RF Electronics Chapter 7: RF Filters Page 212
2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0.
The frequency response for the Butterworth filter is shown in figure 7.2. The group delay
of Butterworth filters is reasonably flat but has a rise near the cut off frequency. The step
response of these filters exhibits some ringing, which degrades its use for data
communications.
Bessel Filters
The bigger the difference between the group delay at low frequency and the maximum
group delay, normally occurring near the filter cut-off frequency of the filter, the bigger
the ringing and overshoot in the step response. The Bessel filter has a maximally flat
group delay and does not have any ringing or overshoot in its step response. As a result,
the Bessel filter type is very suitable for data communication systems. Simple equations
like equations 7.1 and 7.2 do not exist for Bessel filters, so that normalised filter element
values have to be obtained from filter tables. Many filter tables for Bessel filters are
normalised for a group delay of one second, rather than a 3 dB cut-off frequency. The
Bessel filter in figure 7.3 has a cut-off frequency of 500 MHz so that accurate
comparisons between the filter types can be made.
The Bessel filter has a less sharp roll-off of the attenuation characteristic but a flatter
group delay than the Butterworth filter, as can be seen by comparing figure 7.2 and 7.4.
For the Butterworth filter, the 60 dB attenuation level occurs at 1.3 GHz while for the
Bessel filter it occurs at 2.4 GHz.
Figure 7.3. Bessel Lowpass Filter.
Figure 7.4. Bessel Lowpass Filter Frequency Response.
CAP
ID=C2
C=3.34 pF
CAP
ID=C1
C=0.704 pF
CAP
ID=C4
C=14.4 pF
CAP
ID=C3
C=5.53 pF
PORT
P=2
Z=50 Ohm
PORT
P=1
Z=50 Ohm
IND
ID=L3
L=17.7 nH
IND
ID=L2
L=11.2 nH
IND
ID=L1
L=5.19 nH
RF Electronics: Design and Simulation
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