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 Z₁ and Z₂ by capacitors and Z₃ and Z₄ by resistors.