2.4 : Mesh Analysis with Current Sources

Mesh analysis becomes simpler when analyzing circuits with current sources, whether independent or dependent. The presence of current sources reduces the number of equations required for analysis. Two cases illustrate this:

Current Source in One Mesh: The analysis process is straightforward when a current source is found in only one mesh within the circuit. Mesh currents are assigned as usual, with the mesh containing the current source excluded from the analysis. Kirchhoff's voltage law (KVL) is applied to the remaining mesh, resulting in a linear equation. Since the current in the mesh with the source is equal in magnitude but opposite in direction, it allows for easy determination of the current in the first mesh.

Current Source Between Two Meshes: In cases where a current source lies between two meshes, the analysis can be simplified by creating a supermesh. This involves excluding the current source and any elements connected in series with it. Applying KVL to the supermesh yields a linear equation. Additionally, Kirchhoff's current law (KCL) is applied to a node where the branch with the current source is connected, providing another linear equation linking the two branch currents. Solving these equations provides the values of the mesh currents.

Critical properties of a supermesh include:

• The current source within the supermesh imposes a constraint equation necessary for solving the mesh currents.
• A supermesh does not have its own current; it encompasses currents from the individual meshes it encloses.
• KVL and KCL are applied to a supermesh like any other mesh.