Nodal Analysis: Process, Types, And Examples

Do you have doubts about the nodal analysis method? It’s time to sort it out with good examples and explanations. The nodal analysis uses the general process of analyzing the circuit. Also, the node voltages are used as the circuit variables.

The circuits can be analyzed with the help of Kirchhoff circuit law. Again, Kirchhoff’s voltage law should be used if you want to go ahead with the mesh analysis.

Features Of Nodal Analysis Method

You can easily find a variety of features in nodal analysis. The following points are the vital characteristics of the node voltage method or node voltage analysis.

• The alphabet ”n” denotes the node. Also, when n= 1, solving the simultaneous equation is possible with the reference node.
• Kirchhoff’sKirchhoff’s current law (KCL) and its application are the basis of the Nodal Analysis.
• As you further solve the nodal equations, solving n-1 is essential.
• Here, it is pretty interesting to observe that the number of non reference nodes will equal the number of nodal equations.

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How Many Nodes Are Present In Nodal Analysis?

You will be able to observe two types of nodes in nodal analysis. Following is a highlight of it.

Reference Node

It is a node that serves as a focal point for all other nodes. The Datum Node is another.

Non Reference Node 

It is a node with an apparent Node Voltage, such as Nodes 1 and 2 in our example, which are the Non-Reference nodes. It is also called the variation with definite node voltage.

Reference Node Types

Chassis Ground: This reference node is a common node for multiple circuits.

Earth Ground: This type of reference node is known as Earth Ground when earth potential is utilized as a reference in any circuit.

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Circuit Solving Using Nodal Analysis

Fundamental Procedures in Nodal Analysis

• To get the reference node, pick a node. Give the remaining nodes voltages V1, V2,…, Vn-1. About the reference node, the voltages are referred to.
• To each of the non-reference nodes, apply KCL.
• To translate branch currents into node voltages, use Ohm’sOhm’s law.
• Node consistently expects that current in a resistor moves from a more significant potential to a lower potential. The following is how current is expressed. Instead, it speaks about the nodal analysis with current source.
• Get the “n-1” node equations in values of node voltages & resistances after using Ohm’sOhm’s Law.

You can get suitable node voltages. You can solve “n-1” node equations given the values of the node voltages.

Case I: Nodal Analysis Using Voltage Sources If a voltage supply is connected between the node and a non-reference node.

 We can analyze the voltage source by setting the voltage at the non-reference node to the same value as the energy of the voltage source. V1 = 10 volts.

Case II. If the voltage source forms a supernode with the two non-reference nodes, the supernode analysis is performed as follows.

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Supernode Analysis Supernode Definition

When a voltage source, whether independent or dependent, is linked between the two

Supernode Properties

• The voltage difference between any two non-reference nodes at Supernode is always known.
• A supernode has no internal voltage.
• To solve it, KCL and KVL must be applied to a supernode nodal analysis.
• Any element may be linked in parallel with the voltage source constituting the Supernode.
• A Supernode meets the KCL requirements just like a regular node.

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Way To Solve Any Circuit With Supernode

To know the specific way to solve a circuit that contains Supernode following circuit must be considered:

In the above mentioned circuit, you can see that there is a connection between Node 1 and Node 2. Also, the main voltage source over here is 2V. As a result, a supernode is formed with the 10Ω resistor.

You should also note that there will be no difference if any of the elements has a parallel connection. Also, the nodal voltages that form the super node doesn’tdoesn’t make any difference. Always, V1- V2 = 2V.

In addition, there is a provision for 10 Ω electrical circuit to be removed. After that, application of KCL to the super node is represented below:

How To Do Nodal Analysis: Process

When utilizing the node analysis to solve any electrical circuit, you must follow the nodal system steps below:

Step 1:

Choose one to serve as a reference node to determine the central nodes. We shall consider this reference node to be the ground.

Step 2:

Except for the reference node, all node voltages concerning ground from all primary nodes should be labeled.

Step 3:

Each primary node should have a nodal equation, excluding the reference node. Kirchhoff’s current law is used to get the nodal equation, then Ohm’s law.

Step 4:

You can use Step 3 to derive the nodal equations and acquire the node voltages.

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Nodal Analysis Examples Determining Node Voltages

Suppose the above circuit is given to the student. They must determine all the node voltages.

Solution.

The above figure shows the number of nodes present in the particular circuit is 3. Also, each principal nodes in the electrical network is numbered below.

Using Kirchhoff’sKirchhoff’s current law at each node, we get

Node 2 is the reference point. Also, this node’s voltage will be zero.

Using Kirchhoff’sKirchhoff’s current law within each of the nodes, we get

V130+V1−1005+V1−V310=0

(eq.1)This is a result of KCL at node 1

V3−V110+V310+V320=0

(eq.2)This is a result of KCL at node 3

(130+15+110)V1−(110)V3=1005

−(110)V1+(110+110+120)V3=0

Solving the above equations, we get

V1 = 68.2v

V3 = 27.3v

Example 2

Look at the above circuit or the nodal diagram. Here, you will find figuring out voltage va quite quickly. Here, node a connects to the voltage source and the reference node c. As a result, it becomes an accessible node. Here Va = 140 V.

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