Nodspänningar

Nodspänningar, or node voltages, are the electrical potentials measured at the junctions of components within an electrical circuit. In the context of circuit analysis, the term refers to the set of voltages that determine the operating state of the network. By definition, the voltage at a node is set relative to a reference node, often called the ground. All other node voltages are expressed with respect to this reference.

The concept of nodspänningar underpins nodal analysis, a systematic method for solving linear electrical networks. The technique requires selecting a reference node and writing Kirchhoff’s current law (KCL) equations for each of the remaining nodes. Each equation expresses the algebraic sum of currents leaving that node as equal to zero. The currents are expressed in terms of node voltages and the admittances of the connecting impedances, yielding a linear system of equations that can be written in matrix form. Solving this matrix, usually via Gaussian elimination or matrix inversion, produces the unknown node voltages. Once the node voltages are known, branch currents and other circuit variables can be derived easily.

A simple illustrative example is a two‑node circuit: a voltage source in series with a resistor connected to a load resistor. Writing KCL at the non‑ground node gives the familiar voltage divider formula. In more complex networks with multiple sources and impedances, nodal analysis provides a more efficient approach than mesh analysis, especially when the number of nodes significantly exceeds the number of mesh loops.

Nodspänningar are foundational in both analog and digital circuit design, providing the basis for simulation tools such as SPICE. They also appear in power distribution networks, adaptive signal processing, and in the theoretical study of electromagnetics where the concept of node potential continues to be generalized to multidimensional field problems.