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Chapter 8
Ideal Operational Amplifier Circuits and Analysis
 The Ideal Operational Amplifier
o
o
o
The Inverting Amplifier
The Noninverting Amplifier
The Voltage Follower
 Voltage Summation, Subtraction, and Scaling
 Controlled Voltage and Current Sources
o Voltage-Controlled Voltage Sources
o Voltage-Controlled Current Sources
o Current-Controlled Voltage Sources
o Current-Controlled Current Sources
FIGURE 8-1
Operational amplifier symbol, showing inverting (-) and noninverting (+) inputs
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The Inverting Amplifier
FIGURE 8-2 An operational-amplifier application in which signal v1 is connected through R1.
Resistor Rf provides feedback. vo / vi- = - A.
-Avi-
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FIGURE 8-3 Voltages and currents resulting from the application of the signal voltage vi
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FIGURE 8-4 (Example 8-1)
For an ideal op-amp, find:
1. The rms value of vo when vi is 1.5 V rms;
2. The rms value of the current in the 25-kΩ resistor when vi is 1.5V rms; and
3. The output voltage when vi = -0.6 V dc.
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The Noninverting Amplifier
FIGURE 8-5 The operational amplifier in a noninverting configuration
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The Voltage Follower
FIGURE 8-6 The voltage follower
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FIGURE 8-7 (Example 8-2)
In a certain application, a signal source having 60 kΩ of source impedance produces a 1-V-rms
signal. This signal must be amplified to 2.5 V rms and drive a 1-k load. Assuming that the
phase of the load voltage is of no concern, design an op-amp circuit for the application.
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Voltage Summation (inverting version)
FIGURE 8-11 An operational-amplifier circuit that produces an output equal to the
(inverted) sum of three separately scaled input signals
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Example 8-3
1. Design an op-amp circuit that will produce an output equal to –(4v1+ v2 + 0.1v3).
2. Write an expression for the output and sketch its waveform when v1 = 2sinωt V, v2 = + 5V dc,
and v3 = -100 V dc.
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FIGURE 8-12
(Example 8-3)
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Voltage Summation (noninverting version)
FIGURE 8-13 A noninverting linear combination circuit
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Voltage Subtraction
FIGURE 8-14 Using the amplifier in a differential mode to obtain an output
proportional to the difference between two scaled inputs
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Example 8-4
Design an op-amp circuit that will produce the output vo = 0.5v1 – 2v2.
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FIGURE 8-15
(Example 8-4)
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FIGURE 8-16 Using two inverting amplifiers to obtain the output vQ = a1 v1 - a2 v2
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FIGURE 8-17 (Example 8-5) Two (of many) equivalent methods for producing 20v1 - 0.2v2 using two inverting amplifiers
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FIGURE 8-18 (Example 8-6)
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Voltage-Controlled Voltage Sources
Voltage-Controlled Current Sources
(floating load)
FIGURE 8-19 Floating-load, voltage-controlled current sources
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Example 8-7 Design an inverting, voltage-controlled current source
that will supply a constant current of 0.2 mA when the controlling
voltage is 1V. What is the maximum load resistance for this supply if
the maximum amplifier out voltage is 20V?
IL = Vi/R1
RL < R1(|Vmax|/Vi )
FIGURE 8-20
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(Example 8-7)
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Voltage-Controlled Current Sources
(grounded load)
IL = Vi/R
FIGURE 8-21 A voltage-controlled current source with a grounded load
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Example 8-8 Find the current through each resistor and the voltage
at each node of the voltage-controlled current source. What is the
transconductance (gm = 1/R) of the source?
IL = Vi/R
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FIGURE 8-22
(Example 8-8)
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Current-Controlled Voltage Source (inverting)
FIGURE 8-23
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A current-controlled voltage source
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Current-Controlled Voltage Source (noninverting)
FIGURE 8-24 A current-controlled voltage source whose controlling current, Ii,
has a return path to ground
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Current-Controlled Current Source
IL = (R2/R1 +1)Ii
FIGURE 8-25
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A current-controlled current source with floating load
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Example 8-9
It is desired to measure a dc current that ranges from 0 to 1 mA
using an ammeter whose range is 0 to 10 mA. To improve the measurement
accuracy, the current to be measured should be amplified by a factor of 10.
1. Design the circuit.
2. Assuming that the meter resistance is 150Ω and the maximum output voltage
of the amplifier is 15 V, verify that the circuit will perform properly.
FIGURE 8-26 (Example 8-9) The current-controlled current source acts as a current
amplifier, so a 0-1-mA current can be measured by a 0-10-mA ammeter
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Chapter 8 Summary
 An ideal op-amp has infinite input resistance, infinite
differential gain, and zero output resistance.
 There are two basic amplifier configurations: inverting
and noninverting.
 Voltage gain is established by two external resistors.
 A voltage follower is used as a buffer between a highresistance source and a low-resistance load.
 Op-amps can be used for summing and/or subtracting
scaled signals in inverting and noninverting modes.
 Controlled sources can be implemented with operational
amplifiers and can be configured for floating or grounded
loads.