Lecture 10 Op-Amp CircuitsAmp Circuits - Courses | … 10 Op-Amp CircuitsAmp Circuits ELECTRICAL...
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Lecture 10Op Amp CircuitsOp-Amp Circuits
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Characteristics of Ideal Op pAmps
Infinite gain for the differential input signal
Zero gain for the common mode input signalZero gain for the common-mode input signal
Infinite input impedances
Zero output impedance
Infinite bandwidth
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Real Versus Ideal Op Amp
Parameter Typical Range Ideal ValuesOpen-loop gain A 10^5-10^8 ∞Input resistance, Ri 10^5 to 10^13Ω ∞ ΩOutput resistance, Ro 10 to 100Ω 0 Ω
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
741 Op-Amp
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
741 Op-Amp
Current Mirrors
Output Stage
Differential Amplifier
Class A Amplifier
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
SUMMING POINTSUMMING-POINT CONSTRAINT
Operational amplifiers are almost alwaysOperational amplifiers are almost always used with negative feedback, in which part of the output signal is returned to the input inthe output signal is returned to the input in opposition to the source signal.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
In a negative feedback system, the ideal op-amp output voltage attains the value neededamp output voltage attains the value needed to force the differential input voltage and input current to zero. We call this fact thecurrent to zero. We call this fact the summing-point constraint.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Ideal op amp circuits areIdeal op-amp circuits are analyzed by the following steps:
1. Verify that negative feedback is present.
2. Assume that the differential input voltage and the input current of the op amp are forced to zero. (This is the summing-point constraint.)
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
3 Apply standard circuit analysis principles3. Apply standard circuit-analysis principles, such as Kirchhoff’s laws and Ohm’s law, to solve for the quantities of interestsolve for the quantities of interest.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
The Basic Inverter
decreasesvvv xox →<<→> 00
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Applying the Summing Point Constraint
20 RvA
vvvi
vi oinoino −−
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
1
2
1211
22 Rv
ARRR
iR
iin
ov
inoino −==→=→===
Inverting Amplifierg
1Riv
Zin
inin == 0
1
2 =→−= outinout ZvRRV
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
in 1
Summing Amplifierg
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Summing AmplifiergiA
iF
iB
++ BABA VViiiViVi
⎟⎟⎞
⎜⎜⎛
+→+−−
+=+===
BABAoo
B
B
A
ABAF
B
BB
A
AA
VVRVVvvi
RRiii
Ri
Ri
0
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
⎟⎟⎠
⎜⎜⎝
+−=→+===B
B
A
AFo
B
B
A
A
F
o
F
oF RR
RvRRRR
i
Summing Amplifierg
VRA
iA
−−
==
tt
B
BB
A
AA
vvRvi
Rvi
0
V = 0
VA
Vout
RfVB
iout
iB
+−
→+
==
BAout
F
out
F
outout
vvviii
Rv
Rv
i0
VBRB
⎟⎟⎞
⎜⎜⎛
+−=
+=→+=
BAF
BAFBAout
vvRv
RRRiii
⎟⎟⎠
⎜⎜⎝
+=BA
Fout RRRv
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Summing Amplifierg
Input resistance seen by vA = RA
Input resistance seen by vB = RB
Since the output voltage does not depend on the load resistance
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
RL, the output impedance is zero.
Exercise 14.2(a)
Fi d i i i i dFind i1, i2, ix, io and vo:
111
11 mA
kV
Rv
i in =Ω
==
1011011
1
2
12
1
mAVkvRvi
mAii
o −=⎟⎞
⎜⎛ Ω
−=⎟⎟⎞
⎜⎜⎛−==
==
1011110
10111
22
2
kRmAmAmAiiiiii
mAVkk
vRRR
i
oxox
inLL
o
Ω
−=−−=−=→=+
=⎟⎠
⎜⎝ ΩΩ
=⎟⎟⎠
⎜⎜⎝
==
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
)1(1
1010)1)(10(2
2 Vkkv
RRVkmAv ino Ω
Ω−=−=−=Ω−=
Exercise 14.2(b)v
VvmAvi
imAkVi
550
515
2
21
−=→=−
=
==Ω
=
vvv
mAkV
kvi
VvmAk
i
5
515
10
551
3
2
=Ω
=Ω
−=
=→=Ω
=
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Vvk
vk
vvmAmAmAiii o
oo 1515
11055324 −=→
Ω−−
=Ω
−==+=+=
Exercise 14.3
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Exercise 14.3
20110
20 vvo −=
Inverting SummingInverting amplifier
Summingamplifier
22 201 vvv⎟⎞
⎜⎛ ⎞⎛
⎟⎞
⎜⎛
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
212
12 24
101020
10120
101020 vv
kvv
kk
kv
kv
kv oout −=⎟⎟
⎠
⎞⎜⎜⎝
⎛Ω
+⎟⎠⎞
⎜⎝⎛−
ΩΩ−=⎟
⎠
⎞⎜⎝
⎛Ω
+Ω
Ω−=
Positive FeedbackPositive Feedback
With positive feedback the opfeedback, the op amp’s input and output voltagesoutput voltages increase in magnitude until the outputuntil the output voltage reaches one of its extremes.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
of its extremes.
Non-inverting Amplifierg
⎟⎞
⎜⎛+
=→= 10
RRRR
vvv ini
⎟⎟⎞
⎜⎜⎛
+
⎟⎟⎠
⎞⎜⎜⎝
⎛+=
+=→
+=
2
1
2
1
21
21
11
1
1
RvA
vRRv
RRRvv
RRRv
o
ininoo
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
⎟⎟⎠
⎜⎜⎝
+==1
21Rv
Ain
ov
Non-inverting Amplifierg
−0 vi in
−=
=1
vvi
Ri
outinout
inin
iin iout
Vin0 Vout
R1 R2 −=
−→=
2
Rvv
Rv
ii
Ri
outininoutin
out
+=212
21
Rv
Rv
Rv
RR
ininout
⎟⎟⎠
⎞⎜⎜⎝
⎛+=
1
2
212
1RRvv
RRR
inout
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
⎠⎝ 1
NONINVERTING AMPLIFIERS
Under the ideal-op-amp assumption, the p p ,non- inverting amplifier is an ideal pvoltage amplifier having infinite inputg presistance and zero output resistance.
21RR
vvA o
v +==
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
p1in Rv
Voltage Followerg
1011 2 ++Rv
A o 1111
=∞
+=+==Rv
A vin
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Exercise 14.4
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Exercise 14.4
i1 = 0
i2 = 0
inv
+v
inv
+v
ininin vRivv =+=+
vo = vin
in
iiR
vvi
==
=−
= +
12
1
0
0
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
ininout vvRiv =+= 2
Exercise 14.4
0
0
inino vvRRv −=−=
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Voltage-to-Current Converterg
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Voltage-to-Current Converterg
vinin
F
ino R
vi =
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
F
Exercise 14.6
vin
i1i1
v2
i2
i3
1 =Rv
i in
2
212
211
21111212
11
1)(1
)()(
⎟⎟⎞
⎜⎜⎛ +
+⎥⎤
⎢⎡
++++
+=+=+=
RRvRR
vvvviii
RRRv
RRiRiRiv
R
inininin
in
21
21
1
221
1232
1
21
121
1111
2
1213
1)(
1)(
⎟⎟⎠
⎞⎜⎜⎝
⎛ ++++=+=
⎟⎟⎠
⎜⎜⎝
+=⎥⎦
⎢⎣
++=+=+=
RRR
RRv
RRRv
Rivv
RRRR
RRRRRiii
inino
inininin
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2 311 ⎟⎟⎠
⎞⎜⎜⎝
⎛++=++++=
RR
RR
RR
RR
RR
RR
RR
vv
i
o
Design of Simple AmplifiersDesign of Simple Amplifiers
Amplifier design using op amps mainly consists of selecting a suitable circuitconfiguration and values for the feedback resistors.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
If the resistances are too small, an impractical amount of current and power will be needed to operate the amplifier.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Very large resistance may be unstable in y g yvalue and lead to stray coupling of undesired signals.g
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Example 14.3Want the voltage gain to be -10 ± 5 percent:
Varying resistance
%5102 ±Rvout Need R1>>RS so that variability in
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
%5101
2 ±=+
−=RRv Ss
out 1 S yRS is a small percentage change
Example 14.3
Choose R1 = 100Rs = 50kΩChoose R1 100Rs 50kΩ
R1+RS min = 50kΩ
R +R max = 50 5kΩR1+RS max = 50.5kΩ
%15.0505.50minmax ==Ω−Ω
=− kkRR
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
50501 ΩkR
Example 14.3
T t th i f 10 h R 10R 500kΩTo get the gain of 10, choose R2 ≈ 10R1 = 500kΩ
Since R1, RS, R2 can all vary, use 1% tolerance resistors:
R1 = 49.9kΩ ± 499Ω
R2 = 499kΩ ± 4.99kΩ
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.