Question

Given $V_s=20V,V_0=50V,R=50\Omega ,L=20\mu H,D=0.5$. The converter will operate at a switching frequency of _______kHz.

Answer 1

Continuous conduction mode,

$V_{o\left(av\right)}=\frac{V_s}{1-D}=\frac{20}{0.5}=40$
but given, $V_0=50V$
$\therefore$ Discontinuous conduction mode,
$V_{0avg}=\frac{\beta V_s}{\beta -D}$

$50=\frac{20\beta }{\beta -0.5}$

$\Rightarrow \beta =\frac{5}{6}$

$V_{L\left(on\right)}=V_s$

$\Rightarrow L\frac{\Delta I_L}{DT}=20$,

$P_{in}=P_0$

$V_s{I}_{L\left(avg\right)}=50W$
$I_{L\left(avg\right)}=2.5A$

also $I_{L\left(avg\right)}=\frac{1}{2}\times \frac{\Delta I_L\times \beta T}{T}$

$2.5=\frac{1}{2}\times \Delta I_L\times \frac{5}{6}$

$\Rightarrow f=\frac{20\times 0.5}{20\times {10}^{-6}\times 6}=83.33kHz$