Second Order High Pass Butterworth Filter using Op-amp

Second Order High Pass Butterworth Filter

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 the also can be realised by interchanging positions of resistors and capacitors in a second order low pass Butterworth filter. The Fig. 3.9.1 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, 

A_F = Passband gain

= 1.586 to ensure second order butterworth response

and R_f = 0.586 R₁

The frequency response of this filter is shown in the Fig. 3.9.2.

Example 3.9.1 Design a second order Butterworth active high pass filter for a cut-off frequency of 5 kHz.

Dec.-07, May-15, Marks 10

Solution: A second order Butterworth active high pas filter for a cut-off frequency of 5 kHz: The cut-off frequency is f_o = 5 kHz

Choose R = 10 kΩ

For second order Butterworth filter,

R_f / R₁ = 1.585

Choose R = 10 kΩ

hence R_f = 15.85 kΩ

The designed circuit is shown in the Fig. 3.9.3.

Review Question

1. Explain the operation of second order high pass Butterworth filter.