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1123 A separately excited DC motor is rated at 10 kW,
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Operational Ampli ers
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n this chapter we analyze the properties of the ideal ampli er and explore the features of a general-purpose ampli er circuit known as the operational ampli er Understanding the gain and frequency response properties of the operational ampli er is essential for the user of electronic instrumentation Fortunately, the availability of operational ampli ers in integrated circuit form has made the task of analyzing such circuits quite simple The models presented in this chapter are based on concepts that have already been explored at length in earlier chapters, namely, Th venin and Norton equivalent circuits and frequency response e ideas Mastery of operational ampli er fundamentals is essential in any practical application of electronics This chapter is aimed at developing your understanding of the fundamental properties of practical operational ampli ers A number of useful applications are introduced in the examples and homework problems Upon completion of the chapter, you should be able to:
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Analyze and design simple signal-conditioning circuits based on op-amps Analyze and design simple active lters Understand the operation of analog computers Assess and understand the practical limitations of operational ampli ers
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One of the most important functions in electronic instrumentation is that of ampli cation The need to amplify low-level electrical signals arises frequently in a number of applications Perhaps the most familiar use of ampli ers arises in converting the low-voltage signal from a cassette tape player, a radio receiver, or a compact disk player to a level suitable for driving a pair of speakers Figure 121 depicts a typical arrangement Ampli ers have a number of applications of interest to the non electrical engineer, such as the ampli cation of low-power signals from transducers (eg, bioelectrodes, strain gauges, thermistors, and accelerometers) and other, less obvious functions that will be reviewed in this chapter for example, ltering and impedance isolation We turn rst to the general features and characteristics of ampli ers, before delving into the analysis of the operational ampli er
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CD player Source Amplifier Speakers load
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Figure 121 Ampli er in audio system
Ideal Ampli er Characteristics
RS +
vS(t)
Gain, A
vL(t)
The simplest model for an ampli er is depicted in Figure 122, where a signal, vS (t), is shown being ampli ed by a constant factor A, called the gain of the ampli er Ideally, the load voltage should be given by the expression vL (t) = AvS (t) (121)
Source Amplifier
Load
Figure 122 A voltage ampli er
Rout + vin Avin Rin +
vL
Figure 123 Simple voltage ampli er model
Note that the source has been modeled as a Th venin equivalent, and the load as e an equivalent resistance Th venin s theorem guarantees that this picture can be e representative of more complex circuits Hence, the equivalent source circuit is the circuit the ampli er sees from its input port; and RL , the load, is the equivalent resistance seen from the output port of the ampli er What would happen if the roles were reversed That is, what does the source see when it looks into the input port of the ampli er, and what does the load see when it looks into the output port of the ampli er While it is not clear at this point how one might characterize the internal circuitry of an ampli er (which is rather complex), it can be presumed that the ampli er will act as an equivalent load with respect to the source, and as an equivalent source with respect to the load After all, this is a direct application of Th venin s theorem Figure 123 provides e a pictorial representation of this simpli ed characterization of an ampli er The black box of Figure 122 is now represented as an equivalent circuit with the following behavior The input circuit has equivalent resistance Rin , so that the
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