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Lecture 4: Nodal Analysis Nilsson & Riedel 4.1-4.4 ENG17 (Sec. 2): Circuits I Spring 2014 1 April 10, 2014

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Overview Recap on Voltage & Current Dividers Term Definition Node Voltage Method NVM w/Dependent Sources NVM Special Cases 2

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Voltage Divider Wheatstone Bridge –2 voltage dividers in parallel 3

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Current Divider 4 Similar analysis

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Overview Recap on Voltage & Current Dividers Term Definition Node Voltage Method NVM w/Dependent Sources NVM Special Cases 5

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Planar Circuit 6 Planar Not Planar Nodal good for either Mesh good for planar

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Identify Node Essential Node Path Branch Essential Branch Loop Mesh 7

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Simultaneous Equations How many unknown currents? How many equations needed? 8

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Overview Recap on Voltage & Current Dividers Term Definition Node Voltage Method NVM w/Dependent Sources NVM Special Cases 9

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Node Voltage Method – Setting Up Identify essential nodes Define reference node Apply KCL to each non-reference node, express current in terms of node voltages Solve simultaneous equations 10

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Node Equations 11

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Example 12

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Overview Recap on Voltage & Current Dividers Term Definition Node Voltage Method NVM w/Dependent Sources NVM Special Cases 13

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Dependent Sources Only need to add equation to describe relationship of the dependent source 14

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Example 15

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Overview Recap on Voltage & Current Dividers Term Definition Node Voltage Method NVM w/Dependent Sources NVM Special Cases 16

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Source Between Essential Nodes 17

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w/Dependent Source 18

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Supernode 19

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Example 20

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Recap Recap on Voltage & Current Dividers Term Definition Node Voltage Method NVM w/Dependent Sources NVM Special Cases 21

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1 Loop (Mesh) Analysis. 2 Loop Analysis Nodal analysis was developed by applying KCL at each non-reference node. Loop analysis is developed by applying.

1 Loop (Mesh) Analysis. 2 Loop Analysis Nodal analysis was developed by applying KCL at each non-reference node. Loop analysis is developed by applying.

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