Transfer function ConversionI

Obtain Transfer function of 4th order Butterworth High Pass with cut off n = 2 * π * 104 rad/sec.

We know the Transfer function for 4th order Butterworth low pass filter is given by  

\[
T_4(s) = \frac{1}{(s^2 + 1.85 s + 1)(s^2 + 0.765 s + 1)}
\]  

Replace \(s\) by \(\Omega s\)  

\[
s' = \Omega s = 2 \pi \cdot 10^4 s
\]  

Then the new transfer function is  

\[
T_4(s) = \frac{1}{(s^2 + 1.85 \Omega s + 1)(s^2 + 0.765 \Omega s + 1)}
\]  

Substituting the numerical value of \(\Omega\) gives  

\[
T_4(s) = \frac{1}{(s^2 + 116098.1261 s + 3947841760)(s^2 + 48089.419 s + 39478417.6)}
\]