![Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Introduction…
Passive Elements
1. Resistor[R]:
•A resistor opposes the flow of electric current.
•Resistors dissipate energy in the form of heat.
•Resistors exhibit negative temperature effects.
•Obeys ohm’s Law
VαI, V=R I ohms.
Where, R is the Proportionality constant called Resistance measured
in Ohms, V is the Voltage and I is the Current.
•If Resistors are connected in Series. 𝑅 𝑒𝑞 = 𝑖=1
𝑛
𝑅𝑖
•If Resistors are connected in Parallel.
1
𝑅 𝑒𝑞
= 𝑖=1
𝑛 1
𝑅 𝑖
•Power 𝑃 = 𝑉𝑥𝐼 ⇒
𝑉2
𝑅
⇒ 𝐼2 𝑅 𝑊𝑎𝑡𝑡𝑠
Circuit Symbol
R
Resistors are in Series
Resistors are in Parallel](https://image.slidesharecdn.com/introduction-200923061017/85/Introduction-to-Network-Analysis-10-320.jpg)
![Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Introduction…
2. Capacitor [C]:
• Capacitors stores energy in the form of Electrostatic Field.
• 𝑄 = 𝐶𝑉
• v(t)=
1
𝐶
𝑖 𝑡 . 𝑑𝑡; i t = C
dv t
dt
.
• 𝐸 =
1
2
𝐶𝑉2
Joules.
• 𝐶𝑒𝑞 =
1
𝑖=1
𝑛 1/𝐶 𝑖
; If the Capacitors are connected in Series.
• 𝐶𝑒𝑞 = 𝑖=1
𝑛
𝐶𝑖 ; If the Capacitors are connected in Parallel.
• Star to delta and delta to star conversion is applicable to capacitors,
only if it is in Reactance form.
• Capacitive Reactance 𝑋 𝐶 =
1
2𝜋𝑓𝐶
Ohms.
Circuit Symbol
C](https://image.slidesharecdn.com/introduction-200923061017/85/Introduction-to-Network-Analysis-12-320.jpg)
![Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru
Network Theory (19EC33)
Introduction…
3. Inductor [L]:
• Inductors stores energy in the form of Electro Magnetic Field.
• 𝜑 = 𝐿𝐼
• v(t)= L
di t
dt
; i t =
1
𝐿
𝑣 𝑡 . 𝑑𝑡.
• 𝐸 =
1
2
𝐿𝐼2
Joules.
• 𝐿 𝑒𝑞 = 𝑖=1
𝑛
𝐿𝑖 ; If the Inductors are connected in Series.
• 𝐿 𝑒𝑞 =
1
𝑖=1
𝑛 1/𝐿 𝑖
; If the Inductors are connected in Parallel.
• Star to delta and delta to star conversion applicable to Inductors
also, only if it is in Reactance form.
• Inductive Reactance, 𝑋 𝐿 = 2𝜋𝑓𝐿 Ohms.
Circuit Symbol
L](https://image.slidesharecdn.com/introduction-200923061017/85/Introduction-to-Network-Analysis-13-320.jpg)
Introduction to Network Analysis
- 1. Network Theory(19EC33) 2020-21 Class-1: Overview of Syllabus and Introduction to Network Theory 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) Overview of Syllabus • Subject Title : Network Theory • Subject code : 19EC33 • Credits: 04 • Total number of Contact hours : 52 hours • Number of teaching hours per week: 04 hours • 3- CIE’s, 25 marks each • Final CIE=Sum of two best CIE marks and reduced it to 40 marks + 5 marks Assignment + 5 marks Group Activity. • Assignments – Problems • Group Activity – PSPICE Simulation
- 3. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru Network Theory (19EC33) Overview of Syllabus… Pre-requisites: • Engineering Mathematics • Basic Electrical Engineering Objectives: • Different types of Electrical Elements and their characteristics. • Circuit Analysis Techniques such as Circuit simplification, loop analysis and node analysis. • Different Network Theorems and its applications,. • Concepts of Resonance and its importance. • Study of dynamic behavior(Transient and steady state response) of electrical systems using initial conditions • Applications of Laplace Transforms to electrical systems. • Two port networks and its importance in the analysis of electrical circuits.
- 4. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru Network Theory (19EC33) Overview of Syllabus… Contents: Unit-I: Ch-1: Basic Circuit Concepts Unit-II: Ch-1: Network Theorems Ch-2: Resonant Circuits Unit-III: Ch-1: Transient Behaviour and Initial Conditions Unit-IV: Ch-1: Laplace Transforms Unit-V: Ch-1: Two Port Network Parameters
- 5. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru Network Theory (19EC33) Overview of Syllabus… Outcomes: • Apply the network reduction techniques to simplify the electrical circuits and analyze electrical circuits using loop and nodal analysis. • Apply the network theorems to find the load quantities, explain the resonant parameters and the analyze the circuit. • Explain and find the transient behavior of electrical circuits with initial conditions. • Apply the Laplace Transforms for the analysis of electrical circuits. • Define, explain and find the two port network parameters of electrical circuits and derive the relationship between one parameter to other parameter. Pre-Requisite for: • Electronic Circuits • Communications • Power Electronics
- 6. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru Network Theory (19EC33) Overview of Syllabus… • Text Books: • Charles K Alexander and Mathew N O Sadiku, “Fundamentals of Electric Circuits”, 3rd edition, Tata McGraw-Hill, 2009.
- 7. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru Network Theory (19EC33) Introduction Definition: Network Theory Theory: A set of Principles or Ideas are used to perform an activity ( In this context activity is to study and analysis of a Networks). Network ( Electrical ): Interconnection or combination of electrical elements is called an electrical network, generally network. Network Theory: Set of principles or ideas are used to study the behaviour of electrical networks. Circuit and Network: Network- Open loop or Closed Loop Circuit- Closed Loop All circuits are networks but all networks are not circuits Network Network/Circuit
- 8. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru Network Theory (19EC33) Introduction… Electrical Elements Electrical Elements Passive Elements Resistors Capacitors Inductors Active Elements Independent sources Ideal Voltage Current Practical voltage current Dependent sources VCVS VCIS ICVS ICIS
- 9. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru Network Theory (19EC33) Introduction… Basic principles 1. Current: Rate of change of Charge is called current, it is denoted as “I” and unit is Amperes. 𝐼 = 𝑑𝑄 𝑑𝑡 1. Voltage: Rate of change of Flux is called Voltage, it is denoted as “V” and unit is volts. 𝑉 = 𝑑Ø 𝑑𝑡 1. Power: Product of Voltage and Current is called Power, it is denoted as “P” and unit is watts. 𝑃 = 𝑉 × 𝐼 Branch: A Path of element is connecting between two nodes is called Branch. Node: Two or more elements connected at a Point/Junction is called as a Node. Ohm’s law: Ohm’s law states that the voltage across an element is directly proportional to the current flowing through that element. 𝑖. 𝑒., 𝑉𝛼 𝐼
- 10. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru Network Theory (19EC33) Introduction… Passive Elements 1. Resistor[R]: •A resistor opposes the flow of electric current. •Resistors dissipate energy in the form of heat. •Resistors exhibit negative temperature effects. •Obeys ohm’s Law VαI, V=R I ohms. Where, R is the Proportionality constant called Resistance measured in Ohms, V is the Voltage and I is the Current. •If Resistors are connected in Series. 𝑅 𝑒𝑞 = 𝑖=1 𝑛 𝑅𝑖 •If Resistors are connected in Parallel. 1 𝑅 𝑒𝑞 = 𝑖=1 𝑛 1 𝑅 𝑖 •Power 𝑃 = 𝑉𝑥𝐼 ⇒ 𝑉2 𝑅 ⇒ 𝐼2 𝑅 𝑊𝑎𝑡𝑡𝑠 Circuit Symbol R Resistors are in Series Resistors are in Parallel
- 11. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru Network Theory (19EC33) Introduction… Resistors are connected in Star form. Resistors are connected in Delta form. Star to Delta conversion 𝑅 𝑎 = 𝑅1 𝑅2+𝑅2 𝑅3+𝑅1 𝑅3 𝑅1 ; 𝑅 𝑏 = 𝑅1 𝑅2+𝑅2 𝑅3+𝑅1 𝑅3 𝑅2 ; 𝑅 𝑐 = 𝑅1 𝑅2+𝑅2 𝑅3+𝑅1 𝑅3 𝑅3 . Delta to Star conversion 𝑅1 = 𝑅 𝑏 𝑅 𝑐 𝑅 𝑎+𝑅 𝑏+𝑅 𝑐 ; 𝑅2 = 𝑅 𝑎 𝑅 𝑐 𝑅 𝑎+𝑅 𝑏+𝑅 𝑐 ; 𝑅3 = 𝑅 𝑎 𝑅 𝑏 𝑅 𝑎+𝑅 𝑏+𝑅 𝑐 .
- 12. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru Network Theory (19EC33) Introduction… 2. Capacitor [C]: • Capacitors stores energy in the form of Electrostatic Field. • 𝑄 = 𝐶𝑉 • v(t)= 1 𝐶 𝑖 𝑡 . 𝑑𝑡; i t = C dv t dt . • 𝐸 = 1 2 𝐶𝑉2 Joules. • 𝐶𝑒𝑞 = 1 𝑖=1 𝑛 1/𝐶 𝑖 ; If the Capacitors are connected in Series. • 𝐶𝑒𝑞 = 𝑖=1 𝑛 𝐶𝑖 ; If the Capacitors are connected in Parallel. • Star to delta and delta to star conversion is applicable to capacitors, only if it is in Reactance form. • Capacitive Reactance 𝑋 𝐶 = 1 2𝜋𝑓𝐶 Ohms. Circuit Symbol C
- 13. Dept. of ECE, Dr. Ambedkar Institute of Technology, Bengaluru Network Theory (19EC33) Introduction… 3. Inductor [L]: • Inductors stores energy in the form of Electro Magnetic Field. • 𝜑 = 𝐿𝐼 • v(t)= L di t dt ; i t = 1 𝐿 𝑣 𝑡 . 𝑑𝑡. • 𝐸 = 1 2 𝐿𝐼2 Joules. • 𝐿 𝑒𝑞 = 𝑖=1 𝑛 𝐿𝑖 ; If the Inductors are connected in Series. • 𝐿 𝑒𝑞 = 1 𝑖=1 𝑛 1/𝐿 𝑖 ; If the Inductors are connected in Parallel. • Star to delta and delta to star conversion applicable to Inductors also, only if it is in Reactance form. • Inductive Reactance, 𝑋 𝐿 = 2𝜋𝑓𝐿 Ohms. Circuit Symbol L
- 14. 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 ?