The battery system has E 12 V and R 1 Ohm Consider the ver

The battery system has E = 12 V and R = 1 Ohm. Consider the very simple DC-DC converter shown in the figure with R_L = 5 Ohm. Suppose the duty cycle of the switch is D = 0.4. what is the average output voltage? If F is dropped to E = 10 V, to maintain the same average output voltage as in question (1), how should the duly cycle be adjusted to? If E = 12 V, but R is dropped to R = 0.8 Ohm. To maintain the same average output voltage as in question (1), what should be the duty cycle? Consider the converter with R = 5 Ohm, L = 1 H (this is not realistic, but used for easy calculation). The power source is a battery system with E = 11

Solution

Problem 2 Ans) Given E=12 V,R=1 ohms RL=5 ohms

1) D=0.4

Average output Voltage Vo=D*E*RL/(R+RL) Voltage Division rule

Vo=0.4*12*5/6= 4 V

Vo=4 V

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2)Given E=10 V and Vo=4 V

D=Vo*(R+RL)/(E*RL)=(4*6)/(10*5)=24/50

D=0.48

so to get same output voltage D should be adjusted to D=0.48

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3) Given E=12 V, R=0.8

D=Vo*(R+RL)/(E*RL)=(4*5.8)/(12*5)=23.2/60

D=0.3867

so to get same output voltage D should be adjusted to D=0.3867