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© 2013 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill
9-1
ElectronicsElectronics
Principles & ApplicationsPrinciples & ApplicationsEighth EditionEighth Edition
Chapter 9Operational Amplifiers
Charles A. Schuler
© 2013 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill
9-2
• The Differential Amplifier• The Operational Amplifier• Determining Gain• Frequency Effects• Applications• Comparators
INTRODUCTION
© 2013 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill
9-3
Noninverted outputInverted output
A differential amplifier driven at one input
C
BE
C
BE
+VCC
-VEE
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Both outputs are active because Q1 drives Q2.
C
BE
C
BE
+VCC
-VEE
Q1 Q2
Q2 serves as a common-base
amplifier in this mode. It’s driven
at its emitter.
Q1 serves as an emitter-followeramplifier in this mode to drive Q2.
© 2013 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill
9-5
Reduced outputReduced output
A differential amplifier driven at both inputs
C
BE
C
BE
+VCC
-VEE
Common mode input signal
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A differential amplifier driven at both inputs with a common-mode signal shows low gain (usually a loss) because the total emitter current is fairly constant.
C
BE
C
BE
+VCC
-VEE
If the input signalgoes positive, bothtransistors want toincrease theircurrent but can’t.
Constanttotal
current
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Increased outputIncreased output
Driven at both inputs with a differential signal
C
BE
C
BE
+VCC
-VEE
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9-8
A differential amplifier driven at both inputs with a differential signal shows high gain.
+VCCHere, one transistorincreases its currentas the other decreasesso the constant totalcurrent is not a limitingfactor. C
BE
C
BE
-VEE
Constanttotal
current
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9-9
The amplifier has two gains:
• High for differential signals• Low for common-mode signals
The ratio of the two gains is called the common-moderejection ratio (CMRR) and is perhaps the most important feature of this amplifier.
CMRR = 20 x logAV(DIF)
AV(CM)
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9-10
Differential amplifier dc analysis
C
BE
C
BE
+9 V
-9 V
3.9 k
4.7 k4.7 k
10 k10 k
RE
RL
RBRB
RL
VEE
VCC
IRE =
VEE - VBE
RE
9 V - 0.7 V
3.9 k= = 2.13 mA
IE =IRE
2= 1.06 mA
IC = IE = 1.06 mA
VRL = IC x RL
= 1.06 mA x 4.7 k= 4.98 V
VCE = VCC - VRL - VE
= 9 - 4.98 -(-0.7)
= 4.72 V
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9-11
Differential amplifier dc analysis continued
C
BE
C
BE
+9 V
-9 V
3.9 k
4.7 k4.7 k
10 k10 k
RE
RL
RBRB
RL
VEE
VCC
Assume = 200
IB =IC
1.06 mA
=
= 5.3 A
VB = VRB = IB x RB
= 5.3 A x 10 k
= 53 mV
© 2013 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill
9-12
Differential amplifier ac analysis
C
BE
C
BE
+9 V
-9 V
3.9 k
4.7 k4.7 k
10 k10 k
RE
RL
RBRB
RL
VEE
VCC
rE =50 mV
IE
=50 mV
1.06 mA= 47 (50 mV is conservative)
AV(DIF) = RL
2 x rE
AV(CM) = RL
2 x RE
= 504.7 k
2 x 47 =
= 0.6
4.7 k2 x 3.9 k
=
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9-13
Differential amplifier ac analysis continued
C
BE
C
BE
+9 V
-9 V
3.9 k
4.7 k4.7 k
10 k10 k
RE
RL
RBRB
RL
VEE
VCC
CMRR = 20 x logAV(DIF)
AV(CM)
= 20 x log500.6
= 38.4 dB
© 2013 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill
9-14
A current source can replace RE to decrease the common mode gain.
C
BE
C
BE
4.7 k4.7 k
10 k10 k
RL
RBRB
RL
VCC
2 mA*
*NOTE: Arrow shows conventional current flow.
AV(CM) = RL
2 x RE
Replaces thiswith a very highresistance value.
© 2013 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill
9-15
A practical current source
390
5.1 V2.2 k
-9 V
IC = IE = 2 mA
IC
IZ = 9 V - 5.1 V
390 = 10 mA
IE = = 2 mA5.1 V - 0.7 V
2.2 k
© 2013 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill
9-16
6.3 V60 Hz
212 mV1 kHz
The amplitude of thecommon-mode signalis almost 30 times the
amplitude of thedifferential signal.
A demonstration of common-mode rejection
The common-mode signalcannot be seen in the output.
© 2013 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill
9-17
Differential amplifier quiz
When a diff amp is driven at one input,the number of active outputs is _____. two
When a diff amp is driven at both inputs, thereis high gain for a _____ signal. differential
When a diff amp is driven at both inputs, thereis low gain for a ______ signal. common-mode
The differential gain can be found by dividingthe collector load by ________. 2rE
The common-mode gain can be found by dividingthe collector load by ________. 2RE
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Invertinginput
Non-invertinginput
Output
Op amps have two inputs
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Op-amp Characteristics
• High CMRR• High input impedance• High gain• Low output impedance
• Available as ICs• Inexpensive• Reliable• Widely applied
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Imperfections can make VOUT non-zero. The offset null terminals can be used to zero VOUT.
-VEE
+VCC
VOUT
With both inputs grounded through equal resistors, VOUT should be zero volts.
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V
t
Vt
Slew rate =
The output of an op amp cannot change instantaneously.
741
0.5 Vs
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Slew-rate distortion
fMAX = Slew Rate
2 x VP
f > fMAX
VP
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Operational amplifier quiz
The input stage of an op amp is a__________ amplifier. differential
Op amps have two inputs: one is invertingand the other is ________. noninverting
An op amp’s CMRR is a measure of its abilityto reject a ________ signal. common-mode
The offset null terminals can be used to zeroan op amp’s __________. output
The ability of an op amp output to changerapidly is given by its _________. slew rate
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RL
Op-amp follower
AV(OL) = the open loop voltage gain
AV(CL) = the closed loop voltage gain
This is a closed-loopcircuit with a voltage
gain of 1.
It has a high input impedanceand a low output impedance.
© 2013 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill
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RL
Op-amp follower
AV(OL) = 200,000
AV(CL) = 1
The differential inputapproaches zero dueto the high open-loop
gain. Using this model,VOUT = VIN.
VIN
VOUT
VDIF = 0
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RLVIN
VOUT
Op-amp follower
AV(OL) = 200,000
B = 1
The feedback ratio = 1
200,000
(200,000)(1) + 1 1AV(CL) =
AB +1AVIN VOUT
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RLVIN
VOUT
The closed-loop gain is increased by decreasing the feedback with a voltage divider.
RF
R1
200,000
(200,000)(0.091) + 1= 11AV(CL) =
B =R1
RF + R1
100 k
10 k 10 k100 k+ 10 k
=
= 0.091
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RLVIN
VOUT
RF
100 k10 k
VDIF = 0
It’s possible to develop a different model for the closed loop gain
by assuming VDIF = 0.
VIN = VOUT xR1
R1 + RF
=VOUT
VIN
1 +RF
R1
Divide both sides by VOUT and invert:
AV(CL) = 11
R1
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RLVIN VOUT
RF
10 k1 k
VDIF = 0R1
In this amplifier, the assumption VDIF = 0 leads to the conclusion that the inverting op amp terminal is
also at ground potential. This is called a virtual ground.
Virtual ground We can ignore the op amp’s inputcurrent since it is so small. Thus:
IR1 = IRF
VIN
R1
=-VOUT
RF
VOUT
VIN
=-RF
R1
= -10
By Ohm’s Law:
The minus sign designates an inverting amplifier.
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VIN
RF
10 k1 k
VDIF = 0
R1
Virtual ground
Due to the virtual ground, the input impedance of the inverting amplifier is equal to R1.
R2 = R1 RF = 910
Although op amp inputcurrents are small, in
most applications, offseterror is minimized by
providing equal resistance paths for the input
currents.
This resistor reduces offset error.
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Output
A typical op amp has internal frequency
compensation.
Break frequency:
fB = 2RC1
R
C
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100 k10 k1 10 100 1k 1M0
20
80
40
60
100
120
Frequency in Hz
Gain in dB
Bode plot of a typical op amp
Break frequency
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RLVIN
VOUT
RF
100 k1 k
Op amps are typically operated with negative feedback(closed loop). This increases their useful frequency range.
R1
=VOUT
VIN
1 +RF
R1
AV(CL) =
= 1 +100 k1 k
= 101
dB Gain = 20 x log 101 = 40 dB
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100 k10 k1 10 100 1k 1M0
20
80
40
60
100
120
Frequency in Hz
Gain in dB
Using the Bode plot to find closed-loop bandwidth:
Break frequency
AV(CL)
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There are two frequency limitations:Slew rate determines the large-signal bandwidth.
Internal compensation sets the small-signal bandwidth.
0.5 Vs
70 Vs
A 741 op amp slews at A 318 op amp slews at
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100 k10 k1 10 100 1k 1M0
20
80
40
60
100
120
Frequency in Hz
Gain in dB
The Bode plot for a fast op amp showsincreased small-signal bandwidth.
10M
fUNITY
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RLVIN
VOUT
RF
100 k1 k
fUNITY can be used to find the small-signal bandwidth.
R1
=VOUT
VIN
1 +RF
R1
AV(CL) =
= 1 +100 k1 k
= 101
318 Op amp
fB = fUNITY
AV(CL)
10 MHz
101= 99 kHz=
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Op amp feedback quiz
The open loop gain of an op amp is reducedwith __________ feedback negative
The ratio RF/R1 determines the gain of the___________ amplifier. inverting
1 + RF/R1 determines the gain of the___________ amplifier. noninverting
Negative feedback makes the - input of theinverting circuit a ________ ground. virtual
Negative feedback _________ small signalbandwidth. increases
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R
C
Amplitude responseof an RC lag circuit
0 dB
-20 dB
-40 dB
-60 dB
10fbfb 100fb 1000fb
fb = RC1
Vout
Vout
f
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9-40
0o
0.1fb fb 10fb
Phase response ofan RC lag circuit
-90o
-45o
R
C
R
-XC = tan-1
Vout
Vout
f
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Interelectrode capacitance and Miller effect
CBECMiller
CBE
CBC
R
CMiller = AVCBC
CInput = CMiller + CBE
The gain frombase to collector
makes CBC
effectively largerin the input circuit.
fb = RCInput
1
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10 Hz 100 Hz 1 kHz 10 kHz 100 kHz
50 dB
40 dB
30 dB
20 dB
10 dB
0 dB
Bode plot of an amplifier with two break frequencies.
20 dB/decade
40 dB/decade
fb1 fb2
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0o
Multiple lag circuits:
-180o
R1C1
Vout
Vout
f
R2C2
R3C3
Phase reversal
Negative feedback becomes positive!
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Op amp compensation
• Interelectrode capacitances create several break points.
• Negative feedback becomes positive at some frequency due to cumulative phase lags.
• If the gain is > 0 dB at that frequency, the amplifier is unstable.
• Frequency compensation reduces the gain to 0 dB or less.
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9-45
Op amp compensation quiz
Beyond fb, an RC lag circuit’s output dropsat a rate of __________ per decade. 20 dB
The maximum phase lag for one RC networkis __________. 90o
An interelectrode capacitance can be effectivelymuch larger due to _______ effect. Miller
Op amp multiple lags cause negative feedbackto be ______ at some frequency. positive
If an op amp has gain at the frequency wherefeedback is positive, it will be ______. unstable
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9-46
RF
10 k
1 k
1 kHz
3 kHz
3.3 k5 kHz
5 k
Summing Amplifier
Inverted sum of three sinusoidal signals
Amplifier scaling: 1 kHz signal gain is -103 kHz signal gain is -35 kHz signal gain is -2
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RF
1 k
1 k 1 k
Subtracting Amplifier
Difference of twosinusoidal signals
(V1 = V2)
1 k
V1 V2
VOUT = V2 - V1
(A demonstration of common-mode rejection)
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A cascade RC low-pass filter
An active low-pass filter
(A poor performer since later sections load the earlier ones.)
(The op amps provide isolation and better performance.)
© 2013 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill
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Frequency in Hz
Am
pli
tud
e in
dB
0
-20
-40
-60
10 100
Cascade RC
Active filter
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VIN
Active low-pass filterwith feedback VOUT
C1C2
At relatively low frequencies, Vout and Vin
are about the same. Thus, the signal voltageacross C1 is nearly zero. C1 has little effect
at these frequencies.
feedback
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VIN
Active low-pass filterwith feedback VOUT
Frequency
Gain
fC
-3 dBFeedback canmake a filter’sperformanceeven better!
C1C2
As fIN increases and C2
loads the input, Vout
drops. This increasesthe signal voltageacross C1. This
sharpens the knee.
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Frequency in Hz
Am
pli
tud
e in
dB
0
-20
-40
-60
10 100
Active filterusing feedback
(two stages)
Note the flat pass bandand the sharp knee.
The slope eventually reaches24 dB/octave or 80 db/decade
for all the filters (4 RC sections).
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VIN
Active high-pass filter VOUT
Frequency
Gain
fC
-3 dB
feedback
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VIN
Active band-pass filter(multiple feedback)
VOUT
Frequency
Gain
-3 dB
Bandwidth
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VIN Active band-stop filter(multiple feedback)
VOUT
Frequency
Gain
-3 dB
Stopband
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9-56
40 mV
0 V
56.6 mV
0 V
- 56.6 mV
Active rectifier
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VIN
VOUT
Integrator
R
C
Slope = -VIN x1
RC
VsSlope =
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Input Waveforms (Blue) Integrator Output Waveform (Red) Differentiator Output Waveform (Red)
Square
Triangle
Sine
A differentiator shows R and C reversed.
Vout = -(Vin/t)RC
Differentiation is the opposite of integration.
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VIN
VOUT
0 V
1 V +VSAT
-VSAT
1 V
Comparator with a 1 Volt reference
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VIN
VOUT
0 V
1 V +VSAT
-VSAT
1 V
Comparator with a noisy input signal
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9-61
VINVOUT
+VSAT
-VSAT
Schmitt trigger with a noisy input signal
UTP
LTP
Hysteresis = UTP - LTPRF
R1
R1 + RF
R1VSAT x
Trip points:
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VIN
VOUT
R2
R14.7 k
4.7 k
+5 V
3 V
1 V
Window comparator
311
311VUL
VLL VOUT is LOW (0 V) when VIN
is between 1 V and 3 V.
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9-63
VIN
VOUT
+5 V
3 V
1 V
Window comparator
311
311VUL
VLL
Many comparator ICs require pull-up resistors in
applications of this type.
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9-64
VIN
VOUT
R2
R14.7 k
4.7 k
+5 V
3 V
1 V
Window comparator
311
311VUL
VLL VOUT is TTL logic compatible.
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9-65
Op amp applications quiz
A summing amp with different gains for theinputs uses _________. scaling
Frequency selective circuits using op ampsare called _________ filters. active
An op amp integrator uses a _________ asthe feedback element. capacitor
A Schmitt trigger is a comparator with__________ feedback. positive
A window comparator output is active whenthe input is ______ the reference points. between
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REVIEW
• The Differential Amplifier• The Operational Amplifier• Determining Gain• Frequency Effects• Applications• Comparators