SKEE 2073
Signals & Systems
1
Chapter 6:
FILTER DESIGN
Part 2 (BUTTERWORTH)

Steps to design Butterworth Transfer Function
2
1.
Calculate the order number,
n
2.
Calculate
c
and choose
c
with the
p
&
s
that fulfill the given
specification
3.
Determine the normalized Transfer Function,
H
n
(s)
–
refer
a
n
(butterworth
coefficient) from the table
4.
Determine the real/actual Transfer Function: obtained from step 3 and using
the transformation table.
p
(dB) = 20 log
p
s
(dB) = 20 log
s
p
(dB)
&
s
(dB)
can be
calculated from equations
in the next slide

Example: Butterworth Response
1.
Calculate the order number,
n
(circular number)
2.
Sketch the magnitude response of this filter
3.
Determine the normalized Transfer Function,
H
n
(s)
–
refer
a
n
from the table
4.
Determine the real/actual Transfer Function
Design a Butterworth lowpass filter (LPF) with
•
a passband gain between 1 and 0.891 (-1 dB gain) for
0<
ω
<10
•
a stopband not to exceed 0.0316 (-30 dB gain) for
ω≥
20