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Unit 2.2 - Mesh Current Analysis

Unit 2.2 - Mesh Current Analysis - Mesh Current Circuit...

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1 1 Unit 2: Node and Mesh Circuit Analysis Unit 2.2 - Mesh Current Analysis 2 Mesh Current Circuit Analysis f In this lecture, you will learn: How to assign mesh currents, simplifying the solution of large circuits. How to apply Mesh Current Analysis: Learn to identify and assign mesh currents. Learn to write the set of simultaneous algebraic equations. Learn to express the quantities to calculate in terms of the mesh currents in the circuit. To identify and analyze circuits requiring a “Supermesh” approach. 3 Definition Review f Branch : a path that connects two nodes. f Essential branch : a branch that connects two essential nodes. f Loop : any closed connection of branches. f Mesh : a loop that does not contain other loops. 4 Example 1 A R3 R1 R2 2 V + - R4 Mesh 1 Mesh 2 Mesh 3 Outer Loop is not a Mesh Why? 5 Mesh Current Analysis f How many essential nodes (n e )? 4 f How many essential branches (b e )? 6 f 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 6 Mesh Current Method f Mesh current method provides another systematic tool to solve circuit problems. Only applicable to planar circuits. f Use mesh currents as the independent variables and write KVL equations around each mesh.
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2 7 More on Mesh Current Method f Because of the passive sign convention, the direction of the mesh current flow automatically defines the polarity of the branch voltages . f Mesh currents are not necessarily the same as branch currents. f Mesh currents automatically satisfy KCL since a given mesh current both enters and leaves a node. 8 Mesh Current Analysis Methodology 1. Identify all of the meshes 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 the mesh and set them = 0. Passive sign convention is used for all voltage and are determined in relation to the mesh current value In some branches, the current you will use is the difference of two mesh currents. 5. Current sources imply constraints on the mesh currents. More on this later. 9 Example f Assume the mesh currents flow clockwise . f Apply KVL around the mesh Mesh equation becomes: -V + IR 1 + IR 2 = 0 f Same as sign convention as KVL approach studied earlier. R 1 R 2 V I 10 A More Complex Example f Define two mesh currents I 1 and I 2 . f 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 ). f 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 11 A More Complex Example f Now, let’s look at mesh 2.
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