Biomedical Signal Processing - Computational Intelligence in Biomedical Engineering - page 45

2.5.2 Butterworth Filters
Butterworth filters are higher-order filters with the special characteristic that
as the filter order increases, the filter response approaches that of an ideal
filter (Akay, 1994). This can be seen from the transfer characteristics plot
in Figure 2.11, where the attenuation region becomes sharper as the filter
order increases. When designing a Butterworth filter, two important issues
are the filter order, N and the cutoff frequencies, ω c . We will examine the
design of a low-pass Butterworth filter to show how the filter characteristics
are determined from the filter specifications. Figure 2.12 shows a Butterworth
filter circuit, where R i and C i are resistors and capacitors respectively, whereas
UA 741 is an operational amplifier.
The general magnitude of the Butterworth filter response is given as

1
1+( ω/ω c ) 2 N

2 =

| H ( ω ) | (2.110)

⏐ H ⏐

1.0

0.707

n = 4
n = 2
n = 1

0

0 = 2

FIGURE 2.11
A typical frequency response of an nth order Butterworth filter.

R4 15.82 k

R3 27 k

+

V1
− 3/3 V

30 V

UA741

R2 3.3 k R1 3.3 k +

C1 C2

0.047 µ F 0.047 µ F

1 KHz

FIGURE 2.12
Circuit diagram of a Butterworth filter.