Intel 2920 Design Handbook page 52

CHAPTER 5
SUMMARY OF FILTER CHARACTERISTICS
5.0 SUMMARY OF FILTER
CHARACTERISTICS
This section presents a general review of different filter
types and discusses their characteristic weak and strong
points. It then presents a comparative analysis which
aids in the selection of a filter for implementation and
testing.
5.1 Characteristics Of "Ideal" Filters
It is useful to examine the characteristics of transmis-
sion lines and the so-called "ideal" filter as an introduc-
tion to typical filter characteristics.
Distortionless transmission implies that a signal is trans-
mitted through a network or medium and is received
exactly as sent but delayed by some amount. A Fourier
Analysis of the required transfer function shows that it
must have a constant amplitude over all frequencies and
a linear phase shift with frequency. An example of a
distortionless system is a length of transmission line
with a phase slope proportional to its length. Any
amplitude shaping as a function of frequency will
introduce some measure of distortion to the signal. The
problem then is to achieve the required frequency selec-
tivity while minimizing the distortion of the signal.
5.1.1 The Rectangular Filter
An ideal filter can be defined as follows for purposes of
analysis: it has a linear phase characteristic and a band-
limited amplitude response, i.e., unity in the passband
and zero in the stopband. This filter provides the
asymptotic limit in filter selectivity with a minimum of
distortion. Realizable filters can approach this selectiv-
ity by increasing the number of poles or stopband zeros
in their transmission function. Phase linearity must be
maintained either by employing direct linear phase syn-
thesis techniques or by using phase equalizers to
linearize the phase characteristic of the fil ter.
It is of interest to study the pulse transient response of
the rectangular filter as a limiting case of high selectivity
filter development. The pulse response can be calculated
as a function of pulse width and filter bandwidth using
Fourier Analysis techniques. The following equation is
derived for the output response:
5-1
h(t)
=
Kn
V
{
Si
[(B)(t-t o
+~~
-Si
[(B)(t-to-i)]}
where h(t) is the output pulse response
x
Si(x)
=
J
o
sin
y
dy
y
K is the filter passband gain
V is the input pulse amplitude
T
is the pulse width
B is the filter bandwidth
Figure 5-1 illustrates the pulse response as a function of
the TB product.
Do
~
<I:
(a) Lowpass-Fllter Pulse Response
(b) Response 01 Rectangular Lowpass
FIlter to a Unit Input Pulse
TIME
Figure 5-1. Rectangular Filter Pulse Response
As the pulse-duration bandwidth product approaches
infinity, the output pulse shape approaches that of the
input pulse in rise time and amplitude. One important
difference is that overshoot and ringing on the output
pulse does not diminish in amplitude as the bandwidth
of the filter is increased toward infinity. Instead,
overshoot approaches 9070 of the steady-state pulse
height, and settling time approaches zero as bandwidth
approaches infinity. This characteristic is referred to as