AIC_Ch12 - 12 Introduction to Switched-Capacitor Circuits...

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12 Introduction to Switched-Capacitor Circuits Our study of amplifiers in previous chapters has dealt with only cases where the input signal is continuously available and applied to the circuit and the output signal is continuously observed. Called “continuous-time” circuits, such amplifiers find wide application in audio, video, and high- speed analog systems. In many situations, however, we may sense the input only at periodic instants of time, ignoring its value at other times. The circuit then processes each “sample,” producing a valid output at the end of each period. Such circuits are called “discrete-time” or “sampled-data” systems. In this chapter, we study a common class of discrete-time systems called “switched-capacitor (SC) circuits.” Our objective is to provide the foundation for more advanced topics such as filters, comparators, ADCs, and DACs. Most of our study deals with switched-capacitor amplifiers but the concepts can be applied to other discrete-time circuits as well. Beginning with a general view of SC circuits, we describe sampling switches and their speed and precision issues. Next, we analyze switched-capacitor amplifiers, considering unity-gain, noninverting, and multiply-by-two topologies. Finally, we examine a switched-capacitor integrator. 12.1 General Considerations In order to understand the motivation for sampled-data circuits, let us first consider the simple continuous-time amplifier shown in Fig. 12.1(a). Used extensively with bipolar op amps, this circuit presents a difficult issue if implemented in CMOS technology. Recall that, to achieve a high voltage gain, the open-loop output resistance of CMOS op amps is maximized, typically approaching hundreds of kilo-ohms. We therefore suspect that 2 heavily drops the open-loop gain, degrading the precision of the circuit. In fact, with the aid of the simple equivalent circuit 395
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Chapter 12. Introduction to Switched-Capacitor Circuits 396 R 1 2 out V in 1 2 out in A out X X v - (a) (b) Figure 12.1. (a) Continuous-time feedback amplifier, (b) equivalent circuit of (a). shown in Fig. 12.1(b), we can write 1 2 1 1 2 12 1 and hence 2 1 2 1 1 2 1 12 2 Equation (12.2) implies that, compared to the case where 0, the closed-loop gain suffers from inaccuracies in both the numerator and the denominator. Also, the input resistance of the amplifier, approximately equal to 1 , loads the preceding stage while introducing thermal noise. In the circuit of Fig. 12.1(a), the closed-loop gain is set by the ratio of 2 and 1 .Ino rde rto avoid reducing the open-loop gain of the op amp, we postulate that the resistors can be replaced by capacitors [Fig. 12.2(a)]. But, how is the bias voltage at node set? We may add a large feedback out in (a) C 1 2 X out in (a) 1 2 F Figure 12.2. (a) Continuous-time feedback amplifier using capacitors, (b) use of resistor to define bias point.
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This note was uploaded on 06/18/2010 for the course CE 01 taught by Professor Bazgei during the Spring '09 term at UCSC.

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AIC_Ch12 - 12 Introduction to Switched-Capacitor Circuits...

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