The second order high pass Butterworth filter produces a gain roll off at the rate of + 40 dB/decade in the stop band. This filter also can be realised by interchanging the positions of resistors and capacitors in a second order low pass Butterworth filter. The Fig. 2.81 shows the second order high pass Butterworth filter.
The analysis, design and the scaling procedures for this filter is exactly same as that of second order low pass Butterworth filter.
The resulting expression is given here for the convenience of the reader. The voltage gain magnitude equation for the second order high pass filter is
and Rf = 0.586 R1
The frequency response of this filter is shown in the Fig. 2.82.