Download 04_Nodal Method for Circuit Analysis

ELC3314, Nodal Method, Feb. 03, 2017
Nodal Method for Circuit Analysis, AKA “The Circuit Solution Method of Choice”
A node is an equipotential surface, such the junction of two or more branches (i.e., wires, circuit
elements such as resistors, voltage sources, and current sources, etc.)
The reference (i.e., “ground”) node is the one at which the user defines as have zero voltage.
“Major” nodes are those having three or more non-combinable circuit elements attached to them.
Supernodes are perfect voltage sources having no series resistance, connected directly between two
nodes other than the reference node.
Having solved N equations and N unknowns for voltages at all major nodes, the circuit is considered
“solved,” and all branch voltages and currents can be found afterward.
Procedure:
1. Pick a reference node, “i.e., “ground”, to which all other node voltages are referenced. The
reference node is usually at the bottom of a circuit. Reference node voltage is zero by
definition.
2. Identify major nodes and supernodes, and wrap each in an imaginary surface for KCL equations
so that every “puncture” of the surface is easily identified. Supernodes connected to major
nodes are merged with those major nodes to become one super node.
3. If it helps, branch elements in series can be re-arranged in any order for the purpose of writing
KCL equations at major nodes.
4. Current sources – treat them as injectors (plus or minus) at the two nodes to which they are
connected.
5. Write Kirchhoff current law equations (KCL) for each major node, except the reference (because
its voltage is already zero).
6. Place the KCL equations in standard matrix form, and solve for major node voltages using
Gaussian Elimination.