# Nodal Analysis

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## nodal analysis

[′nōd·əl ə′nal·ə·səs]
(electricity)
A method of electrical circuit analysis in which potential differences are taken as independent variables and the sum of the currents flowing into a node is equated to 0.

## Nodal Analysis

(or nodal method), a method of analyzing linear electric networks, that is, a method of determining the currents in the branches of such a network and the voltages between the terminals of the passive elements and active elements (sources of energy) in the network.

In nodal analysis the voltages at the nodes of the network are taken as the unknown quantities. The known quantities are the input impedances (or admittances) of the passive elements and the internal impedances (or admittances) and electromotive forces (or currents) of the active elements. One node is chosen as a reference, or datum, node; the potential at the reference node is usually taken to be zero. Equations are written for all the other nodes in accordance with Kirchhoff’s first law, each of the unknown currents being expressed in terms of the impedances, the electromotive forces, and the voltages at the nodes in accordance with the impedance form of Ohm’s law.

If n is the number of nodes in the network, then n – 1 independent simultaneous equations are obtained. From these equations the voltages at the nodes can be obtained (the voltage at each node is equal to the voltage between the node and the reference node). The branch currents and the voltages between the terminals of the active and passive elements can then be found by means of Ohm’s law. If the voltages for some pairs of nodes are given or the currents in some branches are known, the number of equations is less than n – 1. The equations can be written and solved in matrix form.

It is usually simpler to use nodal analysis than mesh analysis (seeMESH CURRENT METHOD) when the nodal method yields a smaller number of independent equations. The nodal method is particularly effective for networks having parallel branches—for example, a network with only two nodes.

### REFERENCES

Polivanov, K. M. Lineinye elektricheskie tsepi s sosredotochennymi postoiannymi. (Teoreticheskie osnovy elektrotekhniki, vol. 1.) Moscow, 1972.
Osnovy teorii tsepei. Moscow, 1975.

B. IA. ZHUKHOVITSKH

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