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1

### GATE EE 2002

In the chopper circuit shown in fig the input $$dc$$ voltage has a constant value $${{V_s}}$$. the output voltage $${{V_0}}$$ is assumed ripple free. The switch $$S$$ is operated with a switching time period $$T$$ and a duty ratio $$D.$$ What is the value of $$D$$ at the boundary of continuous and discontinuous conduction of the inductor current $${i_L}$$? A
$$D = 1 - {{{V_s}} \over {{V_0}}}$$
B
$$D = {{2L} \over {RT}}$$
C
$$D = 1 - {{2L} \over {RT}}$$
D
$$D = {{RT} \over L}$$
2

### GATE EE 2000

A step down chopper operates from a $$dc$$ voltage source $${V_s}$$ feeds a $$dc$$ motor armature with a back $$e.m.f$$ $$\,\,{E_b}.$$ From oscilloscope traces, it is found that the current increases for time $${t_r}$$ falls to zero over time $${t_f},$$ and remains zero for time $${t_0}$$ in every chopping cycle, then the average $$dc$$ voltage across the freewheeling diode is
A
$${{{V_s}\,{t_r}} \over {\left( {{t_r} + {t_f} + {t_0}} \right)}}$$
B
$${{\left( {{V_s}\,{t_r} + {E_b}\,{t_f}} \right)} \over {\left( {{t_r} + {t_f} + {t_0}} \right)}}$$
C
$${{\left( {{V_s}\,{t_r} + {E_b}\,{t_0}} \right)} \over {\left( {{t_r} + {t_f} + {t_0}} \right)}}$$
D
$${{{V_s}\,{t_r} + {E_b}\left[ {{t_f} + {t_0}} \right]} \over {\left( {{t_r} + {t_f} + {t_0}} \right)}}$$
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