Electrical engineering

Butterworth filter design $(4$ points$)$

We would like to design a fifth$-$order Butterworth highpass filter with cutoff frequency $10ra\frac{d}{s}.$

$($a$)(1$ point$)$ Determine the locations of the poles.

$($b$)(1$ point$)$ Determine the transfer function $H(s).$

$($c$)(1$ point$)$ We implement this filter using first$-$order RC filters and$/$or second$-$order SallenKey filters. Draw the circuit diagram.

$($d$)(1$ point$)$ Suppose that we use $10-k$ resistors. Determine the capacitors in all the stages of the filter.

$2.$ Butterworth filter design $(6$ points$)$

We would like to design a Butterworth lowpass filter that meets the specifications of $|H()|=0\mathrm{.}9$ at $10$ Hz and $|H()|=0\mathrm{.}1$ at $28$ Hz $.$

$($a$)(2$ points$)$ Determine the order and the cutoff frequency of the filter.

$($b$)(1$ point$)$ Determine the locations of the poles.

$($c$)(1$ point$)$ Determine the transfer function $H(s).$

$($d$)(1$ point$)$ We implement this filter using first$-$order RC filters and$/$or second$-$order SallenKey filters. Draw the circuit diagram.

$($e$)(1$ point$)$ Suppose that we use $10-k$ resistors. Determine the capacitors in all the stages of the filter.