Biomedical Engineering Reference
In-Depth Information
Solution
As usual, the design of the filter is done in the phasor domain and uses the work done in the
previous two examples. Note that the elements around the op amp on the left are the low-pass
filter circuit elements, and those on the right are the high-pass filter circuit elements. In fact, when
working with op amps, filters can be cascaded together to form other filters, so a low-pass and
high-pass filter cascaded together will form a band-pass. The phasor domain circuit is given in
the next figure.
1
j
w
C
L
R
b
L
R
b
H
−
−
R
a
L
+
+
R
a
H
+
−
+
+
V
S
1
V
L
V
0
j
w
C
H
−
−
As before the noninverting input to the op amps is connected to ground, which means that the
inverting input is also connected to ground. Summing the currents leaving the inverting input for
each op amp gives
V
s
R
a
L
V
L
1
j
o
C
L
V
L
R
b
L
¼
0
V
L
V
0
R
b
H
¼
0
1
j
o
C
H
R
a
H
þ
Solving the first equation for
V
L
gives
0
@
1
A
1
R
a
L
C
L
1
V
L
¼
V
s
1
R
b
L
C
L
j
o þ
Solving the second equation for
V
0
gives
V
0
¼
R
b
H
R
a
H
j
o
V
L
1
R
a
H
C
H
j
o þ
