Page 420 - Analog and Digital Filter Design

Design Equations 4 1 7

In other words, Cn(Q;,ls)=cosh

For example, consider a fifth-order 0.1 dB ripple Chebyshev filter. What at-
tenuation does it produce at twice the 3dB cutoff frequency?

~=d10~.'"" =0.15262
-1
Q(3 dB)=R.sosh = 2.~0~h(0.513415)=2.26944

Cn(Q) = cosh(iz.cosh-'R) = 740.77

A = 10.10g(l+E'C~z2(Q;2)) dB = lO.log(12783) = 41 dB.

The required filter order is given by:

cos h-l (Crz)
/1 =
cos k-' (Q)
where Cn = d( 10"'" - l), As = desired stopband attenuation and R is the ratio
of stopband to passband frequency.

Equations to Find Chebyshev Element Values

Chebyshev with Zero or Infinite Impedance Load
For a Chebyshev filter with zero or infinite impedance load, the following equa-
tions give the element values. Values are given as C,, that are the nth component.
These are alternating inductors or capacitors, and the sequence depends on the
load, as just described. The passband ripple, in decibels, is Ap.

R = 1,2,3,. . . n