Digital Signal Processing Reference
In-Depth Information
Figure 4.10
Twin-tee bandstop active filter stage.
The general form of the transfer function for this filter is given in (4.41):
⎡
1
⎤
2
K
⋅
s
+
⎣
⎦
2
2
R
C
H
(
s
)
=
c
,
S
⎡
4
−
2
K
+
2
RY
⎤
1
+
2
RY
2
s
+
⋅
s
+
⎣
⎦
RC
2
2
R
C
(4.41)
where again
K
=
1
+
(
R
/
R
)
B
A
(4.42)
Equation (4.43) rewrites this equation in terms of the pole frequency ω
p
and the
zero frequency ω
z
:
2
2
K
⋅
(
s
+
ω
)
z
H
(
s
)
=
c
,
S
2
2
s
+
(
ω
/
Q
)
⋅
s
+
ω
p
p
(4.43)
The transfer function of (4.43) must be matched to the general form of a
bandstop approximation function, as shown in (4.44):
2
G
⋅
(
s
+
a
)
2
H
(
s
)
=
a
,
S
2
s
+
b
⋅
s
+
b
1
2
(4.44)
Depending on the value of
Y
selected, ω
z
may be greater than, equal to, or less
than ω
p
. This will affect the matching of the respective terms in (4.43) and (4.44).
The responses for the transfer function will also change, as indicated in Figure
4.11. Let's look at how the transfer function changes for the three cases.
