ene 104 electric circuit theory -...

ENE 104

Electric Circuit Theory

Lecture 03:

Basic Nodal and Mesh Analysis

http://webstaff.kmutt.ac.th/~dejwoot.kha/

Week #3 : Dejwoot KHAWPARISUTH

Objectives :

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ENE 104

• Implementation of the nodal analysis

• Implementation of the mesh analysis

• Supernodes and Supermeshes

• Basic computer-aided circuit analysis

Basic Nodal and Mesh Analysis

Example: 4.2

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ENE 104 Basic Nodal and Mesh Analysis

find the nodes voltages:

Practice: 4.2

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ENE 104 Basic Nodal and Mesh Analysis

Practice: 4.2

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ENE 104

012

3 2131

vvvvNode 1:

Node 2:

Node 3:

0431

32212

vvvvv

0542

7 32313

vvvvv

1v 2v3v

Basic Nodal and Mesh Analysis

The Supernode: Page 6

ENE 104 Basic Nodal and Mesh Analysis

find the nodes voltages:

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The Supernode: Page 7

ENE 104 Basic Nodal and Mesh Analysis

find the nodes voltages:

i

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The Supernode: Page 8

ENE 104 Basic Nodal and Mesh Analysis

find the nodes voltages:

i

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Practice: 4.3

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ENE 104 Basic Nodal and Mesh Analysis

Compute the voltage across each current source

Practice: 4.3

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ENE 104

042

1

1

31

21

vi

vvNode 1:

Node 2:

Supernode 1-2:

096

1

2

31

12

vi

vv

0946

1

2

31

12

21

1

31

21

vvvvvv

1v 2v

Basic Nodal and Mesh Analysis

Example: 4.4 Page 11

ENE 104 Basic Nodal and Mesh Analysis

Determine the node-to-reference voltages in the circuit below.

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Example: Page 12

ENE 104 Basic Nodal and Mesh Analysis

Determine the node-to-reference voltages in the circuit below.

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Practice: 4.4

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ENE 104 Basic Nodal and Mesh Analysis

Use nodal analysis to find vx, if element A is (a)

a 25 Ω; (b) a 5-A current source, arrow pointing

right; (c) a 10-V voltage source, positive

terminal on the right; (d) a short circuit

Practice:

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ENE 104 Basic Nodal and Mesh Analysis

Use nodal analysis to determine the nodal

voltage in the circuit.

Mesh Analysis: Page 15

ENE 104 Basic Nodal and Mesh Analysis

Mesh analysis is applicable only to those networks which are planar.

Examples of planar and nonplanar networks

Mesh is a loop that doesn’t contain any other loops.

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Path, Closed path, and Loop: Page 16

ENE 104 Basic Nodal and Mesh Analysis

(a) The set of branches identified by the heavy lines is neither a path nor a

loop. (b) The set of branches here is not a path, since it can be traversed

only by passing through the central node twice. (c) This path is a loop but

not a mesh, since it encloses other loops. (d) This path is also a loop but

not a mesh. (e, f) Each of these paths is both a loop and a mesh.

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Example: 4.6 Page 17

ENE 104 Basic Nodal and Mesh Analysis

Determine the two mesh currents, i1 and i2, in the circuit below.

For the left-hand mesh,

-42 + 6 i1 + 3 ( i1 - i2 ) = 0

For the right-hand mesh,

3 ( i2 - i1 ) + 4 i2 - 10 = 0

Solving, we find that i1 = 6 A and i2 = 4 A.

(The current flowing downward through

the 3- resistor is therefore i1 - i2 = 2 A. )

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Practice: 4.5

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ENE 104 Basic Nodal and Mesh Analysis

Determine i1 and i2

Practice: 4.5

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ENE 104

010146 211 iiiMesh 1:

Mesh 2:

051010 212 iii

Basic Nodal and Mesh Analysis

Example: 4.7 Page 20

ENE 104 Basic Nodal and Mesh Analysis

determine the three mesh currents

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Example: Page 21

ENE 104 Basic Nodal and Mesh Analysis

determine the three mesh currents

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Practice: 4.6

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ENE 104 Basic Nodal and Mesh Analysis

Determine i1 and i2

Practice: 4.6

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03410 21 iiMesh 1:

Mesh 2:

Mesh 3:

010954 322212 iiiiii

08103 323 iii

Basic Nodal and Mesh Analysis

The Supermesh: Page 24

ENE 104 Basic Nodal and Mesh Analysis

Find the three mesh currents in the circuit below.

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The Supermesh: Page 25

ENE 104 Basic Nodal and Mesh Analysis

Find the three mesh currents in the circuit below.

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The Supermesh: Page 26

ENE 104 Basic Nodal and Mesh Analysis Week #3

The Supermesh: Page 27

ENE 104 Basic Nodal and Mesh Analysis

Find the three mesh currents in the circuit below.

Creating a “supermesh” from meshes 1 and 3:

-7 + 1 ( i1 - i2 ) + 3 ( i3 - i2 ) + 1 i3 = 0 [1]

Around mesh 2:

1 ( i2 - i1 ) + 2 i2 + 3 ( i2 - i3 ) = 0 [2]

Rearranging,

i1 - 4 i2 + 4 i3 = 7 [1]

-i1 + 6 i2 - 3 i3 = 0 [2]

i1 - i3 = 7 [3]

Solving,

i1 = 9 A, i2 = 2.5 A, and i3 = 2 A.

Finally, we relate the currents in meshes 1 and 3:

i1 - i3 = 7 [3]

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Practice: 4.8 Page 28

ENE 104 Basic Nodal and Mesh Analysis

Find the voltage v3 in the circuit below.

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Practice: 4.8 Page 29

ENE 104 Basic Nodal and Mesh Analysis

Find the voltage v3 in the circuit below.

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Ai

Bi

Practice: 4.8 Page 30

ENE 104 Basic Nodal and Mesh Analysis

Find the voltage v3 in the circuit below.

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Ai

Bi

A comparison: Page 31

ENE 104 Basic Nodal and Mesh Analysis Week #3

A comparison: Page 32

ENE 104 Basic Nodal and Mesh Analysis Week #3

A comparison: Page 33

ENE 104 Basic Nodal and Mesh Analysis Week #3

A comparison: Page 34

ENE 104 Basic Nodal and Mesh Analysis Week #3

Ex: Page 35

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Ch4-26 p.94 Determine each mesh current in the circuit

Basic Nodal and Mesh Analysis

Computer-Aided: Page 36

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Computer-Aided: Page 37

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Example: Page 38

ENE 104 Basic Nodal and Mesh Analysis Week #3

Ch4.58 p.100 Write an appropriate input deck

for SPICE to find v5 in the circuit. Submit a

printout of the output file, with the solution

highlight

Homework: Page 39

ENE 104 Circuit Analysis and Electrical Engineering Week #3

Reference: Page 40

ENE 104 Basic Nodal and Mesh Analysis

W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.

Copyright ©2002 McGraw-Hill. All rights reserved.

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