The Laws of Circuit - you can learn and practice by just reading

Copyright. Charles Kim 2006

Things to know for Node Voltage Method

First thing you remember is a method is not a law. A method can be derived from a law, though. The nodal analysis or node voltage method comes from the KCL (Kirchhoff's Current Law - Sum of all currents-in is the same as the Sum of all currents-out at a node). So I would love to claim that node voltage method is a KCL in disguise. Then why do we have to disguise, instead of using the law? The main reason is that, if you apply KCL directly to a circuit problem, you may have to apply KVL along with KCL to solve the circuit. In other words, KCL and KCL in their original forms would end up with too many a equation to solve. This does not mean the laws cannot solve the problem. It means that they need to change their shape to minimize the number of equations (or variables). So the 'disguise' fits in here. Second, you have to have a clear understanding on the term 'node voltage'. Again all voltages are defined by two terminals and the potential difference between two (i.e., 'voltage across' a and b is Vab). This does not change at any condition. Then, a node voltage is a voltage between a node and the reference node. The reference node is a node in the circuit but selected as a reference (i.e., ground or 0[V]). That means a node voltage is also a voltage between two terminals (a and ref, or b and ref, etc): Va-ref and Vb-ref. However, since the reference is 0 V level, we can symbolize them as: Va0 and Vb0. Again, since the other terminal is always reference with 0 V, we just ignore the ref terminal in our symbol of node voltage: Va and Vb. But don't be fooled by the notation of the node voltages. They are voltages between two points: the other terminal is always the reference. Third, we apply KCL at a node but currents are to be expressed, by applying Ohm's Law,'voltage across' over resistance.  Then, by KCL, all the sum of currents-in (expresssed by Voltage over Resistance) is the same as the sum of currents-out (expressed by Voltage over Resistance) at a node. Fourth, once you have an equation at a node, make sure every term must be of current, whether current directly from a current source or a current expressed by voltage over a resistance.

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