Nodal Analysis

Nodal analysis is a general method for simplifying circuit analysis by using node voltages as circuit variables.

Consider a circuit with three nodes and three resistors.

To find the node voltages in this circuit, first, a reference or datum node is selected, whose voltage is assigned to be zero.

The remaining non-reference nodes are assigned nodal voltages relative to the reference node.

Next, applying Kirchhoff's current law to the non-reference nodes 1 and 2 gives the relation between the branch currents.

Further, using Ohm's law, the branch currents passing through the three resistors are expressed in terms of the node voltages.

Now, the values of the branch currents can be substituted into the equations obtained using Kirchhoff's current law to get two simultaneous equations.

For a circuit with n nodes, n - 1 independent equations are obtained.

If the values of the resistors and source currents are known, they can be substituted into the two equations, which can then be solved to obtain the node voltages.