Biomedical Engineering Reference
In-Depth Information
i
1
i
2
i
4
i
3
FIGURE 9.5
A node with four currents.
connection—must equal zero so no net charge accumulates. This principle is known as
Kirchhoff's current law (KCL), given as
N
1
i
n
ð
t
Þ¼
0
ð
9
:
3
Þ
n
¼
where there are
currents leaving the node. Consider the circuit in Figure 9.5. Using
Eq. (9.3) and applying KCL for the currents
N
leaving
the node gives
i
i
þ
i
þ
i
¼
0
1
2
4
3
The previous equation is equivalently written for the currents
the node, since
entering
i
1
þ
i
2
i
i
¼
0
4
3
It should be clear that the application of KCL is for
all
currents whether they are all leaving
or all entering the node.
In describing a circuit, we define its characteristics with the terms
node, branch, path, closed
path,
and
mesh
as follows:
Node:
A point at which two or more circuit elements have a common connection.
Branch:
A circuit element or connected group of circuit elements. A connected group of
circuit elements usually connect nodes together.
Path:
A connected group of circuit elements in which none is repeated.
Closed Path:
A path that starts and ends at the same node.
Mesh:
A closed path that does not contain any other closed paths within it.
Essential Node:
A point at which three or more circuit elements have a common
connection.
Essential Branch:
A branch that connects two essential nodes.
Figure 9.6 shows five nodes—A, B, C, D, and E—that are all essential nodes. Kirchhoff's
current law is applied to each of the nodes as follows:
Node A
:
i
þ
i
i
¼
0
1
2
3
Node B
:
i
3
þ
i
4
þ
i
i
¼
0
5
6
Node C
:
i
1
i
4
i
8
¼
0
Node D
:
i
i
þ
i
¼
0
7
5
8
Node E
:
i
þ
i
þ
i
¼
0
2
6
7
