1
Characteristics of an Ideal Op-Amp
• Infinite input impedance
• Zero output impedance
• Zero common-mode gain, or, infinite common-mode rejection
• Infinite open-loop gain A
• Infinite bandwidth.
2
Difference Amplifier• A difference amplifier is one that responds to the difference between the two
signals applied at its input and ideally rejects signals that are common to the two inputs.
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IcmvIv −=
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-+
+-
2Idv
22Idv
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2Idv
Icmv
12 IvIvIdv −=
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log20CMRR =
+=
3
More Characteristics of Op-Amp
• Since the ideal op-amp responds only to the difference between the two input signals, the ideal op-amp maintains a zero output signal when the two input signals are equal.
• When the two input signals are unequal, there is what is called a common-mode input signal.
• For the ideal op-amp, the common-mode output signal is zero. This characteristic is referred to as common-mode rejection.
• Another characteristic, because op-amp is biased by both positive and negative power supplies, most op-amps are direct coupled devices (no coupling capacitors are required on the input). Accordingly, the two input voltages can be DC.
• Because the OP is composed of transistors biased in the active region by the DC power supply, the output voltage is limited.
4
Difference Amplifier
R2
R1
R3
R4
vI1
vI2
vo
-
+
5
Figure 8.10
A Single Difference or Differential Amplifier
( )121
2 vvR
Rvout −=
1
2
1
2
R
RdA
IdvR
Routv
=
=
6
Figure 8.14, 8.15
Instrumentation Amplifier Input (a) and output (b) stages of Instrumentation amplifier
+=
−=
1
2
21
21
R
R
R
R
vv
vA Fout
V
7
Design Example: Determine the range required for resistor R1 in the instrumentation amplifier to realize a differential gain adjustable from 5 to
500. Assume RF = 2R, so that the difference amplifier gain is 2.
• Assume R1 is a combination of a fixed resistor R1f and a variable resistor R1v. Assume R1v = 100 kΩ
Ω=Ω=
+=
+=
=
++=
+=
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−=
k 5.752 and k 606.01
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fR
fR
fR
R
fRR
fR
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fR
R
R
R
RFR
vvoutv
VA R1f
R1v
8
Figure 8.35
Op-amp Differentiator
dt
tdvCRtv S
SFout
)()( −=
9
Large Signal Operation of Op Amp
• Like other amplifiers, op amps operate linearly over a limited range of output voltages.
• Another limitation of the operation of op amps is that their output current is limited to a specified maximum. For example, the op amp 741 is specified to have a maximum output current of ±20 mA.
• Read Example 2.5.
• Another phenomenon that can cause nonlinear distortion when large output signals are present is that of slew-rate limiting. This means there is a specific maximum rate of change possible at the output of a real op amp. This maximum is known as the slew rate (SR) of the op amp and isdefined as
maxSR
dtodv
=
10
Design Example. Design a difference amplifier with a specified gain and minimum differential input resistance.
Design the circuit such that the differential gain is 30 and theminimum differential input resistance is Ri = 50 kΩ
kΩ 75042 havemust we
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k 25 3 1
kΩ 5012
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11
Design Example: Calculate the common-mode rejection ratio of a differential amplifier. Consider the difference amplifier shown in page 2.
Let R2/R1 = 10 and R4/R3 = 11. Determine CMRR (dB)
dB 6.410.0833
10.0421020logCMRR(dB)
0833.0;042.10
;0833.0042.10
)2
(10)2
(0833.10
22;
21;2
21 ;12
11020833.101)10(2)111
11)(101(
1)1
2(2
3
41
3
4
)1
21(
21
=
=
==+=+=
−−+=
+=−=+=−=
−=−+
+=
−
++=
+=
cmAdAcmvcmAdvdAovcmvdvov
dvcmvdv
cmvvo
dvcmvvdv
cmvIvIvIvcmvIvIvdv
IvIvIvIvov
IvR
RIv
R
RR
R
R
Rov
vovovo
12
Figure 8.20
Op-amp Circuits Employing Complex Impedances
S
F
S
out
S
F
S
out
Z
Zj
V
V
Z
Zj
V
V
+=
−=
1)(
)(
ω
ω
13
Figure 8.21, 8.23
Active Low-Pass Filter
Normalized Response of Active Low-pass Filter
14
Figure 8.24, 8.25
Active High-Pass Filter
Normalized Response of Active High-pass Filter
15
Figure 8.26, 8.27
Active Band-Pass Filter
Normalized Amplitude Response of Active Band-pass Filter
16
Figure 8.30
Op-amp Integrator
∫∞−
−=t
SFS
out dttvCR
tv )(1
)(
17
Figure 8.35
Op-amp Differentiator
dt
tdvCRtv S
SFout
)()( −=
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