Page 202 - Analog and Digital Filter Design

7
CHAPTER

BANDSTOP FILTERS

There are two categories of bandstop filters: wideband and narrowband. Filters
are classified as wideband if their upper and lower passband cutoff frequencies
are several octaves apart. This is when the upper frequency is many times that
of the lower frequency.

Wideband filters are ideally constructed from odd-order lowpass and highpass
filters connected in parallel. Odd-order filters are necessary because, outside
their passband, these have both high input impedance and high output imped-
ance. High impedance in the stopband prevents loading of the parallel-
connected filter. Otherwise impedance mismatches could occur that would lead
to an incorrect overall frequency response. The denormalization and scaling
process for lowpass and highpass filters has already been described (in Chapters
4 and 5).

This chapter describes how to design narrowband active and passive bandstop
filters to almost any specification. Narrowband filters have upper and lower fre-
quencies that are less than about three octaves apart. The design of these uses
the normalized lowpass filter pole and zero or component values as a starting
point. I use information from previous chapters and give examples where this
helps in the understanding. I also provide formulae for passive designs in the
denormalization and scaling of normalized component values previously given
in Chapter 2, and describe the method of denormalizing pole and zero infor-
mation, given in Chapter 3 for use with active filters.

Bandstop filter design starts with normalized component values, which are con-
verted into normalized highpass values. These highpass values are then scaled
to give a new cutoff frequency, W'. The new cutoff frequency must be made
equal to the difference between upper and lower cutoff frequencies far the
desired bandstop filter. In mathematical terms, W=fi - fi. Figure 7,1 illustrates
this.