Chapter 3 operational amplifier electrical engineering

Electronics chapter 3 applications of operational amplifier

1. Applied Electronics II
Chapter 3: Operational Amplier
Part 1- Op Amp Basics
School of Electrical and Computer Engineering
Addis Ababa Institute of Technology
Addis Ababa University
Daniel D./Getachew T./Abel G.
April 2017
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 1 / 46

2. Overview
1
Introduction
2
The Ideal Op Amp
The Op Amp Terminals
Function and Characteristics of the Ideal Op Amp
3
The Inverting Conguration
Closed-Loop Gain
Eect of Finite Open-Loop Gain
Input and Output Resistances
An Important Application - The Weighted Summer
4
The Noninverting Conguration
The Closed-Loop Gain
Eect of Finite Open-Loop Gain
Application - The Voltage Follower
5
Dierence Ampliers
A Single-Op-Amp Dierence Amplier
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3. Overview
The Instrumentation Amplier
6
Integrators and Dierentiators
The Inverting Integrator
The Op-Amp Dierentiator
7
DC Imperfections
Oset Voltage
Input Bias and Oset Currents
8
Frequency Response
Frequency Dependence of the Open-Loop Gain
Frequency Response of Closed-Loop Ampliers
9
Large-Signal Operation of Op Amps
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4. Introduction
Introduction
The operational amplier (Op amps) have been in use for a long
time, their initial applications being primarily in the areas of
analog computation and sophisticated instrumentation.
Early op amps were constructed from discrete components
(vacuum tubes and then transistors, and resistors).
The introduction of integrated circuit (IC) reduced the cost and
improved the performance.
One of the reasons for the popularity of the op amp is its
versatility.
IC op amp has characteristics that closely approach the assumed
ideal.
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5. The Ideal Op Amp The Op Amp Terminals
The Op Amp Terminals
From a signal point of view the op amp has three terminals: two input
terminals (1) and one output terminal (3).
Most IC op amps require two dc power supplies, as shown in two
terminals,, are brought out of the op-amp package and
connected to a positive voltageVCCand a negative voltageVEE,
respectively.
Some times other terminals can include terminals for frequency
compensation and terminals for oset nulling.
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6. The Ideal Op Amp Function and Characteristics of the Ideal Op Amp
Function and Characteristics of the Ideal Op Amp
Op amp is designed to sense the dierence between the voltage signals
applied at its two input terminals and multiply this by a number A.
v3=A(v2v1)
Characteristics of the Ideal Op Amp
Innite input impedance
Zero output impedance
Zero common-mode gain or, equivalently, innite common-mode
rejection
Innite open-loop gain A
Innite bandwidth
Question:
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7. The Ideal Op Amp Function and Characteristics of the Ideal Op Amp
Function and Characteristics of the Ideal Op Amp
An ampliers input is composed of two components
dierential input (vId)
non-inverting terminals
vId=v2v1
common-mode input (vIcm)
vIcm=
1
2
(v2+v1)
The input signalsv1andv2
v1=vIcmvId=2and 2=vIcm+vId=2
Similarly, two components of gain exist
dierential gain(A)
common-mode gain(Acm)
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 7 / 46

8. The Ideal Op Amp Function and Characteristics of the Ideal Op Amp
Function and Characteristics of the Ideal Op Amp
Figure:
op amp.
Figure:
dierential and common-mode
components.
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 8 / 46

9. The Inverting Conguration
The Inverting Conguration
Op amps are not used alone; rather, the op amp is connected to passive
components in a feedback circuit.
There are two such basic circuit congurations employing an op amp
and two resistors: the
conguration
Figure:
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 9 / 46

10. The Inverting Conguration Closed-Loop Gain
Closed-Loop Gain
Assuming an ideal op amp. How to analyze closed-loop gain for
inverting conguration of an ideal op-amp?
Step 1
Step 2 vois nite , then the voltage between the op-amp input
terminals should be negligibly small and ideally zero.
v2v1=
vo
A
= 0; because 1
A virtual short circuit betweenv1andv2.
A virtual ground exist atv1.
Step 3 i1).
i1=
vIv1
R1
=
vI0
R1
=
vI
R1
Step 4
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 10 / 46

11. The Inverting Conguration Closed-Loop Gain
Closed-Loop Gain
It cannot go into the op amp, since innite input impedance draws zero
current.i1will have to ow throughR2to the low-impedance terminal
3.
Step 5 voin terms of current owing acrossR2.
vo=v1i1R2= 0
vI
R1
R2=
R2
R1
vI G=
R2
R1
Figure:
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 11 / 46

12. The Inverting Conguration Eect of Finite Open-Loop Gain
Eect of Finite Open-Loop Gain
How does the gain expression change if open loop gain (A) is not
assumed to be innite?
One must employ analysis similar to the previous.
The voltage atv1becomes
v2v1=
vo
A
v1=
vo
A
The currenti1becomes
i1=
vIv1
R1
=
vI+
vo
A
R1
The output voltagevobecomes
vo=v1i1R2=
vo
A

vI+
vo
A
R1
R2;vo

1 +
1 +
R2
R1
A
!
=v1
R2
R1
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 12 / 46

13. The Inverting Conguration Eect of Finite Open-Loop Gain
Eect of Finite Open-Loop Gain
The Gain will be
GA<1=
vo
vi
=
R2=R1
1 +

1 +R2=R1
A

Figure:
open-loop gain of the op amp.
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 13 / 46

14. The Inverting Conguration Input and Output Resistances
Input and Output Resistances
The Input Resistance is
Ri=
vi
ii
=
vi
(viv1)=R1
=
vi
vi=R1
=R1
For a Voltage amplicationRimust be large. Then the gain would be
reduced, so such conguration suers from lowRi. Consider the
following circuit and nd the expression of the closed loop gain
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 14 / 46

15. The Inverting Conguration Input and Output Resistances
Input and Output Resistances
The closed loop gain
vo
vi
=
R2
R1

1 +
R4
R2
+
R4
R3

It can be seen a higherRican be achieved without compromising the
closed loop gain.
Since the output of the inverting conguration is taken at the terminals
of the ideal voltage sourceA(v2v1), it follows that the output
resistance of the closed-loop amplier is zero.
Ro= 0
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 15 / 46

16. The Inverting Conguration An Important Application - The Weighted Summer
An Important Application - The Weighted Summer
Weighted Summer
provides an output voltage which is weighted sum of the inputs.
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 16 / 46

17. The Noninverting Conguration
The Noninverting Conguration
The input signalvIis applied directly to the positive input terminal of
the op amp while one terminal ofR1is connected to ground.
Then the polarity / phase of the output is same as input.
Figure:
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18. The Noninverting Conguration The Closed-Loop Gain
The Closed-Loop Gain
For an ideal case the closed-loop gain by using the previous methods.
vo
vi
= 1 +
R2
R1
Figure:
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 18 / 46

19. The Noninverting Conguration Eect of Finite Open-Loop Gain
Eect of Finite Open-Loop Gain
Assuming the op amp to be ideal except for having a nite open-loop
gainA. The closed-loop gain
GA<1=
vo
vi
=
1 +R2=R1
1 +

1 +R2=R1
A

For
A1 +
R2
R1
the closed-loop gain can be approximated by the ideal value.
The percentage error inGresulting from the nite op-amp gainAas
Percentage gain error =
1 +R2=R1
A+ 1 + (R2=R1)
The Riof this closed-loop amplier is ideally innite,
since no current ows into the positive input terminal of the op amp.
The output is taken at the terminals of the ideal voltage source thus
the Roof the noninverting conguration is zero.
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 19 / 46

20. The Noninverting Conguration Application - The Voltage Follower
The Voltage Follower
The property of high input impedance is a very desirable feature
of the noninverting conguration.
It enables using this circuit as a buer amplier to connect a
source with a high impedance to a low-impedance load. Buer
amplier is not required to provide any voltage gain
This circuit is commonly referred to as a, since the
output ollows" the input.
Figure:
circuit model.
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 20 / 46

21. Dierence Ampliers
Dierence Ampliers
A
the two signals applied at its input and ideally rejects signals that are
common to the two inputs.
Ideally, the amp will amplify only the dierential signal (vId) and
reject completely the common-mode input signal (vIcm). However,
a practical circuit will behave as below
vo=AdvId+AcmvIcm
The ecacy of a dierential amplier is measured by the degree of its
rejection of common-mode signals in preference to dierential signals.
CMRR= 20 log
jAdj
Acm
Question:
an op amp?
very high (ideally innite) gain of the op amp
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 21 / 46

22. Dierence Ampliers
Dierence Ampliers
A
the two signals applied at its input and ideally rejects signals that are
common to the two inputs.
Ideally, the amp will amplify only the dierential signal (vId) and
reject completely the common-mode input signal (vIcm). However,
a practical circuit will behave as below
vo=AdvId+AcmvIcm
The ecacy of a dierential amplier is measured by the degree of its
rejection of common-mode signals in preference to dierential signals.
CMRR= 20 log
jAdj
Acm
Question:
an op amp?
very high (ideally innite) gain of the op amp
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 21 / 46

23. Dierence Ampliers A Single-Op-Amp Dierence Amplier
A Single-Op-Amp Dierence Amplier
Analyzing the dierence amplier below using superposition.
vo1=
R2
R1
vI1 vo2=
R4
R3+R4

1 +
R2
R1

vI2
We have to make the two gain magnitudes equal in order to reject
common-mode signals.
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 22 / 46

24. Dierence Ampliers A Single-Op-Amp Dierence Amplier
A Single-Op-Amp Dierence Amplier
R2
R1
=
R4
R3+R4

1 +
R2
R1

R2=R1
1 +R2=R1
=
R4
R3+R4
=
R4=R3
1 +R4=R3
The condition is obtained when
R2
R1
=
R4
R3
Assuming the condition is satised, the output voltage
vo=
R2
R1
(vI2vI1)
In addition to rejecting common-mode signals, a dierence amplier is
usually required to have ahigh input resistance. AssumingR4=R2
andR3=R1and applying a dierential input.
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 23 / 46

25. Dierence Ampliers A Single-Op-Amp Dierence Amplier
A Single-Op-Amp Dierence Amplier
vId=R1iI+ 0 +R1iI
Thus
RId=
vId
iI
= 2R1
Note that if the amplier is required to have a large dierential gain (R2=R1),
thenR1of necessity will be relatively small and the input resistance will be
correspondingly low, a drawback of this circuit.
Another drawback of the circuit is that it is not easy to vary the dierential
gain of the amplier.
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26. Dierence Ampliers The Instrumentation Amplier
The Instrumentation Amplier
The low-input-resistance problem can be solved by using voltage
followers to buer the two input terminals. But why not get some
voltage gain.
Solution: using a Noninverting Op Amp.
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 25 / 46

27. Dierence Ampliers The Instrumentation Amplier
The Instrumentation Amplier
The outputvo
vo=
R4
R3

1 +
R2
R1

(vI2vI1)
The Advantages are
very high input resistance
high dierential gain
symmetric gain (assuming thatA1andA2are matched)
The Disadvantage
AdandAcmare equal in rst stage - meaning that the
common-mode and dierential inputs are amplied with equal gain
need for matching - if two op amps which comprise stage 1 are not
perfectly matched, one will see unintended eects
The Solution R1) connected to node
Xfrom ground and connecting them together.
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 26 / 46

28. Dierence Ampliers The Instrumentation Amplier
The Instrumentation Amplier
For a dierential input applied the gain would remain the same. For a
common mode input voltagevIcman equal voltage appears at the negative
input terminals ofA1andA2, causing the current through R1to be zero.
Thusvo1andvo2will be equal to the input. Thus the rst stage no longer
ampliesvIcm.
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 27 / 46

29. Integrators and Dierentiators The Inverting Integrator
The Inverting Integrator
By placing a capacitor in the feedback path and a resistor at the input, we
obtain the circuit of below. We shall now show that this circuit realizes the
mathematical operation of integration. Let the input be a time-varying
functionvI(t).
The transient description
vO(t) =
1
CR
tZ
0
vI(t)dtvO(t0)
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 28 / 46

30. Integrators and Dierentiators The Inverting Integrator
The Inverting Integrator
The steady-state description
Vo(s)
Vi(s)
=
1
sCR
Thus the integrator transfer function has magnitude of =!CRand
phase= +90

This conguration also known as aMiller integratorhas a
disadvantage.
At!= 0, the magnitude of the integrator transfer function is
innite. This indicates that at dc the op amp is operating with an
open loop.
Solution:
negative feedback is employed to make dc gain \nite".
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 29 / 46

31. Integrators and Dierentiators The Inverting Integrator
The Inverting Integrator
The integrator transfer function becomes
Vo(s)
Vi(s)
=
RF=R
1 +sCRF
The lower the value we select forRF, the higher the corner frequency will be
and the more nonideal the integrator becomes. Thus selecting a value forRF
presents the designer with a trade-o between dc performance and signal
performance.
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32. Integrators and Dierentiators The Op-Amp Dierentiator
The Op-Amp Dierentiator
Interchanging the location of the capacitor and the resistor of the integrator
circuit results in the circuit which performs the mathematical function of
dierentiation.
The transient description
vO(t) =CR
dvI(t)
dt
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 31 / 46

33. Integrators and Dierentiators The Op-Amp Dierentiator
The Op-Amp Dierentiator
The steady-state description
Vo(s)
Vi(s)
=sCR
Thus the integrator transfer function has magnitude of!CRand phase
=90

This conguration as a dierentiator has a disadvantage.
Dierentiator acts as noise amplier, exhibiting large changes in
output from small (but fast) changes in input. As such, it is rarely
used in practice.
When the circuit is used, it is usually necessary to connect a
small-valued resistor in series with the capacitor. This modication,
unfortunately, turns the circuit into a nonideal dierentiator.
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 32 / 46

34. DC Imperfections Oset Voltage
Oset Voltage
Now we consider some of the important nonideal properties of the op amp.
What happens If the two input terminals of the op amp are tied together and
connected to ground.
Ideally sincevid= 0, we expectvO= 0
In practice a nite dc voltage exists at the output.
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 33 / 46

35. DC Imperfections Oset Voltage
Oset Voltage
The causes ofVOSis unavoidable mismatches in the dierential stage
of the op amp. It is impossible to perfectly match all transistors.
General-purpose op amps exhibitVOSin the range of 1 mV to 5 mV.
Also, the value ofVOSdepends on temperature.
Analysis to determine the eect of the op-ampVOSon their
performance is the same for both inverting and the noninverting
amplier congurations.
VO=VOS

1 +
R2
R1

Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 34 / 46

36. DC Imperfections Oset Voltage
Oset Voltage
How to reduced Oset Voltage
oset nulling terminals
reduce the asymmetry present and, in turn, reduce oset.
capacitive coupling
may be used to reduce oset, although it will also lter out dc
signals.
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 35 / 46

37. DC Imperfections Input Bias and Oset Currents
Input Bias and Oset Currents
In order for the op amp to operate, its two input terminals have to be
supplied with dc currents, termed the, IB.
IB=
IB1+IB2
2
IOS=jIB1IB2j
input oset currents, IOS- the dierence between bias current at both
terminals.
The resulting output voltage
VO=IB1R2uIBR2
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 36 / 46

38. DC Imperfections Input Bias and Oset Currents
Input Bias and Oset Currents
To reduce the value of the output dc voltage due to the input bias currents,
logically it is#R2but higherR2needed for gain.
The solution is introducing a resistanceR3in series with the noninverting
input.
The output voltage when calculated
VO=IB2R3+R2(IB1IB2R3=R1)
AssumingIB1=IB2=IB
VO=IB[R2R3(1 +R2=R1)]
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 37 / 46

39. DC Imperfections Input Bias and Oset Currents
Input Bias and Oset Currents
Thus we can reduceVOto zero by selectingR3such that
R3=
R2
1 +R2=R1
=
R1R2
R1+R2
We conclude that to minimize the eect of the input bias currents, one
should place in the positive lead a resistance equal to the equivalent dc
resistance seen by the inverting terminal.
This is the case for op amps constructed using bipolar junction
transistors (BJTs). Those using MOSFETs in the rst (input) stage
do not draw an appreciable input bias current; nevertheless, the input
terminals should have continuous dc paths to ground.
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 38 / 46

40. Frequency Response Frequency Dependence of the Open-Loop Gain
Frequency Dependence of the Open-Loop Gain
The dierential open-loop gainAof an op amp is not innite; rather, it is
nite and decreases with frequency.
It is high at dc, but falls o at a rather low frequency.
Internal compensation - is the presence of internal passive components
(caps) which cause op-amp to demonstrate STC low-pass response.
Frequency compensation - is the process of modifying the open-loop gain
to increase stability.
Figure:
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41. Frequency Response Frequency Dependence of the Open-Loop Gain
Frequency Dependence of the Open-Loop Gain
The gain of an internally compensated op-amp may be expressed as
shown below
The transfer function in Laplace domain:A(s) =
A0
1 +s=!b
The transfer function in Frequency domain:A(|!) =
A0
1 +|!=!b
The transfer function for high frequnecy:A(|!)
A0!b
|!
Magnitude gain for high frequnecy:jA(|!)j
A0!b
!
=
!t
!
Unity gain occurs at!t!t=A0!b
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42. Frequency Response Frequency Response of Closed-Loop Ampliers
Frequency Response of Closed-Loop Ampliers
The eect of limited op-amp gain and bandwidth on the closed-loop
transfer functions of the inverting congurations.
Step 1
open-loop gain (A)
Vo
Vi
=
R2=R1
1 + (1 +R2=R1)=A
Step 2 A
Vo
Vi
=
R2=R1
1 +
1 +R2=R1

A0
1 +s=!b

=
R2=R1
1 +

1+R2=R1
A0

+
s
!b

1+R2=R1
A0

Step 3 A01 +R2=R1
Vo
Vi
=
R2=R1
1 +
s(1+R2=R1)
!t
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 41 / 46

43. Frequency Response Frequency Response of Closed-Loop Ampliers
Frequency Response of Closed-Loop Ampliers
By using the same methods the eect of limited op-amp gain and
bandwidth on the closed-loop transfer functions of the noninverting
congurations.
Vo
Vi
=
1 +R2=R1
1 +
s(1+R2=R1)
!t
3dBfrequency
attenuated 3dBfrom maximum (aka. dc value).
!3dB=
!t
1 +R2=R1
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 42 / 46

44. Large-Signal Operation of Op Amps
Large-Signal Operation of Op Amps
The following are limitations on the performance of op-amp circuits
when large output signals are present.
1
Op amps operate linearly over a limited range of output voltages. If
supply voltage +/- 15V isvOwill saturate around +/- 13V.
2
Another limitation on the operation of op amps is that their output
current is limited to a specied maximum. If the circuit requires a
larger current, the op-amp output voltage will saturate at the level
corresponding to the maximum allowed output current.
3
Slew Rate is the maximum rate of change possible at the output of a
real op amp.
SR=
dvo
dt
max
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 43 / 46

45. Large-Signal Operation of Op Amps
Large-Signal Operation of Op Amps
If slew rate is less than rate of change of input it becomes problematic.
Slewing occurs because the bandwidth of the op-amp is limited, so the
output at very high frequencies is attenuated.
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46. Large-Signal Operation of Op Amps
Large-Signal Operation of Op Amps
4
Op-amp slew-rate limiting can cause nonlinear distortion in
sinusoidal waveforms.
Assume a unity-gain follower with a sine-wave input
vI=Visin!t
The rate of change
dvI
dt
=!Vicos!t
Now if!Viexceeds the slew rate of the op amp, the output
waveform will be distorted in the manner shown.
Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 45 / 46

47. Large-Signal Operation of Op Amps
Large-Signal Operation of Op Amps
Full-power bandwidth fM)
sinusoid with amplitude equal to the rated output voltage of the op
amp begins to show distortion due to slew-rate limiting.
SR=!MVoM ax fM=
SR
2VoM ax
Maximum output voltage VoM ax) AvI).
Output sinusoids of amplitudes smaller thanVoM axwill show
slewrate distortion at frequencies higher thanfM
At a frequency!higher thanfM, the maximum amplitude of the
undistorted output sinusoid is
Vo=VoM ax

!M
!

Chapter 3: Operational Amplier Part 1- Op Amp Basics ()SECE April 2017 46 / 46