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input voltage, vin , is given by vin = Rin vS RS + Rin (122)
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The equivalent input voltage seen by the ampli er is then ampli ed by a constant factor, A This is represented by the controlled voltage source Avin The controlled source appears in series with an internal resistor, Rout , denoting the internal (output) resistance of the ampli er Thus, the voltage presented to the load is vL = Avin RL Rout + RL (123)
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or, substituting the equation for vin , vL = A RL Rin RS + Rin Rout + RL vS (124)
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In other words, the load voltage is an ampli ed version of the source voltage Unfortunately, the ampli cation factor is now dependent on both the source and load impedances, and on the input and output resistance of the ampli er Thus, a given ampli er would perform differently with different loads or sources What are the desirable characteristics for a voltage ampli er that would make its performance relatively independent of source and load impedances Consider, once again, the expression for vin If the input resistance of the ampli er, Rin , were very large, the source voltage, vS , and the input voltage, vin , would be approximately equal: vin vS since
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(125)
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Rin Rin + RS
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By an analogous argument, it can also be seen that the desired output resistance for the ampli er, Rout , should be very small, since for an ampli er with Rout = 0, the load voltage would be vL = Avin (127)
Combining these two results, we can see that as Rin approaches in nity and Rout approaches zero, the ideal ampli er magni es the source voltage by a factor of A: vL = AvS (128)
just as was indicated in the black box ampli er of Figure 122 Thus, two desirable characteristics for a general-purpose voltage ampli er are a very large input impedance and a very small output impedance In the next sections it will be shown how operational ampli ers provide these desired characteristics
THE OPERATIONAL AMPLIFIER
An operational ampli er is an integrated circuit, that is, a large collection of individual electrical and electronic circuits integrated on a single silicon wafer
12
Operational Ampli ers
An operational ampli er or op-amp can perform a great number of operations, such as addition, ltering, or integration, which are all based on the properties of ideal ampli ers and of ideal circuit elements The introduction of the operational ampli er in integrated circuit form marked the beginning of a new era in modern electronics Since the introduction of the rst IC op-amp, the trend in electronic instrumentation has been to move away from the discrete (individual-component) design of electronic circuits, toward the use of integrated circuits for a large number of applications This statement is particularly true for applications of the type the non electrical engineer is likely to encounter: op-amps are found in most measurement and instrumentation applications, serving as extremely versatile building blocks for any application that requires the processing of electrical signals In the following pages, simple circuit models of the op-amp will be introduced The simplicity of the models will permit the use of the op-amp as a circuit element, or building block, without the need to describe its internal workings in detail Integrated circuit technology has today reached such an advanced stage of development that it can be safely stated that for the purpose of many instrumentation applications, the op-amp can be treated as an ideal device Following the introductory material presented in this chapter, more advanced instrumentation applications will be explored in 15 The Open-Loop Model The ideal operational ampli er behaves very much as an ideal difference ampli er, that is, a device that ampli es the difference between two input voltages Operational ampli ers are characterized by near-in nite input resistance and very small output resistance As shown in Figure 124, the output of the op-amp is an ampli ed version of the difference between the voltages present at the two inputs:1 vout = AV (OL) (v + v ) (129)
The input denoted by a positive sign is called the noninverting input (or terminal), while that represented with a negative sign is termed the inverting input (or terminal) The ampli cation factor, or gain, AV (OL) , is called the open-loop voltage gain and is quite large by design, typically of the order of 105 to 107 ; it will soon become apparent why a large open-loop gain is a desirable characteristic Together with the high input resistance and low output resistance, the effect of a large ampli er open-loop voltage gain, AV (OL) , is such that op-amp circuits can be designed to perform very nearly as ideal voltage or current ampli ers In effect, to analyze the performance of an op-amp circuit, only one assumption will be needed: that the current owing into the input circuit of the ampli er is zero, or iin = 0 (1210)
This assumption is justi ed by the large input resistance and large open-loop gain of the operational ampli er The model just introduced will be used to analyze three ampli er circuits in the next part of this section
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