instead of the non-inverting output to the inverting input. In either
case, the unused output terminal may be ignored. 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, then, it is necessary to take feedback from
both output terminals as in figure 28. This circuit is a differential form of the inverting amplifier
since neither output terminal is grounded. ZOUT is ideally zero, and closed loop (differential) gain
. RO
is .
RI
A differential output amplifier may be used to convert a single-ended voltage into a pair of
balanced voltages by grounding either signal input. Such devices as servo motors, push-pull
amplifier stages, and symmetrical transmission lines may be driven by the differential output
amplifier.
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Texas Instruments fully differential operational amplifiers include an additional pin -VOCM. When
used as an output, this pin represents the common mode voltage about which the two outputs
operate. It can also be used as an input, to allow the user to set the common mode operational
point from an external source, such as the reference output of a differential input analog to digital
converter. The designer is cautioned not to rely on this input exclusively to set the correct DC
operating point of the circuit. Voltage divider effects of input and feedback resistors can easily
violate the input common mode range of the operational amplifier, and the low values of
resistors used in modern fully differential circuits can cause unexpected power dissipation levels
in the resistors. For more information on the correct use of the VOCM pin, and setting the correct
DC operating level of a fully differential operational amplifier circuit, consult reference 3.
Ideal-Real Comparison
The idealized operational amplifier has been used as a model throughout this section. Before
progressing into the next section concerning real operational amplifier characteristics, it will be
demonstrated by example that the gain expressions that have been derived are indeed valid in
the real case.
The equivalent circuit of a real operational amplifier might appear as in figure 29.
RI RO
EI
EO
-
+
Figure 29. Equivalent Circuit of a Real Operational Amplifier
Connecting it as in figure 30 gives a X10 amplifier circuit.
EI
EO
ZI = R
-
+
ZO = 10R
Figure 30. Amplifier Circuit Using a Real Operational Amplifier
When the effect of finite gain, input impedance, and output impedance are taken into account,
the gain characteristics are given by:
EO ZO .
1 .
=.
EI ZI
.
.
1+.
where:
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.
ZZ .
ZZ
out out OO
1++ 1 ++
ZZ ZZ
.
O load .
I in
.=
Zout
.
A .
Z
.
O
This may be expanded as:
E . Z
OO 23
=(1..+. .. + ...)
EI ZI
and, where .«1, as is usually the case, simplifies to:
EO . ZO
=(1 . .)
EI ZI
Now, letting the open loop parameters take on the following values which are typical, though
conservatively estimated:
A = 10,000 ZI = 10 k.
Zin = 50 k. ZO = 100 k.
Z = 100 Z = 10 k.
out load
Solving, we get . = 0.0013 (which justifies our assumption above) and the real closed loop gain
is:
E
O =.10.000 + 0.013 =.9.987
EI
instead of -10 which would be ideally expected.
The gain of this circuit is accurate to within 0.13% of the idealized value.
This entire error may be considered as a ‘calibration” error and completely cancelled by a slight
adjustment of the feedback resistor. Once such on adjustment is made, the gain accuracy of the
circuit would be affected less than 0.02% should the gain of the amplifier change by 10%.
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CHARACTERISTICS OF PRACTICAL OPERATIONAL AMPLIFIERS
The modern operational amplifier is a solid state, high gain, DC voltage amplifier. Practical
feedback circuits employing it are based on the circuits that were derived in the preceding
section using the ideal operational amplifier model. Substituting a real for an ideal operational
amplifier will result in some predictable variation from ideal operation that is negligibly small in
many applications. This section is intended to acquaint the reader with the characteristics of the
real devices so that they may be utilized to the fullest possible extent in practical circuits.
Open Loop Characteristics
In the case of the ideal operational amplifier, circuit operation was seen to be dependent entirely
on the feedback used. It is possible to use the real operational amplifier open loop, but control
and stability problems are encountered due to the high open loop gain (X100000 typically at
DC). Random noise from the input circuit and noise generated within the operational amplifier
itself plus any variations in amplifier characteristics due to temperature change or aging
components are all multiplied by open loop gain. Slight variations in the manufactured unit
become noticeable due to this effect; hence open loop specifications are sometimes given
conservative “typical” values.
Open loop operational amplifier specifications have a relatively remote connection to closed loop
operation of a circuit since they do not as much define circuit operation as they do limit it. The
sheer numbers of useful operational amplifier circuits make it impossible for a manufacturer to
completely specify closed loop operation. Since each closed loop circuit is, in essence, a special
case, it is necessary to understand both open and closed loop characteristics before the
intelligent design of circuitry using operational amplifier can begin. Any statements that are to be
made about operational amplifier circuits must be qualified by the information “open loop” or
“closed loop,” and the character of the feedback should be specified for “closed loop”
information.
Figure 31. Input-Output Transfer Relation for the Open Loop Operational Amplifier
The open loop input-output relationship for a rather “well-behaved” practical operational amplifier
is shown in figure 31. The open loop gain, A, is measured by the slope of the curve so it can be
seen that the operational amplifier only amplifies between the saturation values of EO.
The slope of the amplifying portion of the transfer curve is dependent on the frequency of the
input voltage while the saturation voltages remain constant. This relation between input and
output holds regardless of the feedback configuration used as long as the amplifier is not in
overload.
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The “well behaved” aspect of this operational amplifier is the fact that its transfer curve goes
through the origin. In practice, all operational amplifiers exhibit offset, a fault that effectively shifts
the transfer curve from the origin. To complicate matters further, this offset value will wander,
producing drift. Both of these phenomena are of the same order of magnitude as the input
voltage necessary to drive the open loop amplifier into saturation and a necessary part of circuit
design is to minimize their effect.
Open Loop Operation
As an example of open loop operation, consider the Texas Instruments THS4001 used as an
open loop DC amplifier. DC open loop gain is 10000 and output saturation occurs at ±13.5 volts
(for a supply voltage of ±15V). Hence, for linear operation, the input voltage cannot exceed
10,000 X 2.7 millivolts. The open loop amplifier is also subject to the full effect of random noise,
offset, and drift, which may be greater than 2.7 millivolts. Therefore, the open loop amplifier is
not useful for linear operation, because any circuit that is so close to saturation may cause the
output to latch-up.
Output Limiting
Texas Instruments specifications for operational amplifiers give a voltage and a current output
rating, plus output short circuit current. Output saturation voltages are commonly slightly greater
than the rated output value when the nominally specified power supply voltage is used. Texas
Instruments operational amplifiers will supply full output voltage to a load drawing full rated
output current for an indefinite period.
In addition, for lower output voltages, slightly higher output current is available up to the short
circuit conditions. Though the current ratings are conservative, exceeding the rated current
should be attempted only after some calculation, unless the output voltage is extremely low.
Output voltage is self-limiting, and voltage levels above the saturation voltage cannot be
achieved. It is not recommended to operate an operational amplifier saturated for an indefinite
period of time.
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FREQUENCY DEPENDENT PROPERTIES
Introduction
The AC response characteristics of the operational amplifier are very important considerations in
circuit design. DC operational amplifiers will operate successfully at audio, ultrasonic, and radio
frequencies with some predictable variation from DC operation. Circuits designed to operate at
DC are also affected by the AC response since random noise and varying DC levels contain AC
components.
Open Loop Gain and the Bode Plot
The frequency response curve of operational amplifier circuitry is conveniently represented by
the Bode plot. The absolute value of voltage gain is plotted in dB (the hybrid but popular
EO
“decibel” defined by dB = 20log so that a gain of 10 is 20 dB, a gain of 100 is 40 dB, etc.)
EI
versus the orthodox decade logarithmic frequency scale. The Bode plot of a typical operational
amplifier’s open loop gain is shown in figure 32 along with a convenient linear approximation to
the actual curve.
Figure 32. Bode Plot of an Operational Amplifier and its Linear Approximation
Bode Plot Construction
The shape of the Bode plot shown in figure 32 is characteristic of all compensated voltage
feedback operational amplifiers. It is so characteristic, in fact, that any open loop Bode plot may
be approximated rapidly from only two bits of information about the particular operational
amplifier:
1) DC open loop gain
2) The unity-gain crossover frequency (open loop bandwidth).
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For example: An operational amplifier has DC open loop gain of 108 dB and open loop
bandwidth of 1 MHz. From these two values, we can sketch the Bode plot as indicated in figure
33.
Figure 33. Sketching the Bode Plot Approximation for Figure 32
Comparing the shape of this sketch with the typical response of figure 32, the constant gain
bandwidth product sketch is observed to be a conservative approximation to the typical
response. Since the typical gain fall off exceeds 20 dB per decade at some points, there may be
slight peaking at intermediate closed loop gains. Such peaks do not indicate a condition of
instability.
Closed Loop Gain
When feedback is used around an operational amplifier, the closed loop gain of the circuit is
determined by a ratio involving the input and feedback impedances used. If the closed loop gain
called for by the feedback configuration is greater than the open loop gain available from the
operational amplifier for any particular frequency, closed loop gain will be limited to the open
loop gain value. Thus a plot of the closed loop gain of a X100 (40db) amplifier using the amplifier
of figure 33 would appear as in figure 34:
Figure 34. Closed Loop Gain of a X100 (40 dB) Inverting Amplifier
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Stability
As indicated above, the closed loop amplifier circuit cannot supply more gain than is available
from the operational amplifier itself, so at high frequencies, the closed loop Bode plot intersects
and follows the open loop gain curve. The intersection point between the closed and open loop
curves is important because the angle between the two curves - or, more precisely, the “rate of
closure” since the curves aren’t actually straight lines - determines whether the closed loop
amplifier, 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 40 db per decade
the system is likely to be unstable. Bode plots may be varied almost at will to insure stability or to
provide some tailor made frequency response characteristic.
Compensation
The open loop gain of operational amplifiers is tailored or “compensated” with one or more
simple resistor and capacitor combinations (figure 35).
Figure 35. The Effect of Internal Phase Compensation
Phase compensation is effected in order that the majority of popular circuits utilizing operational
amplifiers will be inherently stable, even under conditions of 100% feedback. As a consequence
of internal compensation, the user may connect feedback around the amplifier with relative
impunity. We must hasten to add, though, that each feedback condition is, in essence, a special
case. Superior results may be obtainable by adding external compensation. Knowledge of the
stability criteria and the Bode plot will be adequate in all but the most unorthodox circuits.
If compensation were not provided, certain amplifier circuits would be unstable under normal
operating conditions according to the above “rate of closure” or change of slope principle. The
effect of compensation on closed loop stability can be seen from the Bode plots of figure 36,
showing several different closed loop amplifiers utilizing the same operational amplifiers with and
without compensation.
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Figure 36. Composite Bode Plots Showing Stability Provided by Proper Phase Compensation
Compensation Changes
Operational amplifier compensation for most voltage feedback amplifiers is internal to the die,
and cannot be changed. Texas Instruments supplies voltage feedback amplifiers that are
compensated for gains higher than unity gain, and uncompensated operational amplifiers. The
purpose of decreasing compensation, sacrificing unity gain stability, is to increase the flatness of
the response curve the operational amplifier by changing the 3 dB break point frequency. The
effect of this is shown in figure 37.
Figure 37. The Effect of Internal Compensation for Gains Greater Than 1
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The amplifier can be used at gain levels above the designated gain level, as determined by
external compensation and feedback components, but it cannot be used for lower gains without
readjusting the compensation. Instability would result since the rate of closure may be too large
at low gain values (figure 38).
Figure 38. Instability when an Uncompensated Amplifier is Used at Gains Lower Than the
Designated Level.
Bandwidth
The open loop bandwidth of the operational amplifier is shown explicitly in the Bode plot. The
plot has only two distinguishing frequencies, one being the unity gain crossover frequency and
the second being the 3 dB point. The 3 dB point is considered to be the bandwidth of the open
loop amplifier and used in open loop specifications.
The unity gain crossover frequency may be from 100 kHz for signal amplifiers to 1 GHz or higher
for high-speed amplifiers. An important aspect of bandwidth - besides making high frequency
operational amplifier circuits practical - is to improve the precision of signal amplification. The
loss of high frequency components of non-sinusoidal voltages such as pulses, control signals,
DC steps, or even speech patterns may result in undesirable distortion and phase shift.
Wide bandwidth amplifiers are used maintain high loop gain at lower signal frequencies. For
example, it is necessary to use an operational amplifier with open loop bandwidth of at least 200
MHz to provide a closed loop gain of 40 dB at 1 MHz.
Loop Gain
As indicated in figure 34, loop gain is the gain “difference” between open and closed loop gain.
In actuality, the loop gain is the ratio between open loop gain and closed loop gain since
subtracting on the logarithmic gain scale is equivalent to division.
Open Loop Gain
Loop Gain =
Closed Loop Gain
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In a practical circuit, loop gain is the increase in gain that is observed when the feedback path is
opened, but with all circuit loads intact. Loading effects of finite input and output impedance, as
well as the external feedback components, will lead to reduced loop gain. For example, in a
unity gain inverting configuration, 6 dB is lost due to the voltage divider effect of the input and
feedback resistors. Since the phase compensation network fixes the 3 dB point and roll off rate
of the frequency response, the reduced gain effectively lowers the bandwidth. An inspection of
figure 39 will clarify this effect.
Figure 39. Loss of High Frequency Response When Heavy Feedback is Used
The Significance of Loop Gain
Just as local degeneration around a transistor can reduce circuit sensitivity to certain parameter
changes in that transistor, feedback around an operational amplifier will reduce sensitivity to
open loop parameter changes. Open loop gain, phase shift, input impedance, and output
impedance may vary with temperature, power supply voltage, and time. Loop gain is the
payment made for circuit stability and gain accuracy, and it is a direct measure of the
improvement obtained. Basic stability, however, must be designed into the open loop amplifier.
Noise, drift, and offset will not be affected by loop gain. These parameters are essentially input
functions that, like the signal, will be increased by the closed loop gain. The signal to noise ratio
will remain constant, independent of gain. Loop gain will improve closed loop gain stability,
phase shift, input impedance, and output impedance.
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BODE PLOTS AND BASIC PRACTICAL CIRCUITRY
Voltage Follower
Figure 40. Voltage Follower Circuit
The unity gain follower and its Bode plot are shown in figure 40. Since there is no feedback
impedance loading, the closed loop plot traces out the unity gain line to the open loop unity gain
crossover before rolling off.
Inverter
Figure 41. Voltage Inverter Circuit
A unity gain inverting amplifier is shown in figure 41. The bandwidth is decreased by one octave
(50%) from that of the voltage follower due to the voltage division effect of the input and
feedback resistors mentioned above.
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X1000 Amplifier
NON-INVERTING INVERTING
EI999R
R
EO
-
+
R
1000R
EO
-
+
EI
R + R . R
OI O
E = E = 1000EE = E =.1000E
O II OII
RI RI
Figure 42. 60 dB Amplifier Circuits
Figure 42 shows the Bode plot for either the inverting or non-inverting amplifier with a gain of
X1000 (60db). Negligible bandwidth is last due to the voltage divider effect but is still very much
reduced by the normal roll off of the open loop curve.
Differentiator
Figure 43. Differentiator Circuit
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The Bode plot of the differentiator (figure 43) is slightly more trouble to construct since the ZI
value is dependent on frequency. It is evident that the curve must intersect the unity gain axis at
the frequency where XC = RO (conveniently found from the reactance chart in Appendix A). For
DC, the capacitor represents infinite impedance hence gain is zero. At higher frequencies, XC
drops and the gain increases, which is approximated closely by a straight line rising at 20 dB /
decade.
Since highest gain is encountered at high frequencies, this circuit is very susceptible to random
noise. Even more important, however, is the fact that the rate of closure is about 40 dB / decade,
making the simple differentiator inherently unstable in operation. One practical method of
reducing noise and preventing instability is shown in figure 44.
Figure 44. Differentiator With “Stop”
At high frequencies, XC is negligible and the circuit operates as an amplifier with resistive
1
feedback. The transition “point” is the frequency at which f = . Note that a capacitor,
2.RICI
CO, in parallel with R, would have produced the same results with the significant frequency given
1
by f = .
2.ROCO
Both techniques may be combined to give even better noise rejection (figure 45).
Figure 45. Differentiator With “Double Stop”
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With RO and CO set to break at the same frequency as RI and CI, the total slope change will be
twice that of a single RC combination, hence a roll off of 20 dB / decade is introduced.
INTEGRATOR
Figure 46. Integrator Circuit
The discussion above should make the Bode plot for an integrator simple to deduce (figure 46).
Unity gain crossover occurs at the frequency where XCO = RI. The slope is a negative 20 dB /
decade and gain would ideally go to infinity at DC.
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OTHER IMPORTANT PROPERTIES OF OPERATIONAL AMPLIFIERS
Summing Point Restraints
In the case of the ideal operational amplifier, circuit analysis was simplified by the ideal summing
point restraints of zero voltage and zero current at the inverting input. The real operational
amplifier summing junction comes close to this, as will be shown in an example.
A typical Texas Instruments THS4001 Operational Amplifier has a DC open loop gain of 80 dB
or 10,000, open loop input impedance of 10 M., and a saturation voltage of more than ±13
volts.
Figure 47. DC Summing Point Conditions
For the circuit shown in figure 47 to have a full output of 10 volts, the voltage at the inverting
input must be:
10
E.= = 1 mV
10,000
The current flowing to the inverting input is the voltage at the inverting input divided by the
impedance to the non-inverting input, which is ri. This specification is available from the data
sheet.
1 mV
I.= = 0.1 nA
10 M.
Note that these calculations do not depend on the values of the feedback and input elements. In
fact, they don’t depend on the nature of the closed loop circuit at all, so long as the operational
amplifier is not operating in an overload condition.
Since the dynamic voltage current variations that appear at the summing junction of a real
operational amplifier in a closed loop circuit are so small, they are considered zero - as in the
ideal case -for circuit analysis purposes. It must be noted, however, that this effect is due to the
high open loop gain of the operational amplifier. At high frequencies, the open loop gain falls off
and the summing point voltage 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.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Closed Loop Impedance Levels
Open loop output impedances are given in the specifications and range from 3 . to 5000 ., with
the majority of operational amplifiers having 100 or 200 . open loop output impedance. Since
the input and feedback resistors usually will vary from 1 k. to 1 M., this may represent a rather
poor approximation of the ideal zero output impedance. However, as we shall see, the
equivalent closed loop output impedance is typically less than an ohm.
Open loop input impedances are also specified and run as high as 1015 .. Compared to the
typical feedback impedance levels, this can be a very good approximation of the ideally infinite,
open loop input impedance. Practically, this is of little importance since the input resistor
determines the closed loop input impedance of the inverting amplifier. Calculations will show
that the equivalent input impedance of the non-inverting amplifier may be hundreds or thousands
of M., closed loop.
Output Impedance
IL
EI
ZCLout
Zout
ei
EO
-
+ eo
Figure 48. Voltage Follower
Using the Texas Instruments THS4001 as a voltage follower in the circuit of figure 48, we can
readily determine the effective closed loop output impedance. Loading this circuit with an
incremental output current, .IL, forces the amplifier output, eo, to increase by:
.e =.IZ
o L out
To maintain this .eo, the voltage across the inputs must change by:
.eo
A
Since the inverting input is tied to the output and the input voltage, EI, applied to the non-
inverting input, must decrease by .ei. The effective output impedance is then seen to be:
.E .
.e .
Z .
Z
O o out out
.IA .eA
L .
o
Thus, for the THS4001, the open loop output impedance of 10 . is decreased by the DC gain of
10,000 to an effective 0.001 . at the output plus any lead impedance between the feedback
point and the load.
More general calculations would show that the output impedance is reduced by the loop gain.
The voltage follower is a limiting case in which the loop gain is equal to the open loop gain.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Input Impedance
Closed loop input impedance is also increased by loop gain in non-inverting closed loop
applications. In the inverting or summing closed loop configuration, the summing junction is a
virtual ground and the input impedance is almost exactly the value of the summing impedance,
ZI.
Figure 49. Voltage Follower
In figure 49, the operational amplifier is again shown in the voltage follower circuit with the open
loop input impedance Zin, indicated. For any change in output voltage, .Eo, the voltage across
the inverting and non-inverting input must change by .Eo divided by the open loop gain, A:
.E .E
.ei = o = I
AA
The change of voltage, .ei, across the open loop input impedance, Zin, demands a current, .lin,
equal to .ei divided by Zin.
.ei .E2
.Iin ==
Z AZ
in in
The closed loop input impedance, ZCL in, is the change in input voltage, .E2, divided by the
change in input current, .lin.
.E .
AZ
2 .
in
Z = =.E = AZ
CLin 2 in
.I .E
in .
2
Again, this is a limiting case in which the loop gain is equal to the open loop gain. In the more
general case, the effective input impedance is equal to the open loop input impedance multiplied
by the loop gain. Thus, assuming zero offset currents, the input impedance of the THS4001 is
greater than 10 M. as long as loop gain is greater than 40 dB. Current leakage paths
associated with the input stage tend to limit the input impedance to be achieved in this manner
to about 10 M..
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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Differential Inputs and Common Mode Rejection
The input to most Texas Instruments operational amplifiers is a pair of input pins, neither of
which is connected to ground. Such pair of “floating” input connections is termed “differential
inputs”. Each input connection drives separate, balanced transistor amplifiers. Ideally, the same
voltage connected to each input would produce no net result; hence the operational amplifier
would only detect the difference in the two input voltages. The voltage that both inputs
experience is known as the common mode voltage.
In practice, the voltages on each input are amplified separately and, due to component
variations, never perfectly balance out to zero. The “common mode rejection” properly of a
differential input amplifier also depends on the feedback configuration of the closed loop
application.
The Common Mode Voltage Limit
As stated above, the circuitry within the operational amplifier responds to the voltages appearing
at the two inputs separately. Either input can be overdriven, saturating the input transistor(s).
Since under normal feedback conditions there is only a negligible difference in voltage between
the two inputs (see “Summing Point Restraints”), the input saturation voltage is known as the
common mode voltage limit and appears in Texas Instruments specifications.
For the inverting amplifier, one input terminal is grounded; hence, the common mode input
voltage 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 that a certain input voltage is necessary to balance the operational
amplifier circuit. This input voltage is needed because of a small bias current and voltage
inherently required by the operational amplifier, called offset. When these two bias components
are not externally supplied, they are drawn from the input and feedback networks causing an
output voltage error.
In most applications, this small error is negligible. For highest performance, simple biasing
circuits may be used externally. As an example, a simple bias current injector as shown in figure
50 may correct the current components of input offset.
-
+
RO
-+
RI
Figure 50. Inverting Amplifier with Current Offset Control
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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Drift
The bias values mentioned above will vary with temperature, time, and power supply voltage,
producing a variable output error or drift. Again, this effect is negligible in many cases, but it
should be taken into account in critical applications.
In some Texas Instruments operational Amplifiers, input connections are made directly to the
bases of a matched pair of input transistors. Thus, variations in base current and emitter to base
voltage caused by external changes, i.e. temperature, will tend to cause both input transistors to
vary in the same direction. Since the base currents must flow to ground through the external
feedback network, drift effects can be minimized by: (1) using the lowest resistance levels
consistent with input impedance requirements and output current capability; and (2) balancing
the resistances from the two inputs to ground. For the amplifier shown in figure 51, this latter
consideration is satisfied by connecting a resistor from the non-inverting input to ground equal to
the equivalent resistance from the inverting input to ground.
RI RO
EO
-
+EI
R2
Figure 51. Drift Stabilizing the Inverting Amplifier
Capacitive Loading
The addition of capacitive reactance shunting the load of an operational amplifier may lead to
peaking and finally instability at high frequencies. The capacitive load tends to break with the
output impedance of the amplifier causing the slope of the open loop response to increase. As
the rate of closure approaches 40 dB / decade (see “Stability” above), the closed loop response
begins to peak and possibly oscillate (figure 52). This problem is most severe at low gain levels
and at high frequencies.
Figure 52. Gain Peaking Caused by Capacitive Loading
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
VOLTAGE DETECTORS AND COMPARATORS
When this handbook was first published, there were no comparators. Operational amplifiers
were used in a saturated mode as comparators. This section covered the use of operational
amplifiers as comparators, but Texas Instruments strongly discourages this practice. Reference
1 covers this topic in more detail.
When an operational amplifier absolutely must be used as a comparator, there are a couple of
alternatives:
Voltage Limiting Operational Amplifiers
Texas Instruments manufactures voltage limiting operational amplifiers that are specifically
designed to operate at saturated levels, as set by voltage limiting inputs:
INVERTING NON-INVERTING
OPA68x:
x = 8: unity gain stable+Sup
RO
+Sup
Low Set
EO
-Sup
-Sup
High Set
RI
EI
-
+ L OPA68x
3
RI
H2
3
6
7
4 5
8
4
x = 9: gain >= 4
+
-
H
L
OPA68x
2
6
7
5
8
RO
High Set
EI
EO
Low Set
Figure 53. Voltage Limiting Operational Amplifiers
Voltage limiting operational amplifiers are popular in applications that require clipping, such as
video “sync-stripping” circuits. The High Set and Low Set inputs are used to set the maximum
VOH and VOL of the op amp to values between ±Sup. There is no reason why the High Set and
Low Set values have to be positive and negative voltages, respectively. They can be at ground,
or beyond it. There are limits, of course. The amplifier itself has VOH and VOL specifications that
ultimately limit the set levels. The set levels also have a specified accuracy. Incorrect set level
voltages can also prevent the output from working at all. Consult the data sheets for details.
It is possible to use an operational amplifier with external components simulating the output
clamping circuits fabricated into the voltage limiting operational amplifiers described above.
Figure 54 shows an example of the technique:
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
+15 VDC
-
+
CR1
1N4148-1
Rb
10 k....R2
1 M....EORb'
3 k....R1
100 k....-15 VDC
Ra '
15 k....EI
Ref
Ra
15 k....CR2
1N4148-1
-15 VDC
Figure 54. Fully Clamped Voltage Comparator
R21 M.
Threshold =. Vref =. (.15 VDC)= 1.5 VDC
R1 100 k.
. (+ Vsup )Rb .15 VDC .10 k.
Negative clamping level == =.10 VDC
Ra 15 k.
. (. Vsup )Rb +15 VDC . 3 k.
Positive clamping level == =+3 VDC
Ra 15 k.
EO =.10 VDC for EI > 1.5 VDC
EO =+3 VDC for EI < 1.5 VDC
The slope of the transition is determined by the slew rate of the operational amplifier. The set
points, of course, must be within the normal VOH and VOL of the operational amplifier.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
SECTION II CIRCUIT COLLECTION
A search of literature in the field and Texas Instrument’s collection of application notes turned up
the circuits presented in this section. They have been grouped by general function and ordered
within each group by increasing complexity. It is our hope that one of these will trigger the idea
that develops into your circuit.
Please do not interpret any one circuit as our recommendation for your requirement. Some of
them, due to their simplicity or specialized nature, may perform only over limited ranges and
under controlled conditions. We would welcome the opportunity to suggest a specific circuit for
you, given the details of your application.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
THE VOLTAGE FOLLOWER
EI EO
-
+
E-
Let the voltage at the inverting input with respect to the non-inverting input be E-.
By Kirchoff’s voltage law:
(E .)+ E = E
IO
But by definition:
EO =.A(E .)
where A is the gain of the operational amplifier
Then:
( )E =.
A
EO.
And substituting:
IE . O
A
E = OE
Letting A go to infinity,
A
EO approaches zero, and:
OE = IE
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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BUFFERS AND ISOLATION AMPLIFIERS
The standard inverting and non-inverting amplifier circuits provide impedance isolation due to
their inherently low equivalent output impedance. The following circuits are designed principally
for isolation and not for providing gain.
Inverting Buffer Adjustable Gain
RI R2RO
10 k.
....100 10 k.
....
EO
EI
-
+
Potentiometer in feedback allows gain trimming to compensate for tolerance in resistor values.
Balanced Output
Used for driving balanced loads or push-pull stages when ground reference is critical.
EO-
RI
10 k....-
+
RO
10 k....EO+
-
+
EI
RI
10 k....RO
10 k....
By using EO-terminal at the reference, a p-p swing of 4EI is obtainable at EO+, i.e. a usable
swing greater than the power supply voltage rails. A fully differential operational amplifier
provides this function in a single package, and is therefore the preferable design solution.
VOLTAGE AND CURRENT REFERENCES
The high input impedance and low output impedance levels that can be obtained with the
precision and stability of operational amplifier circuitry make reference supplies practical. Some
circuits are merely reference cells or zener diodes with isolator and multiplying circuits added.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Isolated Standard Cell
ErefEref
-
+
Prevent damage to standard cells induced by drawing current from them with low impedance (20
K. / Volt) measuring devices. See section on Buffers and Isolators for gain error. Offset
adjustments should not be made with standard cell connected.
Constant Current Generator
+15 V
I
R2
300 ....6V Zener VZ
RL
IZ
-
+
R1
330 ....
Convenient current reference up to 20 mA:
V 6
I = Z
== 20 mA
R
2 300
15 . V 9
R = Z == 360 .
1
IZ 25
Saturation Voltage 13.5 V
R
= == 675 .
L min
I 20 mA
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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Buffer Variation
Eref
-
+
TLC265x Eref
Low current drift of chopper -stabilized amplifiers improves stability and cell protection.
Presettable Voltage Source
RO
Decade Box
-
+
TLC265x Eref
Eref
RI
1000 X Eref
RI + RO
E = E
O ref
RI
Gives wide range of very stable reference voltages.
Reference Voltage Supply
R4
90 k.
....
R1
10 k....-
+
-
+
R3
10 k....R0
100 k....-EO
+EO
R2
10 k....Eref
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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THE NON-INVERTING AMPLIFIER
-
+
RO
EI
RII
E-
EO
I
Let the voltage at the inverting input with respect to the non-inverting input be E- and the gain of
the operational amplifier be A (ideally, A =. ).
The voltage at the inverting input is then EI + (E-) and, since the current in RI must equal the
current in RO:
(E .)+ EE . ((E .)+ E )
IO I
=
RI RO
but:
E =.A .(E .)
O
O
(E .)= . E
A
Letting A go to infinity, E- approaches zero and the first equation becomes:
EE . E
I OI
=
RI RO
Solving:
E (R + R )= ER
IOI OI
ER + RR
OOI O
== 1+
ER R
II I
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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THE INVERTING AMPLIFIER
RI
EO
EI
RO
E-
I I
-
+
Let the voltage at the inverting input be E- and the open loop operational amplifier gain be A
(ideally, A =. ).
Since equal currents flow in RO and RI:
E .(E .) E .(E .)
I + O = 0
RI RO
But by definition:
E = A .(E .)
O
EO
(E .)= .
A
Letting A go to infinity, E- approaches zero and:
EE
I + O = 0
RI RO
or:
ER
O =. O
EI RI
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
INTEGRATORS
Assume the validity of the ideal gain expression for the generalized Inverting Amplifier:
. ZO
EO = EIZI
The operational form of capacitive impedance is:
1
CZ =
pC
where the symbol, p, is the operator,
dt
d , or for AC analysis is the complex frequency, j2.f.
For the integrator;
OZ = 1
pC
, IZ = IR
-
+
RI CO
EI
EO
.ZO .EI 1
E = E = =. E dt
OI I
Z RC RC
I IOp IO
PRACTICAL INTEGRATORS
Simple integrator circuits operate successfully but current offset is stored in the feedback
capacitor causing output voltage error. This is corrected with low drift chopper stabilized
amplifier and/or current biasing networks.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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Simple Integrators
CO
1 ....FRI
100 k....-
+
EI
EO
. EIdt
EO = =.10 EIdtRICO
Close switch to reset to zero.
R4
10 k....R1
100 k....R5
10 M....+
R2
10 k....-
+
R3
POTEI
CO
1 mF
-EO
This circuit reduces current offset in operational amplifiers without “Balance” controls. With zero
input and switch open, set R3 for zero output drift.
Regeneration may be used to increase open loop DC gain to infinity.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
R6
1 M....R2
100 k....R10
10 k....R5
2 k....EI
R7
1 M....+
R8
10 k....EO
CO
1 ....F
R9
10 k....R4
1 k....-
+
-
R1
100 k....R3
10 M....ZERO
1.
With input open and regeneration control R5 in approximate center of its range, open
reset switch and adjust zero control, R8, until output remains at zero.
2.
Open reset switch, apply an input signal of either polarity and allow integrator to run up to
some voltage between ±10 VDC, then open circuit signal input.
3.
If integrator output decays toward zero, increase regeneration by increasing R5. If output
continues to grow, decrease regeneration.
4.
If setting of regeneration control is altered, repeat steps (1) and (2) above.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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Summing Integrator
R1
E3
-
+
100 k....R3
100 k....R2
100 k....EO
CO
1 ....F
E2
E1
EO =.1 (E + E + E )dt
123
RC
=.10 (E + E + E )dt
123
One amplifier replaces separate summer and integrator circuits. Any number of inputs may be
used. Zero control and regeneration may be added as in the above circuit.
Double Integrator
CO CO
RI RI 1 µ
....F1 µ
....F
1 M.
....1 M.
....
RO
10 k.
....
CI
1 µ
....F
EI
TLC265x EO
-
+
. 4
E = 2 E dt =.4 E dt
O II
(RC )
II
where :
CR
CO = I ,RO = I
22
Integrates twice with one amplifier.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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Differential Integrator
E =.1 (E . E )dt
OI 2
RICO
= 10 (E . E )dt
21
Integrates difference between two signals.
AC Integrator
-
+
TLC265x
E2
RI
100 k....CO
1 ....F
CO
1 ....F
RI
100 k....EO
E1
R2
100 k....EI
EO
CI
100 ....F
-
+
CO
0.01 ....F
RI
100 k....
Integrates AC component only.
Augmenting Integrator
Sums the input signal and its time integral.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
RI ROCO
10 µ
....F
10 k.
....100 k.
....
EO
-
+
TLC265x
EI
. ROEI 1
EO =. EIdt
R CR
I OI
=.10EI . EIdt
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
DIFFERENTIATORS
1
For the differentiator; Z = R, Z =
O OI
Cp
EO
EI
RO
CI
-
+
.ZO
dE I
E = E =.RCE =.RC
O I OIp I OI
ZI
dt
The ideal differentiator circuit is not generally usable in its simple form. It is susceptible to high
frequency noise that may be greater than the derivative output. Design should include high
frequency response limiting.
With “Stop”
Input resistor sets high frequency cutoff.
CI
RI
RO
EI -
+
EO
1 k....100 k....0.1 ....F
1
High frequency cutoff: F == 0.6 kHz
O 2.
RICI
1
Low frequency cutoff: FI == 16 kHz
2.ROCI
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Low Noise
CO
0.001 µ
....F
CI
0.1 ....F
-
+
RI
1 k....RO
100 k....EO
EI
RC = R C drift compensating resistor
II OO
Double high frequency cutoff.
Augmented Differentiator
EO
-
+
RI
100 k....CI
0.1 ....F
RO
100 k....R2
50 k....EI
. RE dE
OI I
E =. RC
O OI
RI dt
1 dEI
E =.E .OI 100 dt
Sums input and its derivative.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
THE VOLTAGE SUMMER
E3
I3
R3
E1
R1
I2
R2
I1
-
+
RO
IO
EO
E2
Assume the ideal summing paint restraints:
1. Pin (1) is at ground potential
2. . IO + I1 + I2 + I3 + ... = 0
The current, IO, is given by:
. E EEE
O 123
IO = =+++ ...
R RRR
O 123
So that:
.
EE E
123
E =.R .
+++ ...
OO
RR R
.
123
. RO
Thus, each input, En, is multiplied by a factor, , before summing.
Rn
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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SUMMING AND AVERAGING AMPLIFIERS
Voltages are summed by applying the signals to the same input of the amplifier. Amplifying,
averaging, etc., may be accomplished by input resistor scaling. Inputs are effectively isolated
from each other. Any number of inputs may be used in each of these circuits.
Adder
10 k.
....
-
+
10 k....10 k....E3
10 k....EO
E1
E2
E = .(E + E + E )
O 123
Zin = 10 k. for each input
Output is inverted algebraic sum of inputs.
Scaling Adder
R1
EO
-
+
E2
R2
10 k....E3
E1
R0
100 k....1 k....R3
100 k....
.
RR R
00 0
E = .
E + E + E =.100(100E +10E + E )
O 123 123
RR R
.
12 3
Z = 1 k. for E = 10 k. for E = 100 k. for E
in 12 3
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Each input is multiplied by a constant before summing-inverting output.
Direct Addition
R1 R0
10 k.
....20 k.
....
E2
E1
R2
10 k....-
+
R2
10 k....EO
R2
10 k....
E = E + E
O 12
3
Zin = R2 = 15 k. for each input
2
RO = 2RI
Non-inverting output.
Averager
RI
RI
30 k....EO
RO
10 k....E2
E1
E3
30 k....RI
30 k....-
+
. RE + E + E
O 123
E =(E + E + E )=.
O 123
RI 3
RO = RI divided by number of inputs
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Output is inverted average of input signals. Ground unused inputs to preserve scale.
Weighted Average
RO
5.1 k....E2
R2
20 k....R3
30 k....E3
-
+
R1
10 k....RO'
1 k....EO
E1
For E = E = E,setR 'soE = E
123 O OI
Then, R + R'= RR2
OO 1
R3
.(R + R')E (R + R')E (R + R')E .(16.4E + 8.2E + 5.4E )
OO 1 OO 2 OO 3 123
E = ..=
OR RR 30
1 23
Each input is multiplied by a weighting factor before averaging.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
THE DIFFERENTIAL INPUT AMPLIFIER
RO
E1
I2
IOI1
R1
E2
R2 R3
-
+
EO
I3
Assume the ideal input restraints:
1. The input pins reside at the common mode voltage, Ef.
2. IO=I1, I2=I3
Current in the top leg is given by:
E . EE . E
1 f fO
I == 1 R1 RO
Solving for EO:
.
RO
.
RO
E = E 1 +. E
Of 1
RR
.
11
Due to current in the bottom leg, R2 and R3 act as a simple voltage divider:
R3
Ef = E2R2 + R3
Substituting:
.
R .
R .
RR .
R + R .
R
3 OO 31 OO
E = .
1 + E . E = .
E . E
O 21 21
R + RR RRR + RR
.
23 .
1 11 .
23 1
For R2 = R1 and R3 = RO, this reduces to:
RO
EO =
R1
(E2 . E1 )
(Ground reference point does not matter. Input may be “floating” if desired.)
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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Adder-Subtractor or Floating Input Combiner
R
10 k.
....
E1
R
10 k.
....R
10 k.
....E2
RI
10 k.
....
E3
RI
RI
10 k.
....
10 k.
....
EO
E4
-
+
As an adder-subtracter, unused inputs should be grounded.
EO =.E . E + E + E
1234
R and RI not necessarily equal
Two or more “floating” inputs maybe combined by connecting them across E3 to E1 and E4 to E2.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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THE DIFFERENTIAL (BALANCED) OUTPUT AMPLIFIER
I4
RO
I1
Ef
E2
EO + EP
Ef
I3
RI
-
+ EP
E1
I2
EO
RI RO
Assume the ideal input restraints:
1. The inverting and non-inverting inputs reside at the same common mode voltage, Ef
2. I1=I2, I3= I4
Current in the top leg is given by:
E . EE .(E + E )
1 f fOP
I1 ==
RI RO
Current in the bottom leg is given by:
E . EE . E
2 f fP
I3 ==
RI RO
Subtracting these two equations:
E . E . E
12 O
=
RI RO
Or:
RO
EO =(E2 . E1 )
RI
(Ground reference is not critical. Input may be “floating” if desired.)
Note that the values of Ef and EP are not uniquely determined by the above equations. In
practice, this means that EP will reside at same value determined by the internal circuitry of the
operational amplifier itself plus the effects of drift. However, EO will remain accurately fixed by
the differential gain equation above.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
DC AMPLIFIERS
There are two basic circuits, inverting and non-inverting, plus the differential output form.
Simple Inverting sign changing amplifier
RI RO
100 k....1 k....EO
-
+
EI
. RO
E = E =.100E
O II
RI
RORI
resistor == 1 k.
RI + RO
Zin = RI = 1 k.
Chopper Stabilized
Improved drift and stability.
Simple Gain Control
EI
EO
-
+
TLC265x
RO
100 k....RI
1 k....
10 kW
EI
-
+
EO
Wide range gain or attenuation.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Unity gain with R centered. The gain is not linear with potentiometer setting. Zin drops as gain is
increased.
Linear Gain Control
RO
100 k.
....
RI
-
+
EI
EO
10 k....
Variable from 0 to 10
EO = 0 to .10EI
Zin = RI = 10 k.
Simple Non-Inverting
EI
-
+
RO
90 k....RI
10 k....EO
Input common mode voltage limit must be observed.
R + R
E = O IE = 10E
O II
RI
Gain controls and/or trimming may be accomplished as in the variations on the inverting
amplifier above.
Power Booster
Output current of any of the above circuits may be increased by the addition of a power booster.
The operational amplifier -booster combination is substituted directly for the original operational
amplifier.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
20 k.
....
10 k....EI
0.1 ....100 k....47 pF
10 pF
-
+
EO
0.1 ....1 k....-
+
4.7 k....
G = +21
Table 1. Compound Amplifier, Resulting Performance
Parameter OPA277 OPA512 Compound
VOS 20 .V 6 mV 20 .V
Drift 0.15 .V/°C 65 .V/°C 0.15 .V/°C
IB 1 nA 30 nA 1 nA
CMRR 130 dB 100 dB 130 dB
VOUT ± 13 V ± 35 V ± 35 V
IOUT 5 mA 10 A 10 A
SR 0.8 V/.S 2.5 V/.S 2.4 V/.S
This circuit addresses the need for a power output stage with a precision input circuit. The
combination is not available in one device. It is possible to combine the power capabilities of the
OPA512 with the precision of the OPA277. The OPA512 has the highest slew rate and
therefore is operated within a local closed loop. The slower OPA277 is operated within the outer
loop. The 47pF capacitor provides a small amount of phase shift to help stabilize the system.
The resulting performance of the compound amplifier shows that the front-end characteristics of
the OPA277 are joined with the ±35V at 10A drive current capabilities out of the OPA512. The
slew rate of the OPA277 is 0.8V/.s. That slew rate is gained up times three in the OPA512 so
that there is an effective slew rate for the compound amplifier of 2.4V/.s.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Differential Output
RI RO
10 k.
....100 k.
....
-
+
RO
EO
RI
EI
10 k.
....100 k.
....
RO
E = E = 10E
O II
RI
For driving floating load.
Gain Control
-
+
EO10 k....EI
Equivalent to replacing both resistors in the non-inverting amplifier. Observe common mode
voltage limit.
Inverting Gain Control
RO
10 k.
....
-
+
EO
EI
RI
10 k....10 k....R2
EO = (.1 to inf inity)EI
Zin = 10 k.
Convenient gain technique
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
DIFFERENTIAL AMPLIFIERS
In differential amplifiers, separate input signals are applied to the differential inputs of the
operational amplifier. The result is direct subtraction in contrast to the summing amplifier that
adds algebraically.
Subtractor
RI RO
E2
10 k....RI
10 k....RO
10 k....10 k....E1
-
+
EO
EO = E2 . E1
Direct subtraction of two inputs.
Difference Amplifier
1 k.
....100 k.
....
O
E =
.
RRI
(E . E )= 100(E . E1 )
O 12 2
Subtractor with amplification.
RI
1 k....RO
E2
EO
E1
RO
100 k....RI
-
+
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Common Mode Rejection
R1 R0
-
+
R4
10 k....R3
5 k....100 k....E1
E2
1 k....R5
10 k....R2
9.1 k....-
+
EO
. RO
E =(E . E )= 10(E . E )
O 12 21
RI
R + R = R
231
Subtraction by inverting and summing to eliminate common mode voltage.
R3 -common mode adjustment. Set for Zero output when E1 = E2.
Differential Input-Output
EO
RI
1 k....RI
1 k....RO
10 k....-
+
RO
10 k....E2
E1
For use in driving floating loads. Input may be floating source.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
AC AMPLIFIERS
DC Amplifiers with Blocking Capacitors
AC operational amplifier circuits will amplify low frequency signals that are below the range of
more conventional amplifiers (0.1 Hz to 20 kHz) while DC blocking still is present. Only a single
ended supply is required in one circuit. DC and AC operational amplifier circuits are equivalent at
higher frequencies.
Simple Amplifier
Simple RC roll off at low frequency.
CI
RI RO
100 k....-
+
1 ....F
EO
EI
10 k....
RO
E =. E =.10E
O II
RI
Zin = 10 k.
1
Low frequency rolloff begins: f == 16 Hz
.3dB
2.RICI
Single Supply
RI
10 k....RO
100 k....-
+
+ C2
100 ....F
EI
R2
10 k....+Supply
CI
1 ....F
EOR2'
10 k....
Equivalent to above, with the supply “floated” above ground.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Non-Inverting
C2
-
+
R1
10 k....EO
+ C1
100 ....F
R0
90 k....R2
100 k....EI
1 ....F
EO in phase with EI
R + R
EO = OR
I = 10EI
I
1
Low frequency rolloff f == 0.16 Hz
.3dB
2.RICI
Double Rolloff
C2
R0
90 k....EO
+C1
100 ....F
EI
1 ....F
R1
10 k....R2
100 k....-
+
Similar to above.
CR = CR
11 22
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
AC Preamplifier
C2
C3
R1
200 ....+C1
1000 ....F
R2
100 k....1 ....F
R0
100 k....EO
-
+
R3
2.2 k....EI +
10 ....F
R4
10 k....
Completely developed AC amplifier with high Zin and double rolloff rate and gain trim.
ER + R
O 01
== 500
EI R1
R4 -Fine gain adjust
1
Low Frequency rolloff begins f == 1.6 Hz
.3dB
2.R1C1
RC = RC
11 22
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
CURRENT OUTPUT DEVICES
These amplifiers will supply output current to a load in linear correspondence to the input
voltage.
Feedback Loop
R1
1 k.
....RL
EI
I
-
+
E
I = I = E mA
RI
I
Zin = RI = 1 k.
Simple Meter Amplifier
RI
10 k....RO
4.7 k....EI
RO
4.7 k....RO
4.7 k....-
+
EI EI
I == mA
meter
3RI 30
Linear current meter reads AC input voltage.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Meter Amplifier
C1
10 ....F
R0
220 k....R4
47 ....R5
100 ....-
+
R6
100 ....C1
1 ....F
C2
10 ....FR1
220 k....R7
100 ....R8
68 k....EI
0.9EI
Meter reading =(rms)
R4 + R5
R5: gain control (calibration)
Fully developed average reading meter
Current Injector
R1 R0
R3
1 k....EI
1 k....RL
I
1 k....-
+
R2
1 k....
E
I =. I =.EI mA
RL
R1 R0
=
R2 R3
Single terminal current available to ground. Observe common mode voltage limit.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Linear Current Source
R2
100 k.
....
R2
100 k....-
+
-
+
I
R1
100 k....R3
1 k....EI
R0
100 k....CO
RL
R0
100 k....
When RL << R2 ,
IL = R2 = mA1
EI R R31 Volt
CO added for high frequency stability.
Change R3 for current scaling:
Table 2. Current Source Scaling Resistors
R3 IL/EI
1 k. 1 mA / Volt
100 . 10 mA / Volt
10 . 100 mA / Volt
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Deflection Coil Driver
R1 R0
-
+
I
EI
RL
10 k....10 k....R3
10 ....
I . R0
= =.100 mA / Volt
E RR
I 13
Load must be ‘floating,” i.e. ungrounded.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
OSCILLATORS AND MULTI VIBRATORS
Oscillators give a continuous sine wave, output. Multivibrator output fixed voltage level or square
wave similar to flip-flop output.
Simple Oscillator
2C
EO
-
+
R C C
R/2
R
1
f =
2.RC
Double integrator circuit with regenerative feedback. Components R, C, and 2C should be very
low tolerance. Trim R/2 until oscillation is barely sustained.
Wien Bridge Oscillator
C
R
R2
1.8 k....R
EO
R3
220 ....R1
500 ....LP1
GE 1869
-
+
C
1
fO = , 100 to 6000 Hz
2.RC
High purity sine wave generation.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
PHASE LEAD AND LAG NETWORKS
These networks are used to stabilize servo systems by introducing phase shift as desired.
Transient and steady state responses may be tailored semi-independently.
Lag Element
RI RO
1 M.
....10 k.
....
EO
-
+
EI
CO
10 ....F
. RE .10E
OI I
EO ==
R 1+ RCP 10 + P
I OO
Integrating type phase lag.
Adjustable Lag
-
+
....R
RO
10 k....R
10 k....EI
C
10 ....F
EO
1
Non-integrating type. Constant inverting unity gain. Maximum lag for R centered for .=
2
where 0 ...1 is the log setting.
. E . 40E
E = I = I
O 2
1+(... )RCP 40 + P
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Lag value linear with R setting
R
EI
10 k....C
10 ....F
-
+
EO
....R
EI 10EI
EO ==
1+.RCP 10 + P
d
P = operator, or j.
dt
Non-inverting low distortion
Adjustable Lead
RR
EO
EI
....R
10 k....C
10 ....F
-
+
10 k....
EO = .[(. . .2 )RCP]EI
Putting input network from adjustable lag circuit in feedback path gives lead element.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Lead-Lag
R R
10 k.
....10 k.
....
-
+
....2R ....1R
EO
C1
10 ....F
C2
10 ....F
EI
2
1 +(... )RC P
11 1
=EO 1+(. .. 2 )RC P
22 2
Composite lead and log network.
Time Delay
R
0.8C
R/6
3.6C
EI
2R/3R/6
EO
0.8C
3.6C
R/4
-
+
Unity gain phase or time shift.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
ADDITIONAL CIRCUITS
The following are various circuits that do not fall into one of the categories of the previous
sections.
Absolute Value
RR
10 k.
....10 k.
....
-
+
EO EI
+ EI follower circuit
. EI inverter circuit
EO =
EI
Full wave rectification. Reverse diodes to give EO =.
EI
Peak Follower
1 ....F
-
+
EOEI
Peak value memory. Use low leakage capacitor. EO = EI maximum. Common mode input
voltage must be observed.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Precision Rectifier
RI RO
RO
10 k....EO
-
+
10 k....EI
2 k....
. RO
E peak = E peak =.5E peak
O II
RI
Half wave with amplification if desired. Placing rectifiers in feedback loop decreases nonlinearity
to very small value.
AC to DC Converter
R8
R3 R72 k.
....
10 k....R2
10 k....-
+
EO
R1
10 k....10 k....+
C
100 ....F
R6
5 k....==
R4
10 k....EI
-
+
EOaverage = 0.9EIrms
EI = 6 mV to 6 V rms @ 10 to 1000 Hz
Precision conversion for measurement or control. Full wave rectifier with a smoothing filter.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Full Wave Rectifier
R1 RO
2 k.
....2 k.
....
R4
1 k....EI
R3
1 k....-
+
EO
R2
1 k....-
+
R5
1 k....
Precision absolute value circuit.
Rate Limiter
R2
4.7 k....EI -Supply -
+
R1
100 k....+
C0
10 ....F
EO
+Supply
R5
100 k....R0
100 k....-
+
R4
100 k....R3
100 k....
. RO
E = E =.E
O II
RI
Rate limit = 7.5 V/sec
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Time Delay
+
C0
10 ....F
R3
4.7 k....R6
10 k....RELAY SPDT
R5
10 k....R7
10 k....+Supply
R1
100 k....R4
10 k....6 Volt
1 k.... coil
-
+
RICO
Delay =
2KI
Where K is setting of RI, 0, K < 1
Time operated relay. Open switch to reset, close to being timing.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Selective Amplifier
RO
330 k.
....
CI
50 nF
Ca
50 nF
EI
Ra
3.3 k....RI
10 k....Twin-T Network
-
+
EO
Ra
3.3 k....2Ca
100 nF
Ra/21.65 k....Ca
50 nF
Twin T feedback
1
Frequency peak = = 1000 Hz
2.RaCa
RO
Gain at peak = =33 = 30 dB
RI
Set CI so that CIRI >2CaRa and RI < 100 k.
Zin= RI = 10kW
Zout < 200 .
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
Application Report
SBOA092A –October 2001
SECTION III: SELECTING THE PROPER OPERATIONAL AMPLIFIER
Now, with the theory, circuits, and test procedures at our command, we are ready to select an
amplifier. A glance at the representative specifications, given in the Appendix, shows the variety
of ratings available. These represent only a small fraction of the operational amplifiers available
from Burr-Brown alone. This section presents several approaches to selecting the proper
operational amplifier from the wide range of available units.
Focus on Limiting Specifications
To apply the operational amplifier correctly, none of its ratings should be exceeded. It would,
however, be uneconomical to apply the device too conservatively. With so many specifications
and so many amplifiers, the secret is to focus on the limiting specification.
In the majority of DC applications, the limiting factor will be DC drift. Drift in operational amplifiers
is primarily due to temperature effects on the input transistors causing base voltages and base
currents to vary. The input current offset (base current) must flow to ground through the external
feedback network and through the source. The input current drift times the effective resistance to
ground gives a voltage affect 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 tend to cancel as
indicated by the specification, “differential current drift.” A comparison of the input stability
(combined effects of voltage and current drifts over your temperature range) with your input
signal will give a quick indication of the accuracy you can expect.
Specifications other than drift that can help you focus on the proper amplifier are bandwidth,
output capability, and packaging. The requirement for a high gain-bandwidth product may
narrow the field to a few high-speed amplifiers. High power output requirements may rule out the
smaller packages and more economical units. A packaging preference will rule out comparable
units in other configurations.
While any one of seventy or more specifications could be limiting in your application, familiarity
with operational amplifiers will enable you to spot quickly the critical parameter in your case.
Avoid Closed Loop vs. Open Loop Confusion
While an amplifier is never used open loop, in practical applications, open loop specifications are
required to provide the information needed for all possible closed loop applications. As we have
seen in the preceding sections, there may be a vast, but predictable, difference between open
loop and closed loop characteristics such as input impedance, output impedance, and
bandwidth. The amplifier for your application may be completely described with either closed
loop specifications or open loop specifications, but the relationship between the two should be
clearly understood.
Selection Check List
The following is a checklist of the information required to select the proper amplifier for your
needs. Be sure you have enough information.
1. The Source: What type of source do you have? Voltage level? Impedance?
SBOA092A
2.
The Load: What type of load do you have? Voltage level required? Impedance?
3.
Performance: In the closed loop, what is the required gain? Bandwidth? Accuracy?
Linearity? Input Impedance? Output Impedance? DC drift? Noise? In the open loop, what
standard Texas Instruments amplifier will do this? Any exceptions? Formal
specifications? Available in system/instrument?
4.
Environment: Where will the amplifier be used? Temperature range? Other
requirements?
5.
Power Supply: Number of amplifiers per supply? Current drain?
6.
Package: Type of mounting? Controls? Connectors?
7.
Availability: Quantity? Future potential? Delivery requirements? Price?
The above information will define your requirement fully.
Assistance Available from Texas Instruments
The following services are available to you for the asking.
•=
The latest specifications and devices -Operational amplifiers are continually being
improved and new models introduced. Be sure your information is up to date.
•=
Applications assistance - given the information in the preceding checklist, an amplifier will
be recommended with an appropriate circuit.
•=
Availability - Get all the information you need for on-schedule installation at minimum cost.
Contact Texas Instruments or your nearest representative for any or all of these services.
References
1.
Texas Instruments, Op Amps and Comparators - Don't Confuse Them, SLOA067, Bruce
Carter, 09/06/2001
2. Texas Instruments, How (Not) To Decouple High-Speed Operational Amplifiers, SLOA069,
Bruce Carter, 09/12/2001
3.
Texas Instruments, Differential Op Amp Single-Supply Design Techniques, SLOA072,
Bruce Carter, 09/17/2001
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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
SBOA092A –October 2001
HANDBOOK OF OPERATIONAL AMPLIFIER
APPLICATIONS
Bruce Carter and Thomas R. Brown
ABSTRACT
While in the process of reviewing Texas Instruments applications notes, including those
from Burr-Brown – I uncovered a couple of treasures, this handbook on op amp
applications and one on active RC networks. These old publications, from 1963 and
1966, respectively, are some of the finest works on op amp theory that I have ever seen.
Nevertheless, they contain some material that is hopelessly outdated. This includes
everything from the state of the art of amplifier technology, to the parts referenced in the
document – even to the symbol used for the op amp itself:
These numbers in the circles referred to pin numbers of old op amps, which were potted
modules instead of integrated circuits. Many references to these numbers were made in
the text, and these have been changed, of course.
In revising this document, I chose to take a minimal approach to the material out of
respect for the original author, – Thomas R. Brown, leaving as much of the original
material intact as possible while making the document relevant to present day designers.
There were some sections that were deleted or substantially changed:
•=
“Broadbanding” operational amplifier modules – replaced with discussion of uncompensated
operational amplifiers.
•=
Open loop applications and Comparators – Applications showing an operational amplifier
used open loop, as a comparator have been deleted. At the time of original publication,
there were no dedicated comparator components. Good design techniques now dictate
using a comparator instead of an operational amplifier. There are ways of safely using an
operational amplifier as a comparator – if the output stage is designed to be used that way as
in a voltage limiting operational amplifier – or if clamping is added externally that
prevents the output from saturating. These applications are shown.
•=
Testing Operational Amplifiers – a section that had become hopelessly outdated. Testing
techniques are now tailored to the individual amplifier, to test for parameters important to its
intended purpose or target end equipment.
SBOA092A
•=
Some other application circuits were eliminated – if they were deemed impractical in the
light of today’s technology.
This handbook has also been reorganized to eliminate some redundancy, and place all
application circuits in one location.
The reader is cautioned that proper decoupling techniques should be followed with
operational amplifiers. Decoupling components are omitted from applications schematics
in this document for clarity. Consult reference 2 for proper decoupling techniques.
I also cleaned up grammatical and spelling mistakes in the original.
--- Bruce Carter, Texas Instruments Applications
(Excerpts from) Thomas Brown’s original Preface:
The purpose of this handbook is to provide a single source of information covering the proper
design of circuits employing the versatile modem operational amplifier. This manual will be
helpful to the experienced user of operational amplifiers, as well as the new user, in extending
the range of potential applications in which these devices can be used to advantage.
It is assumed that the reader will have a basic knowledge of electronics, but no particular
knowledge of operational amplifiers is needed to use this handbook. The operational amplifier is
treated as a circuit component inherently subject to certain rules of operation. The design of the
operational amplifiers themselves is considered only when necessary to describe their less
evident properties.
Readers with a working knowledge of operational amplifiers will want to refer directly to the
circuit collection. Readers whose job functions have not previously brought them in contact with
operational amplifiers will want to proceed directly through the handbook until the desired degree
of familiarity is obtained.
Refinements are continuously being made in the design and application of operational
amplifiers, yet the basic principles of application remain the same. Please do not hesitate to
contact Texas Instruments at any time with questions or comments arising from the use of this
handbook. It is, after all, intended for you, the user.
---Thomas R. Brown, Jr.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Contents
INTRODUCTION...................................................................................................................................7
Computation Control Instrumentation .............................................................................................7
The Feedback Technique...............................................................................................................7
Notation and Terminology...............................................................................................................8
Input Terminals..............................................................................................................................9
Output Terminals...........................................................................................................................9
Power Connections ......................................................................................................................10
Summary of Notation....................................................................................................................10
Electrical Circuit Models ...............................................................................................................10
Circuit Notation............................................................................................................................11
The Ideal Operational Amplifier ....................................................................................................12
Defining the Ideal Operational Amplifier........................................................................................12
A Summing Point Restraint...........................................................................................................13
CIRCUITS AND ANALYSES USING THE IDEAL OPERATIONAL AMPLIFIER.................................14
The Desirability of Feedback ........................................................................................................14
Two Important Feedback Circuits .................................................................................................15
Voltage Follower..........................................................................................................................15
Non-Inverting Amplifier.................................................................................................................17
INVERTING AMPLIFIER..............................................................................................................18
Intuitive Analysis Techniques........................................................................................................19
Current Output.............................................................................................................................20
Reactive Elements.......................................................................................................................20
Integrator.....................................................................................................................................21
Differentiator................................................................................................................................21
Voltage Adder..............................................................................................................................23
Scaling Summer..........................................................................................................................23
Combining Circuit Functions.........................................................................................................24
Differential Input Amplifier.............................................................................................................24
Balanced Amplifier.......................................................................................................................25
Ideal-Real Comparison.................................................................................................................27
CHARACTERISTICS OF PRACTICAL OPERATIONAL AMPLIFIERS...............................................29
Open Loop Characteristics ...........................................................................................................29
Open LoopOperation..................................................................................................................30
Output Limiting .............................................................................................................................30
FREQUENCY DEPENDENT PROPERTIES........................................................................................31
Introduction..................................................................................................................................31
Open LoopGain and the Bode Plot..............................................................................................31
Bode Plot Construction.................................................................................................................31
Closed Loop Gain.........................................................................................................................32
Stability........................................................................................................................................33
Compensation ..............................................................................................................................33
Compensation Changes...............................................................................................................34
Bandwidth....................................................................................................................................35
Loop Gain....................................................................................................................................35
The Significance of Loop Gain......................................................................................................36
BODE PLOTS AND BASIC PRACTICAL CIRCUITRY........................................................................37
Voltage Follower..........................................................................................................................37
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Inverter........................................................................................................................................ 37
X1000 Amplifier ............................................................................................................................ 38
Differentiator................................................................................................................................ 38
INTEGRATOR............................................................................................................................. 40
OTHER IMPORTANT PROPERTIES OF OPERATIONAL AMPLIFIERS............................................ 41
Summing Point Restraints ............................................................................................................ 41
Closed Loop Impedance Levels....................................................................................................42
Output Impedance.......................................................................................................................42
Input Impedance.......................................................................................................................... 43
Differential Inputs and Common Mode Rejection..........................................................................44
The Common Mode Voltage Limit ................................................................................................ 44
Offset........................................................................................................................................... 44
Drift 45
Capacitive Loading.......................................................................................................................45
VOLTAGE DETECTORS AND COMPARATORS ............................................................................... 46
Voltage Limiting Operational Amplifiers ........................................................................................ 46
THE VOLTAGE FOLLOWER .............................................................................................................. 49
BUFFERS AND ISOLATION AMPLIFIERS .................................................................................. 50
Inverting Buffer Adjustable Gain ................................................................................................... 50
Balanced Output.......................................................................................................................... 50
VOLTAGE AND CURRENT REFERENCES........................................................................................ 50
Isolated Standard Cell .................................................................................................................. 51
Constant Current Generator ......................................................................................................... 51
Buffer Variation............................................................................................................................ 52
Presettable Voltage Source .......................................................................................................... 52
Reference Voltage Supply............................................................................................................52
THE NON-INVERTING AMPLIFIER ....................................................................................................53
THE INVERTING AMPLIFIER ............................................................................................................. 54
INTEGRATORS.................................................................................................................................. 55
PRACTICAL INTEGRATORS.............................................................................................................. 55
Simple Integrators ........................................................................................................................ 56
Summing Integrator.....................................................................................................................58
Double Integrator......................................................................................................................... 58
Differential Integrator....................................................................................................................59
AC Integrator...............................................................................................................................59
Augmenting Integrator .................................................................................................................. 59
DIFFERENTIATORS........................................................................................................................... 61
With “Stop” .................................................................................................................................. 61
Low Noise ................................................................................................................................... 62
Augmented Differentiator.............................................................................................................. 62
THE VOLTAGE SUMMER...................................................................................................................63
SUMMING AND AVERAGING AMPLIFIERS................................................................................ 64
Adder........................................................................................................................................... 64
Scaling Adder..............................................................................................................................64
Direct Addition.............................................................................................................................65
Averager...................................................................................................................................... 65
Weighted Average........................................................................................................................66
THE DIFFERENTIAL INPUT AMPLIFIER............................................................................................ 67
Adder-Subtractor or Floating Input Combiner ............................................................................... 68
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THE DIFFERENTIAL (BALANCED) OUTPUT AMPLIFIER.................................................................69
DC AMPLIFIERS ................................................................................................................................70
Simple Inverting sign changing amplifier.......................................................................................70
Chopper Stabilized......................................................................................................................70
Simple Gain Control......................................................................................................................70
Linear Gain Control ......................................................................................................................71
Simple Non-Inverting....................................................................................................................71
Power Booster.............................................................................................................................71
Differential Output.........................................................................................................................73
Gain Control................................................................................................................................73
Inverting Gain Control...................................................................................................................73
DIFFERENTIAL AMPLIFIERS......................................................................................................74
Subtractor....................................................................................................................................74
Difference Amplifier......................................................................................................................74
Common Mode Rejection.............................................................................................................75
Differential Input-Output................................................................................................................75
AC AMPLIFIERS ................................................................................................................................76
DC Amplifiers with Blocking Capacitors ........................................................................................76
Simple Amplifier .....................................................................................................................................76
Single Supply .........................................................................................................................................76
Non-Inverting..........................................................................................................................................77
Double Rolloff.........................................................................................................................................77
AC Preamplifier ......................................................................................................................................78
CURRENT OUTPUT DEVICES............................................................................................................79
Feedback Loop............................................................................................................................79
Simple Meter Amplifier..................................................................................................................79
Meter Amplifier .............................................................................................................................80
Current Injector............................................................................................................................80
Linear Current Source ..................................................................................................................81
Deflection Coil Driver....................................................................................................................82
OSCILLATORS AND MULTI VIBRATORS .........................................................................................83
Simple Oscillator..........................................................................................................................83
Wien Bridge Oscillator ..................................................................................................................83
PHASE LEAD AND LAG NETWORKS ...............................................................................................84
Lag Element................................................................................................................................84
Adjustable Lag.............................................................................................................................84
Lag value linear with R setting......................................................................................................85
Adjustable Lead...........................................................................................................................85
Lead-Lag .....................................................................................................................................86
Time Delay..................................................................................................................................86
ADDITIONAL CIRCUITS .....................................................................................................................87
Absolute Value .............................................................................................................................87
Peak Follower..............................................................................................................................87
Precision Rectifier........................................................................................................................88
AC to DC Converter......................................................................................................................88
Full Wave Rectifier .......................................................................................................................89
Rate Limiter.................................................................................................................................89
Time Delay..................................................................................................................................90
Selective Amplifier.......................................................................................................................91
SECTION III: SELECTING THE PROPER OPERATIONAL AMPLIFIER ...........................................92
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Focus on Limiting Specifications................................................................................................... 92
Avoid Closed Loop vs. Open Loop Confusion............................................................................... 92
Selection Check List..................................................................................................................... 92
Assistance Available from Texas Instruments............................................................................... 93
References......................................................................................................................................... 93
Figures
Figure 1. Operational Amplifier withFeedback.............................................................................8
Figure 2. Texas Instruments Standard Symbols ........................................................................... 8
Figure 3. Op Amp Package Options...............................................................................................9
Figure 4. Power Supply Connections........................................................................................... 10
Figure 5. Summary of Notation Introduced.................................................................................. 10
Figure 6. Circuit Model of the Single Ended Operational Amplifier ........................................... 10
Figure 7. Circuit Model of the Differential Output Operational Amplifier................................... 11
Figure 8. Notation and Terms Used in Closed Loop Circuits ..................................................... 11
Figure 9. Equivalent Circuit of the Ideal Operational Amplifier .................................................. 12
Figure 10. Open Loop Operation .................................................................................................... 14
Figure 11. Basic Amplifier Circuits................................................................................................. 15
Figure 12. Voltage Follower ............................................................................................................ 15
Figure 13. Feedback Resistor Added to the Voltage Follower ..................................................... 16
Figure 14. Non-Inverting Amplifier ................................................................................................. 17
Figure 15. Non-Inverting Amplifier Re-Drawn to Show Similarity to the Voltage Follower......... 17
Figure 16. Non-Inverting Amplifier Analyzed as a Voltage Divider .............................................. 17
Figure 17. Inverting Amplifier ......................................................................................................... 18
Figure 18. Intuitive Devices for Analysis of Circuits Based on theInverting Amplifier..............19
Figure 19. Inverting Amplifier as a Linear Current Output Device ............................................... 20
Figure 20. General Form of the Inverting Amplifier....................................................................... 20
Figure 21. Integrator Circuit............................................................................................................21
Figure 22. Differentiator Circuit ...................................................................................................... 21
Figure 23. An Intuitive Picture of the Differentiator....................................................................... 22
Figure 24. Voltage Adding Circuit .................................................................................................. 23
Figure 25. Scaling Summer Circuit................................................................................................. 24
Figure 26. Differential Input Amplifier Circuit ................................................................................ 24
Figure 27. Analyzing the Differential Input Amplifier Circuit as Non-Inverting Amplifier ........... 25
Figure 28. The Differential Output Operational Amplifier ............................................................. 26
Figure 29. Equivalent Circuit of aRealOperationalAmplifier......................................................27
Figure 30. Amplifier Circuit Usinga RealOperationalAmplifier..................................................27
Figure 31. Input-Output Transfer Relation for the Open Loop Operational Amplifier................. 29
Figure 32. Bode Plot of anOperational Amplifier and its LinearApproximation........................31
Figure 33. Sketching the Bode Plot Approximation for Figure 32................................................ 32
Figure 34. Closed Loop Gain of a X100 (40 dB) Inverting Amplifier............................................. 32
Figure 35. The Effect of Internal Phase Compensation................................................................. 33
Figure 36. Composite Bode Plots Showing Stability Provided by Proper Phase Compensation34
Figure 37. The Effect of Internal Compensation for Gains Greater Than 1.................................. 34
Figure 38. Instability when an Uncompensated Amplifier is Used at Gains Lower Than the
Designated Level......................................................................................................... 35
Figure 39. Loss of High Frequency Response When Heavy Feedback is Used.......................... 36
Figure 40. Voltage Follower Circuit ................................................................................................ 37
Figure 41. Voltage Inverter Circuit.................................................................................................. 37
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Figure 42. 60 dB Amplifier Circuits.................................................................................................38
Figure 43. Differentiator Circuit ......................................................................................................38
Figure 44. Differentiator With “Stop” .............................................................................................39
Figure 45. Differentiator With “Double Stop”.................................................................................39
Figure 46. Integrator Circuit............................................................................................................40
Figure 47. DC Summing Point Conditions .....................................................................................41
Figure 48. Voltage Follower ............................................................................................................42
Figure 49. Voltage Follower ............................................................................................................43
Figure 50. Inverting Amplifier with Current Offset Control...........................................................44
Figure 51. Drift Stabilizing the Inverting Amplifier ........................................................................45
Figure 52. Gain Peaking Caused byCapacitive Loading..............................................................45
Figure 53. Voltage Limiting Operational Amplifiers ......................................................................46
Figure 54. Fully Clamped Voltage Comparator..............................................................................47
Tables
Table 1. Compound Amplifier,ResultingPerformance.............................................................72
Table 2. Current Source Scaling Resistors ................................................................................81
INTRODUCTION
The operational amplifier is an extremely efficient and versatile device. Its applications span the
broad electronic industry filling requirements for signal conditioning, special transfer functions,
analog instrumentation, analog computation, and special systems design. The analog assets of
simplicity and precision characterize circuits utilizing operational amplifiers.
Computation Control Instrumentation
Originally, the term, “Operational Amplifier,” was used in the computing field to describe
amplifiers that performed various mathematical operations. It was found that the application of
negative feedback around a high gain DC amplifier would produce a circuit with a precise gain
characteristic that depended only on the feedback used. By the proper selection of feedback
components, operational amplifier circuits could be used to add, subtract, average, integrate,
and differentiate.
As practical operational amplifier 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 amplifiers has been extended to include such applications
as DC Amplifiers, AC Amplifiers, Comparators, Servo Valve Drivers, Deflection Yoke Drivers,
Low Distortion Oscillators, AC to DC Converters, Multivibrators, and a host of others.
What the operational amplifier can do is limited only by the imagination and ingenuity of the user.
With a good working knowledge of their characteristics, the user will be able to exploit more fully
the useful properties of operational amplifiers.
The Feedback Technique
The precision and flexibility of the operational amplifier is a direct result of the use of negative
feedback. Generally speaking, amplifiers employing feedback will have superior operating
characteristics at a sacrifice of gain.
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RI RO
-
+
Eoutput
Einput
Eoutput R
=. O
ER
input I
Figure 1. Operational Amplifier with Feedback
With enough feedback, the closed loop amplifier characteristics become a function of the
feedback elements. In the typical feedback circuit, figure 1, the feedback elements are two
resistors. The precision of the “closed loop” gain is set by the ratio of the two resistors and is
practically independent of the “open loop” amplifier. Thus, amplification to almost any degree of
precision can be achieved with ease.
Notation and Terminology
Texas Instruments employs the industry standard operational amplifier symbols shown in figure
2. Power pins are often omitted from the schematic symbol when the power supply voltages are
explicit elsewhere in the schematic. Some op amp symbols also include offset nulling pins,
enable / disable pins, output voltage threshold inputs, and other specialized functions.
-
+
(c)
-
Vocm
+
(a) (b)
Figure 2. Texas Instruments Standard Symbols
•=
Symbol (a) is a buffer op amp
•=
Symbol (b) is a differential input, single ended output op amp. This symbol represents the
most common types of op amps, including voltage feedback, and current feedback. It is
often times pictured with the non-inverting input at the top and the inverting input at the
bottom.
•=
Symbol (c) is a differential input, differential output op amp. The outputs can be thought of
as “inverting” and “non-inverting”, and are shown across from the opposite polarity input for
easy completion of feedback loops on schematics.
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Figure 3. Op Amp Package Options
Figure 3 represents a small number of the many op amp package options offered by Texas
Instruments.
Input Terminals
In figures 2b and 2c, the “-“ pin is the “inverting input” or “summing point,” meaning a positive
voltage produces a negative voltage at the output on symbol (b), and the top (non-inverting)
output on symbol (c). When only one input or output terminal exists, its voltage is measured with
respect to ground. This is indicated by the term, “single ended.” It is a popular ambiguity not to
explain if a circuit, earth, 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 an inverting input, such as in figures 2b and 2c, the voltage at the inverting input
may be measured with respect to the non-inverting input. In use, such an amplifier responds to
the difference between the voltages at the inverting and non-inverting inputs, i.e., a “differential
input.
In many circuits, the non-inverting input is connected to ground. Due to the high gain of
operational amplifiers, only a very small input voltage then appears at the output and the output
is virtually at ground potential. For purposes of circuit analysis, it can be assumed to be ground a
“virtual ground.”
Output Terminals
The relation between the inverting and non-inverting inputs and the output was stated above.
For the symbol of (c) the second output voltage is approximately equal and opposite in polarity
to the other output voltage, each measured with respect to ground. When the two outputs are
used as the output terminals without ground reference, they are known as “differential outputs”.
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Power Connections
-
+
Figure 4. Power Supply Connections
Power is supplied to each of these units at connections as shown in figure 4. Such a connection
is implied in all operational amplifier circuits. The dual supply presents the same absolute value
of voltage to ground from either side, while the center connection ultimately defines the common
line and ground potential. The exceptions to this are AC amplifier circuits that may use a single
power supply. This is accomplished by creating a floating AC ground with DC blocking
capacitors. In such circuits, a source of “half-supply” creates a “virtual ground” exactly half way
between the positive supply and ground potentials.
Summary of Notation
If it is understood that the there may not be two inputs or two outputs, figure 5 is a concise
summary of the notation introduced. The arrows denote the “direction” of the polarity at each
pin.
-
Vocm
+
Figure 5. Summary of Notation Introduced
Electrical Circuit Models
The simplified models of the differential input operational amplifiers are shown in figures 6 and 7.
Figure 6. Circuit Model of the Single Ended Operational Amplifier
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As indicated in figure 6, the operational amplifier can be represented by an ideal voltage source
whose value depends on the input voltage appearing across the inverting and non-inverting
inputs plus the effects of finite input and output impedances. The value, A, is known as the open
loop (without feedback) gain of the operational amplifier.
Figure 7. Circuit Model of the Differential Output Operational Amplifier
The simplified model of the differential output operational amplifier (figure 7) is an accurate
approximation only under special conditions of feedback (see “Balanced Amplifier” later in this
handbook). Figure 6 represents the model of the differential output type when it is used as a
single ended output device; the inverting output simply being ignored.
Circuit Notation
RI RO
Input Resistor Feedback Resistor
Inputvoltage
Common line
Drift stabilizing
resistor -
optional
SummingPoint -
+
-
-
-
+
+
+
Ei
EO
Feedback
Loop
Outputvoltage
EI
Figure 8. Notation and Terms Used in Closed Loop Circuits
A circuit that will become very familiar as we progress into practical amplifier circuits and the
notation we will use are shown in figure 8. Resistors RI and RO are replaced by complex
impedances ZI and ZO in some applications of this circuit.
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The Ideal Operational Amplifier
In order to introduce operational amplifier circuitry, we will use an ideal model of the operational
amplifier to simplify the mathematics involved in deriving gain expressions, etc., for the circuits
presented. With this understanding as a basis, it will be convenient to describe the properties of
the real devices themselves in later sections, and finally to investigate circuits utilizing practical
operational amplifiers.
To begin the presentation of operational amplifier circuitry, then, it is necessary first of all to
define the properties of a mythical “perfect” operational amplifier. The model of an ideal
operational amplifier is shown in figure 9.
Figure 9. Equivalent Circuit of the Ideal Operational Amplifier
Defining the Ideal Operational Amplifier
•=
Gain: The primary function of an amplifier is to amplify, so the more gain the better. It can
always be reduced with external circuitry, so we assume gain to be infinite.
•=
Input Impedance: Input impedance is assumed to be infinite. This is so the driving source
won’t be affected by power being drawn by the ideal operational amplifier.
•=
Output Impedance: The output impedance of the ideal operational amplifier is assumed to
be zero. 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 inverting input so the
response time is assumed to be zero. Phase shift will be 180°. Frequency response will be
flat and bandwidth infinite because AC will be simply a rapidly varying DC level to the ideal
amplifier.
•=
Offset: The amplifier output will be zero when a zero signal appears between the inverting
and non-inverting inputs.
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A Summing Point Restraint
An important by-product of these properties of the ideal operational amplifier is that the summing
point, the inverting input, will conduct no current to the amplifier. This property is to become an
important tool for circuit analysis and design, for it gives us an inherent restraint on our circuit - a
place to begin analysis. Later on, it will also be shown that both the inverting and non-inverting
inputs must remain at the same voltage, giving us a second powerful tool for analysis as we
progress into the circuits of the next section.
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CIRCUITS AND ANALYSES USING THE IDEAL OPERATIONAL AMPLIFIER
A description of the ideal operational amplifier model was presented in the last section, and the
introduction of complete circuits may now begin. Though the ideal model may seem a bit remote
from reality - with infinite gain, bandwidth, etc., it should be realized that the closed loop gain
relations which will be derived in this section are directly applicable to real circuits -to within a
few tenths of a percent in most cases. We will show this later with a convincing example.
The Desirability of Feedback
Load ES
-
+
RS
RO
Source
Figure 10. Open Loop Operation
Consider the open loop amplifier used in the circuit of figure 10. Note that no current flows from
the source into the inverting input - the summing point restraint derived in the previous section hence,
there is no voltage drop across RS and ES appears across the amplifier input. When ES is
zero, the output is zero. If ES takes on any non-zero value, the output voltage increases to
saturation, and the amplifier acts as a switch.
The open loop amplifier is not practical - once an op amp is pushed to saturation, its behavior is
unpredictable. Recovery time from saturation is not specified for op amps (except voltage
limiting types). It may not recover at all; the output may latch up. The output structure of some
op amps, particularly rail-to-rail models, may draw a lot of current as the output stage attempts to
drive to one or the other rail. For more details on op amps in open loop operation, consult
reference 1.
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Two Important Feedback Circuits
(a) Inverting
(b) Non-Inverting
EO
-+
RORI
RI
-
+
EOEI
EI
RO
. R
.
R
E
= OE E = 1 + O .E
OI
O I
R
R
I
.
I
Figure 11. Basic Amplifier Circuits
Figure 11 shows the connections and the gain equations for two basic feedback circuits. The
application of negative feedback around the ideal operational amplifier results in another
important summing point restraint: The voltage appearing between the inverting and non-
inverting inputs approaches zero when the feedback loop is closed.
Consider either of the two circuits shown in figure 11. If a small voltage, measured at the
inverting input with respect to the non-inverting input, is assumed to exist, the amplifier output
voltage will be of opposite polarity and can always increase in value (with infinite output
available) until the voltage between the inputs becomes infinitesimally small. When the amplifier
output is fed back to the inverting input, the output voltage will always take on the value required
to drive the signal between the inputs toward zero.
The two summing point restraints are so important that they are repeated:
1.
No current flows into either input terminal of the ideal operational amplifier.
2.
When negative feedback is applied around the ideal operational amplifier, the differential
input voltage approaches zero.
These two statements will be used repeatedly in the analysis of the feedback circuits to be
presented in the rest of this section.
Voltage Follower
EO
EO = EI
EI
-
+
Figure 12. Voltage Follower
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The circuit in figure 12 demonstrates how the addition of a simple feedback loop to the open
loop amplifier converts it from a device of no usefulness to one with many practical applications.
Analyzing this circuit, we see that the voltage at the non-inverting input is EI, the voltage at the
inverting input approaches the voltage at the non-inverting input, and the output is at the same
voltage as the inverting input. Hence, EO = EI, and our analysis is complete. The simplicity of our
analysis is evidence of the power and utility of the summing point restraints we derived and have
at our disposal.
Our result also may be verified by mathematical analysis very simply. Since no current flows at
the non-inverting input, the input impedance of the voltage follower is infinite. The output
impedance is just that of the ideal operational amplifier itself, i.e. zero. Note also that no current
flows through the feedback loop, so any arbitrary (but finite) resistance may be placed in the
feedback loop without changing the properties of the ideal circuit, shown in figure 13. No voltage
would appear across the feedback element and the same mathematical analysis would hold.
-
+
EO = EI
EO
EI
RO
Figure 13. Feedback Resistor Added to the Voltage Follower
The feedback resistor is of particular importance if the op amp selected is a current-feedback
type. The stability of current-feedback op amps is dependent entirely on the value of feedback
resistor selected, and the designer should use the value recommended on the data sheet for the
device.
Unity gain circuits are used as electrical buffers to isolate circuits or devices from one another
and prevent undesired interaction. As a voltage following power amplifier, this circuit will allow a
source with low current capabilities to drive a heavy load.
The gain of the voltage follower with the feedback loop closed (closed loop gain) is unity. The
gain of the ideal operational amplifier without a feedback loop (open loop gain) is infinity. Thus,
we have traded gain for control by adding feedback. Such a severe sacrifice of gain -from
infinity to unity - is not necessary in most circuits. The rest of the ideal circuits to be studied will
give any (finite) closed loop gain desired while maintaining control through feedback.
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Non-Inverting Amplifier
RO
RI
EI EO
-
+
.
RO
EO =
1 + .
.EI
R
.
I
Figure 14. Non-Inverting Amplifier
The circuit in figure 14 was chosen for analysis next because of its relation to the voltage
follower. It is re-drawn as in figure 15, which makes it evident that the voltage follower is simply a
special case of the non-inverting amplifier.
-
+
RO EO RI
EI
Figure 15. Non-Inverting Amplifier Re-Drawn to Show Similarity to the Voltage Follower
Since no current flows into the inverting input, RO and RI form a simple voltage divider (figure
16).
RO
EO
RI
EI
Figure 16. Non-Inverting Amplifier Analyzed as a Voltage Divider
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The same voltage must appear at the inverting and non-inverting inputs, so that:
(E .)= (E +) = EI
From the voltage division formula:
RI
EI =.EO
RI + RO
ER + RR
OIO O
== 1 +
ER R
II I
The input impedance of the non-inverting amplifier circuit is infinite since no current flows into
the inverting input. Output impedance is zero since output voltage is ideally independent of
R
output current. Closed loop gain is 1 + O hence can be any desired value above unity.
RI
Such circuits are widely used in control and instrumentation where non-inverting gain is required.
INVERTING AMPLIFIER
RI
RO
EO
EI
-
+
OE = OR.
IE IR
Figure 17. Inverting Amplifier
The inverting amplifier appears in figure 17. This circuit and its many variations form the bulk of
commonly used operational amplifier circuitry. Single ended input and output versions were first
used, and they became the basis of analog computation. Today’s modern differential input
amplifier is used as an inverting amplifier by grounding the non-inverting input and applying the
input signal to the inverting input terminal.
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:
EI EO
== 0
RI RO
Hence:
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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EO RO
=.
EI RI
Input impedance to this circuit is not infinite as in the two previous circuits, the inverting input is
at ground potential so the driving source effectively “sees” RI as the input impedance. Output
. RO
impedance is zero as in the two previous circuits. Closed loop gain of this circuit is .
RI
Intuitive Analysis Techniques
The popularity of the inverting amplifier has been mentioned already. In control and
instrumentation applications, its practical value lies in the ease with which desired input
impedance and gain values can be tailored to fit the requirements of the associated circuitry. Its
utility is reflected in the variety of intuitive devices that are commonly used to simplify its
analysis.
RI RO
I EOEI I
Figure 18. Intuitive Devices for Analysis of Circuits Based on the Inverting Amplifier
If we draw the summing point, the inverting input and output of the inverting amplifier as in figure
18, the dotted line serves as a reminder that the inverting input is at ground potential but
conducts no current to ground. The output can supply any needed current, and analysis quickly
becomes rote. Another such device uses the action of a lever to show as vectors the voltage
relations that exist using the inverting input as the fulcrum.
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Current Output
-
+
IL
RI RL
EI
EI
IL =.
RI
Figure 19. Inverting Amplifier as a Linear Current Output Device
So far, we have considered voltage as the output of the inverting amplifier, but it also finds wide
application as a current supplying device. This is accomplished by placing the load in the
feedback loop as in figure 19. Since the inverting input is ground potential, the current through
EI . EI
RI is . No current flows into the inverting input, so IL = , which is independent of RL. In
RI RI
similar configurations, the inverting amplifier can serve as a linear meter amplifier or deflection
coil driver. Input impedance is RI as before.
Reactive Elements
Though only resistances hove been used in the input and feedback loop of the amplifiers
presented so far, the general form of the inverting amplifier is shown in figure 20, where ZO and
ZI are complex impedances in general.
EI
EO
ZO
-
+
ZI
OE =
. OZ
IE IZ
Figure 20. General Form of the Inverting Amplifier
The gain relation may be verified in the same manner as for the resistive case by summing
currents using complex notation. There is an area of control application utilizing this general form
of the inverting amplifier. Many times it is necessary to construct a network with some
specifically designated transfer function.
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By reducing this transfer function to the ratio of two polynomials, a table may be consulted for
suitable passive networks to be used in the inverting amplifier.
Other uses of reactive elements are found in the integrator and differentiator circuits that follow.
Integrator
EO
-
+
CO
EI
RI
.1
E = E dt
ORC I
IO
Figure 21. Integrator Circuit
If a capacitor is used as the feedback element in the inverting amplifier, shown in figure 21, the
result is an integrator. An intuitive grasp of the integrator action may be obtained from the
statement under the section, “Current Output,” that current through the feedback loop charges
the capacitor and is stored there as a voltage from the output to ground. This is a voltage input
current integrator.
Differentiator
CI
RO
EO
EI -
+
dE
E =.RC 1
O OI
dt
Figure 22. Differentiator Circuit
Using a capacitor as the input element to the inverting amplifier, figure 22, yields a differentiator
circuit. Consideration of the device in figure 23 will give a feeling for the differentiator circuit.
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EO
RO
EI IC IR
CI
Figure 23. An Intuitive Picture of the Differentiator
Since the inverting input is at ground potential:
dE
I = C I,andI . I = 0
CI CR
dt
so that:
dE ECI
I + O = 0
dt RO
dE
E =.RC I
O OI
dt
It should be mentioned that of all the circuits presented in this section, the differentiator is the
one that will operate least successfully with real components. The capacitive input makes it
particularly susceptible to random noise and special techniques will be discussed later for
remedying this effect.
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Voltage Adder
In a great many practical applications the input to the inverting amplifier is more than one
voltage. The simplest form of multiple inputs is shown in figure 24.
-
+
E1
E2
RI
RORI
EO
RI
E3
O
E =
.
RRI
(E + E + E + ...)
O 123
Figure 24. Voltage Adding Circuit
Current in the feedback loop is the algebraic sum of the current due to each input. Each source,
E1, E2, etc., contributes to the total current, and no interaction occurs between them. All inputs
. RO
“see” RI as the input impedance, while gain is . Direct voltage addition may be obtained
RI
with RO = RI.
Scaling Summer
A more general form of adder allows scaling of each input before addition (figure 25).
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RO
E3
EO
E1
R2
-
+
E2
R1
R3
SBOA092A
RO
E3
EO
E1
R2
-
+
E2
R1
R3
.
EE E
123
EO =.RO
.
+++ ...
RR R
.
123
Figure 25. Scaling Summer Circuit
The adder above is obviously a special case of this circuit. Each input “sees” its respective input
resistor as the input resistance.
Combining Circuit Functions
The basic inverting amplifier configuration is very flexible - so flexible, in fact, that it would be
difficult to overestimate its usefulness. Additional applications that already may have occurred to
the reader include: a variable gain amplifier using a potentiometer for RI or RO or both; a
summing integrator by using a feedback capacitor in the summing amplifier; and many others.
Differential Input Amplifier
RI RO
RI
E2 EO
RO
E1
-
+
RO
EO =(E2 . E1 )
RI
Figure 26. Differential Input Amplifier Circuit
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Figure 26 shows a circuit utilizing both inputs to the differential operational amplifier. Its
operation can be appreciated best by considering it a combination of the inverting and non-
inverting amplifier, where the input voltage is tapped from the divider formed by the lower RO and
RI (figure 27).
RI RO
E2
RO
RI
EO
-
+
Figure 27. Analyzing the Differential Input Amplifier Circuit as Non-Inverting Amplifier
Hence, the output due to E2 is:
R + R .
ER .
R
OI 2 OO
E = .
= E
O 2
RR + RR
I .
IO I
With E2 grounded, the circuit is simply an inverting amplifier with the non-inverting input
grounded through a resistance (which conducts no current). Hence, the output due to E1 is
. RO
E = E1
O RI
so the total output is:
RO
EO =
RI
(E2 . E1 )
ER
The input pins reside at the voltage level 2 O , however, which may have a detrimental
RI + RO
effect on a real operational amplifier. (See the section on common mode voltage limit.)
Since the action of the voltage divider formed by the bottom RO and RI is independent of the
remainder of the circuit, the voltage common to the input pins is independent of EI. The source of
E2 “sees” RO + RI, the voltage divider itself. Output impedance is zero, as before.
Balanced Amplifier
The differential output type of operational amplifier is redrawn with its ideal equivalent in figure
28.
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RI RO
-
+
EO
E2
E1
RI RO
RO
EO =(E2 . E1 )
RI
Figure 28. The Differential Output Operational Amplifier
Any of the previous single ended output circuits may use the differential output type since the
relation between the inputs and non-inverting output is fixed. The roles of the input terminals
may even be reversed by applying feedback across the bottom feedback pathway (inverting
output to non-inverting input) instead of the non-inverting output to the inverting input. In either
case, the unused output terminal may be ignored. 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, then, it is necessary to take feedback from
both output terminals as in figure 28. This circuit is a differential form of the inverting amplifier
since neither output terminal is grounded. ZOUT is ideally zero, and closed loop (differential) gain
. RO
is .
RI
A differential output amplifier may be used to convert a single-ended voltage into a pair of
balanced voltages by grounding either signal input. Such devices as servo motors, push-pull
amplifier stages, and symmetrical transmission lines may be driven by the differential output
amplifier.
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Texas Instruments fully differential operational amplifiers include an additional pin -VOCM. When
used as an output, this pin represents the common mode voltage about which the two outputs
operate. It can also be used as an input, to allow the user to set the common mode operational
point from an external source, such as the reference output of a differential input analog to digital
converter. The designer is cautioned not to rely on this input exclusively to set the correct DC
operating point of the circuit. Voltage divider effects of input and feedback resistors can easily
violate the input common mode range of the operational amplifier, and the low values of
resistors used in modern fully differential circuits can cause unexpected power dissipation levels
in the resistors. For more information on the correct use of the VOCM pin, and setting the correct
DC operating level of a fully differential operational amplifier circuit, consult reference 3.
Ideal-Real Comparison
The idealized operational amplifier has been used as a model throughout this section. Before
progressing into the next section concerning real operational amplifier characteristics, it will be
demonstrated by example that the gain expressions that have been derived are indeed valid in
the real case.
The equivalent circuit of a real operational amplifier might appear as in figure 29.
RI RO
EI
EO
-
+
Figure 29. Equivalent Circuit of a Real Operational Amplifier
Connecting it as in figure 30 gives a X10 amplifier circuit.
EI
EO
ZI = R
-
+
ZO = 10R
Figure 30. Amplifier Circuit Using a Real Operational Amplifier
When the effect of finite gain, input impedance, and output impedance are taken into account,
the gain characteristics are given by:
EO ZO .
1 .
=.
EI ZI
.
.
1+.
where:
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.
ZZ .
ZZ
out out OO
1++ 1 ++
ZZ ZZ
.
O load .
I in
.=
Zout
.
A .
Z
.
O
This may be expanded as:
E . Z
OO 23
=(1..+. .. + ...)
EI ZI
and, where .«1, as is usually the case, simplifies to:
EO . ZO
=(1 . .)
EI ZI
Now, letting the open loop parameters take on the following values which are typical, though
conservatively estimated:
A = 10,000 ZI = 10 k.
Zin = 50 k. ZO = 100 k.
Z = 100 Z = 10 k.
out load
Solving, we get . = 0.0013 (which justifies our assumption above) and the real closed loop gain
is:
E
O =.10.000 + 0.013 =.9.987
EI
instead of -10 which would be ideally expected.
The gain of this circuit is accurate to within 0.13% of the idealized value.
This entire error may be considered as a ‘calibration” error and completely cancelled by a slight
adjustment of the feedback resistor. Once such on adjustment is made, the gain accuracy of the
circuit would be affected less than 0.02% should the gain of the amplifier change by 10%.
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CHARACTERISTICS OF PRACTICAL OPERATIONAL AMPLIFIERS
The modern operational amplifier is a solid state, high gain, DC voltage amplifier. Practical
feedback circuits employing it are based on the circuits that were derived in the preceding
section using the ideal operational amplifier model. Substituting a real for an ideal operational
amplifier will result in some predictable variation from ideal operation that is negligibly small in
many applications. This section is intended to acquaint the reader with the characteristics of the
real devices so that they may be utilized to the fullest possible extent in practical circuits.
Open Loop Characteristics
In the case of the ideal operational amplifier, circuit operation was seen to be dependent entirely
on the feedback used. It is possible to use the real operational amplifier open loop, but control
and stability problems are encountered due to the high open loop gain (X100000 typically at
DC). Random noise from the input circuit and noise generated within the operational amplifier
itself plus any variations in amplifier characteristics due to temperature change or aging
components are all multiplied by open loop gain. Slight variations in the manufactured unit
become noticeable due to this effect; hence open loop specifications are sometimes given
conservative “typical” values.
Open loop operational amplifier specifications have a relatively remote connection to closed loop
operation of a circuit since they do not as much define circuit operation as they do limit it. The
sheer numbers of useful operational amplifier circuits make it impossible for a manufacturer to
completely specify closed loop operation. Since each closed loop circuit is, in essence, a special
case, it is necessary to understand both open and closed loop characteristics before the
intelligent design of circuitry using operational amplifier can begin. Any statements that are to be
made about operational amplifier circuits must be qualified by the information “open loop” or
“closed loop,” and the character of the feedback should be specified for “closed loop”
information.
Figure 31. Input-Output Transfer Relation for the Open Loop Operational Amplifier
The open loop input-output relationship for a rather “well-behaved” practical operational amplifier
is shown in figure 31. The open loop gain, A, is measured by the slope of the curve so it can be
seen that the operational amplifier only amplifies between the saturation values of EO.
The slope of the amplifying portion of the transfer curve is dependent on the frequency of the
input voltage while the saturation voltages remain constant. This relation between input and
output holds regardless of the feedback configuration used as long as the amplifier is not in
overload.
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The “well behaved” aspect of this operational amplifier is the fact that its transfer curve goes
through the origin. In practice, all operational amplifiers exhibit offset, a fault that effectively shifts
the transfer curve from the origin. To complicate matters further, this offset value will wander,
producing drift. Both of these phenomena are of the same order of magnitude as the input
voltage necessary to drive the open loop amplifier into saturation and a necessary part of circuit
design is to minimize their effect.
Open Loop Operation
As an example of open loop operation, consider the Texas Instruments THS4001 used as an
open loop DC amplifier. DC open loop gain is 10000 and output saturation occurs at ±13.5 volts
(for a supply voltage of ±15V). Hence, for linear operation, the input voltage cannot exceed
10,000 X 2.7 millivolts. The open loop amplifier is also subject to the full effect of random noise,
offset, and drift, which may be greater than 2.7 millivolts. Therefore, the open loop amplifier is
not useful for linear operation, because any circuit that is so close to saturation may cause the
output to latch-up.
Output Limiting
Texas Instruments specifications for operational amplifiers give a voltage and a current output
rating, plus output short circuit current. Output saturation voltages are commonly slightly greater
than the rated output value when the nominally specified power supply voltage is used. Texas
Instruments operational amplifiers will supply full output voltage to a load drawing full rated
output current for an indefinite period.
In addition, for lower output voltages, slightly higher output current is available up to the short
circuit conditions. Though the current ratings are conservative, exceeding the rated current
should be attempted only after some calculation, unless the output voltage is extremely low.
Output voltage is self-limiting, and voltage levels above the saturation voltage cannot be
achieved. It is not recommended to operate an operational amplifier saturated for an indefinite
period of time.
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FREQUENCY DEPENDENT PROPERTIES
Introduction
The AC response characteristics of the operational amplifier are very important considerations in
circuit design. DC operational amplifiers will operate successfully at audio, ultrasonic, and radio
frequencies with some predictable variation from DC operation. Circuits designed to operate at
DC are also affected by the AC response since random noise and varying DC levels contain AC
components.
Open Loop Gain and the Bode Plot
The frequency response curve of operational amplifier circuitry is conveniently represented by
the Bode plot. The absolute value of voltage gain is plotted in dB (the hybrid but popular
EO
“decibel” defined by dB = 20log so that a gain of 10 is 20 dB, a gain of 100 is 40 dB, etc.)
EI
versus the orthodox decade logarithmic frequency scale. The Bode plot of a typical operational
amplifier’s open loop gain is shown in figure 32 along with a convenient linear approximation to
the actual curve.
Figure 32. Bode Plot of an Operational Amplifier and its Linear Approximation
Bode Plot Construction
The shape of the Bode plot shown in figure 32 is characteristic of all compensated voltage
feedback operational amplifiers. It is so characteristic, in fact, that any open loop Bode plot may
be approximated rapidly from only two bits of information about the particular operational
amplifier:
1) DC open loop gain
2) The unity-gain crossover frequency (open loop bandwidth).
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For example: An operational amplifier has DC open loop gain of 108 dB and open loop
bandwidth of 1 MHz. From these two values, we can sketch the Bode plot as indicated in figure
33.
Figure 33. Sketching the Bode Plot Approximation for Figure 32
Comparing the shape of this sketch with the typical response of figure 32, the constant gain
bandwidth product sketch is observed to be a conservative approximation to the typical
response. Since the typical gain fall off exceeds 20 dB per decade at some points, there may be
slight peaking at intermediate closed loop gains. Such peaks do not indicate a condition of
instability.
Closed Loop Gain
When feedback is used around an operational amplifier, the closed loop gain of the circuit is
determined by a ratio involving the input and feedback impedances used. If the closed loop gain
called for by the feedback configuration is greater than the open loop gain available from the
operational amplifier for any particular frequency, closed loop gain will be limited to the open
loop gain value. Thus a plot of the closed loop gain of a X100 (40db) amplifier using the amplifier
of figure 33 would appear as in figure 34:
Figure 34. Closed Loop Gain of a X100 (40 dB) Inverting Amplifier
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Stability
As indicated above, the closed loop amplifier circuit cannot supply more gain than is available
from the operational amplifier itself, so at high frequencies, the closed loop Bode plot intersects
and follows the open loop gain curve. The intersection point between the closed and open loop
curves is important because the angle between the two curves - or, more precisely, the “rate of
closure” since the curves aren’t actually straight lines - determines whether the closed loop
amplifier, 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 40 db per decade
the system is likely to be unstable. Bode plots may be varied almost at will to insure stability or to
provide some tailor made frequency response characteristic.
Compensation
The open loop gain of operational amplifiers is tailored or “compensated” with one or more
simple resistor and capacitor combinations (figure 35).
Figure 35. The Effect of Internal Phase Compensation
Phase compensation is effected in order that the majority of popular circuits utilizing operational
amplifiers will be inherently stable, even under conditions of 100% feedback. As a consequence
of internal compensation, the user may connect feedback around the amplifier with relative
impunity. We must hasten to add, though, that each feedback condition is, in essence, a special
case. Superior results may be obtainable by adding external compensation. Knowledge of the
stability criteria and the Bode plot will be adequate in all but the most unorthodox circuits.
If compensation were not provided, certain amplifier circuits would be unstable under normal
operating conditions according to the above “rate of closure” or change of slope principle. The
effect of compensation on closed loop stability can be seen from the Bode plots of figure 36,
showing several different closed loop amplifiers utilizing the same operational amplifiers with and
without compensation.
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Figure 36. Composite Bode Plots Showing Stability Provided by Proper Phase Compensation
Compensation Changes
Operational amplifier compensation for most voltage feedback amplifiers is internal to the die,
and cannot be changed. Texas Instruments supplies voltage feedback amplifiers that are
compensated for gains higher than unity gain, and uncompensated operational amplifiers. The
purpose of decreasing compensation, sacrificing unity gain stability, is to increase the flatness of
the response curve the operational amplifier by changing the 3 dB break point frequency. The
effect of this is shown in figure 37.
Figure 37. The Effect of Internal Compensation for Gains Greater Than 1
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The amplifier can be used at gain levels above the designated gain level, as determined by
external compensation and feedback components, but it cannot be used for lower gains without
readjusting the compensation. Instability would result since the rate of closure may be too large
at low gain values (figure 38).
Figure 38. Instability when an Uncompensated Amplifier is Used at Gains Lower Than the
Designated Level.
Bandwidth
The open loop bandwidth of the operational amplifier is shown explicitly in the Bode plot. The
plot has only two distinguishing frequencies, one being the unity gain crossover frequency and
the second being the 3 dB point. The 3 dB point is considered to be the bandwidth of the open
loop amplifier and used in open loop specifications.
The unity gain crossover frequency may be from 100 kHz for signal amplifiers to 1 GHz or higher
for high-speed amplifiers. An important aspect of bandwidth - besides making high frequency
operational amplifier circuits practical - is to improve the precision of signal amplification. The
loss of high frequency components of non-sinusoidal voltages such as pulses, control signals,
DC steps, or even speech patterns may result in undesirable distortion and phase shift.
Wide bandwidth amplifiers are used maintain high loop gain at lower signal frequencies. For
example, it is necessary to use an operational amplifier with open loop bandwidth of at least 200
MHz to provide a closed loop gain of 40 dB at 1 MHz.
Loop Gain
As indicated in figure 34, loop gain is the gain “difference” between open and closed loop gain.
In actuality, the loop gain is the ratio between open loop gain and closed loop gain since
subtracting on the logarithmic gain scale is equivalent to division.
Open Loop Gain
Loop Gain =
Closed Loop Gain
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In a practical circuit, loop gain is the increase in gain that is observed when the feedback path is
opened, but with all circuit loads intact. Loading effects of finite input and output impedance, as
well as the external feedback components, will lead to reduced loop gain. For example, in a
unity gain inverting configuration, 6 dB is lost due to the voltage divider effect of the input and
feedback resistors. Since the phase compensation network fixes the 3 dB point and roll off rate
of the frequency response, the reduced gain effectively lowers the bandwidth. An inspection of
figure 39 will clarify this effect.
Figure 39. Loss of High Frequency Response When Heavy Feedback is Used
The Significance of Loop Gain
Just as local degeneration around a transistor can reduce circuit sensitivity to certain parameter
changes in that transistor, feedback around an operational amplifier will reduce sensitivity to
open loop parameter changes. Open loop gain, phase shift, input impedance, and output
impedance may vary with temperature, power supply voltage, and time. Loop gain is the
payment made for circuit stability and gain accuracy, and it is a direct measure of the
improvement obtained. Basic stability, however, must be designed into the open loop amplifier.
Noise, drift, and offset will not be affected by loop gain. These parameters are essentially input
functions that, like the signal, will be increased by the closed loop gain. The signal to noise ratio
will remain constant, independent of gain. Loop gain will improve closed loop gain stability,
phase shift, input impedance, and output impedance.
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BODE PLOTS AND BASIC PRACTICAL CIRCUITRY
Voltage Follower
Figure 40. Voltage Follower Circuit
The unity gain follower and its Bode plot are shown in figure 40. Since there is no feedback
impedance loading, the closed loop plot traces out the unity gain line to the open loop unity gain
crossover before rolling off.
Inverter
Figure 41. Voltage Inverter Circuit
A unity gain inverting amplifier is shown in figure 41. The bandwidth is decreased by one octave
(50%) from that of the voltage follower due to the voltage division effect of the input and
feedback resistors mentioned above.
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X1000 Amplifier
NON-INVERTING INVERTING
EI999R
R
EO
-
+
R
1000R
EO
-
+
EI
R + R . R
OI O
E = E = 1000EE = E =.1000E
O II OII
RI RI
Figure 42. 60 dB Amplifier Circuits
Figure 42 shows the Bode plot for either the inverting or non-inverting amplifier with a gain of
X1000 (60db). Negligible bandwidth is last due to the voltage divider effect but is still very much
reduced by the normal roll off of the open loop curve.
Differentiator
Figure 43. Differentiator Circuit
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The Bode plot of the differentiator (figure 43) is slightly more trouble to construct since the ZI
value is dependent on frequency. It is evident that the curve must intersect the unity gain axis at
the frequency where XC = RO (conveniently found from the reactance chart in Appendix A). For
DC, the capacitor represents infinite impedance hence gain is zero. At higher frequencies, XC
drops and the gain increases, which is approximated closely by a straight line rising at 20 dB /
decade.
Since highest gain is encountered at high frequencies, this circuit is very susceptible to random
noise. Even more important, however, is the fact that the rate of closure is about 40 dB / decade,
making the simple differentiator inherently unstable in operation. One practical method of
reducing noise and preventing instability is shown in figure 44.
Figure 44. Differentiator With “Stop”
At high frequencies, XC is negligible and the circuit operates as an amplifier with resistive
1
feedback. The transition “point” is the frequency at which f = . Note that a capacitor,
2.RICI
CO, in parallel with R, would have produced the same results with the significant frequency given
1
by f = .
2.ROCO
Both techniques may be combined to give even better noise rejection (figure 45).
Figure 45. Differentiator With “Double Stop”
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With RO and CO set to break at the same frequency as RI and CI, the total slope change will be
twice that of a single RC combination, hence a roll off of 20 dB / decade is introduced.
INTEGRATOR
Figure 46. Integrator Circuit
The discussion above should make the Bode plot for an integrator simple to deduce (figure 46).
Unity gain crossover occurs at the frequency where XCO = RI. The slope is a negative 20 dB /
decade and gain would ideally go to infinity at DC.
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OTHER IMPORTANT PROPERTIES OF OPERATIONAL AMPLIFIERS
Summing Point Restraints
In the case of the ideal operational amplifier, circuit analysis was simplified by the ideal summing
point restraints of zero voltage and zero current at the inverting input. The real operational
amplifier summing junction comes close to this, as will be shown in an example.
A typical Texas Instruments THS4001 Operational Amplifier has a DC open loop gain of 80 dB
or 10,000, open loop input impedance of 10 M., and a saturation voltage of more than ±13
volts.
Figure 47. DC Summing Point Conditions
For the circuit shown in figure 47 to have a full output of 10 volts, the voltage at the inverting
input must be:
10
E.= = 1 mV
10,000
The current flowing to the inverting input is the voltage at the inverting input divided by the
impedance to the non-inverting input, which is ri. This specification is available from the data
sheet.
1 mV
I.= = 0.1 nA
10 M.
Note that these calculations do not depend on the values of the feedback and input elements. In
fact, they don’t depend on the nature of the closed loop circuit at all, so long as the operational
amplifier is not operating in an overload condition.
Since the dynamic voltage current variations that appear at the summing junction of a real
operational amplifier in a closed loop circuit are so small, they are considered zero - as in the
ideal case -for circuit analysis purposes. It must be noted, however, that this effect is due to the
high open loop gain of the operational amplifier. At high frequencies, the open loop gain falls off
and the summing point voltage 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.
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Closed Loop Impedance Levels
Open loop output impedances are given in the specifications and range from 3 . to 5000 ., with
the majority of operational amplifiers having 100 or 200 . open loop output impedance. Since
the input and feedback resistors usually will vary from 1 k. to 1 M., this may represent a rather
poor approximation of the ideal zero output impedance. However, as we shall see, the
equivalent closed loop output impedance is typically less than an ohm.
Open loop input impedances are also specified and run as high as 1015 .. Compared to the
typical feedback impedance levels, this can be a very good approximation of the ideally infinite,
open loop input impedance. Practically, this is of little importance since the input resistor
determines the closed loop input impedance of the inverting amplifier. Calculations will show
that the equivalent input impedance of the non-inverting amplifier may be hundreds or thousands
of M., closed loop.
Output Impedance
IL
EI
ZCLout
Zout
ei
EO
-
+ eo
Figure 48. Voltage Follower
Using the Texas Instruments THS4001 as a voltage follower in the circuit of figure 48, we can
readily determine the effective closed loop output impedance. Loading this circuit with an
incremental output current, .IL, forces the amplifier output, eo, to increase by:
.e =.IZ
o L out
To maintain this .eo, the voltage across the inputs must change by:
.eo
A
Since the inverting input is tied to the output and the input voltage, EI, applied to the non-
inverting input, must decrease by .ei. The effective output impedance is then seen to be:
.E .
.e .
Z .
Z
O o out out
.IA .eA
L .
o
Thus, for the THS4001, the open loop output impedance of 10 . is decreased by the DC gain of
10,000 to an effective 0.001 . at the output plus any lead impedance between the feedback
point and the load.
More general calculations would show that the output impedance is reduced by the loop gain.
The voltage follower is a limiting case in which the loop gain is equal to the open loop gain.
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Input Impedance
Closed loop input impedance is also increased by loop gain in non-inverting closed loop
applications. In the inverting or summing closed loop configuration, the summing junction is a
virtual ground and the input impedance is almost exactly the value of the summing impedance,
ZI.
Figure 49. Voltage Follower
In figure 49, the operational amplifier is again shown in the voltage follower circuit with the open
loop input impedance Zin, indicated. For any change in output voltage, .Eo, the voltage across
the inverting and non-inverting input must change by .Eo divided by the open loop gain, A:
.E .E
.ei = o = I
AA
The change of voltage, .ei, across the open loop input impedance, Zin, demands a current, .lin,
equal to .ei divided by Zin.
.ei .E2
.Iin ==
Z AZ
in in
The closed loop input impedance, ZCL in, is the change in input voltage, .E2, divided by the
change in input current, .lin.
.E .
AZ
2 .
in
Z = =.E = AZ
CLin 2 in
.I .E
in .
2
Again, this is a limiting case in which the loop gain is equal to the open loop gain. In the more
general case, the effective input impedance is equal to the open loop input impedance multiplied
by the loop gain. Thus, assuming zero offset currents, the input impedance of the THS4001 is
greater than 10 M. as long as loop gain is greater than 40 dB. Current leakage paths
associated with the input stage tend to limit the input impedance to be achieved in this manner
to about 10 M..
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Differential Inputs and Common Mode Rejection
The input to most Texas Instruments operational amplifiers is a pair of input pins, neither of
which is connected to ground. Such pair of “floating” input connections is termed “differential
inputs”. Each input connection drives separate, balanced transistor amplifiers. Ideally, the same
voltage connected to each input would produce no net result; hence the operational amplifier
would only detect the difference in the two input voltages. The voltage that both inputs
experience is known as the common mode voltage.
In practice, the voltages on each input are amplified separately and, due to component
variations, never perfectly balance out to zero. The “common mode rejection” properly of a
differential input amplifier also depends on the feedback configuration of the closed loop
application.
The Common Mode Voltage Limit
As stated above, the circuitry within the operational amplifier responds to the voltages appearing
at the two inputs separately. Either input can be overdriven, saturating the input transistor(s).
Since under normal feedback conditions there is only a negligible difference in voltage between
the two inputs (see “Summing Point Restraints”), the input saturation voltage is known as the
common mode voltage limit and appears in Texas Instruments specifications.
For the inverting amplifier, one input terminal is grounded; hence, the common mode input
voltage 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 that a certain input voltage is necessary to balance the operational
amplifier circuit. This input voltage is needed because of a small bias current and voltage
inherently required by the operational amplifier, called offset. When these two bias components
are not externally supplied, they are drawn from the input and feedback networks causing an
output voltage error.
In most applications, this small error is negligible. For highest performance, simple biasing
circuits may be used externally. As an example, a simple bias current injector as shown in figure
50 may correct the current components of input offset.
-
+
RO
-+
RI
Figure 50. Inverting Amplifier with Current Offset Control
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Drift
The bias values mentioned above will vary with temperature, time, and power supply voltage,
producing a variable output error or drift. Again, this effect is negligible in many cases, but it
should be taken into account in critical applications.
In some Texas Instruments operational Amplifiers, input connections are made directly to the
bases of a matched pair of input transistors. Thus, variations in base current and emitter to base
voltage caused by external changes, i.e. temperature, will tend to cause both input transistors to
vary in the same direction. Since the base currents must flow to ground through the external
feedback network, drift effects can be minimized by: (1) using the lowest resistance levels
consistent with input impedance requirements and output current capability; and (2) balancing
the resistances from the two inputs to ground. For the amplifier shown in figure 51, this latter
consideration is satisfied by connecting a resistor from the non-inverting input to ground equal to
the equivalent resistance from the inverting input to ground.
RI RO
EO
-
+EI
R2
Figure 51. Drift Stabilizing the Inverting Amplifier
Capacitive Loading
The addition of capacitive reactance shunting the load of an operational amplifier may lead to
peaking and finally instability at high frequencies. The capacitive load tends to break with the
output impedance of the amplifier causing the slope of the open loop response to increase. As
the rate of closure approaches 40 dB / decade (see “Stability” above), the closed loop response
begins to peak and possibly oscillate (figure 52). This problem is most severe at low gain levels
and at high frequencies.
Figure 52. Gain Peaking Caused by Capacitive Loading
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
VOLTAGE DETECTORS AND COMPARATORS
When this handbook was first published, there were no comparators. Operational amplifiers
were used in a saturated mode as comparators. This section covered the use of operational
amplifiers as comparators, but Texas Instruments strongly discourages this practice. Reference
1 covers this topic in more detail.
When an operational amplifier absolutely must be used as a comparator, there are a couple of
alternatives:
Voltage Limiting Operational Amplifiers
Texas Instruments manufactures voltage limiting operational amplifiers that are specifically
designed to operate at saturated levels, as set by voltage limiting inputs:
INVERTING NON-INVERTING
OPA68x:
x = 8: unity gain stable+Sup
RO
+Sup
Low Set
EO
-Sup
-Sup
High Set
RI
EI
-
+ L OPA68x
3
RI
H2
3
6
7
4 5
8
4
x = 9: gain >= 4
+
-
H
L
OPA68x
2
6
7
5
8
RO
High Set
EI
EO
Low Set
Figure 53. Voltage Limiting Operational Amplifiers
Voltage limiting operational amplifiers are popular in applications that require clipping, such as
video “sync-stripping” circuits. The High Set and Low Set inputs are used to set the maximum
VOH and VOL of the op amp to values between ±Sup. There is no reason why the High Set and
Low Set values have to be positive and negative voltages, respectively. They can be at ground,
or beyond it. There are limits, of course. The amplifier itself has VOH and VOL specifications that
ultimately limit the set levels. The set levels also have a specified accuracy. Incorrect set level
voltages can also prevent the output from working at all. Consult the data sheets for details.
It is possible to use an operational amplifier with external components simulating the output
clamping circuits fabricated into the voltage limiting operational amplifiers described above.
Figure 54 shows an example of the technique:
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
+15 VDC
-
+
CR1
1N4148-1
Rb
10 k....R2
1 M....EORb'
3 k....R1
100 k....-15 VDC
Ra '
15 k....EI
Ref
Ra
15 k....CR2
1N4148-1
-15 VDC
Figure 54. Fully Clamped Voltage Comparator
R21 M.
Threshold =. Vref =. (.15 VDC)= 1.5 VDC
R1 100 k.
. (+ Vsup )Rb .15 VDC .10 k.
Negative clamping level == =.10 VDC
Ra 15 k.
. (. Vsup )Rb +15 VDC . 3 k.
Positive clamping level == =+3 VDC
Ra 15 k.
EO =.10 VDC for EI > 1.5 VDC
EO =+3 VDC for EI < 1.5 VDC
The slope of the transition is determined by the slew rate of the operational amplifier. The set
points, of course, must be within the normal VOH and VOL of the operational amplifier.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
SECTION II CIRCUIT COLLECTION
A search of literature in the field and Texas Instrument’s collection of application notes turned up
the circuits presented in this section. They have been grouped by general function and ordered
within each group by increasing complexity. It is our hope that one of these will trigger the idea
that develops into your circuit.
Please do not interpret any one circuit as our recommendation for your requirement. Some of
them, due to their simplicity or specialized nature, may perform only over limited ranges and
under controlled conditions. We would welcome the opportunity to suggest a specific circuit for
you, given the details of your application.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
THE VOLTAGE FOLLOWER
EI EO
-
+
E-
Let the voltage at the inverting input with respect to the non-inverting input be E-.
By Kirchoff’s voltage law:
(E .)+ E = E
IO
But by definition:
EO =.A(E .)
where A is the gain of the operational amplifier
Then:
( )E =.
A
EO.
And substituting:
IE . O
A
E = OE
Letting A go to infinity,
A
EO approaches zero, and:
OE = IE
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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BUFFERS AND ISOLATION AMPLIFIERS
The standard inverting and non-inverting amplifier circuits provide impedance isolation due to
their inherently low equivalent output impedance. The following circuits are designed principally
for isolation and not for providing gain.
Inverting Buffer Adjustable Gain
RI R2RO
10 k.
....100 10 k.
....
EO
EI
-
+
Potentiometer in feedback allows gain trimming to compensate for tolerance in resistor values.
Balanced Output
Used for driving balanced loads or push-pull stages when ground reference is critical.
EO-
RI
10 k....-
+
RO
10 k....EO+
-
+
EI
RI
10 k....RO
10 k....
By using EO-terminal at the reference, a p-p swing of 4EI is obtainable at EO+, i.e. a usable
swing greater than the power supply voltage rails. A fully differential operational amplifier
provides this function in a single package, and is therefore the preferable design solution.
VOLTAGE AND CURRENT REFERENCES
The high input impedance and low output impedance levels that can be obtained with the
precision and stability of operational amplifier circuitry make reference supplies practical. Some
circuits are merely reference cells or zener diodes with isolator and multiplying circuits added.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Isolated Standard Cell
ErefEref
-
+
Prevent damage to standard cells induced by drawing current from them with low impedance (20
K. / Volt) measuring devices. See section on Buffers and Isolators for gain error. Offset
adjustments should not be made with standard cell connected.
Constant Current Generator
+15 V
I
R2
300 ....6V Zener VZ
RL
IZ
-
+
R1
330 ....
Convenient current reference up to 20 mA:
V 6
I = Z
== 20 mA
R
2 300
15 . V 9
R = Z == 360 .
1
IZ 25
Saturation Voltage 13.5 V
R
= == 675 .
L min
I 20 mA
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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Buffer Variation
Eref
-
+
TLC265x Eref
Low current drift of chopper -stabilized amplifiers improves stability and cell protection.
Presettable Voltage Source
RO
Decade Box
-
+
TLC265x Eref
Eref
RI
1000 X Eref
RI + RO
E = E
O ref
RI
Gives wide range of very stable reference voltages.
Reference Voltage Supply
R4
90 k.
....
R1
10 k....-
+
-
+
R3
10 k....R0
100 k....-EO
+EO
R2
10 k....Eref
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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THE NON-INVERTING AMPLIFIER
-
+
RO
EI
RII
E-
EO
I
Let the voltage at the inverting input with respect to the non-inverting input be E- and the gain of
the operational amplifier be A (ideally, A =. ).
The voltage at the inverting input is then EI + (E-) and, since the current in RI must equal the
current in RO:
(E .)+ EE . ((E .)+ E )
IO I
=
RI RO
but:
E =.A .(E .)
O
O
(E .)= . E
A
Letting A go to infinity, E- approaches zero and the first equation becomes:
EE . E
I OI
=
RI RO
Solving:
E (R + R )= ER
IOI OI
ER + RR
OOI O
== 1+
ER R
II I
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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THE INVERTING AMPLIFIER
RI
EO
EI
RO
E-
I I
-
+
Let the voltage at the inverting input be E- and the open loop operational amplifier gain be A
(ideally, A =. ).
Since equal currents flow in RO and RI:
E .(E .) E .(E .)
I + O = 0
RI RO
But by definition:
E = A .(E .)
O
EO
(E .)= .
A
Letting A go to infinity, E- approaches zero and:
EE
I + O = 0
RI RO
or:
ER
O =. O
EI RI
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
INTEGRATORS
Assume the validity of the ideal gain expression for the generalized Inverting Amplifier:
. ZO
EO = EIZI
The operational form of capacitive impedance is:
1
CZ =
pC
where the symbol, p, is the operator,
dt
d , or for AC analysis is the complex frequency, j2.f.
For the integrator;
OZ = 1
pC
, IZ = IR
-
+
RI CO
EI
EO
.ZO .EI 1
E = E = =. E dt
OI I
Z RC RC
I IOp IO
PRACTICAL INTEGRATORS
Simple integrator circuits operate successfully but current offset is stored in the feedback
capacitor causing output voltage error. This is corrected with low drift chopper stabilized
amplifier and/or current biasing networks.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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Simple Integrators
CO
1 ....FRI
100 k....-
+
EI
EO
. EIdt
EO = =.10 EIdtRICO
Close switch to reset to zero.
R4
10 k....R1
100 k....R5
10 M....+
R2
10 k....-
+
R3
POTEI
CO
1 mF
-EO
This circuit reduces current offset in operational amplifiers without “Balance” controls. With zero
input and switch open, set R3 for zero output drift.
Regeneration may be used to increase open loop DC gain to infinity.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
R6
1 M....R2
100 k....R10
10 k....R5
2 k....EI
R7
1 M....+
R8
10 k....EO
CO
1 ....F
R9
10 k....R4
1 k....-
+
-
R1
100 k....R3
10 M....ZERO
1.
With input open and regeneration control R5 in approximate center of its range, open
reset switch and adjust zero control, R8, until output remains at zero.
2.
Open reset switch, apply an input signal of either polarity and allow integrator to run up to
some voltage between ±10 VDC, then open circuit signal input.
3.
If integrator output decays toward zero, increase regeneration by increasing R5. If output
continues to grow, decrease regeneration.
4.
If setting of regeneration control is altered, repeat steps (1) and (2) above.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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Summing Integrator
R1
E3
-
+
100 k....R3
100 k....R2
100 k....EO
CO
1 ....F
E2
E1
EO =.1 (E + E + E )dt
123
RC
=.10 (E + E + E )dt
123
One amplifier replaces separate summer and integrator circuits. Any number of inputs may be
used. Zero control and regeneration may be added as in the above circuit.
Double Integrator
CO CO
RI RI 1 µ
....F1 µ
....F
1 M.
....1 M.
....
RO
10 k.
....
CI
1 µ
....F
EI
TLC265x EO
-
+
. 4
E = 2 E dt =.4 E dt
O II
(RC )
II
where :
CR
CO = I ,RO = I
22
Integrates twice with one amplifier.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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Differential Integrator
E =.1 (E . E )dt
OI 2
RICO
= 10 (E . E )dt
21
Integrates difference between two signals.
AC Integrator
-
+
TLC265x
E2
RI
100 k....CO
1 ....F
CO
1 ....F
RI
100 k....EO
E1
R2
100 k....EI
EO
CI
100 ....F
-
+
CO
0.01 ....F
RI
100 k....
Integrates AC component only.
Augmenting Integrator
Sums the input signal and its time integral.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
RI ROCO
10 µ
....F
10 k.
....100 k.
....
EO
-
+
TLC265x
EI
. ROEI 1
EO =. EIdt
R CR
I OI
=.10EI . EIdt
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
DIFFERENTIATORS
1
For the differentiator; Z = R, Z =
O OI
Cp
EO
EI
RO
CI
-
+
.ZO
dE I
E = E =.RCE =.RC
O I OIp I OI
ZI
dt
The ideal differentiator circuit is not generally usable in its simple form. It is susceptible to high
frequency noise that may be greater than the derivative output. Design should include high
frequency response limiting.
With “Stop”
Input resistor sets high frequency cutoff.
CI
RI
RO
EI -
+
EO
1 k....100 k....0.1 ....F
1
High frequency cutoff: F == 0.6 kHz
O 2.
RICI
1
Low frequency cutoff: FI == 16 kHz
2.ROCI
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Low Noise
CO
0.001 µ
....F
CI
0.1 ....F
-
+
RI
1 k....RO
100 k....EO
EI
RC = R C drift compensating resistor
II OO
Double high frequency cutoff.
Augmented Differentiator
EO
-
+
RI
100 k....CI
0.1 ....F
RO
100 k....R2
50 k....EI
. RE dE
OI I
E =. RC
O OI
RI dt
1 dEI
E =.E .OI 100 dt
Sums input and its derivative.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
THE VOLTAGE SUMMER
E3
I3
R3
E1
R1
I2
R2
I1
-
+
RO
IO
EO
E2
Assume the ideal summing paint restraints:
1. Pin (1) is at ground potential
2. . IO + I1 + I2 + I3 + ... = 0
The current, IO, is given by:
. E EEE
O 123
IO = =+++ ...
R RRR
O 123
So that:
.
EE E
123
E =.R .
+++ ...
OO
RR R
.
123
. RO
Thus, each input, En, is multiplied by a factor, , before summing.
Rn
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
SUMMING AND AVERAGING AMPLIFIERS
Voltages are summed by applying the signals to the same input of the amplifier. Amplifying,
averaging, etc., may be accomplished by input resistor scaling. Inputs are effectively isolated
from each other. Any number of inputs may be used in each of these circuits.
Adder
10 k.
....
-
+
10 k....10 k....E3
10 k....EO
E1
E2
E = .(E + E + E )
O 123
Zin = 10 k. for each input
Output is inverted algebraic sum of inputs.
Scaling Adder
R1
EO
-
+
E2
R2
10 k....E3
E1
R0
100 k....1 k....R3
100 k....
.
RR R
00 0
E = .
E + E + E =.100(100E +10E + E )
O 123 123
RR R
.
12 3
Z = 1 k. for E = 10 k. for E = 100 k. for E
in 12 3
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Each input is multiplied by a constant before summing-inverting output.
Direct Addition
R1 R0
10 k.
....20 k.
....
E2
E1
R2
10 k....-
+
R2
10 k....EO
R2
10 k....
E = E + E
O 12
3
Zin = R2 = 15 k. for each input
2
RO = 2RI
Non-inverting output.
Averager
RI
RI
30 k....EO
RO
10 k....E2
E1
E3
30 k....RI
30 k....-
+
. RE + E + E
O 123
E =(E + E + E )=.
O 123
RI 3
RO = RI divided by number of inputs
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Output is inverted average of input signals. Ground unused inputs to preserve scale.
Weighted Average
RO
5.1 k....E2
R2
20 k....R3
30 k....E3
-
+
R1
10 k....RO'
1 k....EO
E1
For E = E = E,setR 'soE = E
123 O OI
Then, R + R'= RR2
OO 1
R3
.(R + R')E (R + R')E (R + R')E .(16.4E + 8.2E + 5.4E )
OO 1 OO 2 OO 3 123
E = ..=
OR RR 30
1 23
Each input is multiplied by a weighting factor before averaging.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
THE DIFFERENTIAL INPUT AMPLIFIER
RO
E1
I2
IOI1
R1
E2
R2 R3
-
+
EO
I3
Assume the ideal input restraints:
1. The input pins reside at the common mode voltage, Ef.
2. IO=I1, I2=I3
Current in the top leg is given by:
E . EE . E
1 f fO
I == 1 R1 RO
Solving for EO:
.
RO
.
RO
E = E 1 +. E
Of 1
RR
.
11
Due to current in the bottom leg, R2 and R3 act as a simple voltage divider:
R3
Ef = E2R2 + R3
Substituting:
.
R .
R .
RR .
R + R .
R
3 OO 31 OO
E = .
1 + E . E = .
E . E
O 21 21
R + RR RRR + RR
.
23 .
1 11 .
23 1
For R2 = R1 and R3 = RO, this reduces to:
RO
EO =
R1
(E2 . E1 )
(Ground reference point does not matter. Input may be “floating” if desired.)
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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Adder-Subtractor or Floating Input Combiner
R
10 k.
....
E1
R
10 k.
....R
10 k.
....E2
RI
10 k.
....
E3
RI
RI
10 k.
....
10 k.
....
EO
E4
-
+
As an adder-subtracter, unused inputs should be grounded.
EO =.E . E + E + E
1234
R and RI not necessarily equal
Two or more “floating” inputs maybe combined by connecting them across E3 to E1 and E4 to E2.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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THE DIFFERENTIAL (BALANCED) OUTPUT AMPLIFIER
I4
RO
I1
Ef
E2
EO + EP
Ef
I3
RI
-
+ EP
E1
I2
EO
RI RO
Assume the ideal input restraints:
1. The inverting and non-inverting inputs reside at the same common mode voltage, Ef
2. I1=I2, I3= I4
Current in the top leg is given by:
E . EE .(E + E )
1 f fOP
I1 ==
RI RO
Current in the bottom leg is given by:
E . EE . E
2 f fP
I3 ==
RI RO
Subtracting these two equations:
E . E . E
12 O
=
RI RO
Or:
RO
EO =(E2 . E1 )
RI
(Ground reference is not critical. Input may be “floating” if desired.)
Note that the values of Ef and EP are not uniquely determined by the above equations. In
practice, this means that EP will reside at same value determined by the internal circuitry of the
operational amplifier itself plus the effects of drift. However, EO will remain accurately fixed by
the differential gain equation above.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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DC AMPLIFIERS
There are two basic circuits, inverting and non-inverting, plus the differential output form.
Simple Inverting sign changing amplifier
RI RO
100 k....1 k....EO
-
+
EI
. RO
E = E =.100E
O II
RI
RORI
resistor == 1 k.
RI + RO
Zin = RI = 1 k.
Chopper Stabilized
Improved drift and stability.
Simple Gain Control
EI
EO
-
+
TLC265x
RO
100 k....RI
1 k....
10 kW
EI
-
+
EO
Wide range gain or attenuation.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Unity gain with R centered. The gain is not linear with potentiometer setting. Zin drops as gain is
increased.
Linear Gain Control
RO
100 k.
....
RI
-
+
EI
EO
10 k....
Variable from 0 to 10
EO = 0 to .10EI
Zin = RI = 10 k.
Simple Non-Inverting
EI
-
+
RO
90 k....RI
10 k....EO
Input common mode voltage limit must be observed.
R + R
E = O IE = 10E
O II
RI
Gain controls and/or trimming may be accomplished as in the variations on the inverting
amplifier above.
Power Booster
Output current of any of the above circuits may be increased by the addition of a power booster.
The operational amplifier -booster combination is substituted directly for the original operational
amplifier.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
20 k.
....
10 k....EI
0.1 ....100 k....47 pF
10 pF
-
+
EO
0.1 ....1 k....-
+
4.7 k....
G = +21
Table 1. Compound Amplifier, Resulting Performance
Parameter OPA277 OPA512 Compound
VOS 20 .V 6 mV 20 .V
Drift 0.15 .V/°C 65 .V/°C 0.15 .V/°C
IB 1 nA 30 nA 1 nA
CMRR 130 dB 100 dB 130 dB
VOUT ± 13 V ± 35 V ± 35 V
IOUT 5 mA 10 A 10 A
SR 0.8 V/.S 2.5 V/.S 2.4 V/.S
This circuit addresses the need for a power output stage with a precision input circuit. The
combination is not available in one device. It is possible to combine the power capabilities of the
OPA512 with the precision of the OPA277. The OPA512 has the highest slew rate and
therefore is operated within a local closed loop. The slower OPA277 is operated within the outer
loop. The 47pF capacitor provides a small amount of phase shift to help stabilize the system.
The resulting performance of the compound amplifier shows that the front-end characteristics of
the OPA277 are joined with the ±35V at 10A drive current capabilities out of the OPA512. The
slew rate of the OPA277 is 0.8V/.s. That slew rate is gained up times three in the OPA512 so
that there is an effective slew rate for the compound amplifier of 2.4V/.s.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Differential Output
RI RO
10 k.
....100 k.
....
-
+
RO
EO
RI
EI
10 k.
....100 k.
....
RO
E = E = 10E
O II
RI
For driving floating load.
Gain Control
-
+
EO10 k....EI
Equivalent to replacing both resistors in the non-inverting amplifier. Observe common mode
voltage limit.
Inverting Gain Control
RO
10 k.
....
-
+
EO
EI
RI
10 k....10 k....R2
EO = (.1 to inf inity)EI
Zin = 10 k.
Convenient gain technique
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
DIFFERENTIAL AMPLIFIERS
In differential amplifiers, separate input signals are applied to the differential inputs of the
operational amplifier. The result is direct subtraction in contrast to the summing amplifier that
adds algebraically.
Subtractor
RI RO
E2
10 k....RI
10 k....RO
10 k....10 k....E1
-
+
EO
EO = E2 . E1
Direct subtraction of two inputs.
Difference Amplifier
1 k.
....100 k.
....
O
E =
.
RRI
(E . E )= 100(E . E1 )
O 12 2
Subtractor with amplification.
RI
1 k....RO
E2
EO
E1
RO
100 k....RI
-
+
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Common Mode Rejection
R1 R0
-
+
R4
10 k....R3
5 k....100 k....E1
E2
1 k....R5
10 k....R2
9.1 k....-
+
EO
. RO
E =(E . E )= 10(E . E )
O 12 21
RI
R + R = R
231
Subtraction by inverting and summing to eliminate common mode voltage.
R3 -common mode adjustment. Set for Zero output when E1 = E2.
Differential Input-Output
EO
RI
1 k....RI
1 k....RO
10 k....-
+
RO
10 k....E2
E1
For use in driving floating loads. Input may be floating source.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
AC AMPLIFIERS
DC Amplifiers with Blocking Capacitors
AC operational amplifier circuits will amplify low frequency signals that are below the range of
more conventional amplifiers (0.1 Hz to 20 kHz) while DC blocking still is present. Only a single
ended supply is required in one circuit. DC and AC operational amplifier circuits are equivalent at
higher frequencies.
Simple Amplifier
Simple RC roll off at low frequency.
CI
RI RO
100 k....-
+
1 ....F
EO
EI
10 k....
RO
E =. E =.10E
O II
RI
Zin = 10 k.
1
Low frequency rolloff begins: f == 16 Hz
.3dB
2.RICI
Single Supply
RI
10 k....RO
100 k....-
+
+ C2
100 ....F
EI
R2
10 k....+Supply
CI
1 ....F
EOR2'
10 k....
Equivalent to above, with the supply “floated” above ground.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Non-Inverting
C2
-
+
R1
10 k....EO
+ C1
100 ....F
R0
90 k....R2
100 k....EI
1 ....F
EO in phase with EI
R + R
EO = OR
I = 10EI
I
1
Low frequency rolloff f == 0.16 Hz
.3dB
2.RICI
Double Rolloff
C2
R0
90 k....EO
+C1
100 ....F
EI
1 ....F
R1
10 k....R2
100 k....-
+
Similar to above.
CR = CR
11 22
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
AC Preamplifier
C2
C3
R1
200 ....+C1
1000 ....F
R2
100 k....1 ....F
R0
100 k....EO
-
+
R3
2.2 k....EI +
10 ....F
R4
10 k....
Completely developed AC amplifier with high Zin and double rolloff rate and gain trim.
ER + R
O 01
== 500
EI R1
R4 -Fine gain adjust
1
Low Frequency rolloff begins f == 1.6 Hz
.3dB
2.R1C1
RC = RC
11 22
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
CURRENT OUTPUT DEVICES
These amplifiers will supply output current to a load in linear correspondence to the input
voltage.
Feedback Loop
R1
1 k.
....RL
EI
I
-
+
E
I = I = E mA
RI
I
Zin = RI = 1 k.
Simple Meter Amplifier
RI
10 k....RO
4.7 k....EI
RO
4.7 k....RO
4.7 k....-
+
EI EI
I == mA
meter
3RI 30
Linear current meter reads AC input voltage.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Meter Amplifier
C1
10 ....F
R0
220 k....R4
47 ....R5
100 ....-
+
R6
100 ....C1
1 ....F
C2
10 ....FR1
220 k....R7
100 ....R8
68 k....EI
0.9EI
Meter reading =(rms)
R4 + R5
R5: gain control (calibration)
Fully developed average reading meter
Current Injector
R1 R0
R3
1 k....EI
1 k....RL
I
1 k....-
+
R2
1 k....
E
I =. I =.EI mA
RL
R1 R0
=
R2 R3
Single terminal current available to ground. Observe common mode voltage limit.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Linear Current Source
R2
100 k.
....
R2
100 k....-
+
-
+
I
R1
100 k....R3
1 k....EI
R0
100 k....CO
RL
R0
100 k....
When RL << R2 ,
IL = R2 = mA1
EI R R31 Volt
CO added for high frequency stability.
Change R3 for current scaling:
Table 2. Current Source Scaling Resistors
R3 IL/EI
1 k. 1 mA / Volt
100 . 10 mA / Volt
10 . 100 mA / Volt
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Deflection Coil Driver
R1 R0
-
+
I
EI
RL
10 k....10 k....R3
10 ....
I . R0
= =.100 mA / Volt
E RR
I 13
Load must be ‘floating,” i.e. ungrounded.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
OSCILLATORS AND MULTI VIBRATORS
Oscillators give a continuous sine wave, output. Multivibrator output fixed voltage level or square
wave similar to flip-flop output.
Simple Oscillator
2C
EO
-
+
R C C
R/2
R
1
f =
2.RC
Double integrator circuit with regenerative feedback. Components R, C, and 2C should be very
low tolerance. Trim R/2 until oscillation is barely sustained.
Wien Bridge Oscillator
C
R
R2
1.8 k....R
EO
R3
220 ....R1
500 ....LP1
GE 1869
-
+
C
1
fO = , 100 to 6000 Hz
2.RC
High purity sine wave generation.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
PHASE LEAD AND LAG NETWORKS
These networks are used to stabilize servo systems by introducing phase shift as desired.
Transient and steady state responses may be tailored semi-independently.
Lag Element
RI RO
1 M.
....10 k.
....
EO
-
+
EI
CO
10 ....F
. RE .10E
OI I
EO ==
R 1+ RCP 10 + P
I OO
Integrating type phase lag.
Adjustable Lag
-
+
....R
RO
10 k....R
10 k....EI
C
10 ....F
EO
1
Non-integrating type. Constant inverting unity gain. Maximum lag for R centered for .=
2
where 0 ...1 is the log setting.
. E . 40E
E = I = I
O 2
1+(... )RCP 40 + P
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Lag value linear with R setting
R
EI
10 k....C
10 ....F
-
+
EO
....R
EI 10EI
EO ==
1+.RCP 10 + P
d
P = operator, or j.
dt
Non-inverting low distortion
Adjustable Lead
RR
EO
EI
....R
10 k....C
10 ....F
-
+
10 k....
EO = .[(. . .2 )RCP]EI
Putting input network from adjustable lag circuit in feedback path gives lead element.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Lead-Lag
R R
10 k.
....10 k.
....
-
+
....2R ....1R
EO
C1
10 ....F
C2
10 ....F
EI
2
1 +(... )RC P
11 1
=EO 1+(. .. 2 )RC P
22 2
Composite lead and log network.
Time Delay
R
0.8C
R/6
3.6C
EI
2R/3R/6
EO
0.8C
3.6C
R/4
-
+
Unity gain phase or time shift.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
ADDITIONAL CIRCUITS
The following are various circuits that do not fall into one of the categories of the previous
sections.
Absolute Value
RR
10 k.
....10 k.
....
-
+
EO EI
+ EI follower circuit
. EI inverter circuit
EO =
EI
Full wave rectification. Reverse diodes to give EO =.
EI
Peak Follower
1 ....F
-
+
EOEI
Peak value memory. Use low leakage capacitor. EO = EI maximum. Common mode input
voltage must be observed.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Precision Rectifier
RI RO
RO
10 k....EO
-
+
10 k....EI
2 k....
. RO
E peak = E peak =.5E peak
O II
RI
Half wave with amplification if desired. Placing rectifiers in feedback loop decreases nonlinearity
to very small value.
AC to DC Converter
R8
R3 R72 k.
....
10 k....R2
10 k....-
+
EO
R1
10 k....10 k....+
C
100 ....F
R6
5 k....==
R4
10 k....EI
-
+
EOaverage = 0.9EIrms
EI = 6 mV to 6 V rms @ 10 to 1000 Hz
Precision conversion for measurement or control. Full wave rectifier with a smoothing filter.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Full Wave Rectifier
R1 RO
2 k.
....2 k.
....
R4
1 k....EI
R3
1 k....-
+
EO
R2
1 k....-
+
R5
1 k....
Precision absolute value circuit.
Rate Limiter
R2
4.7 k....EI -Supply -
+
R1
100 k....+
C0
10 ....F
EO
+Supply
R5
100 k....R0
100 k....-
+
R4
100 k....R3
100 k....
. RO
E = E =.E
O II
RI
Rate limit = 7.5 V/sec
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Time Delay
+
C0
10 ....F
R3
4.7 k....R6
10 k....RELAY SPDT
R5
10 k....R7
10 k....+Supply
R1
100 k....R4
10 k....6 Volt
1 k.... coil
-
+
RICO
Delay =
2KI
Where K is setting of RI, 0, K < 1
Time operated relay. Open switch to reset, close to being timing.
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
SBOA092A
Selective Amplifier
RO
330 k.
....
CI
50 nF
Ca
50 nF
EI
Ra
3.3 k....RI
10 k....Twin-T Network
-
+
EO
Ra
3.3 k....2Ca
100 nF
Ra/21.65 k....Ca
50 nF
Twin T feedback
1
Frequency peak = = 1000 Hz
2.RaCa
RO
Gain at peak = =33 = 30 dB
RI
Set CI so that CIRI >2CaRa and RI < 100 k.
Zin= RI = 10kW
Zout < 200 .
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
Application Report
SBOA092A –October 2001
SECTION III: SELECTING THE PROPER OPERATIONAL AMPLIFIER
Now, with the theory, circuits, and test procedures at our command, we are ready to select an
amplifier. A glance at the representative specifications, given in the Appendix, shows the variety
of ratings available. These represent only a small fraction of the operational amplifiers available
from Burr-Brown alone. This section presents several approaches to selecting the proper
operational amplifier from the wide range of available units.
Focus on Limiting Specifications
To apply the operational amplifier correctly, none of its ratings should be exceeded. It would,
however, be uneconomical to apply the device too conservatively. With so many specifications
and so many amplifiers, the secret is to focus on the limiting specification.
In the majority of DC applications, the limiting factor will be DC drift. Drift in operational amplifiers
is primarily due to temperature effects on the input transistors causing base voltages and base
currents to vary. The input current offset (base current) must flow to ground through the external
feedback network and through the source. The input current drift times the effective resistance to
ground gives a voltage affect 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 tend to cancel as
indicated by the specification, “differential current drift.” A comparison of the input stability
(combined effects of voltage and current drifts over your temperature range) with your input
signal will give a quick indication of the accuracy you can expect.
Specifications other than drift that can help you focus on the proper amplifier are bandwidth,
output capability, and packaging. The requirement for a high gain-bandwidth product may
narrow the field to a few high-speed amplifiers. High power output requirements may rule out the
smaller packages and more economical units. A packaging preference will rule out comparable
units in other configurations.
While any one of seventy or more specifications could be limiting in your application, familiarity
with operational amplifiers will enable you to spot quickly the critical parameter in your case.
Avoid Closed Loop vs. Open Loop Confusion
While an amplifier is never used open loop, in practical applications, open loop specifications are
required to provide the information needed for all possible closed loop applications. As we have
seen in the preceding sections, there may be a vast, but predictable, difference between open
loop and closed loop characteristics such as input impedance, output impedance, and
bandwidth. The amplifier for your application may be completely described with either closed
loop specifications or open loop specifications, but the relationship between the two should be
clearly understood.
Selection Check List
The following is a checklist of the information required to select the proper amplifier for your
needs. Be sure you have enough information.
1. The Source: What type of source do you have? Voltage level? Impedance?
SBOA092A
2.
The Load: What type of load do you have? Voltage level required? Impedance?
3.
Performance: In the closed loop, what is the required gain? Bandwidth? Accuracy?
Linearity? Input Impedance? Output Impedance? DC drift? Noise? In the open loop, what
standard Texas Instruments amplifier will do this? Any exceptions? Formal
specifications? Available in system/instrument?
4.
Environment: Where will the amplifier be used? Temperature range? Other
requirements?
5.
Power Supply: Number of amplifiers per supply? Current drain?
6.
Package: Type of mounting? Controls? Connectors?
7.
Availability: Quantity? Future potential? Delivery requirements? Price?
The above information will define your requirement fully.
Assistance Available from Texas Instruments
The following services are available to you for the asking.
•=
The latest specifications and devices -Operational amplifiers are continually being
improved and new models introduced. Be sure your information is up to date.
•=
Applications assistance - given the information in the preceding checklist, an amplifier will
be recommended with an appropriate circuit.
•=
Availability - Get all the information you need for on-schedule installation at minimum cost.
Contact Texas Instruments or your nearest representative for any or all of these services.
References
1.
Texas Instruments, Op Amps and Comparators - Don't Confuse Them, SLOA067, Bruce
Carter, 09/06/2001
2. Texas Instruments, How (Not) To Decouple High-Speed Operational Amplifiers, SLOA069,
Bruce Carter, 09/12/2001
3.
Texas Instruments, Differential Op Amp Single-Supply Design Techniques, SLOA072,
Bruce Carter, 09/17/2001
HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS
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enhancements, improvements, and other changes to its products and services at any time and to discontinue
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