Mesh current analysis is known as an effective method to determine the current and potential difference of planar circuits. But when it comes to branched-circuits, node voltage method is more suitable to define the voltage.
Also known as branch current method, it uses Kirchhoff’s laws as the basis of analysis. When mesh analysis uses Kirchhoff’s voltage law (KVL) to conduct the, node analysis uses Kirchhoff’s current law (KCL) to define the voltage between nodes.
What Is Node Analysis?
Before proceeding any further, it’s essential to know what node analysis is. Node analysis or nodal voltage analysis is a specific method used to determine the potential difference (voltage) between branches or nodes in an electrical circuit.
In layman’s terms, node analysis is the right method to analyze circuits with four, five, or more nodes in it. Nodes can be described as points where wires or branches connect in an electrical circuit, including DC circuit.
Kirchhoff’s current law is used to conduct the analysis. It also uses nodal equations, which means equation for each node to determine the potential differences around the electrical circuit. After getting all the nodal voltages, the sum of all the voltages must be zero.
Given that, supposing that there are n nodes, there must be n-1 nodal equations. Resolving the equations will be sufficient to define and resolve the electrical circuit.
Node Analysis Procedure
There are some specific procedures to conduct node voltage method. The procedures include noting all the connected wires (nodes) and choose one to become the reference. Please note that the reference does not generally effect the final result as it is only convention matter.
To make it easier, nodal analysis procedures will be explained in the following steps.
- List all the existing nodes in the electrical circuit. The nodes can be found from the connected wire segments.
- Choose one note as a reference node. To simplify the analysis, make sure to choose a node which has the most connections. A circuit with ‘n’ nodes must have nodal equations as many as ‘n-1’.
- If there are nodes with unknown voltage, determine a variable of each node. For nodes which potential difference is already known, determining a variable is not necessarily needed.
- For each node with unknown potential difference, use Kirchhoff’s current law to form an equation.
- Resolve the equation and get the voltages. The obtained current between two points is the same as the branch with higher potential subtracted by the branch with lower potential.
In some cases, voltage source may present among two unknown voltages. In this condition, the two nodes must be joined and it is known as supernode. This kind of node requires different node voltage method which will be discussed later.
Basic Nodes and Super Nodes
Generally, there are two types of nodes in electrical circuits: basic nodes and supernodes. Each type of node comes with different characteristics which require different analysis method to determine the potential difference.
Basic nodes or basic case is where a circuit only have one unknown voltage. As the name implies, this case is simple to solve and calculate. This kind of circuit typically has three or more nodes which currents are already known.
After knowing the direction of the currents, use Kirchhoff’s current law to solve the equation. This is how you can solve the unknown voltage. Once the unknown voltage is obtained, the unknown currents can be calculated easily.
On the other hand, supernodes occure when an electrical circuit has two unknown voltages. It requires supernode technique in which the nodes are combined in one equation. Then, another equation for potential difference is required. In this method, the currents of the joined nodes must be zero.
Even the littlest thing in this world has advantages. Many people consider that node analysis is better for analyzing circuit. What makes node analysis more preferred than other methods? There are some benefits of using node voltage method to define the potential difference.
Compared to other electrical circuit analysis such as mesh current analysis, Kirchhoff’s law, or Thevenin’s theorem, node analysis offers a number of advantages. Aside from being a general analysis method, other advantages include:
- Node analysis offers a direct solution for node voltages. When using this method, the potential differences can be found without involving complex math calculation.
- This method works effectively for electrical circuits with several nodes. Unlike mesh analysis that works best for planar circuits, node analysis can be used for ‘branched circuits’.
- Although it works best for circuit with nodes, node analysis also works well for any circuit. In other words, this method is more general than other circuit analysis.
- Current and voltage sources can be easy.
Nodal Analysis vs Mesh Analysis
As circuit analysis methods, both nodal analysis and mesh analysis are often considered similar. As a matter of fact, node analysis is considered more general than mesh analysis as it works well for any circuits.
There are some other differences such as the variables. While nodal method uses nodal voltages as circuit variables, mesh method uses mesh currents as its variables. It allows you to significantly reduce equations that must be resolved.
Besides, nodal method uses Kirchhoff’s current law to determine nodal potential difference while mesh method incorporates Kirchhoff’s voltage law to define the mesh currents. Additionally, mesh is planar network without branches while node is a circuit with a few branches.
When it comes to analysis procedure, mesh method is far simpler than node method. It requires at least three steps: assign mesh currents, apply Kirchhoff’s law, and resolve the equations simultaneously. However, both node and mesh analysis also have super case which requires different analysis technique.
Things to Note
When it comes to node voltage method, there are some important things to keep in mind to help understand this circuit analysis method. Before resolving the current for each node, assume that the unknown current of each branch is considered one. Besides, it is also necessary to follow the same sign convention. The currents are considered positive when entering the node, while currents are considered negative when leaving the node. The last but not least, converting the existing voltage source into equivalent current sources can also be conducted.