Page 422 - Analog and Digital Filter Design
P. 422
Design Equations 419
The values obtained for even-order filters should be increased in value by
Load Impedance for Even-Order Chebyshev Filters
For even-order Chebyshev filters, equal source and load impedance is not pos-
sible. It must have a normalized load of greater than unity if the first compo-
nent is a series inductor (the last component is therefore a shunt capacitor). The
(3
minimum value of the normalized load is RL 2~0th~ - . Conversely, if the
first component is a shunt capacitor, the last component is a series inductor. and
the load must be less than unity. The maximum value of the normalized load is
RL I tanh'i$).
Inverse Chebyshev Filter Equations
To find the filter order required for Inverse Chebyshev filters, use the following
equation.
Where Cn = lilo""-1, with A being the desired attenuation, and Q is the ratio
of stopband to passband.
For example, if the 3dB point is at lOHz and the stopband begins at IjMz,
Q = 1.5. If 20dB of stopband attenuation is required, Cn = 9.95; n = 2.98810.9624
= 3.1; the filter order must be 4 or more.
Inverse Chebyshev filters have to be adjusted to give a 3dB passband edge
a.t w = 1 radls. Consider a third-order lowpass filter, as shown in Figure A.1,
having equal source and load impedance and a stopband beginning at w =
1 radls:
