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
- AF = 1.586 = pass band gain for the second order Butterworth response
- f = frequency of the input signal in Hertz.
- fL = 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.