TABLE OF CONTENTS The basic concepts of transferring charge among capacitors will be given in this section. The emulation of resistors with circuits containing switches and capacitors will be developed. This will be followed by a review of circuit analysis techniques that allow the analysis of switched capacitor circuits. A first-order, low-pass filter will be examined to illustrate the methods developed.
The first recorded use of switches and capacitors to emulate (measure) resistance is found in a text written by James Clerk Maxwell in 1873 [ [4]]. On pages 420 through 425 he describes how to measure the resistance of a galvanometer by connecting it in series with a battery, ammeter, and capacitor and periodically reversing the capacitor. Using a similar approach, we can illustrate how to emulate a resistor. Consider the switched capacitor circuit of Fig. 9.1-1(a). This configuration is called the parallel switched capacitor equivalent resistor. Next, we show how Fig. 9.1-1(a) is equivalent to the resistor R in Fig. 9.1-1(b).
The parallel switched capacitor equivalent resistor circuit in Fig. 9.1-1(a) consists of two independent voltage sources, v 1( t) and v 2( t), two controlled switches, S 1 and S 2, and a capacitor, C. The switches, S 1 and S 2, are controlled by the clock waveforms. These clock waveforms are illustrated in Fig. 9.1-2. There...
