Odd Order Butterworth Narrow Band Pass Filter with Passive
This page describes a somewhat simplified approach to
deriving narrow band pass filters from normalized
low pass filters.
The transformation required is illustrated by the image
Starting from any of the low pass filter configurations, denormalized low
pass values are calculated assuming a 3dB frequency equal to
the required bandwidth of the band pass filter.
Inductors are then added in parallel with the capacitors
and capacitors added in series with the inductors as shown
Values of the added components are calculated to make their
resonant frequency equal to the center frequency wo of the band pass
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 pass filters. Fn = 1, 2, 3 and 4 show 3rd, 5th, 7th and 9th
order band pass 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 ninth order passive band pass Butterworth filter
RS = 100W, RL = 120W, Center freq = 5KHz, BW = 1kHz,
Impedance scaling factor is 100.0.
Components in green are low pass components. Those in yellow are
the ones which must be added to the low pass to transform it to
a band pass filter.
Image below shows what happens if capacitor C3 is 5% larger than
its correct value. The spikes in the phase are "spurious".
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COPYRIGHT © 2011 Cuthbert Nyack.