Odd Order Butterworth Narrow Band Stop Filter with Passive
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
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".
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COPYRIGHT © 2011 Cuthbert Nyack.