lecture7 - only for circuits containing resistors and...

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Mesh Analysis Nodal vs. Mesh In nodal analysis , circuit variables are node voltages Nodal analysis applies KCL to find unknown voltages In mesh analysis , circuit variables are mesh currents Mesh analysis applies KVL to find unknown currents Both methods result in a system of linear equations Mesh analysis is only applicable to a circuit that is planar Planar vs. Non-planar Planar circuit : it can be drawn on a plane surface where no element cross any other element Non-planar circuit : there is no way to redraw it and avoid the branches crossing C C C What is a mesh/mesh current? • A mesh is a loop that does not contain any other loops within it The current through a mesh is known as mesh current a b c d e
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Steps of Mesh Analysis 1. Assign a mesh current to each mesh. 2. Apply KVL to each mesh --- express voltages in terms of mesh currents. 3. Solve the resulting linear equations. Example V a R 1 R 2 R 3 V b Mesh Equations by Visual Inspection
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Unformatted text preview: ( only for circuits containing resistors and independent voltage sources ) • Left-hand side: − Diagonal terms is the sum of resistances in the related mesh − Off-diagonal terms are the negatives of the resistances common to the meshes. • Right-hand side: − Algebraic sum of voltage rises of all independent voltage sources in the related mesh Example 2 Ω 1 Ω 1 Ω 1 Ω 3 Ω 4 Ω 2 Ω 12 V 24 V 18 V 6 V Mesh Analysis with Current Sources Two cases: • a current source exists only in one mesh • a current source exists between two meshes Mesh Analysis with Current Sources (I) o o + V o-4 mA 2 mA 4 k Ω 2 k Ω 6 k Ω 4 k Ω 3 V Find V o Mesh Analysis with Current Sources (II) 20 V 6 A 6 Ω 10 Ω 2 Ω 4 Ω Mesh Analysis with Current Sources (II) 5 A 8 Ω 40 Ω 80 Ω 64 V- + I 2 I 1 2I 2 2.5I 1 Find I 1 , I 2 ....
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