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
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