NodeVoltage

Nodevoltage, commonly referred to as the node-voltage method or nodal analysis, is a systematic technique in circuit analysis used to determine the voltages at the nodes of an electrical circuit relative to a chosen reference node (ground). The method relies on Kirchhoff's current law: at each node, the algebraic sum of currents leaving the node is zero. The essential steps are straightforward: select a reference node, assign a voltage variable to every other node with respect to ground, and write a KCL equation for each node.

Currents through circuit elements are expressed in terms of node voltages. For resistors, the current from node i to node j is (Vi − Vj)/R or, using conductance G = 1/R, G(Vi − Vj). If a voltage source lies between two nonreference nodes, a supernode is formed that encloses both nodes, and the voltage constraint of the source is added as an extra equation. Current sources contribute their specified currents to the KCL equations. The resulting system is a set of linear equations in the unknown node voltages, often written in matrix form as YV = I, where Y is the admittance matrix, V is the vector of node voltages, and I is the current source vector. After solving for node voltages, branch currents and voltages can be computed.

In AC analysis, the method applies in the phasor domain with impedances replacing resistances. Nodevoltage is particularly efficient for circuits with many nodes and resistive networks and is often contrasted with mesh analysis, which can be more convenient for loop-centric problems. Limitations arise with numerous voltage sources and dependent sources, where extended techniques (supernodes, rewriting equations) are required.