MFBP Circuit for Narrow Band Pass Butterworth Filter.

Cuthbert Nyack
Wideband Butterworth filters can be obtained by connecting a low pass filter in series with a high pass filter. The 3dB frequency of the high pass filter must be the lower 3dB frequency of the band pass filter and the 3dB frequency of the low pass filter must be the upper 3dB frequency of the bandpass filter.
If the upper 3dB frequency of the band pass filter is less than twice the lower 3dB frequency then narrow band pass filters must be used. The Circuit below can be used to implement a second order narrow bandpass filter and several sections can be put in series to implement higher order filters.
The applet below can be used to calculate component values for narrow band pass Butterworth filters with orders 2 to 5. The function of the applet is determined by Fn which is set by scrollbar (0). Fn = 1 to 4 shows 2 to 5th order filters.
Scrollbars (3, 4) are used to set the center frequency of the filter.
Scrollbar (5) sets the Q of the filter.
Scrollbar (6) sets the gain of the filter.
Scrollbars (7,8) are used to set the value of the capacitors.
Scrollbars (11 to 35) are used to change the component values by ± 20%.
Denormalized component values are shown in green on the applet.



The Image below shows a 5th order filter (Fn = 4) implemented with 5 sections and 5 opamps(15 resistors and 10 capacitors). Denormalized components are shown in green. In this case, the center frequency is 1kHz and the bandwidth is 100Hz. The capacitors are set to 0.1µF.
Pink and Cyan plots show the magnitude and phase error introduced when the capacitor C2 in section 1 is 10% larger than its correct value.
Numerical values of the errors can be seen at the bottom by using scrollbar 43 to move the white line. The blue/magenta plots are the magnitude response of the different sections.

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COPYRIGHT 2010 Cuthbert Nyack.