nodanalys

Nodanalys, or nodal analysis, is a method in circuit analysis used to determine the voltages at the nodes of an electrical network relative to a reference ground. The technique is grounded in Kirchhoff's current law (KCL), which states that the algebraic sum of currents entering a node is zero.

The procedure begins by selecting a reference node (ground) and identifying essential nodes—points in the circuit where currents meet and are not simply connected by a single element. For each essential node, KCL is applied to form a linear equation in the unknown node voltages. Currents through impedances are expressed in terms of node voltages, typically as (V_node − V_other)/Z or V_node/Z for elements connected to a ground. In circuits containing voltage sources between non-reference nodes, a supernode is formed, and additional equations relate the voltages to the sources.

The resulting system of linear equations is solved to obtain the node voltages. Once node voltages are known, branch currents and power in each element can be computed from Ohm's law or impedance relations. Nodanalys is readily extended to alternating current (AC) analysis by using impedances in the complex domain or to time-domain problems via Laplace-transformed impedances. A common practical variation is modified nodal analysis (MNA), which augments the equations to accommodate voltage sources and dependent sources more systematically and is widely used in circuit simulators such as SPICE.

Nodanalys is valued for its systematic handling of networks with many nodes and its clear separation between topology and element values, making it a fundamental tool in electronics and electrical engineering.