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4. Circuit analysis using matrix methods
Consider a circuit made up of B branches connected to N nodes. Analysis of the circuit is complete if we know the voltages across these B branches and the currents flowing through them. Since currents are deduced from voltages (and vice versa), it seems that B unknowns are needed to analyze the circuit. In fact, since the branches form meshes and the nodes are each connected to one or more branches, verification of Kirchhoff's laws shows that the number of independent unknowns required to analyze the circuit is less than B.
4.1 Choice of unknowns
To determine the number of independent unknowns, we start by defining a tree for the circuit: this is a set of N – 1 branches of the circuit that form no closed contour. For example, for the circuit of
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Circuit analysis using matrix methods
Analysis by state variables
