Mesh Analysis

MESH ANALYSIS

Mesh and nodal analysis are the two basic techniques used to find solutions for a network. The suitability of either mesh or nodal analysis to a particular problem mainly depends on the number of voltage sources or current sources. If a network has a large number of voltage sources, it is useful to use mesh analysis. If any current source in a circuit they converted into equivalent voltage source. If the network has more current sources, nodal analysis is more useful.

A Mesh is defined as a loop which does not contain any other loops within it. Consider a simple network as shown in fig 1.23

Steps to be followed to find out the mesh current and branch current are

Step 1: Each mesh is assigned a seperate mesh current. Assume all mesh currents directions are clockwise. Consider fig 1.23, it consists of two meshes (ABDA and BCDB) and two mesh currents (i1 and i2).

Step 2: If two mesh currents (i1 and i2) are flowing through a network element, the actual current in the circuit element is the algebraic sum of the two (i1 and i2). In the above network mesh currents i1 and i2 are flowing in R2. First consider the direction B to D, current is i1 –i2 and consider the direction D to B. current is i2 – i1.

Step 3: Write equation for each mesh in terms of mesh currents by applying KVL. In this equation potential rise is mentioned as positive sign (+) and potential drop as negative sign (-).

Step 4: If any one mesh current becomes negative the actual or true direction of the current is anticlockwise.

We apply KVL to the fig 1.23

Mesh ABDA

− i1 R1 − (i1 – i2) R2 + V1 = 0

− i1 R1 − i1 R2 +  i2 R2 + V1 = 0

− i1 ( R1 + R2 ) – i2 R2 + V1 = 0

i1 ( R1 + R2 ) – i2 R2 = V1

Mesh BCDB

− i2 R3 − V2 − ( i2 − i1 ) R2 = 0

− i2 R3 − V2 −  i2 R2 − i1 R2 = 0

i1 R2 −  i2 (R2 + R3) = V2

The mesh currents i1 and i2 can be found by solving the equations V1 and V2.

Step 5: The branch current can easily found by using the mesh currents i1 and i2.