Announcements 1 Announcements EECS 70 A Network Analysis

Announcements: 1. Announcements EECS 70 A: Network Analysis Lecture 7 & 8 12/5/2020 EECS 70 A © 2014 P. J. Burke 1

Nodal analysis summary 1. 2. 3. 4. 5. 12/5/2020 Define reference node Label remaining nodes (e. g. V 1, V 2, V 3, …) Apply KCL + Ohm’s law Solve for nodal voltages (e. g. using Kramer’s rule) Solve for currents EECS 70 A © 2014 P. J. Burke 2

Nodal analysis example 1. 2. 3. Define a reference node. Label remaining nodes. Apply KCL + ohm. i 1 i 2 R 1 i 3 R 3 i 5 R 4 i 6 3 A R 2 i 4 i 7 R 6 i 8 R 7 i 9 i 10 R 9 i 11 R 11 i 12 R 12 Typical notation: i 1 is current through R 1. (Same as before) V 1 is voltage of node 1 relative to reference node. (Different from before) We will do this entire problem in class… Using these techniques, you can attempt the “monster problem” as extra credit on HW 3… 12/5/2020 EECS 70 A © 2014 P. J. Burke 3

Mesh analysis summary 1. 2. 3. 4. 12/5/2020 Assign mesh currents i 1, i 2, … in Apply KVL to each mesh Solve for mesh currents (e. g. using Kramer’s rule) Then solve for voltages EECS 70 A © 2014 P. J. Burke 4

Assigning mesh currents R 1 V 1 12/5/2020 + - R 2 R 3 + - V 2 EECS 70 A © 2014 P. J. Burke 5

Nodal vs. mesh analysis? 12/5/2020 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 6

Nodal analysis example 12/5/2020 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 7

5 W - + 3 W 4 W + - 1 W - + 1 W + 12/5/2020 - 2 V 4 V 6 V 2 W Nodal vs. Mesh Analysis 3 V EECS 70 A © 2014 P. J. Burke 8

5 W - + 3 W 4 W + - 1 W - + 1 W + 12/5/2020 - 2 V 4 V 6 V 2 W Nodal vs. Mesh Analysis 3 V EECS 70 A © 2014 P. J. Burke 9

3 A (Monster HW problem) 7 W 3 V 7 W 7 W 2 i 1 3 i 1 5 W 2 W 7 W 7 W 7 W 5 W 3 A 3 A 2 W + - + 7 W 3 A 7 W 7 W + 7 W 3 i 1 7 W 3 W + 7 W 3 V 3 A 3 V 3 V 3 V 5 W 3 W 7 W - 7 W 3 A 2 W i 1 + - + + 3 A EECS 70 A © 2014 P. J. Burke 7 W 5 W 7 W 3 A 7 W 7 W 12/5/2020 7 W 2 W - 7 W 7 W 10

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Compartmentalization: Need for simplicity Power brick image. And ask class to show their own… Demo: Computer? 12/5/2020 EECS 70 A © 2014 P. J. Burke 16

Thevenin’s Theorem I a + Linear two-terminal circuit Load b Equivalent to: Vth Rth a + + - Load b 12/5/2020 EECS 70 A © 2014 P. J. Burke 17

Finding Vth, Rth a + Linear twoterminal circuit b Equivalent to: Vth Rth + - a + b 12/5/2020 EECS 70 A © 2014 P. J. Burke 18

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. 12/5/2020 EECS 70 A © 2014 P. J. Burke 19

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. 12/5/2020 EECS 70 A © 2014 P. J. Burke 20

Example Find Thevenin equivalent circuit: R 1 + V 1 - R 2 12/5/2020 EECS 70 A © 2014 P. J. Burke 21

Norton’s Theorem I a + Linear two-terminal circuit Load b Equivalent to: a RN IN + Load b 12/5/2020 EECS 70 A © 2014 P. J. Burke 22

Finding Vth, Rth a + Linear twoterminal circuit b Equivalent to: - a + + - RN + a IN Vth Rth b 12/5/2020 b EECS 70 A © 2014 P. J. Burke 23

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 12/5/2020 EECS 70 A © 2014 P. J. Burke 24

3 V 3 A (Monster HW problem: Part 2): Find the Thevenin & Norton equivalent circuit of the circuit below with respect to terminals a and b: 7 W 7 W 7 W + 3 V 3 i 1 2 i 1 3 V 3 V 5 W 3 W 7 W - 7 W + 3 A 2 W i 1 - + a + - - + - 7 W 7 W 7 W 5 W 5 W 7 W 2 W 3 A 7 W 7 W + 7 W 3 i 1 3 A 7 W 3 V 3 A 3 W 7 W 2 W b + 3 A EECS 70 A © 2014 P. J. Burke 7 W 5 W 7 W 3 A 7 W 7 W 12/5/2020 7 W 2 W - 7 W 7 W 25

Power Vth Rth + - a Arrow means RL variable (e. g. by a knob) + - RL Power delivered to load = ? 12/5/2020 EECS 70 A © 2014 P. J. Burke 26

Questions? 12/5/2020 EECS 70 A © 2014 P. J. Burke 27

Ground? ? Ground Reference Earth 12/5/2020 EECS 70 A © 2014 P. J. Burke 28

Symbol library Iab I=5 A a b 12/5/2020 + - + a - b EECS 70 A © 2014 P. J. Burke 29

Symbol library + - 2 + - + 12/5/2020 + - 2 i 1 - 3 i 1 + 3 A i 7 3 V 2 W i 7 - EECS 70 A © 2014 P. J. Burke 30

Symbol & circuit library 12/5/2020 EECS 70 A © 2014 P. J. Burke 31