Nodal and Mesh Analysis Simplification by Introducing a Theorem-Based Preliminary Step

This brief proposes a new and simplified method for the analysis of linear circuits that combines the classical mesh-current or node-voltage method with a recently-stated theorem. The beforehand application of such a theorem, which involves the insertion of an open or short circuit, in a circuit with N meshes or nodes results in a system of N - 1 linear equations for N - 1 unknowns, instead of N equations for N unknowns obtained using the conventional approach. Therefore, if the circuit is analyzed in matrix form, the resulting coefficient matrix is square of order N - 1, instead of N, thus facilitating the hand calculations. Examples of circuit analysis are provided to demonstrate the applicability and advantages of the proposed analysis method in comparison with the conventional approach.

Automated summary

This brief introduces a new and simplified method for analyzing linear circuits, which combines classical mesh-current or node-voltage methods with a recently-stated theorem. By applying this theorem, a simplified system of linear equations can be obtained, making the analysis process easier compared to the conventional approach.