Biomedical Engineering Reference
In-Depth Information
EXAMPLE PROBLEM 9.15
Write the node equations for the following circuit for
t
0 if the initial conditions are zero.
L
1
R
2
C
1
+
−
v
s
(t)
R
1
C
2
Solution
With the reference node at the bottom of the circuit, we have two essential nodes, as shown
in the following redrawn circuit. Recall that the node involving the voltage source is a known
voltage and that we do not write a node equation for it. When writing the node-voltage equations,
the current through a capacitor is
i
c
¼
C
D
v
, where
D
v
is the derivative of the voltage across the
Z
t
1
L
i
L
¼
D
vd
l þ
i
L
0
ðÞ
, where
D
v
is the voltage
capacitor, and the current through an inductor is
0
across the inductor. Since the initial conditions are zero, the term
i
L
ð
0
Þ¼
0
:
L
1
2
1
+
+
R
2
C
1
+
v
s
(t)
R
1
v
1
C
2
v
2
−
−
−
Summing the currents leaving node 1 gives
Þ
v
1
R
1
þ
v
1
v
2
v
1
v
s
C
1
ð
R
2
¼
0
