EE302Lecture15 - Me C nt C sh urre ircuit Analysis I n the...

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1 Mesh Current Circuit Analysis In these lectures, you will learn: How to apply Mesh Current Analysis: Learn to identify and assign mesh currents. Learn to writetheset of simultaneous algebraic equations. Learn to express thequantities to calculatein terms of the mesh currents in the circuit. To identify and analyzecircuits requiring a “Supermesh” approach.
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2 Definitions Branch : a path that connects two nodes. Essential branch : a branch that connects two essential nodes. Loop : any closed connection of branches. Mesh : a loop that does not contain other loops.
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3 Example 1 A R3 R1 R2 2 V + - R4 Mesh 1 Mesh 2 Mesh 3 Outer Loop is not a Mesh Why?
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4 Mesh Current Analysis How many essential nodes (n e )? 4 How many essential branches (b e )? 6 Number of mesh currents? 3 In general, number mesh currents = b e - (n e -1) In our case, number mesh currents = 6 - (4 - 1) = 3
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5 Mesh Current Method Mesh current method provides another systematic tool to solve circuit problems. Only applicableto planar circuits. Not an issue in EE302. Use mesh currents as the independent variables and write KVL equations around each mesh.
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6 Moreon Mesh Current Method Becauseof thepassivesign convention, the direction of the mesh current flow automatically defines thepolarity of the branch voltages . Mesh currents arenot necessarily thesameas branch currents. Mesh currents automatically satisfy KCL sinceeach mesh current both enters and leaves each nodeit encounters.
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7 Mesh Current Analysis Methodology 1. Identify all of themeshes in the circuit. 2. Define the current in each mesh as flowing clockwise. 3. Assign each mesh current a name: (I 1 , I 2 , I 3 ) or (I A , I B , I C ) 4. Using KVL, sum the voltage drops around themesh and set them = 0. Passivesign convention is used for all voltage and are determined in relation to the mesh current value In some branches, the current you will useis the difference of two mesh currents. 5. Current sources imply constraints on themesh currents. More on this later.
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8 Example Assume the mesh currents flow clockwise . Apply KVL around themesh Mesh equation becomes: -V + IR 1 + IR 2 = 0 Thesign of each term in theKVL equation is thesame sign as first encountered in going around the loop as indicated by the arrow. R 1 R 2 V I
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9 A More Complex Example Definetwo mesh currents I 1 and I 2 . Let’s look at mesh 1. Current in R 1 is I 1 . Sign convention follows I 1 . What is the current in R 3 ? Net current in R 3 = (I 1 - I 2 ). KVL around mesh 1: -V 1 + I 1 R 1 + (I 1 -I 2 )R 3 = 0 R 1 R 3 V 1 R 2 V 2 I 1 I 2
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10 A More Complex Example Now, let’s look at mesh 2. Current in R 2 is I 2 . Sign convention follows I 2 . What is thecurrent in R 3 ? Net current in R3 = (I 2 – I 1 ). KVL around mesh 2: (I 2 -I 1 )R 3 +I 2 R 2 + V 2 = 0 R 1 R 3 V 1 R 2 V 2 I 1 I 2
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11 KVL around mesh 1: -V 1 + I 1 R 1 + (I 1 -I 2 )R 3 = 0 KVL around mesh 2: (I 2 -I 1 )R 3 +I 2 R 2 + V 2 = 0 For each mesh, the sign convention follows that mesh current.
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