Notes
on
the
Node
Method
and
the
Loop
Method
The steps
in
the node method
are:
1.
Identify one node as the ground node, so that by definition, the potential at the
node is 0 V. You may choose any node as ground, but often a judicious choice
will simplify things later on. If there is only one source, make the negative
terminal of the source ground. If there are several sources, all with a common
node, make that node ground. Otherwise, choose one source, and make one of
its terminals (usually the negative terminal) ground.
2. Label the potential of each node. Of course the ground node is at 0 V. Most
of the other nodes will be unknown. Label them as
e
1
,
e
2
, etc. For voltage
sources, use the constitutive relation to label one of the nodes. For example,
if the negative terminal is at ground, and the source has strength
V
1
, then the
positive terminal is at
V
1
. If the negative terminal is at, say,
e
2
, then the positive
terminal is at
V
1
+
e
2
.
Generally, this process will lead to a unique (but perhaps unknown) voltage at
each node. Furthermore, Kirchhoff’s voltage law will be satisfied automatically
for each loop.
This process can fail in one situation: If any loop in the network consists of
only voltage sources, then that loop will not satisfy KVL (unless the source
strengths happen to sum to zero around the loop). Physically, such a situation
would lead to infinite current ﬂow, and so should be avoided!
3. For each node with unknown potential, apply Kirchhoff’s Current Law. This
will lead to an equation in the unknown node voltage. (The equation will also
involve other nodes that are connected to the node of interest by other elements.)
There is no need to apply KCL at nodes with known voltage. Indeed, such
nodes are connected to voltage sources, and the constitutive relation of voltage
sources gives no information about the current ﬂow through the source; hence,
it adds no new information that would allow one to find the unknown node
voltages.
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 Fall '05
 MarkDrela
 Equations, Voltage source, Constitutive equation

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