Problem $2(25$ points$)$:

The following circuit shows a CLC filter which is commonly used in resonant converters:

m$1$

The transfer function linking the input voltage to the output voltage is defined in the

frequency domain via:

$H(j)=\frac{V_2(j)}{V_1(j)}$

The circuit contains three ideal energy conversion elements $($i$.$e$.$ two capacitors and one

inductor$).$

$($a$)$ Compute the transfer function in terms of $L,C_1$ and $C_2.$

$($b$)$ Given the values of $L=100H,C_1=0\mathrm{.}1F,$ and $C_2=0\mathrm{.}1F$ compute and plot

$|H(j)|\frac{,}{{?}_H}(j).$

$($c$)$ Compute the values of $L,C_1,$ and $C_2$ such that the resonant frequency of the

circuit to be $60$ kHz $.$