Mesh Analysis

Mesh Analysis

Mesh analysis (or the mesh current method) is a method that is used to solve planar circuits for the currents (and indirectly the voltages) at any place in the circuit. Planar circuits are circuits that can be drawn on a plane surface with no wires crossing each other. A more general technique, called loop analysis (with the corresponding network variables called loop currents) can be applied to any circuit, planar or not. Mesh analysis and loop analysis both make use of Kirchhoff’s voltage law to arrive at a set of equations guaranteed to be solvable if the circuit has a solution. Mesh analysis is usually easier to use when the circuit is planar, compared to loop analysis.

Steps to determine mesh currents:

1.)    Assign mesh currents i1,i2, . . . . in to the n meshes.

2.)    Apply KVL to each of the n meshes. Use Ohm’s law to express the voltages in terms of the mesh currents.

3.)    Solve the resulting n simultaneous equations to get the mesh currents

Essential meshes of the planar circuit labeled 1, 2, and 3. R₁, R₂, R₃, 1/sc, and Ls represent the impedance of the resistors, capacitor, and inductor values in the s-domain. V_s and i_s are the values of the voltage source and current source, respectively.

 Circuit with mesh currents labeled as i₁, i₂, and i₃. The arrows show the direction of the mesh current.

What is Super mesh?

A super mesh occurs when a current source is contained between two essential meshes. The circuit is first treated as if the current source is not there. This leads to one equation that incorporates two mesh currents. Once this equation is formed, an equation is needed that relates the two mesh currents with the current source. This will be an equation where the current source is equal to one of the mesh currents minus the other. The following is a simple example of dealing with a super mesh.

 

Circuit with a super mesh. Super mesh occurs because the current source is in between the essential meshes.

OVERVIEW AND INSIGHTS

A mesh current is a current that loops around and the equations are set solved in terms of them. A mesh current may not correspond to any physically flowing current, but the physical currents are easily found from them. It is usual practice to have all the mesh currents loop in the same direction. This helps prevent errors when writing out the equations. The convention is to have all the mesh currents looping in a clockwise direction.

in  Mesh analysis it is a method that is used to solve planar circuits for the currents at any place in the circuit. Planar circuits are circuits that can be drawn on a plane.

From my own understanding a mesh I a loop that does not contain any other loop within it.