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Chapter 2 Operational amplifiers
 General-purpose integrated circuit
 Perform addition or integration of signals
 Op amps are most useful when part of the output signals is
returned to the input through a feedback network.
(closed-loop condition)
 The characteristics of IC op amp (with resistive feedback
network) depends on the circuit configuration and the
resistive values, but only weekly on the op amp.
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Outline
 The ideal operational amplifier
 The summing-point constraints
 The inverting amplifier
 The noninverting amplifier
 Integrators and Differentiators
 Large-signal operation
 DC imperfection
 Acitve filter
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2.1 The ideal operational amplifier
Figure 2.1 Circuit symbol for the op amp.
Figure 2.3 Op-amp symbol showing power supplies.
Characteristics of an ideal operational amplifier
Input resistance Ri
voltage gain AdoL  , Acm =0
Output resistance Ro=0
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2.2 The summing-point constraint
 The differential input voltage and the
input current are zero
v+ = v-
i+ = i-=0
 Ideal op-amp analysis
 Verify that negative feedback is present.
v+
 Using summing point constraint.
v-
 Apply standard circuit analysis principles
to solve for the quantities of interest.
i+c
i-
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2.3 The inverting amplifier
i2
i1
Negative feedback?
Indicate v+
, v- ,i+
and i-
 What is the value of v+?
 Applying the summing point constraint, What is the value of v-?
 Find expressions for the currents flowing through R1 and R2, i1
and i2, in terms of node voltages.
 Applying KCL, find an equation for i1, i2 and i Derive the closed loop voltage gain Av=vo/vi
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2.3 The inverting amplifier
 Why is it called inverting amplifier?
 Input impedance and output impedance
Zin=R1, Zo=0
 The virtual-short-circuit (virtual open-circuit) concept
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2.3 The inverting amplifier
Variation 1
Figure 2.6 An inverting amplifier that achieves high gain with a smaller
range of resistor values than required for the basic inverter.P52）
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2.3 The inverting amplifier
Variation 2
Figure 2.7 Summing amplifier. See Exercise 2.1.P53
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2.3 The inverting amplifier
Example
Figure 2.9 Circuit of Exercise 2.3, p53
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2.4 The noninverting amplifier
Figure 2.11 Noninverting amplifier. P55
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2.4 The noninverting amplifier
Figure 2.12 Voltage follower.
Figure 2.14 Differential amplifier. See Exercise 2.5.
P56, refer to p72 figure2.34
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Instrumentation-quality differential amplifier P72
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Voltage-current converter P73
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Current-voltage converter P74
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2.5 Integrators and Differentiators P76
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2.5 Integrators and Differentiators
Exercise: Derive the expression for the output voltage vo.
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2.6 Large-signal operation
 Output voltage swing (Vomin, Vomax)
The range of allowed output
voltages before clipping occurs
depends on the type of op amp
in use, on the load resistance,
and on the values of the powersupply voltages.
Figure 2.28 For a real op amp, clipping occurs if the
output voltage reaches certain limits.
Transfer characteristic
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2.6 Large-signal operation
 Output current limit (Iomax, mA)
The maximum current that an op amp can supply to a load.
 Slew-rate limitation (105~8V/s)
The magnitude of the rate of change of the output is limited.
 Full-power bandwidth~(SR,Vomax)
The range of frequencies for which the op amp can produce
an undistorted sinusoidal output with peak amplitude equal to
the guaranteed maximum output voltage.
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2.7 DC imperfections
 bias current IB
The average of the DC currents
 Offset current Ioff
The difference between the bias currents
 Offset voltage Voff
The output voltage may not be zero for zero
input voltage. The op amp behaves as if a
small DC source is in series with one of the
input terminal.
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2.7 DC imperfections
 Cancellation of the effects of bias currents
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Pictures of Op Amps
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2.8 Active Filter
 Frequency response (P30)
 The complex gain: The ratio of the phasor for the output signal to
the input signal
 Bode plot (P271)
 How circuit functions can be quickly and easily plotted against
frequency? (straight line approximation & smart scale)
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2.8 Active Filter
Logarithmic Frequency Scale
A decade is a range of frequencies for which the ratio
of the highest frequency to the lowest is 10.
An octave is a two-to-one change in frequency.
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Example
A filter circuit is designed using an operational amplifier and is
shown in the following figure
(1) Determine the ratio
R1
R2
R
~
~
Vs
R,C,R1,R2.
-
+
C
~
VO
~ ~
a function of
vo vas
s
(2) Identify whether the circuit is a low-pass,
high-pass or band-pass filter, and give
reasons.
(3) If RC=0.1 and R1/R2=3, sketch the bode
plot and find the cut-off frequency.
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Summary
 Characteristics of an ideal op amp.
 The summing-point constraint applies when ideal op
amps are used in circuits with negative feedback.
 The steps to analyze an ideal op amp circuits.
 The inverting/noninverting amplifier
 The summing/differentiating amplifier
 The integrator/differentiator
 The design of simple op amp circuits
Exercise
2.1, 2.3, 2.5, 2.6, 2.7, 2.9, 2.10, 2.18, 2.19, 2.20, 2.21, 2.22, 2.23(optional)
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