Odd Order Chebyshev Low Pass Filter with Passive Components Applet.

Cuthbert Nyack
Analytic expressions are available for calculating component values for odd Chebyshev filters with equal terminations. Odd order Chebyshev filters are symmetric and the impedance of each half can be scaled independently to derive component values for unequal terminations.
The circuits for third and ninth order filters and their duals are shown below.
For all cases at low frequencies, the impedance of the inductors is small and that of the capacitors is large, so the output Vo ~ VS (RL/(RL + RS)). At high frequencies the output goes to zero.
The applet below can be used to calculate component values for low pass odd order Chebyshev filters with RS = 1 and variable RL and passband ripple.

The function of the applet is controlled by Fn which is set scrollbar 0.
Fn = 1 to 4 shows filters with order 3, 5, 7 and 9. Fn = 5 to 8 shows dual circuit filters with orders 3, 5, 7 and 9.
Fn = 9 to 16 show only the values without the plots.
Normalized component values are shown in green and denormalized values in yellow.
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 Chebyshev Filter. Denormalized values shown in yellow are for a filter with RS = 100W, RL = 100W, a 3dB frequency of 10KHz a passband ripple of 1dB and an impedance scaling factor of 100.0. All resistances are in ohms, all inductances in henries and all capacitances in farads.

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COPYRIGHT 2011 Cuthbert Nyack.