**Second Order High Pass Butterworth Filter Derivation:**

As in the case of a first order filter, a second order high pass filter can be formed from a second order low pass filter by simply interchanging the frequency determining resistance and capacitor. Figure 15.13 (a) shows a Second Order High Pass Butterworth Filter Derivation.

The voltage gain magnitude equation of the second order high pass filter is given by

where

A_{F} = 1.586 = pass band gain for the second order Butterworth response

f = frequency of the input signal in Hertz.

f_{L} = low cutoff frequency

This voltage gain equation can be mathematically determined by using Eq. (15.27), and replacing Z_{1} and Z_{2} by capacitors and Z_{3} and Z_{4} by resistors.