Calculate the capacitance necessary to produce vout so that

Question

Assignment :1.

1. Consider the circuit shown in Fig. 1. Prior to t=0, the switch has been open for a very long time. At t=0, the switch closes. Calculate and sketch v_L(t) and i_L(t) for t>0. Show your work! Note in this case, there is no return path for the inductor current when the switch is open, so the switch stays closed after t>0!

2. Consider the half-wave rectifier seen in Fig. 2. The diode direction has been reversed. The frequency of the input sinusoidal voltage, f = 60 Hz. Adopt the constant voltage drop model, to sketch the input sinusoid, the diode voltage drop, V_D, and the output voltage V_O. You may assume the voltage drop across the diode during conduction is 0.7 V.

3. A half-wave peak rectifier with a 1 k? load operates from a 120 V (rms) 60 Hz household supply through a 10-to-1 step down  transformer. So 120 V (rms) appears at the primary side of the transformer. The output of the rectifier will be referred to as "Vout." Note that the primary and secondary of the transformer are in phase. Assume the ideal diode model.

a. Calculate the capacitance necessary to produce Vout so that its peak to peak ripple voltage (equation given in class) is 10% of the magnitude (or maximum value) of the voltage that appears across the transformer secondary.

b. Repeat part (a) if it is desired that the peak to peak ripple voltage of Vout is 5% of the magnitude of the voltage cross the transformer secondary. Note, the lower the ripple desired, the higher the capacitance necessary. Thus the capacitor is acting like a filter.

c. Calculate the DC load current.

4. It is required to use a full-wave peak bridge rectifier to design a DC power supply that provides an average DC output voltage of 15 V on which a maximum of +/- 1 V ripple is allowed. The rectifier feeds a load of 150 ?. The rectifier is fed from the line voltage (120 V rms, 60 Hz) through a transformer. The diodes have a 0.7 V drop when conducting (at all currents).

a. Specify the rms voltage that must appear across the transformer secondary.

b. Find the required value of the filter capacitor.