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The Nodal Analysis - Definition, Features and Examples

The Nodal Analysis – Definition, Features and Examples

Bobbi Smith
Bobbi Smith
September 27, 2022
The nodal analysis is a way to extract the voltage between the nodes. Now, you must be wondering about what node is. Those are the points where the branches or elements get connected. You can now use nodal analysis with the help of Kirchhoff’s circuit law. The nodal analysis method helps clarify a circuit’s proper voltage.

What is nodal analysis?

What is nodal analysis?
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Nodal analysis is a process through which circuits can be analyzed. Here, you need to use the node voltages as the circuit variable. Another name for node analysis is node voltage method.

The following are some Nodal Analysis features:

  • Based on Kirchhoff’s Current Law, nodal analysis is built (KCL).
  • There will be “n-1” simultaneous equations to solve with “n” nodes.
  • You can find The nodes’ voltages by solving ‘n-1’ equations.
  • The number of possible nodal equations equals the number of non reference nodes.

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Learn how to use reference node

Learn how to use reference node

When employing Nodal analysis to solve any electrical network or circuit, the following are the steps.

Choose one of the central nodes to serve as the reference node in nodal system steps.

  • Step 1. That reference node will be regarded as the Ground.
  • Step 2: Label all primary node voltages concerning Ground, excluding the reference node.
  • Step 3: Leaving the reference node, write nodal equations at each central node. KCL is used first, followed by Ohm’s law, to produce the nodal equation.
  • Step 4: To get the node voltages, solve the nodal equations you received in Step 3. We can now identify the stream flowing.

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Node types in a nodal analysis

Node types in a nodal analysis
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Non Reference Node: A non reference node has a fixed Node Voltage. e.g., The Non Reference Nodes, in this case, are Node 1 and Node 2.

A reference node serves as a point of reference for all other nodes in the network. The Datum Node is another name for it. Electrical Sources

Independent and dependent electrical sources are the two categories under which they fall.

A circuit is connected to a separate electrical source that outputs a predetermined amount of current or voltage. The only sources here are power supply and batteries. In this case, the power supply provides a stable fixed value while the batteries eventually provide a stable, limited value without recharging. You must know the node voltage analysis as well.

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Linear Dependent Sources

The four categories of linearly dependent sources are as follows.

  • Voltage-controlled voltage source
  • Current-controlled current source
  • Current-controlled voltage source
  • Voltage-controlled current source
  • You will be able to observe a number of nodal equations.

The o/p of a voltage-controlled voltage source is “V,” the voltage gain is “AV,” and the parameter being detected is “VCD.” This linear dependent source is related by the equation shown below.

V = Av VCD

In a voltage source controlled by current, the o/p is V, the resistance is RM, and the measured parameter is IC. The equation below can be combined through a nodal analysis with  voltage source with current control.

V = RvM IC

The current gain and the parameter detected are the o/p and Ai, respectively, in the current-controlled current source. A current-controlled current source can be used to connect the following equation.

I = AI Ic

The o/p in a voltage-controlled current source is “I,” the conductance is “GM,” and the parameter being measured is “VCD.”

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Differences between nodal analysis and mesh

Differences between nodal analysis and mesh
The following are some ways that mesh and nodal analysis differ from one another.

In contrast to mesh analysis, which uses current values in a specific branch of a circuit, nodal analysis of electricity systems allows for observing voltages at a given unit.

Mesh analysis is one technique used in the electrical network to solve planar circuits, specifically for the current flow at any branch. Without putting any wires in contact with one another, these circuits can be sketched on a flat surface. Any course employs a more all-encompassing technique called loop analysis.

The KCL (Kirchhoff’s Current Law) application is necessary for nodal analysis. There will be “n-1” instantaneous equations to solve if the circuit has n nodes.

Fundamental Procedures in Nodal Analysis

Fundamental Procedures in Nodal Analysis
To serve as 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’s law.

Node consistently expects that the current in a resistor moves from a more significant potential to a lower potential. The following is how current is expressed.

Nodal analysis with current source

Nodal analysis with current source

The following nodal analysis examples include a discussion on using nodal analysis. Also, it uses an electrical circuit.

In the below-mentioned circuit, we can see three nodes. One is a reference node, and the other is nonreference nodes – Node 1 and Node 2. The above mentioned nodal diagram creates a clarity in electrical circuit.

Calculate the nodal voltage for the circuit in the example below. The nodal voltages also play a vital role here.

The following circuit has three nodes, one of which is a reference node and the other two nonreference nodes, such as nodes 1 and 2.


Node voltages are denoted with the letters v1 and v2 in step 1, and branch current directions can also be marked about the reference point nodes.

Step 2:

Apply Kirchoff’s current law to two nodes, such as nodes 1 and 2, in this stage.

When the circuit as mentioned above node 1 is subjected to the Kirchoff current law

i1 =i2+i3…… (1)

Likewise, at node 2

i2+i4 = i1+i5… (2)

Step 3:

When KCL equations are used with Ohm’s law

Using the elimination process

20 = 3V1-V2

60 = -3V1+5V2

4V2 = 80

V2= 20

When V2 = 20 is used as a substitution in equation (3), we obtain

20 = 3V1-V2

20 = 3V1-20 => V1 = 40/3 = 13.3 V

Consequently, the definite node voltage such as v1 = 13.33 V & v2 = 20 V is observed.

Similar calculations can be made for nodal analysis with voltage source.

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What is a Super Node?

What is a Super Node?

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A voltage source linked between the two non-reference nodes forms a generalized node. The specific node is referred to as the super node.

Specifications of supernode nodal analysis

Below are the characteristics of Supernode analysis 

  • At the super node, it is possible to calculate the voltage difference between two non-reference nodes.
  • Supernodes lack their internal voltage.
  • Kirchhoff’s voltage law and Kirchhoff’s current law are used to solve the super node.
  • You can also check it with a nodal analysis calculator.

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Frequently Asked Questions

What is nodal analysis?

Nodal analysis is a method of calculating voltage distribution among the circuit. The nodal equations obtained from the calculation help solve problems of an electrical circuit.

What is the nodal analysis formula?

Identification of the principal nodes is essential when dealing with the nodal analysis of the electrical circuit.

What are the steps of nodal analysis?

Here are the steps of nodal analysis. One can apply it to all the node voltages.

  1. List every node.
  2. Select a referencing node. Use the reference (Ground) symbol to identify it.
  3. Give the other nodes voltage parameters (these are node voltages.)
  4. For every node, create a KCL equation (sum the currents leaving the node and set equal to zero).

Where is a nodal analysis used?

Nodal analysis is an optimization technique used to identify and forecast solutions to production issues. It can be used in an electrical circuit. This method may indicate a well’s inflow performance. Also, you can get critical pressure for artificial lifts.

It will allow the fresh bailing operation to be scheduled appropriately. The skin damage inside an existing well can also be estimated using this method, and the results can be utilized to support digging farther or re-stimulating the new.

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