Question

A step up dc converter with ideal components has $V_d=8V,V_0=24V$ (regulated), $f_s=20kHz$ and C = $470\mu F$. The value of $L_{min}$ required for keeping the operation of step up dc converter in continuous conduction mode (assuming $P_0\ge 5W$) will be

Answer 1

Given, $V_d=8V,V_0=24V,f=20kHz,C=470\mu F,P_0\ge 5W$

Using, $P_0=V_0{I}_0$ (at operation boundary)

$I_0=\frac{5W}{24V}=0.2083A$

Case-I:

$V_d=8V,\frac{V_0}{V_d}=\frac{24}{8}=3=\frac{1}{1-D}$

Also, $3=\frac{1}{1-D}or1-D=\frac{1}{3}$

$D=\frac{2}{3}=0.667$

Using relation, $I_0=\frac{T_s{V}_0}{2L_c}D(1-D{)}^2$

i.e, $0.2083=\frac{24\times 0.667\times (1-0.667{)}^2}{2\times 20\times {10}^3\times L_c}$

$L_c=0.213mH$