Page 207 - Analog and Digital Filter Design

204 Analog and Digital Filter Design

L1=186.5nH L3=186.5nH
Rs=50

Cl=1.326uF C3=1.326uF
Source
R=50
Figure 7.6
Bandstop Filter.
Denormalized with
504 Load Resistance

Having gone through this laborious process, readers will be pleased to know that
there are formulae that allow the whole process to be completed in one step.
These formulae are similar to those used in the bandpass filter design process.
Care must be taken to use the correct formulae for each stage of the design.

Formula for Passive Bandstop Filter Denormalization

The series and shunt subscripts indicate which circuit element is being consid-
ered. A series subscript indicates the series arm (which is parallel resonant). A
shunt subscript indicates the shunt arm (which is series resonant). In the equa-
tions, the factor Xis the normalized lowpass element value taken from the tables
in Chapter 2. The same value of Xmust be used for both components in a single
branch. Remember that each branch in the all-pole lowpass filter has one com-
ponent, while branches in the bandstop have two components that are either
series or parallel resonant.

It may be helpful to redesign the third-order Butterworth filter to illustrate the
use of these formulae. Since it is a symmetrical design, only the first three
branches need to be calculated. As before R = 50, F,, = (320 + 1.2) kHz =
321.2kHz, FL=(320- 1.2) kHz= 318.8kHz.