Page 248 - Analog and Digital Filter Design

Phase-Shift Networks (All-Pass Filters) 245

s:= 1,2.. 1000 A:= 1

2

1

JY 0
-

-1

Figure 9.1
-2
Band-Limited impulse 0 500 IO00
Response r:

The Bessel filter is unique in that the distortion produced is due entirely to band-
width restrictions. It has a constant group delay. This is important if an impul-
sive signal is applied to the filter input; the phase relationship between the
harmonic signals is the same at the output as it was at the input. This must be
true because all the transmitted harmonics are delayed by the same amount.

Bessel filters have a serious disadvantage. Beyond the cutoff point the attenua-
tion increases slowly with frequency. Even at twice the -3dB cutoff frequency
there is very little difference in attenuation between a third- and tenth-order
filter. So, despite their constant group delay, Bessel filters are rarely used. They
may be suitable for some electromagnetic interference (EM) reducing applica-
tions. They could also be used for anti-aliasing filters prior to a delta-sigma
analog-to-digital converter, where the sampling frequency is many tirnes greater
than the signal bandwidth.

The use of Butterworth, Chebyshev, and Cauer filters is preferred because
they have a steeper rate of attenuation beyond the filter’s cutoff frequency.
Unfortunately, these filters have a group delay that depends on frequency. Cen-
erally. the group delay increases as the cutoff frequency is approached, peaking
just below the cutoff frequency and then failing rapidly above the cutoff fre-
quency. The higher the filter order: the greater the change in group delay. Also.