Nodal Analysis

A close examination of appearing reveals that the subscript voltage at the node in which kirchhoff's current law is applied is multiplied by the sum of the conductance attached to that node. Note also that the other nodal voltages within the same equation are multiplied by the negative of the conductance between the two nodes.
The current source are represented to the right of the equals sign with a positive sign if they supply current to the node and with a negative sign if they draw the current from the node.

These conclusion can be expanded to include networks with any numbers of nodes. This allows us to write nodal equations rapidly and in a from that is convenient for the use of determined . A major requirement  however is that all voltage sources must first be converted to current source before the procedure is applied . 
        Note the parallelism between the following steps of application and required for mesh analysis in section.


Nodal Analysis Procedure

• Choose a reference node and assign a subscripted voltage label to the (N-1) remaining nodes of the network.
• The number of equations requirement for a complete solution is equal to the number of subscripted voltages (N-1) . Column 1of each equation is formed by summing the conductances tried to the node of interest and multiplying the result by that subscripted nodal voltage.
• We must now consider the mutual terms that as noted in the preceding example, are always subtracted from the first column. In is possible to have more than one mutual term if the nodal voltage of current interest has an element in common with more with more than one other nodal voltage.