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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 Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. 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- Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 8-3 Voltages and currents resulting from the application of the signal voltage vi Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. 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. Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. The Noninverting Amplifier FIGURE 8-5 The operational amplifier in a noninverting configuration Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. The Voltage Follower FIGURE 8-6 The voltage follower Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. 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. Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. 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 Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. 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. Bogart/Beasley/Rico Electronic Devices and Circuits, 6e FIGURE 8-12 (Example 8-3) Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Voltage Summation (noninverting version) FIGURE 8-13 A noninverting linear combination circuit Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Voltage Subtraction FIGURE 8-14 Using the amplifier in a differential mode to obtain an output proportional to the difference between two scaled inputs Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Example 8-4 Design an op-amp circuit that will produce the output vo = 0.5v1 – 2v2. Bogart/Beasley/Rico Electronic Devices and Circuits, 6e FIGURE 8-15 (Example 8-4) Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 8-16 Using two inverting amplifiers to obtain the output vQ = a1 v1 - a2 v2 Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 8-17 (Example 8-5) Two (of many) equivalent methods for producing 20v1 - 0.2v2 using two inverting amplifiers Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 8-18 (Example 8-6) Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Voltage-Controlled Voltage Sources Voltage-Controlled Current Sources (floating load) FIGURE 8-19 Floating-load, voltage-controlled current sources Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. 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 Bogart/Beasley/Rico Electronic Devices and Circuits, 6e (Example 8-7) Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Voltage-Controlled Current Sources (grounded load) IL = Vi/R FIGURE 8-21 A voltage-controlled current source with a grounded load Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. 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 Bogart/Beasley/Rico Electronic Devices and Circuits, 6e FIGURE 8-22 (Example 8-8) Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Current-Controlled Voltage Source (inverting) FIGURE 8-23 Bogart/Beasley/Rico Electronic Devices and Circuits, 6e A current-controlled voltage source Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Current-Controlled Voltage Source (noninverting) FIGURE 8-24 A current-controlled voltage source whose controlling current, Ii, has a return path to ground Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Current-Controlled Current Source IL = (R2/R1 +1)Ii FIGURE 8-25 Bogart/Beasley/Rico Electronic Devices and Circuits, 6e A current-controlled current source with floating load Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. 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 Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. 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.