Announcements 1 Announcements EECS 70 A Network Analysis

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Announcements: 1. Announcements EECS 70 A: Network Analysis Lecture 6 12/12/2021 EECS 70 A

Announcements: 1. Announcements EECS 70 A: Network Analysis Lecture 6 12/12/2021 EECS 70 A © 2010 P. J. Burke 1

Today’s Agenda • Review of Nodal Analysis • Mesh Analysis – Introduction • What

Today’s Agenda • Review of Nodal Analysis • Mesh Analysis – Introduction • What is a Mesh? • Mesh Current – Method • Mesh Analysis with Current Source 12/12/2021 EECS 70 A © 2010 P. J. Burke 2

Node Voltage(review) a i R 1 i b R 2 i c Vab is

Node Voltage(review) a i R 1 i b R 2 i c Vab is the voltage drop across resistor 1 12/12/2021 EECS 70 A © 2010 P. J. Burke 3

Nodal Analysis(Review) Based on KCL, Use node voltages as circuits variables. 1. Define a

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. 12/12/2021 EECS 70 A © 2010 P. J. Burke 4

Apply KCL + Ohm to All Nodes and Supernodes R 2 R 1 3

Apply KCL + Ohm to All Nodes and Supernodes R 2 R 1 3 A R 3 R 7 R 6 R 8 R 10 R 9 R 11 12/12/2021 R 5 R 4 R 12 EECS 70 A © 2010 P. J. Burke 5

Nodal Analysis-Example 0. 2 W i 1 + + V 0 0. 2 W

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 - 12/12/2021 EECS 70 A © 2010 P. J. Burke 6

Mesh Analysis-Introduction What is a Mesh? 12/12/2021 • A loop is a closed path

Mesh Analysis-Introduction What is a Mesh? 12/12/2021 • A loop is a closed path with no node passed more than once. • A mesh is a loop that does not contain any other loops within it. EECS 70 A © 2010 P. J. Burke 7

Mesh Analysis-Introduction Mesh Current vs. Element Current - • + V 2 • V

Mesh Analysis-Introduction Mesh Current vs. Element Current - • + V 2 • V 3 + - V 1 - + • - + 12/12/2021 V 4 EECS 70 A © 2010 P. J. Burke The current through a mesh is known as mesh current. Direction of the mesh current is arbitrary-conventionally assumed to be clockwise. The current through an element can be the same as mesh current or the subtraction of two mesh currents. 8

Mesh Analysis-Method • • • 10 v Assign mesh currents i 1 , i

Mesh Analysis-Method • • • 10 v Assign mesh currents i 1 , i 2 , …in Apply KVL+ Ohm’s law to each mesh Solve the equations for i 1 , i 2 , …in 3 W 5 W + - 10 W 12/12/2021 + 7 W - 5 v 2 W EECS 70 A © 2010 P. J. Burke 9

Apply KVL+ Ohm’s Law to Each Mesh R 1 10 v + + R

Apply KVL+ Ohm’s Law to Each Mesh R 1 10 v + + R 3 - R 2 12/12/2021 R 4 - 5 v R 5 EECS 70 A © 2010 P. J. Burke 10

7 W Mesh Analysis - Example i 2 W 1 W + - 4

7 W Mesh Analysis - Example i 2 W 1 W + - 4 W + 2 i - 5 v 3 W 12/12/2021 EECS 70 A © 2010 P. J. Burke 11

Mesh Analysis with Current Sources • CASE 1: current source only in one mesh.

Mesh Analysis with Current Sources • CASE 1: current source only in one mesh. already have the current for that mesh => no need to write KVL for that mesh 3 W + 10 v - 5 W 7 W 10 W 12/12/2021 5 A 2 W EECS 70 A © 2010 P. J. Burke 12

Mesh Analysis with Current Sources • CASE 2: current source exits between two meshes.

Mesh Analysis with Current Sources • CASE 2: current source exits between two meshes. => create a supermesh – Apply KVL to the supermesh – Apply KCL to the supermesh 3 W 10 v 5 A + - 7 W 3 W 10 W 12/12/2021 5 W 2 W EECS 70 A © 2010 P. J. Burke 13

Mesh Analysis- Example 6+v 4 W 2 W + 1 W 5 W 12/12/2021

Mesh Analysis- Example 6+v 4 W 2 W + 1 W 5 W 12/12/2021 - 12 v 3 A EECS 70 A © 2010 P. J. Burke 14

5 W Mesh Analysis- Example 2 W 12/12/2021 3 W 7 W 3 A

5 W Mesh Analysis- Example 2 W 12/12/2021 3 W 7 W 3 A 5 A EECS 70 A © 2010 P. J. Burke 15

Nodal Versus Mesh Analysis • The method that results in fewer number of equations

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 12/12/2021 EECS 70 A © 2010 P. J. Burke 5 A But also depends on the type of the sources. i 4 3 W R 5 R 10 R 12 16

Symbol library Iab I=5 A a b 12/12/2021 + - + a - b

Symbol library Iab I=5 A a b 12/12/2021 + - + a - b EECS 70 A © 2010 P. J. Burke 17

Symbol library + - 2 + - + 12/12/2021 + - 2 i 1

Symbol library + - 2 + - + 12/12/2021 + - 2 i 1 - 3 i 1 + 3 A i 7 3 V 2 W i 7 - EECS 70 A © 2010 P. J. Burke 18

Symbol & circuit library 12/12/2021 EECS 70 A © 2010 P. J. Burke 19

Symbol & circuit library 12/12/2021 EECS 70 A © 2010 P. J. Burke 19