Page 424 - Analog and Digital Filter Design

Design Equations 42 1

capacitor: C2 = 1/p'L. But the new zero is at p/@dB and the new inductor value
is LC&dB.

In
other
So C2 = @dB'/P2L~;dB. This simplifies to C2 = Q~~/~~L. words, C2 is
also multiplied by @dB-
(2K - 1)n
un. =
2 n

K= 1, 2,. . . , n

An equation exists to find the 3 dB point for any Inverse Chebyshev filter:

1
OM5 =
COS 17 1
L J

The 3dB cutoff frequency depends on both the stopband attenuation Ks and
the filter order n. Component values, or pole positions in the case of active
filters, can be scaled to give a 3dB cutoff point.

Elliptic or Cauer Filter Equations

The filter order required for a given passband ripple, stopband attenuation, and
ratio of passband to stopband frequency can be calculated by use of compli-
cated algorithms. These algorithms use something called an elliptic integral.
Elliptic integrals are easier than they look, and examples will be given to show
this. To find the filter order required we must note the passband ripple and fre-
quency as well as the stopband ripple and frequency.

ripple = maximum passband ripple (in dB).

amin = minimum stopband ripple (in dB).
pass = passband frequency (cutoff frequency).
stop = stopband frequency (where the stopband has been reached j.

The ratio of stopband + passband is given as k. Another variable, L, is
dependent upon the passband ripple and the stopband attenuation.