Biomedical Engineering Reference
In-Depth Information
Solution
By treating the op amp as ideal, note that the noninverting input is connected to ground and,
therefore, the inverting input is also connected to ground. The operation of this filter is readily
apparent because at low frequencies, the capacitor acts like an open circuit, reducing the circuit
to an inverting amplifier that passes low-frequency signals. At high frequencies, the capacitor acts
like a short circuit, which connects the output terminal to the inverting input and ground.
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.
1
j w C
R b
R a
+
V 0
V S
Summing the currents leaving the inverting input gives
V s
R a
V 0
1
V 0
R b ¼
0
j
o
C
Collecting like terms and rearranging yields
0
@
1
A ¼
1
1
j o C
1
R b
V s
R a
þ
V 0
After further manipulation,
0
@
1
A
0
@
1
A
V 0
V s ¼
1
R a
1
1
R a
1
¼
1
1
1
R b
1
R b
þ
j o C þ
j
o
C
0
@
1
A
V 0
V s ¼
1
R a C
1
1
R b C
j o þ
Continued
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