Maschenstromanalyse

Maschenstromanalyse, also known as mesh‑current analysis, is a systematic technique used in electrical engineering for determining the currents flowing in the fundamental loops (meshes) of a planar circuit. The method applies Kirchhoff’s Voltage Law (KVL) to each independent mesh, generating a set of linear equations that can be solved simultaneously. It is particularly useful for circuits that are two‑dimensional, where all elements lie in a single plane and no components cross each other.

The procedure begins with the identification of independent meshes, followed by the assignment of a hypothetical mesh current to each loop, usually in a consistent clockwise or counter‑clockwise direction. For every mesh, KVL is written by summing the voltage drops across resistors, voltage sources, and other elements, expressed in terms of the mesh currents. When a component lies on the border of two meshes, its voltage contribution includes the difference of the adjacent mesh currents. The resulting system of equations is then solved using algebraic methods such as substitution, matrix inversion, or computer‑assisted techniques.

Maschenstromanalyse offers advantages over nodal analysis in circuits where the number of meshes is smaller than the number of nodes, leading to fewer equations and reduced computational effort. It also provides direct insight into loop currents, which can simplify the evaluation of power dissipation and the design of protective devices. However, the method is limited to planar circuits; for non‑planar (three‑dimensional) networks, the technique must be combined with other approaches or transformed into an equivalent planar representation.

In practice, the mesh‑current method is taught in undergraduate courses on circuit theory and is implemented in many electronic design automation (EDA) tools for the analysis of printed‑circuit boards, power distribution networks, and analog integrated circuits.