Continued
The shape factors for the Bandpass Filters and Band Reject Filters
listed later on these pages and the can be determined by
dividing the frequency difference between the 20dB points or the
40dB points (rejection bandwidth) by the frequency difference
between the 3dB points (passband). The specified upper and lower
3, 20 or 40dB points should be geometrically symmetrical to the
center frequency. The relationship of the band edges (F_{1}
& F_{2}) to the center frequency (F_{0}) in a filter that has geometric
symmetry is defined as F_{0} =
F_{0}
x F_{2}.
The Linear Phase Flat Delay Bandpass Filters on
later pages have arithmetric symmetry to the center
frequency. This type of symmetry is defined by F_{0 = }
½(F_{1} x F_{2}). This type of filter will always
have at least one half of the passband on either side of the
center frequency.
In this filter catalog, all the Iowpass and bandpass shape
factors will result in a number greater than one, while the
shape factors in the

 highpass and
band reject filters will be less than one. In all cases,
however, the shape factor improves as the number approaches
one.
As the shape factor requirement for a particular filter
approaches one, the necessary number and quality factor of
its capacitors and inductors increases. Extensive experience
and knowledge of components, along with the ultimate in
computer aided design and computer controlled test
equipment, are required to manufacture LC Filters that
exhibit these very low shape factors. Allen Avionics offers
a wide range of shape factors for each of the Lowpass,
Highpass, Bandpass and Band Reject type of filter. By taking
advantage of the tables of shape factors for each filter
type, you can pick just the right amount of filtering to do
your job. Buying more filter than you need can cost a lot.
The characteristics that the Lowpass, Highpass, Bandpass
or Band Reject Filters exhibit are determined by the type of
design as well as the number of elements. The Butterworth,
Chebyshev, Elliptical, Bessel, Gaussian and the Transitional
Gaussian are the best known and most useful designs that are
currently used in the filter industry. 
The Butterworth Design is characterized
by a ripplefree passband as well as a smooth stop band.
Increased attenuation is achieved as the frequencies get further
from the passband. For a given shape factor, this design
requires more components than the Chebyshev or Elliptic types
but the required quality factor of its components is not as
high. When a Butterworth filter is specified for a filter
application, the additional sections needed to meet a given
shape factor will increase over other filter types and can
result in increased size and cost.  
The
Chebyshev design is characterized by a predetermined amount of
passband ripple. The stop band exhibits smooth rolloff and
infinite attenuation is approached as the frequency increases.
This design requires less components than the Butterworth to
realize a given shape factor. Reductions in cost and size can be
realized with this type of filter over the Butterworth even
though the quality factor demanded of its components is much
greater. (See Fig. A and B.)
