Biomedical Engineering Reference
In-Depth Information
As before, the phasor method will be used to solve this problem by first transforming the
circuit into the phasor domain, as shown in the following figure.
R
b
R
a
1
j
w
C
+
V
S
V
0
−
Summing the currents leaving the inverting input gives
V
s
V
0
R
b
¼
0
1
j
o
C
R
a
þ
Rearranging yields
V
0
V
s
¼
R
b
R
a
þ
¼
R
b
R
a
j
o
1
j
o
C
1
R
a
C
j
o þ
100
rad
s
1
R
a
C
. The magnitude of
V
0
V
s
At cutoff frequency o
c
¼
¼
is given by
¼
R
b
V
0
V
s
o
o
2
s
2
R
a
1
R
a
C
þ
and at the cutoff frequency,
p ¼
R
b
5
o
c
s
2
R
a
1
R
a
C
o
2
c
þ
1
R
a
C
¼
100
rad
s
With
100 and o
c
¼
, gives
1
R
a
C
100
2
p ¼
R
b
5
o
c
o
2
¼
R
b
R
a
¼
R
b
R
a
100
100
¼
R
b
s
q
p
R
a
2
R
a
100
2
1
R
a
C
þ
c
þ
Thus,
R
b
R
a
¼
5. Since we have three unknowns and two equations, one can select a convenient
value for one of the elements—say,
R
b
¼
20 k
O
—and the other two elements are determined as
R
a
¼
R
5
¼
20000
5
¼
4k
O