lec4 - Fundamentals of Electrical Engineering 2009...

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Fundamentals of Electrical Engineering 2009 Danang University of Technology
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Lecture 4 Techniques of Circuit Analysis (chapter 4)
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Preview Use the node-voltage method to solve a circuit Use the mesh-current method to solve a circuit Be able to decide if the N-V method or the M-C method is the suitable approach for a particular circuit Use source transformation to solve a circuit Understand the The’venin & Norton equivalent circuits and be able to construct a The’venin or Norton equivalent for a circuit Known the condition for maximum power transfer to a resistive load and be able to
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Terminology Node: a point where 2 or more elements join Essential node: a node where 3 or more elements join Branch: a path that connects two nodes Essential branch: a branch which connects two essential nodes without passing through an essential node Loop: a path whose last node is the same as the starting node Mesh: a loop that does not enclose any other loops Planar circuit: a circuit that can be drawn on a plane with no crossing branches
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Example Nodes: a, b, c, d Essential nodes: a, b, d Paths: 60-80, etc. Branches: 4, 20, 60, 80, 10, 30 Essential branches: d-4-a, d-20-a, d-80-b, d-30-10-b, a-60-b Meshes: 20-4, 60-80-20, 10-30-80 Loops that are not meshes: 60-80-4, 60-10-30-20, 60-10-30-4
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How many equations ? Number of unknown currents equals number of branches (b=6 in ex.) Must have b independent equations to solve a circuit If we have n nodes, we can derive n-1 ind. eqs. by applying KCL Need to apply KVL to loops (meshes) to derive b-(n-1) ind eqs In the example: n = 4 3 ind eqs (KCL) b = 6 5 unknown currents, need 2 ind eqs (KVL)
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Essential things ? Note that all currents in an essential branch are equal: opportunity to reduce number of eqs Essential nodes n e = 3 n e – 1 = 2 ind eqs (KCL) Essential branches b e = 5 b e – (n-1) ind eqs (KCL) 4 unknown currents 2 more ind eqs needed
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How to solve ? Essential nodes: (KCL)
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lec4 - Fundamentals of Electrical Engineering 2009...

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