The Laws of Circuit
- you can learn
and practice by just reading
Copyright. Charles Kim 2006
- Node Voltage Method
- Why the 3 laws are not enough?
- You learned about the most fundamental
laws in electrical engineering: Ohm's Law, Kirchhoff's
Current Law (KCL), and Kirchhoff's Voltage Law (KVL). You
also learned about the Passive Convention in current flow
direction, voltage polarity, and power calculation. And
you guys, I hope, had a lot practice time to apply the
above concepts, and could solve all the
problems using only the laws and the convention.
There is no doubt that you can solve all circuit problems
however complex or big they are. Of course with a
lot of practices. However, when there are a lot of
variables involved in analysis, a direct application of
the laws and the convention may cause some practical
problems: too many equations to be solved. Apparently, we
need some easier application of the Law for somewhat
complex circuit problems.
- KCL in Disguise
- One of the "methods" we can
apply is "a disguised KCL" at nodes. This
"KCL in disguise" is called "node voltage
method." In other words, Node voltage
method is nothing but KCL. However, there is a big
difference. In KCL, all the terms in your KCL
equations are expressed in current; in Node voltage
method, all the terms in the equations are expressed by
a current equivalent, namely, Node voltage over Resistance, obtained by
applying the Ohm's Law. So
instead of using current proper (unless there is a current
source involved), we express the current by the
voltage across over the resistance. The
"voltage across" must be expressed by the
difference in node voltages in the nodal
analysis. All in all, I summarize it
- * Node voltage method is actually
"KCL in disguise."
- * Node voltage method applies KCL at
- * Instead of directly using the KCL in
current form, we rephrase the currents (by applying Ohm's
Law) in (voltage across) over (resistance) form.
- Node Voltage vs. "Voltage
- Then, why do we use 'node voltage'
instead of just 'voltage'? It's all because of
equation complexities and the desire to minimize the
number of unknown variables. By the way, voltage
is a potential different between two points. That's
why we use the term 'voltage across' a resistor. Node
voltage is a voltage between a node referred and the designated
reference node (like ground).
- Node Method Application Order
- Here is the order of node voltage method
- a. Select an essential node as the
- b. Remember a node voltage is
a voltage between a node and the reference node
- c. Assign node voltages to the remaining
- d. At each of the nodes, express the
branch currents in terms of node voltages (using
- e. Apply KCL to each node
- f. Solve the resulting simultaneous
equations to obtain the unknown node voltages.