Teilvermaschte

Teilvermaschte (German for “partial mesh”) is a term used in electrical circuit theory and network analysis to denote a subset of a complete mesh (or loop) within a planar circuit. While a full mesh comprises a closed path that encloses no other meshes, a Teilvermaschte represents a smaller, often convenient, loop that may share branches with other meshes or lie entirely inside a larger one. The concept assists in simplifying the application of Kirchhoff’s voltage law (KVL) when the circuit contains numerous interconnected loops.

In practice, engineers identify Teilvermaschten to reduce the number of simultaneous equations required for analysis. By selecting strategically placed partial loops, currents can be expressed in terms of a limited set of mesh currents, easing the solution of linear systems derived from KVL. The method is particularly valuable in circuits with dependent sources, transformers, or bridge configurations where a full-mesh approach would generate redundant equations.

Mathematically, a Teilvermaschte is defined by a set of branch impedances and voltage sources that together form a closed contour. The algebraic sum of the voltage drops around this contour equals zero, consistent with KVL. When multiple Teilvermaschten are used, their equations must be combined with appropriate constraints to avoid over‑determination.

The notion of partial meshes is related to the loop‑current method, supermesh technique, and graph‑theoretic approaches such as spanning tree analysis. In modern computer‑aided design (CAD) tools, algorithms automatically detect optimal Teilvermaschten to streamline circuit simulation and synthesis.