Digital Signal Processing Reference
In-Depth Information
Figure 4.5
Sallen-Key highpass active filter stage.
2
K
⋅
s
H
H
(
s
)
=
c
,
[
]
2
s
+
1
/
R
C
+
1
/
R
C
+
(
−
K
)
/
R
C
⋅
s
+
1
/
R
R
C
C
2
2
2
1
1
1
1
2
1
2
(4.22)
where again
K
=
1
+
(
R
/
R
)
B
A
(4.23)
We can use the same procedure in selecting the component values as we used
in the lowpass case by letting
R
1
=
R
2
and
C
1
=
C
2
. The result is shown in (4.24),
where we see that the denominator is identical to the lowpass case in (4.8):
2
K
⋅
s
H
(
s
)
=
c
,
H
[
]
2
2
2
s
+
(
−
K
)
/
RC
⋅
s
+
1
/
R
C
(4.24)
This equation can then be matched to the quadratic factors from the
approximation functions that have the form shown in (4.25)
2
G
⋅
s
H
(
s
)
=
a
,
H
2
s
+
b
⋅
s
+
b
1
2
(4.25)
When the equation for the approximation function is compared to the
equation for the active filter stage, we see that the relationships between terms are
identical to those of the lowpass case. Therefore, if we pick the same value of
capacitor, the resistor values will be identical to those of the lowpass case, as
shown below:
2
R
=
1
/
b
C
2
(4.26)
