ACTIVE_FILTERS_Theory_and_Design

Introduction 15
effect of a constant group delay in a filter is that all frequency components of a signal
transmitted through it are delayed by the same amount, i.e., there is no dispersion of
signals passing through the filter. Accordingly, because a pulse contains signals of
different frequencies, no dispersion takes place, i.e., its shape will be retained when
it is filtered by a network that has a linear phase response or constant group delay.
Just as the Butterworth filter is the best approximation to the ideal of “perfect
flatness of the amplitude response” in the filter passband, so the Bessel filter provides
the best approximation to the ideal of “perfect flatness of the group delay” in the
passband, because it has a maximally flat group delay response. However, this applies
only to low-pass filters because high-pass and band-pass Bessel filters do not have
the linear-phase property. Figure 1.11 compares the amplitude (a) and phase response
0
−2
Butterworth
Magnitude/dB
−4
−6
Bessel
−8
−10
0.1 0.2 0.4 0.6 0.8 1.0 2.0
ω
(a)
0
−90
Bessel
Phase/degrees
−180
−270
−360
Butterworth
−450
−540
0 1 2
ω
(b)
FIGURE 1.11 Response of Butterworth and Bessel: (a) amplitude, (b) phase.