Announcements 1 Announcements EECS 70 A Network Analysis

Announcements: 1. Announcements EECS 70 A: Network Analysis Lecture 6 1/16/2022 EECS 70 A © 2014 P. J. Burke 1

Nodal Analysis(Review) Based on KCL, Use node voltages as circuits variables. 1. Define a reference node. 2. Label remaining nodes. (n-1 nodes) 3. Apply KCL + ohm to all nodes and supernodes 1. Express all I’s in terms of v’s 4. Apply KVL to loops with voltage source 5. Solve the n-1 simultaneous equations, to find V’s 6. Use Ohm’s law to find the currents. 1/16/2022 EECS 70 A © 2014 P. J. Burke 2

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Example Nodal Problem (detailed solution) R 2 R 1 3 A R 3 R 7 R 6 R 8 R 10 R 9 R 11 1/16/2022 R 5 R 4 R 12 EECS 70 A © 2014 P. J. Burke 4

1. 2. 3. Same circuit: Nodal analysis Define a reference node. Label remaining nodes. Apply KCL + ohm. i 1 i 2 R 1 i 3 R 3 i 6 3 A i 5 R 4 i 7 R 6 i 8 R 7 i 9 i 10 R 9 i 11 1/16/2022 R 2 i 4 R 11 i 12 R 12 EECS 70 A © 2014 P. J. Burke 5

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Nodal Analysis-Example 0. 2 W i 1 + + V 0 0. 2 W - 0. 5 W + i 1 2 V 0 1 W 5 V 1 W 0. 5 W - 1/16/2022 EECS 70 A © 2014 P. J. Burke 10

Mesh Analysis(Review) Based on KVL, use mesh currents as circuits variables. 1. Assign mesh currents i 1 , i 2 , …in A. Create supermesh if current source 2. Apply KVL+ Ohm’s law to each mesh 3. Solve the equations for mesh currents i 1 , i 2 , …in 4. Find voltage drops 1/16/2022 EECS 70 A © 2014 P. J. Burke 11

Mesh Analysis- Example 6+v 4 W 2 W + 1 W 5 W 1/16/2022 - 12 v 3 A EECS 70 A © 2014 P. J. Burke 12

Nodal Versus Mesh Analysis • The method that results in fewer number of equations is more suitable. – Mesh analysis for networks with many series connected elements – Nodal Analysis for networks with many parallel connected elements i 2 2 W 2 W + R 3 3 A 3 W i 3 5 W R 2 R 1 - 10 V 2 A 5 A i 1 7 W R 4 R 7 R 6 R 8 R 9 R 11 1/16/2022 EECS 70 A © 2014 P. J. Burke 5 A But also depends on the type of the sources. i 4 3 W R 5 R 10 R 12 13

Nodal vs. mesh analysis? 1/16/2022 7 W i 2 2 W i 3 i 4 5 W 3 W 5 A 2 A i 1 EECS 70 A © 2014 P. J. Burke 14

Nodal vs. mesh analysis? 1/16/2022 7 W i 2 2 W i 3 i 4 5 W 3 W 5 A 2 A i 1 EECS 70 A © 2014 P. J. Burke 15

5 W - + 3 W 4 W + - 1 W - + 1 W + 1/16/2022 - 2 V 4 V 6 V 2 W Nodal vs. Mesh Analysis 3 V EECS 70 A © 2014 P. J. Burke 16

Nodal vs. Mesh Analysis R 2 R 1 3 A R 3 R 7 R 6 R 8 R 10 R 9 R 11 1/16/2022 R 5 R 4 R 12 EECS 70 A © 2014 P. J. Burke 17

Compartmentalization: Need for simplicity Power brick image. And ask class to show their own… Demo: Computer? 1/16/2022 EECS 70 A © 2014 P. J. Burke 18

Thevenin’s Theorem I a + Linear two-terminal circuit Load b Equivalent to: Vth Rth a + + - Load b 1/16/2022 EECS 70 A © 2014 P. J. Burke 19

Finding Vth, Rth a + Linear twoterminal circuit b Equivalent to: Vth Rth + - a + b 1/16/2022 EECS 70 A © 2014 P. J. Burke 20

Source/load Rsource Vsource + Rload - Derivation: Case 1: Thevenin Thm: Any circuit can be represented by this equivalent circuit. Case 2: We say Rload “loads down” the source. 1/16/2022 EECS 70 A © 2014 P. J. Burke 21

Source/load Rsource Vsource + Rload - Derivation: Case 1: Thevenin Thm: Any circuit can be represented by this equivalent circuit. Case 2: We say Rload “loads down” the source. 1/16/2022 EECS 70 A © 2014 P. J. Burke 22

Example Find Thevenin equivalent circuit: R 1 + V 1 - R 2 1/16/2022 EECS 70 A © 2014 P. J. Burke 23

Norton’s Theorem I a + Linear two-terminal circuit Load b Equivalent to: a RN IN + Load b 1/16/2022 EECS 70 A © 2014 P. J. Burke 24

Finding Vth, Rth a + Linear twoterminal circuit b Equivalent to: - a + + - RN + a IN Vth Rth b 1/16/2022 b EECS 70 A © 2014 P. J. Burke 25

Find the Thevenin & Norton equivalent circuit of the circuit below with respect to terminals a and b: Example + 60 W - + - 2 Vx + a Vx 30 V 12 W b 1/16/2022 EECS 70 A © 2014 P. J. Burke 26

“Baby” monster problem Find the Thevenin & Norton equivalent circuit of the circuit below with respect to terminals a and b: 3 V 3 A 7 W 7 W 7 W + 5 W 3 i 1 2 i 1 3 V 3 V + - + EECS 70 A © 2014 P. J. Burke 3 V - + - 1/16/2022 7 W - 7 W 3 W + 3 A 2 W i 1 - + a - 27