Super
Mesh Analysis :
DEFINETION:
“Super
mesh is defined as the combination of two meshes which have current source on
their boundary”.
Example :
From the above circuit :
If a current source is located on only one mesh (1-A ICS in the circuit), the mesh current can be directly found from the current source and we do not need to write any KVL:
i1 = -1 A………(1)
If a current source is located on the boundary between two meshes (2-A ICS in the circuit),KVL on these meshes (mesh 2 or 3 in the above circuit) contain the voltage across the 2-A ICS which is unknown. We need two equations to substitue for the two KVLs on meshes
2 and 3 that are not useful now. The first one is found from the i-v characteristics of the
current source (its current should be 2 A):
i3 - i2 = 2 A……..(2)
The second equation can be found by noting that KVL can be written over any closed loop.
While KVL on mesh 2 or on mesh 3 both include the voltage across the 2-A current source that is unknown, KVL on the supermesh does not include that:
Supermesh 2&3: 2(i2 - i1) + 2(i3 - i1) + 6i3 - 10 = 0 . -4i1 + 2i2 + 8i3 = 10………(3)
Solving above three equations gives i1=-1A , i2=-1A , i3=1A.
Steps to be followed:
Example :
From the above circuit :
If a current source is located on only one mesh (1-A ICS in the circuit), the mesh current can be directly found from the current source and we do not need to write any KVL:
i1 = -1 A………(1)
If a current source is located on the boundary between two meshes (2-A ICS in the circuit),KVL on these meshes (mesh 2 or 3 in the above circuit) contain the voltage across the 2-A ICS which is unknown. We need two equations to substitue for the two KVLs on meshes
2 and 3 that are not useful now. The first one is found from the i-v characteristics of the
current source (its current should be 2 A):
i3 - i2 = 2 A……..(2)
The second equation can be found by noting that KVL can be written over any closed loop.
While KVL on mesh 2 or on mesh 3 both include the voltage across the 2-A current source that is unknown, KVL on the supermesh does not include that:
Supermesh 2&3: 2(i2 - i1) + 2(i3 - i1) + 6i3 - 10 = 0 . -4i1 + 2i2 + 8i3 = 10………(3)
Solving above three equations gives i1=-1A , i2=-1A , i3=1A.
Steps to be followed:
1. Check if circuit is planar.
2. Identify meshes, mesh currents, and supermeshes.
a) Rearrange the circuit if possible to position current source on a single mesh.
b) Use i-v characteristic equations of ICS to find mesh currents and reduce the number of unknowns.
3. Write KVL at each mesh and supermesh.
4. Solve for mesh currents.
5. Calculate problem unknowns from mesh currents. If you need to calculate the voltage across a current source you may have to write KVL around a mesh containing the current source.
6. For consistency and elimination of errors, always mark all mesh currents in clockwise direction and write down KVLs in the same direction.
2. Identify meshes, mesh currents, and supermeshes.
a) Rearrange the circuit if possible to position current source on a single mesh.
b) Use i-v characteristic equations of ICS to find mesh currents and reduce the number of unknowns.
3. Write KVL at each mesh and supermesh.
4. Solve for mesh currents.
5. Calculate problem unknowns from mesh currents. If you need to calculate the voltage across a current source you may have to write KVL around a mesh containing the current source.
6. For consistency and elimination of errors, always mark all mesh currents in clockwise direction and write down KVLs in the same direction.
