Page 418 - Analog and Digital Filter Design

4
Design Equations

F5r example, suppose you want to know the frequency at which a 3dB
normalized fifth-order filter has 1 dB attenuation.

In order for the filter to have 1dB attenuation at cr) = 1: pole positions or
component values must be scaled to give the filter a higher 3dB attenuation
frequency. The scaling factor will be

1
K, = -, which is approximately 1.1447.
mK,l

Normalized Component Values for Butteworth Filter with
RL >> RS or RL e< RS

For zero or infinite impedance load, the following equations give the element
values. Values are given as C,, and are the nth component. The components are
alternating inductors and capacitors; the sequence depends on the load, as just
described.

(2 R - l)n'
aR =sin[ 2n j ~=1,2,3, ... n

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

These equations produce component values in an order that assumes they are
normalized against source impedance, rather than the load (Rs = I).

Normalized Component Values for Butterworth Filter:
Source and Load Impedances within a Factor of Ten

The following equations are used to find the element values.

4RL
Termination factor, T =
(RL + 1)'