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Unformatted text preview: Attia, John Okyere. “Operational Amplifiers.” Electronics and Circuit Analysis using MATLAB. Ed. John Okyere Attia Boca Raton: CRC Press LLC, 1999 © 1999 by CRC PRESS LLC CHAPTER ELEVEN OPERATIONAL AMPLIFIERS The operational amplifier (Op Amp) is one of the versatile electronic circuits. It can be used to perform the basic mathematical operations: addition, subtrac tion, multiplication, and division. They can also be used to do integration and differentiation. There are several electronic circuits that use an op amp as an integral element. Some of these circuits are amplifiers, filters, oscillators, and flipflops. In this chapter, the basic properties of op amps will be discussed. The nonideal characteristics of the op amp will be illustrated, whenever possi ble, with example problems solved using MATLAB. 11.1 PROPERTIES OF THE OP AMP The op amp, from a signal point of view, is a threeterminal device: two inputs and one output. Its symbol is shown in Figure 11.1 . The inverting input is designated by the ‘’ sign and noninverting input by the ‘+’ sign. Figure 11.1 Op Amp Circuit Symbol An ideal op amp has an equivalent circuit shown in Figure 11.2 . It is a differ ence amplifier, with output equal to the amplified difference of the two inputs. An ideal op amp has the following properties: • infinite input resistance, • zero output resistance, • zero offset voltage, • infinite frequency response and • infinite commonmode rejection ratio, • infinite openloop gain, A. © 1999 CRC Press LLC © 1999 CRC Press LLC V 1 V 2 A(V 2 V 1 ) Figure 11.2 Equivalent Circuit of an Ideal Op Amp A practical op amp will have large but finite openloop gain in the range from 10 5 to 10 9 . It also has a very large input resistance 10 6 to 10 10 ohms. The out put resistance might be in the range of 50 to 125 ohms. The offset voltage is small but finite and the frequency response will deviate considerably from the infinite frequency response. The commonmode rejection ratio is not infinite but finite. Table 11.1 shows the properties of the general purpose 741 op amp. Table 11.1 Properties of 741 Op Amp Property Value (Typical) Open Loop Gain 2x10 5 Input resistance 2.0 M Output resistance 75 Ω Offset voltage 1 mV Input bias current 30 nA Unitygain bandwidth 1 MHz Commonmode rejection ratio 95 dB Slew rate 0.7 V/ µ V Whenever there is a connection from the output of the op amp to the inverting input as shown in Figure 11.3 , we have a negative feedback connection © 1999 CRC Press LLC © 1999 CRC Press LLC Z 2 Z 1 I 2 I 1 ( a ) Z 2 Z 1 I 2 I 1 ( b ) Figure 11.3 Negative Feedback Connections for Op Amp (a) Inverting (b) Noninverting configurations With negative feedback and finite output voltage, Figure 11.2 shows that ( ) V A V V O = − 2 1 (11.1) Since the openloop gain is very large, ( ) V V V A O 2 1 − = ≅ (11.2) © 1999 CRC Press LLC © 1999 CRC Press LLC Equation (11.2) implies that the two input voltages are also equal. Equation (11....
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This note was uploaded on 12/19/2009 for the course ELECTRONIC elm 461 taught by Professor Oğuzkucur during the Spring '09 term at Gebze Institute of Technology.
 Spring '09
 Oğuzkucur
 Amplifier, Operational Amplifier

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