Intel 2920 Design Handbook page 54

SUMMARY OF FILTER CHARACTERISTICS
The pulse response of the elliptic function filter is
approximately the same as for Chebyshev filters, and
possibly even better for the same selectivity. The phase
and time delay characteristics are sufficiently bad that
this type of filter is seldom used where signal distortion
is a strong consideration.
5.2.4 Bessel and Gaussian Filters
These filters are nearly identical to each other in both
time and frequency domains. The Bessel is also known
as the Thompson and the maximally flat time delay
filter. Unlike the high selectivity filters described above,
these filters are primarily designed for linear phase and
good transient response. Their selectivity is roughly
comparable to a single stage RC section within the first
6 dB regardless of the number of poles. Well outside
their passband the rolloff approaches 6 dB/octave-
bandwidth per pole.
The pulse response is characterized by a fast rise time
and little or no overshoot regardless of the number of
poles. One application of this filter is as a matched filter
to receive pulse signals in a noisy but otherwise
interference-free environment.
5.2.5 Transitional Gaussian/Butterworth Filters
This useful filter provides the skirt selectivity of a But-
terworth but the passband characteristics of a Gaussian
filter. The transitional point is established by varying a
parameter in the transfer function, transition points
values of 6 dB or 12 dB being common. This means that
the filter exhibits a Gaussian amplitude response down
to the transition amplitude, and then assumes a Butter-
worth amplitude response. The filter has good phase
linearity in the passband, though not as good as a con-
ventional Gaussian filter, and a transient response
which has substantially reduced overshoot compared to
a Butterworth.
5.2.6 Other Minimum Phase Filters
Many other transfer functions can be described, such as
equal ripple phase, parabolic, monotonic L, etc. Their
characteristics are combinations of those already
described. The important aspect of minimum phase
filters is the unique relationship between amplitude and
phase. The transient response is affected by both
parameters, so that flexibility is limited with respect to
simultaneously achieving good selectivity and low
distortion.
5-3
5.2.7 Comparison of Minimum Phase Filters
Lowpass prototype filters have been discussed which
meet various magnitude or phase requirements. For
minimum phase networks, the specification of one
parameter (magnitude or phase) necessarily constrains
the other. Thus, both amplitude and phase cannot be
specified independently.
Filters synthesized for specific amplitUde properties
include Butterworth (maximally flat amplitude),
Chebyshev (equal ripple passband amplitude), and
elliptic function (equal ripple amplitude passband and
stopband). Optimal phase filters include Bessel (max-
imally flat phase), equal ripple time delay (equal ripple
phase error), and transitional (compromised amplitUde
and phase). Some of these filter types and the cor-
responding properties are iisted in Table 5-1. A com-
parison can be made in both the time domain and fre-
quency domain to illustrate the different properties.
Table 5-1. Summary of Analog Filter Types
• Butterworth "maximally flat amplitude"
- Flat in passband
- Monotonic in stopband to zero gain at
00
Hz
- High selectivity
- High overshoot transient response
• Chebyshev "equal ripple amplitude"
. - Small ripples in passband
- Monotonic in stopband to zero gain at
00
Hz
- Higher selectivity
- Higher overshoot transient response
• Elliptic or cauer "equal ripple amplitude"
- Ripples in passband
- Ripples in stopband to Amin
- Highest selectivity
- Highest overshoot transien
t
response
• Bessel "maximally flat delay"
- Monotonic amplitude in passband and stopband
- Poor selectivity
- Nearly linear phase and flat time delay
- Zero overshoot transient response
• Allpass
- Flat amplitude (constant gain)
- Used to equalize phase or delay characteristics of
networks