CH 3 Nodal and Loop analysis Techniques, Slides of Electronics engineering

Download CH 3 Nodal and Loop analysis Techniques and more Slides Electronics engineering in PDF only on Docsity!

Chapter 3

Nodal and Loop analysis

Techniques

Nodal analysis

• To determine every voltage

and current in a circuit by

using KCL

Example

@ NODE 1

Write the KCL equations

@ NODE 2

Compute all the voltages and currents in this circuit

The strategy for node analysis

@ Va :  I 1  I 2  I 3  0

k

V V

k

V

k

V a Vs a a b

Reference

VS Va Vb Vc

@ V (^) b :  I 3  I 4  I 5  0 @ Vc :  I 5  I 6  0

0 3 4 9



  



k

V V

k

V

k

V (^) b Va b b c 0 9 3

 



k

V

k

Vc Vb c

An example of node analysis

@ v 1

@ v 2

@ v 3

2 2 1 2 

k

V V

k

V

V mA

V mA k

V

k k

6 mA

k

V

k

V

V mA V 2 (^)  12 V

 V 1 (^)   16 V 1 @ 1 : 2 6 0 2

V V mA mA k

  

Node analysis

Learning Example: Circuit with Voltage-Controlled Current

2 [ / ]

4

1 2 3

A V

R k i mAi mA

R k R R k

A B



Learning Extension: Find Node Voltages

1 1 2 1 

k

V V

mA k

V

V

Node Equations

2 1 2 2   

k

V

I

k

V V

V O

k

V

IO

1 

Two nodes are connected to the reference through voltage

sources. Hence, those node voltages are known!!!

Only one KCL is necessary

0 6 12 12

2 2 3 2 1 

 

  k

V V

k

V V

k

V

Circuits with Independent Voltage Sources

6 [ ]

12 [ ]

3

1

V V

V V

 



V 1  3 V

2 1 2   

Ix k

V

k

V V

KCL@ V 2

k

V

Ix 6

2 

2 1 2 2   

k

V

k

V

k

V V

V 2  2 V 1  0  V 2  6 V

mA k

V V

IO 1

1 2 

FIND IO

Learning Example

V V

V V

4

1

 

SUPERNODE

V 3  V 2  12 V

KCL @ SUPERNODE

k

V

k

V

k

V

k

V

mA k

V

IO 3. 8

3 OHM'SLAW  

Current Controlled Voltage Source

V (^) 2  V 1  2 kIx 0 2

1 2      k

V

mA k

V

mA k

V

Ix 2

1 

 V 1 (^)  2 kIx  V 2  2 V 1 3 V 2 (^)  8 [ V ] mA k

V

IO

2  