**Second Order High Pass Butterworth Filters:**

The second order high pass Butterworth filters produces a gain roll off at the rate of + 40 dB/decade in the stop band. This filter also can be realized by interchanging the positions of resistors and capacitors in a second order low pass Butterworth filters. The Fig. 2.81 shows the second order high pass Butterworth filters.

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

where

- f = input frequency in Hz
- f
_{L }= lower cut off frequency in Hz ≈1/2πRC - R
_{2}= R_{3}= R and C_{2}= C_{3}= C - A
_{F }= passband gain - = 1.586 to ensure second order butterworth response

and

The frequency response of this filter is shown in the Fig. 2.82.