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Find the diode current during one capacitor-charging cycle in the recti er circuit of Fig. 2-15(a) if C 47 F; RL 1 k; and vS 90 cos 2000t V. (Hint: The approximate ripple formula cannot be used, as it implicitly assumes zero capacitor charging time. Instead, solve for capacitor current and load current, and add.) Ans: iD 8:49 sin 2000t 0:68 A for 2:966 ms t < 3:142 ms In the circuit of Fig. 2-32, R1 RL 10 . If the diode is ideal and vS 10 sin !t V, nd the average value of the load voltage vL . Ans: 3:18 V Rework Problem 2.20 with the diode of Fig. 2-18(b) reversed and all else unchanged. (The circuit is now a positive clamping circuit.) Ans: vo 10 sin !t V for 0 t < T=2, 0 for T=2 t < 3T=4, and 10 1 sin !t V for t ! 3T=4 Four diodes are utilized for the full-wave bridge of Fig. 2-48. Assuming that the diodes are ideal and that vS Vm sin !t, (a) nd the output voltage vL and (b) nd the average value of vL . Ans: a vL Vm j sin !tj V; b VL0 2Vm = A shunt lter capacitor (see Example 2.13) is added to the full-wave recti er of Problem 2.50. Show that the ripple factor is given by Fr 2= 4fRL C 1 % 1=2fRL C. Add a 470 F lter capacitor across points a; b in the full-wave recti er circuit of Fig. 2-48. If RL 1 k p and vS 120 2 sin 120t V, use SPICE methods to determine (a) the magnitude (peak-to-peak) of the output ripple voltage and (b) the average value of output voltage. (Netlist code available at author website.) Ans: a vL 2:79 V; b VL0 168:34 V The level-discriminator circuit (Fig. 2-49) has an output of zero, regardless of the polarity of the input signal, until the input reaches a threshold value. Above the threshold value, the output duplicates the input. Such a circuit can sometimes be used to eliminate the e ects of low-level noise at the expense of slight distortion. Relate vo to vi for the circuit. Ans: vo vi 1 A=jvi j for jvi j > A, and 0 for jvi j A
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Fig. 2-48
Fig. 2-49
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SEMICONDUCTOR DIODES
The diode of Fig. 2-39(a) is reversed, but all else remains the same. Write an equation relating v and i when (a) the switch is open and (b) the switch is closed. Ans: a v R i I ; b v R i I for i < I, and v 0 for i ! I The Zener diode in the voltage-regulator circuit of Fig. 2-45 has vZ VZ 18:6 V at a minimum iZ of 15 mA. If Vb 24 3 V and RL varies from 250  to 2 k, (a) nd the maximum value of RS to maintain regulation and (b) specify the minimum power rating of the Zener diode. Ans: a 26:8 ; b 4:65 W The regulator circuit of Fig. 2-45 is modi ed by replacing the Zener diode with two Zener diodes in series to obtain a regulation voltage of 20 V. The characteristics of the two Zeners are Zener 1: VZ 9:2 V for 15 iZ 300 mA Zener 2: VZ 10:8 V for 12 iZ 240 mA (a) if iL varies from 10 mA to 90 mA and Vb varies from 22 V to 26 V, size RS so that regulation is preserved. (b) Will either Zener exceed its rated current Ans: a 19:6  ; b for Vb 26 V, iZ1 iZ2 296 mA, which exceeds the rating of Zener 2 The two Zener diodes of Fig. 2-50 have negligible forward drops, and both regulate at constant VZ for 50 mA iZ 500 mA. If R1 RL 10 , VZ1 8 V, and VZ2 5 V, nd the average value of load voltage when vi is a 10-V square wave. Ans: 0:75 V
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