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One of the important applications of the semiconductor diode is recti cation of AC signals, that is, the ability to convert an AC signal with zero average (DC) value to a signal with a nonzero DC value The application of the semiconductor diode as a recti er is very useful in obtaining DC voltage supplies from the readily available AC line voltage Here, we illustrate the basic principle of recti cation, using an ideal diode for simplicity, and also because the large-signal model is appropriate when the diode is used in applications involving large AC voltage and current levels Consider the circuit of Figure 820, where an AC source, vi = 15556 sin t, is connected to a load by means of a series ideal diode From the analysis of Example 81, it should be apparent that the diode will conduct only during the positive half-cycle of the sinusoidal voltage that is, that the condition vD 0 will be satis ed only when the AC source voltage is positive and that it will act as an open circuit during the negative half-cycle of the sinusoid (vD < 0) Thus, the appearance of the load voltage will be as shown in Figure 821, with the negative portion of the sinusoidal waveform cut off The recti ed waveform clearly has a nonzero DC (average) voltage, whereas the average input waveform voltage was zero When the diode is conducting, or vD 0, the unknowns vL and iD can be found by using the following equations: iD = and vL = iD RL (810) vi RL when vi > 0 (89)
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The load voltage, vL , and the input voltage, vi , are sketched in Figure 821 From equation 810, it is obvious that the current waveform has the same shape as the load voltage The average value of the load voltage is obtained by integrating the load voltage over one period and dividing by the period: vload, DC = 2
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15556 sin t dt =
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15556 = 4952 V
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The circuit of Figure 820 is called a half-wave recti er, since it preserves only half of the waveform This is not usually a very ef cient way of rectifying an AC signal, since half the energy in the AC signal is not recovered It will be shown in a later section that it is possible to recover also the negative half of the AC waveform by means of a full-wave recti er
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Offset Diode Model
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While the ideal diode model is useful in approximating the large-scale characteristics of a physical diode, it does not account for the presence of an offset voltage,
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Electronics
vi (V)
005 006 007 Time (s) 60-Hz source voltage
01 iD (mA) 10 Physical diode
vL (V)
0 5 0 001 002 003 004 005 006 Time (s) Rectified voltage 007 008 009 01 Offset diode model (thick line)
Figure 821 Ideal diode recti er input and output voltages
vD (V)
which is an unavoidable component in semiconductor diodes (recall the discussion of the contact potential in Section 82) The offset diode model consists of an ideal diode in series with a battery of strength equal to the offset voltage (we shall use the value V = 06 V for silicon diodes, unless otherwise indicated) The effect of the battery is to shift the characteristic of the ideal diode to the right on the voltage axis, as shown in Figure 822 This model is a better approximation of the large-signal behavior of a semiconductor diode than the ideal diode model According to the offset diode model, the diode of Figure 822 acts as an open circuit for vD < 06 V, and it behaves like a 06-V battery for vD 06 V The equations describing the offset diode model are as follows: vD 06 V vD < 06 V Diode 06-V battery Diode Open circuit (812)
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