Page 421 - Analog and Digital Filter Design

4 1 8 Analog and Digital Filter Design

Now, the component values are given by CR

Chebyshev Filter with Source and Load Impedances within
a Factor of Ten
If the load is not much greater than or less than the source, either shunt C or
series L can be used as the first component. The last component will depend on
whether the filter has an odd or even order. The following equations are used
to find the element values.

4RL
Termination factor, T = (odd order)
(RL +1)?
4RL 100.'"/'
T= (even order)
(RL + 1)'
(2R - 1)n
aR =sin[ 211 ] R = 1,2, 3,. . . ri
6 = sin "[ (+) sin P( y)]
4-T

y = sin h( $)

(::)
b, = y2+6' -2y6cos - +sin- '( g) R = 1,2,3,. . . rz

c, =- 2a 1
Y -6
4aRaR-I
CR = R = 2, 3,4,. . . n
bR-C R-I

Component values must be normalized for a 3dB cutoff frequency. This is
done by increasing all values, by multiplying those obtained in the formulae by
cos 12 = [: - . cos I2-I (i)] for odd order. For example, for a fifth-order 0.1 dB

Chebyshev ater, component values must be multiplied by 1.13472.