Page 176 - Analog and Digital Filter Design

CHAPTER
6

BANDPASS FILTERS

There are two categories of bandpass filters: wideband and narrowband. Filters
are classified as wideband if their upper and lower passband cutoff frequencies
are more than an octave apart. This is when the upper frequency is over
twice that of the lower frequency. Wideband filters are ideally constructed
from lowpass and highpass filters connected in series. The denormalization and
scaling process for these has already been described in Chapters 4 and 5. This
chapter describes how to design narrowband analog active or passive bandpass
filters. Narrowband filters have upper and lower frequencies that are an octave
or less apart.

Passive bandpass filter designs will be based on the tables of normalized lowpass
component values in Chapter 2. Formulae will be given for the denormalization
and scaling of these component values to produce a bandpass design. The
equations are more complex than for lowpass or highpass transformations, but
examples of their application will be given.

Active bandpass filter designs will be based on the normalized lowpass pole and
zero locations, given in Chapter 3. Formulae will be given for denormalizing this
pole and zero information, which will allow component values to be obtained.
The equations are complex. but they are broken down into easier steps in order
to simplify the process and reduce the chance of errors. Examples of how to use
the equations will be given.

Lowpass to Bandpass Transformation

There is a close relationship between the bandwidth of a bandpass filter and the
normalized lowpass filter from which it is derived. The bandwidth of a lowpass
filter is from DC to the cutoff frequency, and the bandwidth of a bandpass filter
is between the lower and upper cutoff frequencies. To obtain a particular band-
width in a bandpass filter, first scale the normalized lowpass design to have this
bandwidth. and then transform this into a bandpass filter design. The resultant