Network Simplification Technique

1. Network Theory(19EC33)
2020-21
Class-6: Source Transformation, Source shifting and star-delta
conversion with Examples
MOHANKUMAR V.
ASSISTANT PROFESSOR
D E P A R TM E N T O F E L E C TR O N I C S A N D C O M M U N I C A TI O N E N G I N E E R I N G
D R . A M B E D K A R I N S TI TU TE O F TE C H N O L O G Y , B E N G A L U R U - 5 6
E - M A I L : MO H A N K U MA R . V @ D R - A I T . O R G

2. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
6. Find the Current IL in the circuit shown in figure.
Identify the load element and remove it,
then name the load terminals

3. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
Apply Voltage source shifting for
10 V source
Convert voltage sources[(10 V, 5 Ω) , (5 V, 10 Ω) ]
into current sources

4. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
Combine Current sources (1A , 0.5A)
and parallel Resistors (5 Ω, 10 Ω)
Combine Voltage sources (8.33 V , 18 V)
and Series Resistors (6 Ω, 3.33Ω)

5. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
Re-arranging the elements Convert voltage sources[(10 V, 10 Ω) ,
(26.33 V, 9.33 Ω) ] into current sources
Combine Current sources (1A , 2.82 A)
and parallel Resistors (9.33 Ω, 10 Ω)

6. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
Apply current division formula
𝑰 𝑳 = 𝟑. 𝟖𝟐
𝟒. 𝟖𝟐
𝟒. 𝟖𝟐 + 𝟏𝟎
𝑰 𝑳 = 𝟏. 𝟐𝟒𝑨
Connect the load element across AB

7. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Star to delta and delta to start conversion

8. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Delta to Star Conversion Formula
Delta to Start Conversion
𝑹 𝑨 =
𝑹 𝟏 𝑹 𝟑
𝑹 𝟏 + 𝑹 𝟐 + 𝑹 𝟑
𝑹 𝑩 =
𝑹 𝟏 𝑹 𝟐
𝑹 𝟏 + 𝑹 𝟐 + 𝑹 𝟑
𝑹 𝑪 =
𝑹 𝟐 𝑹 𝟑
𝑹 𝟏 + 𝑹 𝟐 + 𝑹 𝟑
NOTE: Denominator is common

9. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Star to delta Conversion Formula
Star to Delta Conversion
𝑹 𝟏 =
𝑹 𝑨 𝑹 𝑩 + 𝑹 𝑩 𝑹 𝑪 + 𝑹 𝑪 𝑹 𝑨
𝑹 𝑪
𝑹 𝟐 =
𝑹 𝑨 𝑹 𝑩 + 𝑹 𝑩 𝑹 𝑪 + 𝑹 𝑪 𝑹 𝑨
𝑹 𝑨
𝑹 𝟑 =
𝑹 𝑨 𝑹 𝑩 + 𝑹 𝑩 𝑹 𝑪 + 𝑹 𝑪 𝑹 𝑨
𝑹 𝑩
NOTE: Star to delta and delta to start conversion applicable to
Capacitors and Inductors also, but should be in reactance format.
NOTE: Numerator is common

10. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
7. Convert the given network into equivalent star network
𝑹 𝟏 =
𝟓𝒙𝟏𝟎
𝟓 + 𝟏𝟎 + 𝟏𝟓
⇒ 𝟏. 𝟔𝟔𝟕 𝜴
𝑹 𝟐 =
𝟏𝟎𝒙𝟏𝟓
𝟓 + 𝟏𝟎 + 𝟏𝟓
⇒ 𝟓𝜴
𝑹 𝟑 =
𝟓𝒙𝟏𝟓
𝟓 + 𝟏𝟎 + 𝟏𝟓
⇒ 𝟐. 𝟓 𝜴

11. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
8. Convert the given network into equivalent Delta network
𝑅31 =
1.67𝑥2.5 + 2.5𝑥5 + 5𝑥1.67
5
⇒ 𝟓 𝜴
𝑅12 =
1.67𝑥2.5 + 2.5𝑥5 + 5𝑥1.67
2.5
⇒ 𝟏𝟎 𝜴
𝑅23 =
1.67𝑥2.5 + 2.5𝑥5 + 5𝑥1.67
1.67
⇒ 𝟏𝟓 𝜴

12. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
9. Find the equivalent resistance between the terminals A and B

13. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
Combine the Series connected resistors

14. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples

15. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
𝑹 𝑨𝑩 = 𝟑. 𝟔𝟗 𝜴

16. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
10. Find the equivalent resistance between the terminals A and B

17. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples

18. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples

19. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
11. Find the equivalent resistance between the terminals A and B

20. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples
Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Examples

21. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Disclaimer
Some Contents and Images showed in this PPT
have been taken from the various internet
sources for educational purpose only.
Thank You
?