0195136047.pdf

7.2 DIODES 357

WithD 2 at its breakpoint, the circuit is drawn in Figure E7.2.7(c). It follows thatv 1 =10 V

andD 1 must be on to carryi 1 =v 1 / 4 = 2 .5 A. Thus, the second breakpoint is ati= 2 .5 A and

v=3 V (becausev= 2 i− 12 +v 1 ).

The completei–vcharacteristic based on our results is shown in Figure E7.2.7(d). It can be

seen that bothD 1 andD 2 will be on over the middle region− 2 <v<3.

Rectifier Circuits

A simplehalf-wave rectifierusing an ideal diode is shown in Figure 7.2.8(a). The sinusoidal
source voltagevSis shown in Figure 7.2.8(b). During the positive half-cycle of the source, the
ideal diode is forward-biased and closed so that the source voltage is directly connected across
the load. During the negative half-cycle of the source, the ideal diode is reverse-biased so that the
source voltage is disconnected from the load and the load voltage as well as the load current are
zero. The load voltage and current are of one polarity and hence said to be rectified. The output
current through the load resistance is shown in Figure 7.2.8(c).
In order to smooth out the pulsations (i.e., to eliminate the higher frequency harmonics) of
the rectified current, a filter capacitor may be placed across the load resistor, as shown in Figure
7.2.9(a). As the source voltage initially increases positively, the diode is forward-biased since
the load voltage is zero and the source is directly connected across the load. Once the source
reaches its maximum valueVSand begins to decrease, while the load voltage and the capacitor
voltage are momentarily maintained atVS, the diode becomes reverse-biased and hence open-
circuited. The capacitor then discharges over time intervalt 2 throughRLuntil the source voltage
vS(t) has increased to a value equal to the load voltage. Since the source voltage at this point
in time exceeds the capacitor voltage, the diode becomes once again forward-biased and hence
closed. The capacitor once again gets charged toVS. The output current of the rectifier with the
filter capacitor is shown in Figure 7.2.9(b), and the circuit configurations while the capacitor gets
charged and discharged are shown in Figure 7.2.9(c). The smoothing effect of the filter can be
improved by increasing the time constantCRLso that the discharge rate is slowed and the output
current more closely resembles a true dc current.

vS vS(t) = VS sin ωtRL iL(k)

vS iL

VS

VS

RL

Diode

closed

Diode

closed

Diode

open

tt

Load

resistance

Ideal diode

(a)

(b)

(c)

−

+

Figure 7.2.8Simple half-wave

rectifier. (a) Circuit with ideal

diode.(b)Input source voltage.(c)

Output current through load resis-

tance.