Method
The MNA uses the element's Branch Constitutive Equations or BCE, i.e., their voltage - current characteristic and the Kirchhoff's circuit laws. According to the method is done in four steps, but it can be reduced to three.
Step 1
Write the KCL of the circuit. At each node of an electric circuit one writes the currents coming in and out of the node. Take care however in the MNA the current of the independent voltage sources is taken from the "plus" to the "minus". See Figure 1. Also note that the right hand side of each equation is always equal to zero. So that the branch currents that come inside the node are given a negative sign, whereas the branch currents coming out are given a positive sign.
Step 2
Use the BCE in terms of the node voltages of the circuit to eliminate as many branch currents as possible. Writing the BCE's in terms of the node voltages saves one step. If the BCE's were written in terms of the branch voltages, one more step, i.e., replacing the branches voltages for the node ones, would be necessary. In this article the letter "e" is used to name the node voltages, while the letter "v" is used to name the branch voltages.
Step 3
Finally, write down the unused equations.
Read more about this topic: Modified Nodal Analysis
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