# Exercise repeat the above example if a 1 resistor is

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Exercise Repeat the above example if a 1- resistor is placed in series with the diode. Input/Output Characteristics Electronic circuits process an input and generate a corre- sponding output. It is therefore instructive to construct the input/output characteristics of a circuit by varying the input across an allowable range and plotting the resulting output. An example, consider the circuit depicted in Fig. 3.9(a), where the output is defined as the voltage across . If , is reverse biased, reducing the circuit to that in Fig. 3.9(b). Since no current flows through , we have . If , then is forward bi- ased, shorting the output and forcing [Fig. 3.9(c)]. Figure 3.9(d) illustrates the overall input/output characteristic. 3.1.3 Application Examples Recall from Fig. 3.2 that we arrived at the concept of the ideal diode as a means of converting to . Let us now design a circuit that performs this function. We may naturally construct the circuit as shown in Fig. 3.10(a). Unfortunately, however, the cathode of the diode is “floating,” the output current is always equal to zero, and the state of the diode is ambiguous. We therefore modify the circuit as depicted in Fig. 3.10(b) and analyze its response to a sinusoidal input [Fig. 3.10(c)]. Since has a tendency to maintain the cathode of near zero, as rises, is forward biased, shorting the output to the input. This state holds for the positive half cycle. When falls below zero, turns off and ensures that because . The circuit of Fig. 3.10(b) is called a “rectifier.” It is instructive to plot the input/output characteristic of the circuit as well. Noting that if , is off and , and if , is on and , we obtain the Note that without , the output voltage is not defined because a floating node can assume any potential.

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 68 (1) 68 Chap. 3 Diode Models and Circuits 1 D V V (a) (b) R 1 out V in V R 1 out V in V in < 0 V R 1 out V in V in > 0 (c) out V in 1 (d) Figure 3.9 (a) Resistor-diode circuit, (b) equivalent circuit for negative input, (c) equivalent circuit for positive input, (d) input/output characteristic. behavior shown in Fig. 3.10(d). The rectifier is a nonlinear circuit because if then . Example 3.8 Is it a coincidence that the characteristics in Figs. 3.7(d) and 3.10(d) look similar? Solution No, we recognize that the output voltage in Fig. 3.10(b) is simply equal to in Fig. 3.7(a). Thus, the two plots differ by only a scaling factor equal to . Exercise Construct the characteristic if the terminals of are swapped. We now determine the time average (dc value) of the output waveform in Fig. 3.10(c) to arrive at another interesting application. Suppose , where denotes the frequency in radians per second and the period. Then, in the first cycle after , we have (3.3) (3.4) To compute the average, we obtain the area under and normalize the result to the period: (3.5) (3.6)
BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 69 (1) Sec. 3.1 Ideal Diode 69 V (a) (b) out V in D 1 V out V in D 1 R 1 t t in V V in out V V in T 0 2 T T 2 3 T 2 V (c) out V in 1 (d) Rectified Half Cycles R 1 R 1 Figure 3.10

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