Basic circuit can be analyzed using a few basic analysis tools such as Ohm’s law or Kirchhoff’s laws. But when it comes to large networks, the involved math will be too complex so there should be another way to lessen the calculation. At this point, mesh analysis offer a huge advantage.
Mesh current analysis is known to be effective to simplify the math of electrical circuit analysis. This classic method allows you to define circuit variables such as current or voltage without giving too much effort. Here are some important things you need to know about loop analysis.
What Is Mesh Analysis?
Mesh current analysis is a method used to solve planar circuit to define the voltages and currents at any desired place in the circuit. Planar circuit is an electrical circuit which can be drawn on a surface without crossing wires.
Mesh analysis is sometimes called as loop analysis, though loop analysis is more general. Loop analysis can be used in any kind of circuit, either planar circuits or others. However, mesh current analysis is more suitable for planar circuits as it gives a great advantages especially in calculation.
Both analyses use Kirchhoff’s voltage law (KVL) to define the currents at a specific area. After mesh currents are found, Ohm’s law can be used to determine the voltage at any place.
How to Analyze Using Mesh Current Analysis
Before analyzing a mesh current, it’s essential to know what mesh current means. A mesh current refers to a current which goes around the essential mesh. This current may not correspond to physical current that flows through the electrical circuit but physical current can be found from it.
There are several steps you need to take to analyze using mesh current analysis. The following steps may help you define the current of a planar circuit.
- Check if there is possibility to alternate all current sources in the circuit to voltage sources.
- Assign the directions of current to each mesh in a circuit. Make sure each mesh follows the same direction.
- Apply Kirchhoff’s law to every mesh and then simplify the equations.
- Find the mesh currents by resolving the equations of various meshes. These equations are exactly the same as the quantity of meshes in the network.
It is necessary to make sure all the currents are in the same direction before starting mesh analysis. It helps avoid errors when writing and calculating the equations. The mesh currents mesh loop must be in a clockwise direction.
Instead of applying KCL and KVL, solving mesh currents directly can significantly reduce the required calculation. The reason is that present mesh currents are fewer than physical branch currents.
Equations are essential for mesh analysis. Every mesh comes with one equation. When a voltage source is included in the loop, you need to subtract or add the voltage in a specific condition. When it is a voltage rise, the voltage source should be added. But when it is a voltage drop, subtraction is needed.
If a current source is not contained among two meshes, the mesh current is going to take either positive or negative value of the source. It depends on the direction of the current source, whether in the same or opposite direction. Once the equations are found, you can use any technique to solve the linear equations.
The Special Cases
When it comes to mesh current, there are two special cases: super mesh and dependent sources. Super mesh analysis can be used when unknown voltage passes across the current source. It will be difficult to use basic mesh current method so supermesh technique can be the solution.
A supermesh takes place when a current source exists between 2 essential meshes. In other words, two adjacent meshes have one current source in common. At first, the circuit is considered like the current source does not exist. It will lead to one equation that uses 2 mesh currents which is called super mesh.
When the equation is obtained, another equation is required so that the 2 mesh currents can be related to the current source. In this equation, the current source will be equal to one among the mesh currents subtracted by the other.
Meanwhile, a dependent source refers to a source which depends on current or potential difference of other element in the electrical circuit. If an essential mesh contains a dependent source, the given source should be considered as an independent source.
Once the mesh equation is obtained, another equation for the dependent source is required. The equation is commonly known as a constraint equation. It relates the variable of dependent source to the current or voltage where the source depends on.
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Mesh Analysis vs Node Analysis
Mesh analysis and node analysis are often used interchangeably. Both of them are used in electric circuit analysis and are often considered similar. In fact, mesh current method and node voltage method are different.
When analyzing a circuit, you can use either nodal analysis using KCL or mesh analysis using KVL. While mesh analysis can be used in planar circuits, nodal analysis works effectively to analyze circuits with four or mode nodes.
Nodal analysis is also known as branch current method as it determines the potential difference between nodes or branch connect in electrical circuits. This analysis needs equation at every node.
Nodal analysis delivers a set of equations which is compact for the network. In a small size, it can be solved by hand or using linear algebra when needed. As it offers compact system, a lot of circuit simulation programs use this kind of analysis.
Finding node voltages is pretty simple. The following steps are required to find the node voltages in a circuit:
- Choose a reference node. Determine all the rest nodes voltages with v1, v2, and so on.
- Use Ohm’s law or Kirchhoff’s law to every non-reference branch and node currents.
- Resolve the equation and get the node voltages.