
33-6 Electrical Variables
Two classes of low-pass lters are commonly used in making noise measurements. e rst has n real
po
les,
a
ll
w
ith
t
he
s
ame
f
requency,
h
aving
t
he
m
agnitude-squared
t
ransfer
f
unction
g
iven
b
y
| ( )|
( )
A f
A
f f
n
v
vo
/
2
2
0
2
1
=
+
(33.14)
where
f
0
is the pole frequency. e second is an n-pole Butterworth lter having the magnitude-squared
transfer function given by
| ( )|
( )
A f
A
f f
n
v
vo
/
2
2
3
2
1
=
+
(3
3
.15
)
where
f
3
is the −3 dB frequency. Table 33.1 gives the noise bandwidths as a function of the number of
poles n for 1 ≤ n ≤ 5. For the real-pole lter, B
n
is given as a function of both f
0
and f
3
. For the Butterworth
lter, B
n
is g ...