2.4:
Mesh Analysis with Current Sources
Mesh analysis is simpler in circuits with current sources because they require fewer equations for analysis.
Consider a two-mesh circuit with a current source in only one mesh.
The mesh currents are assigned, and the branch containing the current source is excluded from mesh analysis.
Kirchhoff's voltage law is applied to the remaining mesh to obtain a linear equation.
As the current in the second mesh is equal in magnitude but opposite in direction to the source current, the simplified equation allows for determining the current in the first mesh.
Now, consider another circuit with a current source between both meshes.
A larger supermesh is created by excluding the current source and elements connected in series with it.
Again, applying Kirchhoff's voltage law to the supermesh results in a linear equation.
Additionally, Kirchhoff's current law is applied to a node where the branch with the current source is connected, yielding another linear equation that links the two branch currents.
The solutions of the simultaneous equations provide the values of the mesh currents.
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.