Determine the circuit component needed for a $2^{nd}-$order Butterworth prototype filter

Solution:

The transfer function for circuit $is$

$q,H(s)=\frac{V_o}{V_g}=\frac{\frac{\frac{R}{s}C}{R+\frac{1}{s}C}}{sL+\frac{\frac{R}{s}C}{R+\frac{1}{s}C}}=\frac{\frac{1}{LC}}{s^2+\frac{s}{RC}+\frac{1}{LC}}=\frac{\frac{1}{LC}}{s^2+\frac{s}{C}+\frac{1}{LC}}$

Problem $1$:

For the circuits of the following figures, sketch the Bode SLA of the transfer function $V_o\frac{s}{V_g}(s)$ on log$-$log paper

diamond where $R=R_1=R_2=1,$ and $C=C_1=C_2=1F$