# Example 310 sketch the time average of in fig 311c

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Example 3.10 Sketch the time average of in Fig. 3.11(c) for a sinusoidal input as the battery voltage, ,

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 71 (1) Sec. 3.1 Ideal Diode 71 varies from to . Solution If is very negative, is always on because . In this case, the output average is equal to [Fig. 3.12(a)]. For , turns off at some point in the negative half cycle and remains off in the positive half cycle, yielding an average greater than but less than . For , the average reaches . Finally, for , no limiting occurs and the average is equal to zero. Figure 3.12(b) sketches this behavior. (a) V out V (b) out V t V p V B V p < in V out V V p V B V p in V < V B = V B V B t out V V p V B in V V B t = 0 out V V p V B t + V B V p < + B V p + V p V p V p π 1 Figure 3.12 . Exercise Repeat the above example if the terminals of the diode are swapped. Example 3.11 Is the circuit of Fig. 3.11(b) a rectifier? Solution Yes, indeed. The circuit passes only negative cycles to the output, producing a negative average. Exercise How should the circuit of Fig. 3.11(b) be modified to pass only positive cycles to the out- put.
BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 72 (1) 72 Chap. 3 Diode Models and Circuits 3.2 PN Junction as a Diode The operation of the ideal diode is somewhat reminiscent of the current conduction in junc- tions. In fact, the forward and reverse bias conditions depicted in Fig. 3.3(b) are quite similar to those studied for junctions in Chapter 2. Figures 3.13(a) and (b) plot the I/V characteristics of the ideal diode and the junction, respectively. The latter can serve as an approximation of the former by providing “unilateral” current conduction. Shown in Fig. 3.13 is the constant-voltage model developed in Chapter 2, providing a simple approximation of the exponential function and also resembling the characteristic plotted in Fig. 3.11(a). V I D D V I j j V I D D (c) (a) (b) V D,on V D,on V D,on Figure 3.13 Diode characteristics: (a) ideal model, (b) exponential model, (c) constant-voltage model. Given a circuit topology, how do we choose one of the above models for the diodes? We may utilize the ideal model so as to develop a quick, rough understanding of the circuit’s operation. Upon performing this exercise, we may discover that this idealization is inadequate and hence employ the constant-voltage model. This model suffices in most cases, but we may need to resort to the exponential model for some circuits. The following examples illustrate these points. Example 3.12 Plot the input/output characteristic of the circuit shown in Fig. 3.14(a) using (a) the ideal model and (b) the constant-voltage model. Solution (a) We begin with , recognizing that is reverse biased. In fact, for , the diode remains off and no current flows through the circuit. Thus, the voltage drop across is zero and .

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