Odd Order Chebyshev Narrow Band Pass Filter with Passive Components Applet.

Cuthbert Nyack
This page describes a very simplified approach to deriving Chebyshev narrow band pass filters from normalized low pass filters.
The transformation required is illustrated by the image below.
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 above.
Values of the added components are calculated to make their resonant frequency equal to the center frequency wo of the band pass 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 Chebyshev band pass filters for different RL and passband ripple. 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 Chebyshev filter RS = 100W, RL = 120W, Ripple = 0.5dB, 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.

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COPYRIGHT 2011 Cuthbert Nyack.