Q$1.$ AP $15\mathrm{.}4-$b$.$ A second$-$order filter circuit is shown in the figure. Derive the transfer function of the filter $H(s)($Show clearly your derivation a step by step$)(10$pts$).$

a$.$ Find $R_1$ and $R_2$ that yield a second$-$order prototype Butterworth filter with $C=1F.$

The circuit in the Time domain

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Figure $15\mathrm{.}25A$ second$-$order Butterworth highpass filter circuit.

Draw your circuit labeling the component values