Digital Signal Processing Reference
In-Depth Information
(
)
R
/
R
=
2
−
b
1
/
b
B
A
2
(4.27)
The adjustment of gain for the highpass case is handled in a similar manner to
the lowpass case. As (4.24) indicates, the
K
value of each stage can be determined
by allowing the frequency to approach infinity, as opposed to zero in the lowpass
case.
K
tot
can then be easily determined, and with the approximation function
gain, the gain adjustment factor
GA
can be determined as shown previously in
(4.14). A resistive voltage divider is used at the output of the last stage of the
active filter. If necessary, a buffer amplifier can be used after this voltage divider
if the impedance of the network being driven by the filter is too small.
If an odd-order highpass approximation factor is to be implemented, an active
filter stage as shown in Figure 4.6 can be used as the first stage of the active filter.
The only difference between this stage and the lowpass first-order stage is the
interchange of
R
and
C
values.
Figure 4.6
First-order highpass filter with buffer amp.
The transfer function for this stage is given in (4.28), while the approximation
function for a first-order highpass factor is shown in (4.29):
s
H
c
(
s
)
=
s
+
1
/
RC
(4.28)
G
⋅
s
H
a
(
s
)
=
s
+
b
2
(4.29)
As in the second-order case, the resistor value will be the same as the lowpass
value assuming that the same value of capacitor is picked.
R
=
1
/
b
C
2
(4.30)
Example 4.2 Chebyshev Highpass Active Filter Design
Problem:
Determine the resistor and capacitor values to implement a
Chebyshev highpass active filter to meet the following specifications:
