Question

In the chopper circuit shown in figure, the input 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 $\alpha$. At the boundary condition of continuous and discontinuous condition of the inductor current $I_0$, the value of critical inductance $L_C$ will be_________

• A. $L_C=\frac{V_s\left(2f{I}_0\right)}{(1-\alpha )I_0^2}$
• B. $L_C=\frac{V_0(1-f)}{2\alpha I_0}$
• C. $L_C=\frac{V_s(1-{\alpha }^2)}{2I_{0}f}$
• D. $L_C=\frac{\alpha V_s(1-\alpha )}{2I_{0}f}$

Answer 1

The correct option is D $L_C=\frac{\alpha V_s(1-\alpha )}{2I_{0}f}$

Given chopper is a Buck chopper so,

Output voltage, $V_0=\alpha V_s$





$\Delta I=\frac{V_0{T}_{off}}{L}$

$=2I_L=2I_0$

This is applicable only at boundary of continuous and discontinuous condition.
Hence,

$L_C=\frac{\alpha V_s(1-\alpha )}{2I_{0}f}$