Odd Order Butterworth Narrow Band Stop Filter with Passive Components Applet.

Cuthbert Nyack
This page describes a somewhat simplified approach to deriving narrow band stop filters from normalized low pass filters.
The first step is to transform the low pass filter to a high pass configuration as shown below.
The high pass is normalized to a 3dB frequency equal to the bandwidth of the band stop filter.
To transform the high pass to a band stop configuration, inductors are added in parallel with the capacitors and capacitors are added in series with the inductors.
Values of the added components are calculated to make their resonant frequency equal to the center frequency wo of the band stop filter.
ie L1 = 1/(wo 2 C1), C2 = 1/(wo 2 L2), L3 = 1/(wo 2 C3), etc. Applet below can be used to calculate component values of Butterworth band stop filters. Fn = 1, 2, 3 and 4 show 3rd, 5th, 7th and 9th order band stop filters. The sensitivity of the transfer function to variation in component values can be seen by changing scrollbars 11 to 30.



Image below shows a 7th order passive band pass Butterworth filter RS = 100W, RL = 100W, Center freq = 500Hz, BW = 90Hz, Impedance scaling factor is 100.0.

Components in green are high pass components. Those in yellow are the ones which must be added to the high pass to transform it to a band stop filter.
Image below shows what happens if inductor L2 is 3% smaller than its correct value. The spikes in the phase are "spurious".

Return to main page
Return to page index
COPYRIGHT 2011 Cuthbert Nyack.