Question

In a step-down converter, consider all component to be ideal. Let output voltage $V_0$ be held constant at 5 V by controlling the switch duty ratio D. Calculate the minimum inductance L required to keep the converter operation in a continuous-conduction mode under all conditions if $V_{s}is10-40V,P_0\ge 5W$ and $f_s=50kHz.$

• A. $21.5\mu H$
• B. $28.37\mu H$
• C. $43.75\mu H$
• D. $52.25\mu H$

Answer 1

The correct option is C $43.75\mu H$

For continuous conduction,
$I_{L\text{min}}\ge 0$
$\Rightarrow I_0-\frac{\Delta I_L}{2}\ge 0$
$\Rightarrow I_0\ge \frac{\Delta I_L}{2}$
$\Delta I_L=\frac{D(1-D)V_s}{fL}$
$\Rightarrow I_0\ge \frac{D(1-D)V_s}{2fL}$
For continuous conduction, at boundary condition
$V_s=40V,$
$P_0=5\times I_0$
$\Rightarrow I_0=\frac{5}{5}=1A$
$D=\frac{5}{40}=0.125$
$\therefore 1\ge \frac{0.125(1-0.125)\times 40}{2\times 50\times {10}^3\times L}$
$L\ge 43.75\mu H$