### CIRCUIT ANALYSIS AND TECHNIQUES Node Voltage Method

The wise selection of loop currents can significantly reduce the number of simultaneous equations to be solved in a given problem. Consider the figure below:

Clearly the circuit has 3 essential nodes (n).

• The first step is to select an essential node as a reference node. The choice is arbitrary, the node with the most branches attached is often a good choice. The node 3 is selected as the reference node.
•  Then the node voltages can be defined as the voltage at a given node with respect to the reference node.
• Finally the Kirchoff's current law is applied to all the non-reference nodes.

On the above circuit there are 3 essential nodes, so only 2 equations are needed ((n-1)=2) in order to describe the circuit.

At node 1:

..................(1)

At node 2:

.........................(2)

From ....(1) =>

..........................(3)

From .....(2) =>

..........................(4)

From ......(3) =>

................................(5)

Substitute (5) into (4) =>

...................................(6)

Substitute (6) into (5) =>