2Mesh Analysis (Loop Analysis) Mesh = A closed loop path which has no smaller loops inside
3Mesh Analysis Procedure Count the number of meshes. Let the number equal N.Define mesh current on each mesh. Let the values be I1, I2, I3, …Use Kirchoff’s voltage law (KVL) on each mesh, generating N equationsSolve the equations
4ExampleUse mesh analysis to find the power consumption in the resistor 3 ΩI1I2Mesh current (loop current)
5I1I2Loop 1Equation 1Loop 2Equation 2I1 = 6A, I2 = 4A, The current that pass through R 3Ω is 6-4 = 2A (downward)Power = 12 W
8SupermeshWhen there is a current source in the mesh path, we cannot use KVL because we do not know the voltage across the current source.We have to use supermesh, which is a combination of 2 meshes to be a big mesh, and avoid the inclusion of the current source in the mesh path.
13How to choose between Node and Mesh Analysis The hardest part in analyzing circuits is solving equations. Solving 3 or more equations can be time consuming.Normally, we will count the number of equations according to each method and select the method that have lesser equations.
14Example From the previous example, if we want to use Nodal Analysis 7V
18Superposition Theorem In a linear circuit, we can calculate the value of current (or voltage) that is the result from each voltage source and current source independently.Then, the real value is the sum of all current (or voltage) from the sources.
20ImplementationWhen calculating the effect of a source, the other sources will be set to zero.For voltage sources, when set as 0V, it will be similar to short circuitFor current sources, when set as 0A, it will be similar to open circuit