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

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

Voltage Divider Wheatstone Bridge –2 voltage dividers in parallel 3

Current Divider 4 Similar analysis

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

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

Identify Node Essential Node Path Branch Essential Branch Loop Mesh 7

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

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

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

Node Equations 11

Example 12

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

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

Example 15

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

Source Between Essential Nodes 17

w/Dependent Source 18

Supernode 19

Example 20

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

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