Fundamentals-of-Microelectronics-Behzad-Razavi.pdf

Noninverting amplifier with a zero and b infinite

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Noninverting amplifier with (a) zero and (b) infinite value for . Exercise Suppose the circuit is designed for a nominal gain of 2.00 but the and suffer from a mismatch of 5% (i.e., ). What is the actual voltage gain? Let us now take into account the finite gain of the op amp. Based on the model shown in Fig. 8.1(b), we write (8.10) and substitute for from (8.6): (8.11) As expected, this result reduces to (8.9) if . To avoid confusion between the gain of the op amp, , and the gain of the overall amplifier, , we call the former the “open-loop” gain and the latter the “closed-loop” gain. Equation (8.11) indicates that the finite gain of the op amp creates a small error in the value of . If much greater than unity, the term can be factored from the denominator to permit the approximation for : (8.12) Called the “gain error,” the term must be minimized according to each appli- cation’s requirements. Example 8.3 A noninverting amplifier incorporates an op amp having a gain of 1000. Determine the gain error if the circuit is to provide a nominal gain of (a) 5, or (b) 50. Solution For a nominal gain of 5, we have , obtaining a gain error of: (8.13)
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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 380 (1) 380 Chap. 8 Operational Amplifier As A Black Box On the other hand, if , then (8.14) In other words, a higher closed-loop gain inevitably suffers from less accuracy. Exercise Repeat the above example if the op amp has a gain of 500. With an ideal op amp, the noninverting amplifier exhibits an infinite input impedance and a zero output impedance. For a nonideal op amp, the I/O impedances are derived in Problem 7. 8.2.2 Inverting Amplifier Depicted in Fig. 8.7(a), the “inverting amplifier” incorporates an op amp along with resistors and while the noninverting input is grounded. Recall from Section 8.1 that if the op amp gain is infinite, then a finite output swing translates to ; i.e., node bears a zero potential even though it is not shorted to ground. For this reason, node is called a “virtual ground.” Under this condition, the entire input voltage appears across , producing a current of , which must then flow through if the op amp input draws no current [Fig. 8.7(b)]. Since the left terminal of remains at zero and the right terminal at , R 1 R X 2 in V out V R 1 R 2 in V out V in V R 2 X Virtual Ground R 2 R 1 A B (a) (b) (c) Figure 8.7 (a) Inverting amplifier, (b) currents flowing in resistors, (c) analogy with a seesaw. (8.15) yielding (8.16)
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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 381 (1) Sec. 8.2 Op-Amp-Based Circuits 381 Due to the negative gain, the circuit is called the “inverting amplifier.” As with its noninverting counterpart, the gain of this circuit is given by the ratio of the two resistors, thereby experiencing only small variations with temperature and process.
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