The input voltage $${V_{DC}}$$ of the buck-boost converter shown below varies from $$32$$ $$V$$ to $$72$$ $$V.$$ Assume that all components are ideal, inductor current is continuous, and output voltage is ripple free. The range of duty ratio $$D$$ of the converter for which the magnitude of the steady state output voltage remains constant at $$48$$ $$V$$ is

For the switching converter shown in the following figure, assume steady-state operation. Also assume that the components are ideal, the inductor current is always positive and continuous and switching period is $${T_s}.$$ If the voltage $${V_L}$$ is as shown, the duty cycle of the switch $$S$$ is __________.

The circuit shown is meant to supply a resistive load $${R_L}$$ from two separate $$DC$$ voltage sources. The switches $$S1$$ and $$S2$$ are controlled so that only one of them is ON at any instant. $$S1$$ is turned on for $$0.2$$ $$ms$$ and $$S2$$ is turned on for $$0.3$$ $$ms$$ in a $$0.5$$ $$ms$$ switching cycle time period. Assuming continuous conduction of the inductor current and negligible ripple on the capacitor voltage, the output voltage $${V_0}$$ (in Volt) across $${R_L}$$ is __________.

A self commutating switch $$SW,$$ operated at duty cycle $$\delta $$ is used to control the load voltage as shown in the figure

Under steady state operating conditions, the average voltage across the indicator and the capacitor respectively, are