The nodal analysis is a popular method of circuit analysis. We use nodal analysis very often. It is a very straight forward method of solving circuit parameters. Besides, it is also simple. Here we follow a few steps. These steps are enough to find out the different parameters of a circuit. The steps are as follows.
Steps of Nodal Analysis
Firstly, we have to find out the necessary junction points (nodes) in the circuit. Here, we only consider the junctions which connect more than two branches. The junctions connecting only two branches do not come into our consideration for nodal analysis.
Secondly, we define arbitrary voltages to selected nodes. Also among those nodes, we assign zero potential arbitrarily to one node.
Thirdly, we express the current through the branches. We do it, by dividing the voltage difference across the branch by its impedance. It is one of the main tasks of nodal analysis.
Fourthly, we write one KCL equation for each considered junction. We do it with the current expressions and with the real current of any other branch connected to the node.
Lastly, we solve those KCL equations. Then, we get the required parameters of the circuit.
Example of Nodal Analysis
Let us take an example.
Here, in the above figure, there are two nodes where three branches meet. We name these nodes as A and B.
Now, we consider V as the voltage of node A. At the same time we connect node B to the ground. We do this to make the voltage of node B to zero. Although for nodal analysis purpose, we might have made node A grounded, instead. In that case, we had to assign voltage V at node B.
Then we concentrate on node A. First we assume that the voltage of this node is maximum for the time being. It is the general practice to assume the dealing node as the maximum potential point of the circuit. So, the expression of the current from A to B through the 200Ω resistor is
The expression of the current from A to B through the central 100Ω resistor is
Lastly, the expression of the current from A to B through the right side 100Ω resistor is
Now, we apply Kirchhoff’s Current Law at node A, we get
At last, we solve the above equation. Then, we get,
So, we have got the value of V. Hence, we can easily get the value of branch currents, too, from their expression. So we have seen how simple is the nodal analysis.
Here, we should note that in our example, we have assumed all the branch currents were leaving from node A. After putting the value of the node voltage in any current expression we get either a negative or a positive value of current. If it is positive, then our assumption was correct. That means in the practical circuit, the direction of the current was outward of the node. But if it is negative, then we can say the direction of current was inward the node.
Nodal Analysis with a General Circuit
Let us take a circuit as shown below.
Here, A, B, and C are only those nodes of the circuit which connect more than two branches. First, we assign arbitrary voltage VA and VB at node A and B, respectively. Also, we make grounded the third node that is C.
The KCL for node A and node B are as follows.
By solving these two equations, we get the value of VA and VB and thereby currents in each branch of the circuit.
Nodal Analysis with Current Sources
Now we discuss the nodal analysis with one or more current sources or current in one or more branches.
Here, one branch connected with node B has a current I. E is the emf of the voltage source connected to node A. Now the KCL at node A and node B are as follows.
By solving these two equations, we get the value of VA and VB.
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