Exercise repeat the above example for and compare the

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Exercise Repeat the above example for and compare the results. The reader may wonder why the line originating at must rise at a slope of 20 dB/dec (rather than 40 or 60 dB/dec) toward the vertical axis. Recall from Examples 12.41 and 12.43 that, for adequate phase margin, the gain crossover must occur below the second pole. Thus, the magnitude response of the compensated amplifier does not “see” the second pole as it approaches ; i.e., the magnitude response bears a slope of only dB/dec.

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 666 (1) 666 Chap. 12 Feedback 12.8.6 Miller Compensation In Example 12.42, we noted that a capacitor can be tied from node to ground to compensate the amplifier. The required value of this capacitor may be quite large, necessitating a large area on an integrated circuit. But recall from Miller’s theorem in Chapter 11 that the apparent value of a capacitor increases if the device is connected between the input and output of an inverting amplifier. We also observe that the two-stage amplifier of Fig. 12.73(a) can employ Miller mul- tiplication because the second stage provides some voltage gain. Illustrated in Fig. 12.76, the V DD M 1 M M V b1 V b2 V b3 4 3 M 2 M in V M V out V 5 6 A B X b4 C C V DD M 1 M M V b1 V b2 V b3 4 3 M 2 M in V M V out V 5 6 A B X b4 C eq Figure 12.76 Example of Miller compensation. idea is to introduce the compensation capacitor between the input and output of the second stage, thereby creating an equivalent grounded capacitance at given by (12.195) (12.196) Called “Miller compensation,” this technique reduces the required value of by a factor of . Miller compensation entails a number of interesting side effects. For example, it shifts not only the dominant pole but also the output pole. Such phenomena are studied in more advanced texts, e.g., [1]. 12.9 Chapter Summary Negative feedback can be used to regulate the behavior of systems that are otherwise “un- tamed” and poorly controlled. A negative feedback system consists of four components: forward system, output sense mechanism, feedback network, and input comparison mechanism. The loop gain of a feedback system can, in principle, be obtained by breaking the loop, injecting a test signal, and calculating the gain as the signal goes around the loop. The loop gain determines many properties of feedback systems, e.g., gain, frequency response, and I/O impedances. The loop gain and closed-loop gain should not be confused with each other. The latter refers to the overall gain from the main input to the main output while the feedback loop is closed. If the loop gain is much greater than unity, the closed-loop gain becomes approximately equal to the inverse of the feedback factor. Making the closed-loop gain relatively independent of the open-loop gain, negative feed- back provides many useful properties: it reduces the sensitivity of the gain to component variations, load variations, frequency variations, and signal level variations.
BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 667 (1) Sec. 12.9

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