Nodal analysis

Nodal analysis is a systematic method for determining the voltages at each node of an electrical circuit relative to a reference node (ground). It applies Kirchhoff's current law at each node to generate a set of linear equations, which can be solved by matrix inversion or Gaussian elimination. The method is particularly efficient for circuits with many parallel branches, where mesh analysis would produce more equations than necessary. Nodal analysis is the computational backbone of modern circuit simulators such as SPICE, which use modified nodal analysis to handle voltage sources and dependent sources. The voltage at each node is not merely a numerical quantity; it is a coordinate in the circuit's state space, and nodal analysis is the map from component values to that coordinate system.