Nodal analysis:is a method of determining the voltage (potential difference) between "nodes" (points where elements or branches connect) in an electrical circuit in terms of the branch currents.

In analyzing a circuit using Kirchhoff's circuit laws, one can either do nodal analysis using Kirchhoff's current law (KCL) or mesh analysis using Kirchhoff's voltage law (KVL). Nodal analysis writes an equation at each electrical node, requiring that the branch currents incident at a node must sum to zero. The branch currents are written in terms of the circuit node voltages.

• Node:

A point in a circuit where terminals of atleast two electric components meet. This point can be on any wire, it is infinitely small and dimensionless.

• Major Node:

This point is a node. A set of these nodes is used to create constraint equations.

• Reference Node:

The node to which Voltages of other nodes is read with regard to. This can be seen as ground ( V = 0).

• Branch:

This is a circuit element(s) that connect two nodes.

Manual Nodal Analysis Algorithm:

1.) Choose a reference node. ( Rule of thumb: take the node with most branches connecting to it )

2.) Identify and number major nodes. ( Usually 2 or 3 major Nodes )

3.) Apply KCL to identified major nodes and formulate circuit equations.

4.) Create matrix system from KCL equations obtained.

5.) Solve matrix for unknown node voltages by using Cramer's Rule (Cramer's Rule is simpler, although you can still use the Gaussian method)

6.) Use solved node voltages to solve for the desired circuit entity.

Case 1: If the voltage source (dependent or independent) is connected between two non-reference nodes, the two non-reference nodes form a generalized node or supernode, we apply both KCL and KVL to determine the node voltages.

Case 2: if a voltage source is connected between the reference node and a non-reference node, we simply set the voltage at the non-reference node equal to the voltage of the voltage source

A supernode is formed by enclosing a (dependent or independent) voltage source connected between two non-reference nodes and any elements connected in parallel with it.

In figure 2 node 2 and node 3 form a supernode. Applying KCL at super node which are node 2 and 3 we get,

                                        i₁ + i₄  = i₂ + i₃

To apply KVL redrawing the figure 2 circuit to figure 3 and going around the loop in the clockwise direction gives,

                       – v₂ + 10 + v₃ = 0

                        Or  v₂ – v₃ = 10      ————————— (ii)

From equation (i),(ii) we will obtain node voltages using any solution method.

With Dennis James Matildo