The document defines key terms related to network topology and graph theory, including circuit elements, nodes, branches, paths, loops, and different types of graphs. It provides definitions for each term and discusses how they relate to representing electrical networks as graphs.
This document provides instructions for an experiment on staircase wiring to control one lamp from two points using two SPDT switches. The theory section explains that the wiring allows a bulb to be turned on or off from an upper or lower switch by breaking the wiring circuit. The procedure lists the required materials and instructs students to connect the lamp and switches as shown in the diagram and check the connections with a multimeter before operating the lamp. The conclusion restates that the wiring allows controlling a bulb from two switches simultaneously by switching it off and on from either the upper or lower switch.
The document provides an overview of power electronic devices. It begins by defining power electronic devices as semiconductor devices used to convert or control electric power. It then discusses the key features of power electronic devices, including that they must handle large power levels and typically operate in switching states. The document outlines the basic configuration of a power electronic system and classifications of devices. It provides details on uncontrolled diodes, half-controlled thyristors, and fully-controlled devices. It also discusses characteristics, specifications, applications and history.
Per unit analysis is used to normalize variables in power systems to avoid difficulties in referring impedances across transformers. It involves choosing base values for voltage, power, impedance and current, then expressing all quantities as ratios of their actual to base values. This allows transformer impedances to be treated as single values regardless of which side they are referred to. It also keeps per unit quantities within a narrow range and clearly shows their relative values. The procedure is demonstrated through an example circuit solved first using single phase and then three phase per unit analysis with the same result.
This document provides an overview of DC machines and motors. It discusses:
1) The fundamentals of DC generators and motors, including how voltage is induced in a conductor moving through a magnetic field and how a force is induced on a current-carrying conductor in a magnetic field.
2) The construction of DC machines, including the stationary stator with field poles and rotating armature/rotor with windings.
3) Different types of DC motors like shunt, series, and compound motors and how their field and armature windings are connected. Speed control methods for DC motors are also discussed.
4) Workings of DC motors are explained through equivalent circuits and equations for induced voltage
The document describes a two port network and provides information about various parameter representations of two port networks, including:
- Z parameters define the input and transfer impedances between the two ports.
- Y parameters define the input and transfer admittances between the two ports.
- Transmission parameters (A,B,C,D) define relationships between voltages and currents at the two ports.
- Hybrid parameters also define relationships between voltages and currents at the two ports.
Examples are provided to demonstrate calculating the parameter representations for given two port networks. Additionally, the document discusses how modifying a two port network impacts its parameter representations.
This document provides instructions for an experiment on staircase wiring to control one lamp from two points using two SPDT switches. The theory section explains that the wiring allows a bulb to be turned on or off from an upper or lower switch by breaking the wiring circuit. The procedure lists the required materials and instructs students to connect the lamp and switches as shown in the diagram and check the connections with a multimeter before operating the lamp. The conclusion restates that the wiring allows controlling a bulb from two switches simultaneously by switching it off and on from either the upper or lower switch.
The document provides an overview of power electronic devices. It begins by defining power electronic devices as semiconductor devices used to convert or control electric power. It then discusses the key features of power electronic devices, including that they must handle large power levels and typically operate in switching states. The document outlines the basic configuration of a power electronic system and classifications of devices. It provides details on uncontrolled diodes, half-controlled thyristors, and fully-controlled devices. It also discusses characteristics, specifications, applications and history.
Per unit analysis is used to normalize variables in power systems to avoid difficulties in referring impedances across transformers. It involves choosing base values for voltage, power, impedance and current, then expressing all quantities as ratios of their actual to base values. This allows transformer impedances to be treated as single values regardless of which side they are referred to. It also keeps per unit quantities within a narrow range and clearly shows their relative values. The procedure is demonstrated through an example circuit solved first using single phase and then three phase per unit analysis with the same result.
This document provides an overview of DC machines and motors. It discusses:
1) The fundamentals of DC generators and motors, including how voltage is induced in a conductor moving through a magnetic field and how a force is induced on a current-carrying conductor in a magnetic field.
2) The construction of DC machines, including the stationary stator with field poles and rotating armature/rotor with windings.
3) Different types of DC motors like shunt, series, and compound motors and how their field and armature windings are connected. Speed control methods for DC motors are also discussed.
4) Workings of DC motors are explained through equivalent circuits and equations for induced voltage
The document describes a two port network and provides information about various parameter representations of two port networks, including:
- Z parameters define the input and transfer impedances between the two ports.
- Y parameters define the input and transfer admittances between the two ports.
- Transmission parameters (A,B,C,D) define relationships between voltages and currents at the two ports.
- Hybrid parameters also define relationships between voltages and currents at the two ports.
Examples are provided to demonstrate calculating the parameter representations for given two port networks. Additionally, the document discusses how modifying a two port network impacts its parameter representations.
This document introduces several important network theorems: superposition, Thevenin's, Norton's, maximum power transfer, Millman's, substitution, and reciprocity. It provides definitions and procedures for applying each theorem, such as replacing network elements with voltage/current sources and determining equivalent resistances and voltages. The theorems allow analyzing complex networks, determining outputs when components change, and maximizing power transfer between networks.
This document discusses source transformation examples in network theory. It begins with key points about applying source transformation to practical sources. Next, it outlines the procedure for simplifying electrical networks using source transformation and source shifting. The remainder of the document works through examples of simplifying circuits using these techniques to obtain equivalent single voltage or current sources between load terminals. It concludes with a practice problem and disclaimer about content taken from other sources.
1) DC generators convert mechanical energy to electrical energy through Faraday's law of electromagnetic induction. When a conductor moves through a magnetic field, an EMF is induced in the conductor.
2) The main components of a DC generator are the yoke, field electromagnets, armature, commutator, and brushes. The armature is wound with coils and rotates within the magnetic field produced by the field electromagnets to generate an EMF.
3) As the armature rotates, the commutator and brushes are used to periodically reverse the direction of current in the external circuit, thereby producing direct current. Losses in the generator arise from copper, iron, and mechanical components
This chapter provides complete description of two port network parameters. It also provides relationship between different parameters. Also it provides condition for symmetry and reciprocity.
Chopper basically uses a Thyristor for high power applications. The process of turning off a conducting Thyristor is known as commutation. Here Thyristor is turned off by a current pulse that is why it is called a Current Commutated Chopper.
Power System Analysis was a core subject for Electrical & Electronics Engineering, Based On Anna University Syllabus. The Whole Subject was there in this document.
Share with it ur friends & Follow me for more updates.!
This document discusses parameters of transmission lines and cables. It begins by describing different types of transmission lines based on voltage level, including extra-high voltage lines, high voltage lines, sub-transmission lines, and distribution lines. It then covers the typical components of transmission lines, such as conductors, insulators, towers, and foundations. The document provides examples of commonly used tower designs and conductor types. It concludes by deriving equations to calculate the resistance, inductance, and capacitance of transmission lines based on conductor and geometry properties.
The document provides an overview of the Analog and Digital Electronics course taught at Matoshri College of Engineering & Research Centre. It includes information about the course's teaching scheme, examination scheme, objectives, and outcomes. The objectives are to design logical, sequential and combinational digital circuits using K-maps and to develop concepts related to operational amplifiers and rectifiers. The document also provides details of the topics to be covered in the first unit including Boolean algebra, K-maps, and the design of combinational circuits. It introduces concepts such as logic gates, number systems, and digital signals.
The document describes an experiment on instrument transformers conducted at the STANI Memorial College of Engineering & Technology. The aim was to study the design considerations of current transformers (CTs) and potential transformers (PTs) for measurement and protection. The theory section explains that instrument transformers are used to isolate or transform voltage and current levels to safely operate meters and relays. It then provides details on CTs and PTs, including their construction, ratios, and errors. The procedure measures errors in CTs and PTs. Observations were recorded and calculations were made to analyze the results. In conclusion, the experiment successfully studied instrument transformers and their design considerations for measurement.
EXPERIMENTAL DETERMINATION AND ANALYSIS OF TRANSMISSION LINE PERFORMANCEijiert bestjournal
Ā
It is necessary to calculate the voltage,current a nd power at any point on a transmission line provided the values at one point are known. We are aware that in three phase circuit problems it is sufficient to compute results in one phase and subsequently predict results in the other two phases by exploiting the three phase symm etry. Although the lines are not spaced equilaterally and not transposed,the resulting asy mmetry is slight and the phases are considered to be balanced. As such the transmission line calcu lations are also carried out on per phase basis. For that purpose in the transmission line demo pane l we will be designed to ļæ½To study the performance of the line.1)e.g. Relation between sen ding end quantity and receiving end quantity,Ferranti effect,efficiency of power line etc.2) To demonstrate fault clearing process using distance relay(Future Scope)
The document discusses DC machines and motors. It provides explanations of Maxwell's corkscrew rule and Fleming's left-hand and right-hand rules for determining the direction of magnetic fields. It also describes the construction and working principles of DC generators and motors, including their components like the armature, commutator, and field windings. Various types of DC machines are classified based on their excitation and winding configurations. The document also covers topics like armature reaction, speed control methods, and applications of different DC motor types.
This document provides instructions for an experiment to determine the voltage and current ratios of a single-phase transformer. The experiment uses a single-phase transformer, auto-transformer, ammeters, voltmeters and a load bank. Students are instructed to vary the primary voltage and load, and record primary and secondary voltage and current readings. They will then calculate and compare the average voltage and current ratios to determine if they are equal, as dictated by the transformer's turns ratio.
Three phase Induction Motor (Construction and working Principle)Sharmitha Dhanabalan
Ā
The three phase induction motor consists of a stationary stator and a rotating rotor. The stator contains three-phase windings that generate a rotating magnetic field. This rotating field induces currents in the rotor windings, causing the rotor to turn. There are two common types of rotors - squirrel cage and wound rotor. A squirrel cage rotor has embedded conductors inside its core that are permanently short-circuited. A wound rotor has three insulated windings connected to slip rings to allow external resistance control. Due to slight differences in speed, the rotor always rotates at a slightly slower synchronous speed than the stator's magnetic field.
Kirchhoff's laws deal with the conservation of charge and energy in electrical circuits. There are two Kirchhoff's laws:
1. Kirchhoff's current law (KCL) states that the algebraic sum of currents in a network meeting at a point is zero.
2. Kirchhoff's voltage law (KVL) states that the directed sum of the potential differences around any closed network is zero.
Circuit analysis methods like mesh analysis, nodal analysis, and superposition theorem can be used to solve circuits using Kirchhoff's laws. Mesh analysis uses KVL to analyze loops in a planar circuit. Nodal analysis uses KCL to analyze connections (nodes) in a circuit. Superposition
The document discusses transient analysis of first order differential equations that model circuits containing energy storage elements like capacitors and inductors. It explains that when the circuit conditions change, there will be a transient response before reaching the steady-state. The complete solution consists of the natural/homogeneous response and the particular/forced response. The natural response dies out over time, while the forced response depends on the external excitation. Circuits are solved using the time constant, which relates to how long it takes for the transient response to decay to the steady-state.
This document discusses various network topology concepts including nodes, branches, loops, trees, and different matrix representations of networks. It defines key terms like nodes, branches, loops, meshes, and oriented graphs. It also describes tree concepts such as twigs, links, and co-trees. Finally, it discusses different matrix representations of networks including the incidence matrix, loop matrix, tie-set matrix, cut-set matrix, and formulations of network equilibrium equations in node, mesh, and cut-set forms.
Network theorems for electrical engineeringKamil Hussain
Ā
The document discusses several circuit analysis theorems and methods. Kirchhoff's laws describe the conservation of charge and energy in circuits. Mesh analysis and nodal analysis are methods to solve circuits by assigning currents or voltages and setting up equations based on Kirchhoff's laws. The superposition theorem allows analyzing circuits with multiple sources by solving for each source independently and summing the results.
This document introduces several important network theorems: superposition, Thevenin's, Norton's, maximum power transfer, Millman's, substitution, and reciprocity. It provides definitions and procedures for applying each theorem, such as replacing network elements with voltage/current sources and determining equivalent resistances and voltages. The theorems allow analyzing complex networks, determining outputs when components change, and maximizing power transfer between networks.
This document discusses source transformation examples in network theory. It begins with key points about applying source transformation to practical sources. Next, it outlines the procedure for simplifying electrical networks using source transformation and source shifting. The remainder of the document works through examples of simplifying circuits using these techniques to obtain equivalent single voltage or current sources between load terminals. It concludes with a practice problem and disclaimer about content taken from other sources.
1) DC generators convert mechanical energy to electrical energy through Faraday's law of electromagnetic induction. When a conductor moves through a magnetic field, an EMF is induced in the conductor.
2) The main components of a DC generator are the yoke, field electromagnets, armature, commutator, and brushes. The armature is wound with coils and rotates within the magnetic field produced by the field electromagnets to generate an EMF.
3) As the armature rotates, the commutator and brushes are used to periodically reverse the direction of current in the external circuit, thereby producing direct current. Losses in the generator arise from copper, iron, and mechanical components
This chapter provides complete description of two port network parameters. It also provides relationship between different parameters. Also it provides condition for symmetry and reciprocity.
Chopper basically uses a Thyristor for high power applications. The process of turning off a conducting Thyristor is known as commutation. Here Thyristor is turned off by a current pulse that is why it is called a Current Commutated Chopper.
Power System Analysis was a core subject for Electrical & Electronics Engineering, Based On Anna University Syllabus. The Whole Subject was there in this document.
Share with it ur friends & Follow me for more updates.!
This document discusses parameters of transmission lines and cables. It begins by describing different types of transmission lines based on voltage level, including extra-high voltage lines, high voltage lines, sub-transmission lines, and distribution lines. It then covers the typical components of transmission lines, such as conductors, insulators, towers, and foundations. The document provides examples of commonly used tower designs and conductor types. It concludes by deriving equations to calculate the resistance, inductance, and capacitance of transmission lines based on conductor and geometry properties.
The document provides an overview of the Analog and Digital Electronics course taught at Matoshri College of Engineering & Research Centre. It includes information about the course's teaching scheme, examination scheme, objectives, and outcomes. The objectives are to design logical, sequential and combinational digital circuits using K-maps and to develop concepts related to operational amplifiers and rectifiers. The document also provides details of the topics to be covered in the first unit including Boolean algebra, K-maps, and the design of combinational circuits. It introduces concepts such as logic gates, number systems, and digital signals.
The document describes an experiment on instrument transformers conducted at the STANI Memorial College of Engineering & Technology. The aim was to study the design considerations of current transformers (CTs) and potential transformers (PTs) for measurement and protection. The theory section explains that instrument transformers are used to isolate or transform voltage and current levels to safely operate meters and relays. It then provides details on CTs and PTs, including their construction, ratios, and errors. The procedure measures errors in CTs and PTs. Observations were recorded and calculations were made to analyze the results. In conclusion, the experiment successfully studied instrument transformers and their design considerations for measurement.
EXPERIMENTAL DETERMINATION AND ANALYSIS OF TRANSMISSION LINE PERFORMANCEijiert bestjournal
Ā
It is necessary to calculate the voltage,current a nd power at any point on a transmission line provided the values at one point are known. We are aware that in three phase circuit problems it is sufficient to compute results in one phase and subsequently predict results in the other two phases by exploiting the three phase symm etry. Although the lines are not spaced equilaterally and not transposed,the resulting asy mmetry is slight and the phases are considered to be balanced. As such the transmission line calcu lations are also carried out on per phase basis. For that purpose in the transmission line demo pane l we will be designed to ļæ½To study the performance of the line.1)e.g. Relation between sen ding end quantity and receiving end quantity,Ferranti effect,efficiency of power line etc.2) To demonstrate fault clearing process using distance relay(Future Scope)
The document discusses DC machines and motors. It provides explanations of Maxwell's corkscrew rule and Fleming's left-hand and right-hand rules for determining the direction of magnetic fields. It also describes the construction and working principles of DC generators and motors, including their components like the armature, commutator, and field windings. Various types of DC machines are classified based on their excitation and winding configurations. The document also covers topics like armature reaction, speed control methods, and applications of different DC motor types.
This document provides instructions for an experiment to determine the voltage and current ratios of a single-phase transformer. The experiment uses a single-phase transformer, auto-transformer, ammeters, voltmeters and a load bank. Students are instructed to vary the primary voltage and load, and record primary and secondary voltage and current readings. They will then calculate and compare the average voltage and current ratios to determine if they are equal, as dictated by the transformer's turns ratio.
Three phase Induction Motor (Construction and working Principle)Sharmitha Dhanabalan
Ā
The three phase induction motor consists of a stationary stator and a rotating rotor. The stator contains three-phase windings that generate a rotating magnetic field. This rotating field induces currents in the rotor windings, causing the rotor to turn. There are two common types of rotors - squirrel cage and wound rotor. A squirrel cage rotor has embedded conductors inside its core that are permanently short-circuited. A wound rotor has three insulated windings connected to slip rings to allow external resistance control. Due to slight differences in speed, the rotor always rotates at a slightly slower synchronous speed than the stator's magnetic field.
Kirchhoff's laws deal with the conservation of charge and energy in electrical circuits. There are two Kirchhoff's laws:
1. Kirchhoff's current law (KCL) states that the algebraic sum of currents in a network meeting at a point is zero.
2. Kirchhoff's voltage law (KVL) states that the directed sum of the potential differences around any closed network is zero.
Circuit analysis methods like mesh analysis, nodal analysis, and superposition theorem can be used to solve circuits using Kirchhoff's laws. Mesh analysis uses KVL to analyze loops in a planar circuit. Nodal analysis uses KCL to analyze connections (nodes) in a circuit. Superposition
The document discusses transient analysis of first order differential equations that model circuits containing energy storage elements like capacitors and inductors. It explains that when the circuit conditions change, there will be a transient response before reaching the steady-state. The complete solution consists of the natural/homogeneous response and the particular/forced response. The natural response dies out over time, while the forced response depends on the external excitation. Circuits are solved using the time constant, which relates to how long it takes for the transient response to decay to the steady-state.
This document discusses various network topology concepts including nodes, branches, loops, trees, and different matrix representations of networks. It defines key terms like nodes, branches, loops, meshes, and oriented graphs. It also describes tree concepts such as twigs, links, and co-trees. Finally, it discusses different matrix representations of networks including the incidence matrix, loop matrix, tie-set matrix, cut-set matrix, and formulations of network equilibrium equations in node, mesh, and cut-set forms.
Network theorems for electrical engineeringKamil Hussain
Ā
The document discusses several circuit analysis theorems and methods. Kirchhoff's laws describe the conservation of charge and energy in circuits. Mesh analysis and nodal analysis are methods to solve circuits by assigning currents or voltages and setting up equations based on Kirchhoff's laws. The superposition theorem allows analyzing circuits with multiple sources by solving for each source independently and summing the results.
The document provides an introduction to graph theory. It begins with a brief history, noting that graph theory originated from Euler's work on the Konigsberg bridges problem in 1735. It then discusses basic concepts such as graphs being collections of nodes and edges, different types of graphs like directed and undirected graphs. Key graph theory terms are defined such as vertices, edges, degree, walks, paths, cycles and shortest paths. Different graph representations like the adjacency matrix, incidence matrix and adjacency lists are also introduced. The document is intended to provide an overview of fundamental graph theory concepts.
This document discusses graphs and networks. It defines key terms related to graphs like nodes, branches, trees, and loops. It explains properties of trees, including that a tree with n nodes will have n-1 branches and no closed paths. It also discusses incidence matrices, cut-set matrices, and loop matrices which relate to representing graphs and networks mathematically through matrices. Formulas are provided for relationships between the number of trees, branches, and nodes in a graph.
International Journal of Analysis of Electrical Machines
is a peer-reviewed journal that publishes original research concerning electrical machines. Journal accepts both experimental and theoretical papers and publishes original research articles and review papers. Journal also promotes the practical application of the research that could prove to be beneficial to the society.
The document lists various subjects related to different engineering fields and vocational/trades that eLearning software solutions can be provided for. It includes subjects for mechanical engineering, electrical engineering, electronics engineering, civil engineering, first year engineering, information technology/computer science engineering, and vocational/trades. In total it covers over 200 subjects across these disciplines.
IEEE PRESENTATION ON WIRELESS PILGRIM TRACKINGSOUMYA PANDA
Ā
This document summarizes a presentation about a wireless sensor network system developed for pilgrim tracking in Hajj. The system uses mobile and fixed sensor units to monitor the location of pilgrims in real-time. It was tested on a small group of pilgrims in Hajj with 5m accuracy. The system aims to address issues like identification, medical emergencies, and congestion management for pilgrims. Future work will focus on improving efficiency and scalability of the mobile units to expand tracking to all pilgrims in Hajj.
The document discusses the history and development of the city of San Diego, California from its founding in 1769 by Spanish missionaries to its growth into a major city and tourist destination by the early 20th century. It provides details on the establishment of early settlements and missions by Spanish explorers, the shift to Mexican control in the 1820s, the influx of American settlers in the mid-19th century following the Mexican-American War, and the city's expansion through tourism and the development of Balboa Park, Harbor Island, and other attractions in the 1900s.
A Perspective on Graph Theory and Network ScienceMarko Rodriguez
Ā
The graph/network domain has been driven by the creativity of numerous individuals from disparate areas of the academic and the commercial sector. Examples of contributing academic disciplines include mathematics, physics, sociology, and computer science. Given the interdisciplinary nature of the domain, it is difficult for any single individual to objectively realize and speak about the space as a whole. Any presentation of the ideas is ultimately biased by the formal training and expertise of the individual. For this reason, I will simply present on the domain from my perspective---from my personal experiences. More specifically, from my perspective biased by cognitive and computer science.
This is an autobiographical lecture on my life (so far) with graphs/networks.
This document summarizes different graph theory concepts and methods for solving systems of linear and nonlinear equations using graph theory. It defines what graph theory is, provides examples of different graph types, and discusses the Laplacian matrix. It also outlines Gaussian elimination and other methods for solving linear systems, as well as Newton's method and the secant method for nonlinear systems. An example using Gaussian elimination to solve a system of 3 linear equations is also included.
This document discusses graph theory and Leonhard Euler's solution to the Kƶnigsberg bridge problem in the 18th century. It explains that a graph will contain an Euler path if it contains at most two vertices of odd degree, and will contain an Euler circuit if all vertices have even degree. An example is given of a police officer wanting to patrol a neighborhood while walking as little as possible, which relates to finding an Euler circuit in a graph.
This document outlines the terms and conditions for a rental agreement between John Doe and Jane Smith for the lease of an apartment located at 123 Main St from January 1, 2023 through December 31, 2023. The tenant agrees to pay $1000 per month in rent and a $500 security deposit. The landlord and tenant agree to abide by their respective responsibilities regarding maintenance, repairs, guests, and noise disturbances as detailed in the contract.
Network analysis and synthesis question and answer...Manash Deka
Ā
The document discusses the results of a study on the impact of climate change on coffee production. Researchers found that suitable land for coffee production could decline by up to 50% by 2050 due to rising temperatures and changing rain patterns associated with climate change. The study concludes that climate change poses a major threat to the coffee industry worldwide as suitable land decreases substantially in the coming decades if greenhouse gas emissions are not reduced.
This document discusses the superposition theorem for electrical circuits. The superposition theorem states that the response in any branch of a linear circuit with multiple independent sources is equal to the sum of the responses from each source acting alone. It works by replacing all other sources with their internal impedances (short circuits for voltage sources, open circuits for current sources) and calculating the contribution of each source individually. The superposition theorem is important for circuit analysis and is used to convert circuits into equivalent Norton or Thevenin circuits. It applies to linear networks containing independent sources, linear dependent sources, resistors, inductors, and capacitors.
This document discusses Y or admittance parameters, which describe the behavior of linear two-port electrical systems using equations that relate currents and voltages. The Y parameters - Y11, Y12, Y21, and Y22 - are short circuit admittances that can be used to find the currents at each port if the voltages are known and one port is short circuited. Y parameters are useful for analyzing two-port networks and assessing the small signal stability of electrical systems.
The superposition theorem states that for a linear circuit with multiple independent sources, the total response at any point in the circuit is equal to the sum of the individual responses produced by each independent source acting alone. To determine the individual contribution of each source, all other sources are replaced by their internal impedances. The theorem can be applied to circuits containing resistors, inductors, capacitors, transformers, and independent and dependent sources, as long as the elements have linear responses. The document provides an example using the superposition theorem to calculate the voltage drop and current across a resistor in a circuit with two independent voltage sources.
The superposition theorem allows the analysis of circuits with multiple sources by considering each source independently and adding their effects. It can be applied when circuit elements are linear and bilateral. To use it, all ideal voltage sources except one are short circuited and all ideal current sources except one are open circuited. Dependent sources are left intact. This allows the circuit to be solved for each source individually and the results combined through superposition. Examples demonstrate finding currents through specific elements in circuits with multiple independent and dependent sources. A limitation is that superposition cannot be used to determine total power due to power being related to current squared.
Simulating communication systems with MATLAB: An introductionAniruddha Chandra
Ā
This document outlines a presentation on simulating communication systems with MATLAB. It discusses simulating both analog and digital communication systems. For analog systems, it covers simulating amplitude modulation (AM) by generating a message signal, modulating it with a carrier, and demodulating to recover the message. It demonstrates adding noise to simulate a channel. For digital systems, it states it will cover binary phase-shift keying (BPSK) but does not provide details. The objective is for attendees to be able to write MATLAB scripts to simulate communication links and compare results to theory. It assumes a basic understanding of MATLAB, communications concepts, and performance metrics like bit error rate.
This lecture discusses energy band diagrams and doping of semiconductors. It introduces energy band diagrams as a way to represent carrier energy in semiconductors. Intrinsic semiconductors have equal numbers of electrons and holes, while doping with impurities creates excess carriers by introducing donors or acceptors. N-type doping uses group V donors to generate excess electrons, while p-type uses group III acceptors to generate excess holes. Doping allows tailoring of semiconductor properties for device applications.
The document provides an overview of the Network Theory syllabus for the 2020-21 academic year. It discusses the course details including credits, contact hours, assessments, pre-requisites and outcomes. The syllabus covers topics such as basic circuit concepts, network theorems, resonant circuits, transient behavior, Laplace transforms, and two-port networks. It also introduces some basic concepts of network theory including different electrical elements, circuit analysis techniques, and passive elements like resistors, capacitors, and inductors.
The document outlines the teaching and examination scheme for the second year of a four-year B.Tech program in Electrical Engineering. It lists the courses, credit hours, and assessment details for semesters 3 through 8. Students take courses in subjects like power electronics, circuit analysis, electrical machines, computer programming, and mathematics. Labs are also included for hands-on learning in areas like power electronics, electrical circuits, and programming.
This document outlines the objectives, outcomes, and content of the Basic Electronics course taught at Matrusri Engineering College. The course objectives include understanding the characteristics and design concepts of diodes, transistors, biasing, feedback amplifiers, and oscillators. The outcomes are for students to analyze various circuit types, including rectifiers, regulators, amplifiers, and logic gates. Course content includes the construction and operation of BJTs and JFETs, small signal models, amplifier analysis, and characteristics of FETs and MOSFETs.
This document provides notes on electronic devices and circuits from Lendi Institute of Engineering and Technology. It begins with definitions of key terms like electronic device, circuit, and semiconductor. It then discusses semiconductor materials like silicon, germanium, and gallium arsenide. It compares the properties of insulators, semiconductors, and conductors based on factors like conductivity, resistivity, and band structure. Examples of materials in each category are given along with diagrams. The document continues with explanations of energy levels and band structures in insulators, semiconductors, and metals. In summary, the document provides introductory concepts on electronic devices, circuits, and semiconductor physics.
The document outlines the syllabus scheme for the Bachelor of Technology degree in Electrical Engineering at Punjab Technical University for the 2002 batch. It details all courses over 8 semesters, including course codes, subjects, credit hours, internal and external marks allocation, and total marks. Laboratory courses and workshops are also included, along with the duration of examinations. The syllabus covers topics in various areas of electrical engineering including circuits, electronics, power systems, control systems, measurements, and more.
The document outlines the objectives and outcomes of a course on electrical engineering concepts. The objectives include introducing concepts of electrical circuits and components, magnetic circuits, DC and AC circuits, electrical machines, transformers, and electrical installations. The outcomes are to analyze circuits using laws and theorems, understand electric and magnetic circuits, study electrical machines, and introduce low voltage installations. The first unit covers basics of DC circuits including circuit elements, voltage and current sources, Kirchhoff's laws, circuit analysis techniques, and time-domain analysis of RL and RC circuits. It also defines electricity in terms of protons, electrons, and the charges resulting from excesses or deficits of electrons in neutral bodies.
This document outlines the contents and learning objectives of a course on basic electrical and electronics engineering. The course is intended for mechanical engineering and automobile engineering students and covers topics like electric and magnetic circuits, AC circuits, transformers, motors, electronic components, signals, diodes, and bipolar junction transistors. The course aims to help students understand and apply electrical and electronics engineering principles in industrial processes and determine things like voltage, current, and use components safely. It consists of 6 units that will briefly cover the basics of each topic.
The document is a presentation on magnetically coupled circuits submitted by Rifat Bhuiyan to lecturer Naznin Sultana. It discusses (1) what magnetically coupled circuits are, (2) why they are important, (3) the significance of using the DOT convention for coupled circuits, and (4) applications of magnetically coupled circuits. The DOT convention establishes the correct sign for mutually induced voltages in coupled circuits by marking identical dots on terminals belonging to different coils.
This document proposes and validates an equivalent circuit model for a wireless power transfer system capable of transferring 220W of power over a 30cm air gap with 95% efficiency. The model represents the transmitter and receiver coils as inductors with low mutual coupling. Analytical expressions for the model are derived and validated using finite element analysis and experimental results. Loss analysis is also performed to investigate skin effect and proximity effect losses at high operating frequencies. A new coil spatial design is proposed to reduce such losses compared to conventional coil designs.
Field Effect Transistor, JFET, Metal Oxide Semiconductor Field Effect Transistor, Depletion MOSFET, Enhancement MoSFET, Construction, Basic operation, Regions of Operation, Drain Characteristics, Transfer Characteristics, Biasing, Non-Ideal Characteristics of E-MOSFET, DC Analysis, AC equivalent circuit and Parameters, E-MOSFET as an Amplifier, AC analysis, MOSFET as a Switch, MOSFET as a diode, MOSFET as a resistor, High frequency equivalent circuit, Miller Capacitance, Frequency Response, NMOS and CMOS inverter
This document contains the overview and introduction presented by Mohankumar V for the Network Theory course. It outlines the syllabus, including topics covered, evaluation criteria, prerequisites and outcomes. The class covered basic concepts in network theory including different electrical elements, circuit simplification techniques using source transformation, and provided examples applying these techniques.
Circuit Theory: Nodes, Branches and Loops of a CircuitDr.Raja R
Ā
This document discusses the key concepts of nodes, branches, and loops in electric circuits. It defines nodes as junction points where two or more circuit elements are connected. Branches refer to the path between two nodes through a circuit element. Loops are closed paths in a circuit formed by branches that start and end at the same node without crossing any intermediate nodes twice. The document uses diagrams to illustrate these concepts and their application in representing electric circuits.
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1) A list of courses in the 3rd and 4th semesters, including course codes, titles, credit hours, and assessment details.
2) An overview of the 5th through 8th semesters, including additional required courses and electives in various specializations.
3) Detailed course contents for selected courses covering topics like mathematics, network analysis, electronic devices and circuits, measurements, and programming.
The document thus provides a comprehensive summary of the curriculum, course requirements, and academic plans for students in this Electronics and Communication
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EE-304 Electrical Network Theory [Class Notes1] - 2013
1. Network Topology and Graph Theory
EE-304 ENT credits: 4 L{3} P{0} T{1}
Lairenlakpam Joyprakash Singh, PhD
Department of ECE,
North-Eastern Hill University (NEHU),
Shillong ā 793 022
jplairen@nehu.ac.in
August 8, 2013
1 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
2. Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
3. Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
4. Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
5. Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
6. Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
7. Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
8. Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
9. Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology
- Graph and its types
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
10. Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology
- Graph and its types
Tree
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
11. Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology
- Graph and its types
Tree
Twigs
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
12. Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology
- Graph and its types
Tree
Twigs
Co-tree
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
13. Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology
- Graph and its types
Tree
Twigs
Co-tree
Links or Chords
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
14. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - I
Circuit elements:
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
15. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - I
Circuit elements:
- The mathematical models of a two terminal electrical devices,
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
16. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - I
Circuit elements:
- The mathematical models of a two terminal electrical devices,
- Completely characterized by its voltage-current relationship,
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
17. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - I
Circuit elements:
- The mathematical models of a two terminal electrical devices,
- Completely characterized by its voltage-current relationship,
- Can not be subdivided into other two-terminal devices.
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
18. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - I
Circuit elements:
- The mathematical models of a two terminal electrical devices,
- Completely characterized by its voltage-current relationship,
- Can not be subdivided into other two-terminal devices.
Node:
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
19. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - I
Circuit elements:
- The mathematical models of a two terminal electrical devices,
- Completely characterized by its voltage-current relationship,
- Can not be subdivided into other two-terminal devices.
Node:
- A point at which two or more circuit elements have a common
connection,
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
20. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - I
Circuit elements:
- The mathematical models of a two terminal electrical devices,
- Completely characterized by its voltage-current relationship,
- Can not be subdivided into other two-terminal devices.
Node:
- A point at which two or more circuit elements have a common
connection,
- The number of branches incident to a node is known as the
degree of that node.
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
21. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - I
Circuit elements:
- The mathematical models of a two terminal electrical devices,
- Completely characterized by its voltage-current relationship,
- Can not be subdivided into other two-terminal devices.
Node:
- A point at which two or more circuit elements have a common
connection,
- The number of branches incident to a node is known as the
degree of that node.
Branch:
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
22. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - I
Circuit elements:
- The mathematical models of a two terminal electrical devices,
- Completely characterized by its voltage-current relationship,
- Can not be subdivided into other two-terminal devices.
Node:
- A point at which two or more circuit elements have a common
connection,
- The number of branches incident to a node is known as the
degree of that node.
Branch:
- A single path, containing one circuit element, which connnects
one node to any other node,
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
23. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - I
Circuit elements:
- The mathematical models of a two terminal electrical devices,
- Completely characterized by its voltage-current relationship,
- Can not be subdivided into other two-terminal devices.
Node:
- A point at which two or more circuit elements have a common
connection,
- The number of branches incident to a node is known as the
degree of that node.
Branch:
- A single path, containing one circuit element, which connnects
one node to any other node,
- Represented by a line in the graph.
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
24. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - I
Circuit elements:
- The mathematical models of a two terminal electrical devices,
- Completely characterized by its voltage-current relationship,
- Can not be subdivided into other two-terminal devices.
Node:
- A point at which two or more circuit elements have a common
connection,
- The number of branches incident to a node is known as the
degree of that node.
Branch:
- A single path, containing one circuit element, which connnects
one node to any other node,
- Represented by a line in the graph.
Path:
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
25. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - I
Circuit elements:
- The mathematical models of a two terminal electrical devices,
- Completely characterized by its voltage-current relationship,
- Can not be subdivided into other two-terminal devices.
Node:
- A point at which two or more circuit elements have a common
connection,
- The number of branches incident to a node is known as the
degree of that node.
Branch:
- A single path, containing one circuit element, which connnects
one node to any other node,
- Represented by a line in the graph.
Path:
- A set of elements that may be traversed in order without passing
through the same node twice.
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
26. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - II
Loop:
1Engineering Circuit Analysis, 8e
4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
27. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - II
Loop:
- A close path or a closed contour selected in a network/circuit,
1Engineering Circuit Analysis, 8e
4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
28. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - II
Loop:
- A close path or a closed contour selected in a network/circuit,
- A path that may be started from a prticular node to other nodes
through branches and comes to the original/starting node,
1Engineering Circuit Analysis, 8e
4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
29. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - II
Loop:
- A close path or a closed contour selected in a network/circuit,
- A path that may be started from a prticular node to other nodes
through branches and comes to the original/starting node,
- Also known as closed path or circuit.
1Engineering Circuit Analysis, 8e
4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
30. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - II
Loop:
- A close path or a closed contour selected in a network/circuit,
- A path that may be started from a prticular node to other nodes
through branches and comes to the original/starting node,
- Also known as closed path or circuit.
Mesh1
[2]:
1Engineering Circuit Analysis, 8e
4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
31. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - II
Loop:
- A close path or a closed contour selected in a network/circuit,
- A path that may be started from a prticular node to other nodes
through branches and comes to the original/starting node,
- Also known as closed path or circuit.
Mesh1
[2]:
- A loop that does not contain any other loops within it,
1Engineering Circuit Analysis, 8e
4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
32. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - II
Loop:
- A close path or a closed contour selected in a network/circuit,
- A path that may be started from a prticular node to other nodes
through branches and comes to the original/starting node,
- Also known as closed path or circuit.
Mesh1
[2]:
- A loop that does not contain any other loops within it,
- Any mesh is a circuit/loop but any loop/circuit may not be a
mesh.
1Engineering Circuit Analysis, 8e
4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
33. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - II
Loop:
- A close path or a closed contour selected in a network/circuit,
- A path that may be started from a prticular node to other nodes
through branches and comes to the original/starting node,
- Also known as closed path or circuit.
Mesh1
[2]:
- A loop that does not contain any other loops within it,
- Any mesh is a circuit/loop but any loop/circuit may not be a
mesh.
Network:
1Engineering Circuit Analysis, 8e
4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
34. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - II
Loop:
- A close path or a closed contour selected in a network/circuit,
- A path that may be started from a prticular node to other nodes
through branches and comes to the original/starting node,
- Also known as closed path or circuit.
Mesh1
[2]:
- A loop that does not contain any other loops within it,
- Any mesh is a circuit/loop but any loop/circuit may not be a
mesh.
Network:
- The interconnection of two or more circuit elements forms an
electical network.
1Engineering Circuit Analysis, 8e
4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
35. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - II
Loop:
- A close path or a closed contour selected in a network/circuit,
- A path that may be started from a prticular node to other nodes
through branches and comes to the original/starting node,
- Also known as closed path or circuit.
Mesh1
[2]:
- A loop that does not contain any other loops within it,
- Any mesh is a circuit/loop but any loop/circuit may not be a
mesh.
Network:
- The interconnection of two or more circuit elements forms an
electical network.
Circuit:
1Engineering Circuit Analysis, 8e
4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
36. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - II
Loop:
- A close path or a closed contour selected in a network/circuit,
- A path that may be started from a prticular node to other nodes
through branches and comes to the original/starting node,
- Also known as closed path or circuit.
Mesh1
[2]:
- A loop that does not contain any other loops within it,
- Any mesh is a circuit/loop but any loop/circuit may not be a
mesh.
Network:
- The interconnection of two or more circuit elements forms an
electical network.
Circuit:
- Network that contains at least one closed path,
1Engineering Circuit Analysis, 8e
4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
37. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - II
Loop:
- A close path or a closed contour selected in a network/circuit,
- A path that may be started from a prticular node to other nodes
through branches and comes to the original/starting node,
- Also known as closed path or circuit.
Mesh1
[2]:
- A loop that does not contain any other loops within it,
- Any mesh is a circuit/loop but any loop/circuit may not be a
mesh.
Network:
- The interconnection of two or more circuit elements forms an
electical network.
Circuit:
- Network that contains at least one closed path,
- Every circuit is a network, but not all networks are circuits.
1Engineering Circuit Analysis, 8e
4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
38. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - II
Loop:
- A close path or a closed contour selected in a network/circuit,
- A path that may be started from a prticular node to other nodes
through branches and comes to the original/starting node,
- Also known as closed path or circuit.
Mesh1
[2]:
- A loop that does not contain any other loops within it,
- Any mesh is a circuit/loop but any loop/circuit may not be a
mesh.
Network:
- The interconnection of two or more circuit elements forms an
electical network.
Circuit:
- Network that contains at least one closed path,
- Every circuit is a network, but not all networks are circuits.
Planar circuit:
1Engineering Circuit Analysis, 8e
4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
39. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - II
Loop:
- A close path or a closed contour selected in a network/circuit,
- A path that may be started from a prticular node to other nodes
through branches and comes to the original/starting node,
- Also known as closed path or circuit.
Mesh1
[2]:
- A loop that does not contain any other loops within it,
- Any mesh is a circuit/loop but any loop/circuit may not be a
mesh.
Network:
- The interconnection of two or more circuit elements forms an
electical network.
Circuit:
- Network that contains at least one closed path,
- Every circuit is a network, but not all networks are circuits.
Planar circuit:
- A circuit that may drawn on a plane surface in such a way that
no branch passes over or under any other branch.
1Engineering Circuit Analysis, 8e
4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
40. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - III
Topology:
5 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
41. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - III
Topology:
- Deals with properties of networks which are unaļ¬ected when the
network is stretched, twisted, or otherwise distorted the size and
the shape,
5 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
42. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - III
Topology:
- Deals with properties of networks which are unaļ¬ected when the
network is stretched, twisted, or otherwise distorted the size and
the shape,
- Not concerned with the particular types of elements appearing in
the circuit, but only with the way in which branches and nodes
are arranged.
5 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
43. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - III
Topology:
- Deals with properties of networks which are unaļ¬ected when the
network is stretched, twisted, or otherwise distorted the size and
the shape,
- Not concerned with the particular types of elements appearing in
the circuit, but only with the way in which branches and nodes
are arranged.
Graph:
5 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
44. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - III
Topology:
- Deals with properties of networks which are unaļ¬ected when the
network is stretched, twisted, or otherwise distorted the size and
the shape,
- Not concerned with the particular types of elements appearing in
the circuit, but only with the way in which branches and nodes
are arranged.
Graph:
- A graph corresponding to a given network is obtained by
replacing all circuit elements with lines.
5 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
45. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - III
Topology:
- Deals with properties of networks which are unaļ¬ected when the
network is stretched, twisted, or otherwise distorted the size and
the shape,
- Not concerned with the particular types of elements appearing in
the circuit, but only with the way in which branches and nodes
are arranged.
Graph:
- A graph corresponding to a given network is obtained by
replacing all circuit elements with lines.
- Connected graph: A graph in which at least one path exists
between any two nodes of the graph. If the network has a
transformer as one of the element, then the resulted graph is
unconnected
5 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
46. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - III
Topology:
- Deals with properties of networks which are unaļ¬ected when the
network is stretched, twisted, or otherwise distorted the size and
the shape,
- Not concerned with the particular types of elements appearing in
the circuit, but only with the way in which branches and nodes
are arranged.
Graph:
- A graph corresponding to a given network is obtained by
replacing all circuit elements with lines.
- Connected graph: A graph in which at least one path exists
between any two nodes of the graph. If the network has a
transformer as one of the element, then the resulted graph is
unconnected
- Directed or Oriented graph: A graph that has all the nodes
and branches numbered and also directions are given to the
branches.
5 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
47. Network Toplogy Terms & Definitions
Network Topology: Terms and Deļ¬nitions - III
Topology:
- Deals with properties of networks which are unaļ¬ected when the
network is stretched, twisted, or otherwise distorted the size and
the shape,
- Not concerned with the particular types of elements appearing in
the circuit, but only with the way in which branches and nodes
are arranged.
Graph:
- A graph corresponding to a given network is obtained by
replacing all circuit elements with lines.
- Connected graph: A graph in which at least one path exists
between any two nodes of the graph. If the network has a
transformer as one of the element, then the resulted graph is
unconnected
- Directed or Oriented graph: A graph that has all the nodes
and branches numbered and also directions are given to the
branches.
- Subgraph: The subset of a graph. If the number of nodes and
branches of a subgraph is less than that of the graph, the
subgraph is said to be proper.
5 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
48. Network Toplogy Network Circuits & Their Graphs
Network Topology: An example
A circuit with topologically equivalent graphs:
1
2
3
4
+
āVs
Is
R1
IR1
R2
IR2
R3
IR3
C
IC
L
IL
1
2
3
4
1
2
3
4
i) A Circuit ii) its graph iii) directed graph
1
2
3
4
1
2
3
4
1
2
3
4
Three topologically equivalent graphs of ļ¬gure ii).
6 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
49. Network Toplogy Network Circuits & Their Graphs
An Electrical Network & its Graph - I
1 2 3
4
5 A
R1 R2
R4CR3
(a)
1
2
3
4
a b
c
d e f
(b)
Figure 1 : (a) A circuit and (b) its graph.
Note:
The maximum number of branches possible, in a circuit, will be equal
to the number of nodes or vertices.
There are at least two branches in a circuit.
7 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
50. Network Toplogy Network Circuits & Their Graphs
An Electrical Network & its Graph - II
1 2 3
4
5 A
R1
IR1
R2
IR2
R4
IR4
C
IC
R3
IR3
(a)
1
2
3
4
a b
c
d e f
(b)
Figure 2 : (a) A circuit and (b) its directed graph.
Note:
Each of the lines of the graph is indicated a reference direction by an
arrow, and the resulted graph is called oriented/directed graph.
8 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
51. Network Toplogy Network Circuits & Their Graphs
An Electrical Network & its Graph - III
1
2
3
4
5
+
āVs
Is
R
R1
I1
R2
I2
R3
I3
C
IC
L
IL
(a)
1
2
3
4
5
a
b c
fe
d
g
(b)
1
2
3
4, 5
a
b c
fed
(c)
Figure 3 : (a) A circuit, (b) its directed graph and (c) simpliļ¬ed directed
graph of (b).
Note:
The active element branch is replaced by its internal resistance to
simplify analysis and computation.
9 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
52. Network Toplogy Network Circuits & Their Graphs
An Electrical Network & its Graph - IV
1
2
3
4
+
āVs
Ivs
R
R1
I1
R2
I2
IIsC
IC
L
IL
(a)
1
2
3
4
a
b c
ed
(b)
1
2
3
4
a
b c
e
d
(c)
Figure 4 : (a) A circuit, and (b),(c) its directed graphs.
Note:
The active elements are excluded from the graph to simplify analysis
and computation.
10 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
53. Network Toplogy Network Circuits & Their Graphs
An Electrical Network & its Graph - V
1 A
1 ā¦
1 ā¦
1 ā¦
1 ā¦
1 ā¦
+ā
1 V
(a) (b) (c)
Figure 5 : (a) A circuit, and its- (b) simpliļ¬ed graph and (c) directed
graph.
Note:
When voltage source is not in series with any passive element in the
given network, it is kept in the graph as a branch.
11 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
54. Network Toplogy Terms & Deļ¬nitions
Network Topology: Terms and Deļ¬nitions - IV
Tree:
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
55. Network Toplogy Terms & Deļ¬nitions
Network Topology: Terms and Deļ¬nitions - IV
Tree:
- A connected subgraph having all the nodes of a graph without
any loop.
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
56. Network Toplogy Terms & Deļ¬nitions
Network Topology: Terms and Deļ¬nitions - IV
Tree:
- A connected subgraph having all the nodes of a graph without
any loop.
- Thus, a tree is a subgraph that has the following properties:
- It must consist of all nodes of a complete graph.
- For a graph having n number of nodes, the tree of the given graph
will have n ā 1 branches.
- There exists one and only one path between any pair of nodes.
- A tree should not have any closed path.
- The rank of a tree is (n ā 1). This is also the rank of the graph to
which the tree belongs.
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
57. Network Toplogy Terms & Deļ¬nitions
Network Topology: Terms and Deļ¬nitions - IV
Tree:
- A connected subgraph having all the nodes of a graph without
any loop.
- Thus, a tree is a subgraph that has the following properties:
- It must consist of all nodes of a complete graph.
- For a graph having n number of nodes, the tree of the given graph
will have n ā 1 branches.
- There exists one and only one path between any pair of nodes.
- A tree should not have any closed path.
- The rank of a tree is (n ā 1). This is also the rank of the graph to
which the tree belongs.
Twigs:
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
58. Network Toplogy Terms & Deļ¬nitions
Network Topology: Terms and Deļ¬nitions - IV
Tree:
- A connected subgraph having all the nodes of a graph without
any loop.
- Thus, a tree is a subgraph that has the following properties:
- It must consist of all nodes of a complete graph.
- For a graph having n number of nodes, the tree of the given graph
will have n ā 1 branches.
- There exists one and only one path between any pair of nodes.
- A tree should not have any closed path.
- The rank of a tree is (n ā 1). This is also the rank of the graph to
which the tree belongs.
Twigs:
- The branches of a tree are known as twigs,
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
59. Network Toplogy Terms & Deļ¬nitions
Network Topology: Terms and Deļ¬nitions - IV
Tree:
- A connected subgraph having all the nodes of a graph without
any loop.
- Thus, a tree is a subgraph that has the following properties:
- It must consist of all nodes of a complete graph.
- For a graph having n number of nodes, the tree of the given graph
will have n ā 1 branches.
- There exists one and only one path between any pair of nodes.
- A tree should not have any closed path.
- The rank of a tree is (n ā 1). This is also the rank of the graph to
which the tree belongs.
Twigs:
- The branches of a tree are known as twigs,
Links or Chords:
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
60. Network Toplogy Terms & Deļ¬nitions
Network Topology: Terms and Deļ¬nitions - IV
Tree:
- A connected subgraph having all the nodes of a graph without
any loop.
- Thus, a tree is a subgraph that has the following properties:
- It must consist of all nodes of a complete graph.
- For a graph having n number of nodes, the tree of the given graph
will have n ā 1 branches.
- There exists one and only one path between any pair of nodes.
- A tree should not have any closed path.
- The rank of a tree is (n ā 1). This is also the rank of the graph to
which the tree belongs.
Twigs:
- The branches of a tree are known as twigs,
Links or Chords:
- The branches that are removed from the graph while forming a
tree are termed as links or chords,
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
61. Network Toplogy Terms & Deļ¬nitions
Network Topology: Terms and Deļ¬nitions - IV
Tree:
- A connected subgraph having all the nodes of a graph without
any loop.
- Thus, a tree is a subgraph that has the following properties:
- It must consist of all nodes of a complete graph.
- For a graph having n number of nodes, the tree of the given graph
will have n ā 1 branches.
- There exists one and only one path between any pair of nodes.
- A tree should not have any closed path.
- The rank of a tree is (n ā 1). This is also the rank of the graph to
which the tree belongs.
Twigs:
- The branches of a tree are known as twigs,
Links or Chords:
- The branches that are removed from the graph while forming a
tree are termed as links or chords,
- Links are complement of twigs.
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
62. Network Toplogy Terms & Deļ¬nitions
Network Topology: Terms and Deļ¬nitions - IV
Tree:
- A connected subgraph having all the nodes of a graph without
any loop.
- Thus, a tree is a subgraph that has the following properties:
- It must consist of all nodes of a complete graph.
- For a graph having n number of nodes, the tree of the given graph
will have n ā 1 branches.
- There exists one and only one path between any pair of nodes.
- A tree should not have any closed path.
- The rank of a tree is (n ā 1). This is also the rank of the graph to
which the tree belongs.
Twigs:
- The branches of a tree are known as twigs,
Links or Chords:
- The branches that are removed from the graph while forming a
tree are termed as links or chords,
- Links are complement of twigs.
Co-tree:
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
63. Network Toplogy Terms & Deļ¬nitions
Network Topology: Terms and Deļ¬nitions - IV
Tree:
- A connected subgraph having all the nodes of a graph without
any loop.
- Thus, a tree is a subgraph that has the following properties:
- It must consist of all nodes of a complete graph.
- For a graph having n number of nodes, the tree of the given graph
will have n ā 1 branches.
- There exists one and only one path between any pair of nodes.
- A tree should not have any closed path.
- The rank of a tree is (n ā 1). This is also the rank of the graph to
which the tree belongs.
Twigs:
- The branches of a tree are known as twigs,
Links or Chords:
- The branches that are removed from the graph while forming a
tree are termed as links or chords,
- Links are complement of twigs.
Co-tree:
- The graph constituted with links is known as co-tree.
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
64. Network Toplogy Terms & Deļ¬nitions
Tree and Cotree
Given a Graph:
1 2 3
4
a b
c d e
f
Tree Twigs of tree Links of cotree
1
2 3
4
a b
c d e
f
{a,b,d} {c,e,f}
1
2 3
4
a b
c d e
f
{a,d,f} {c,b,e}
13 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
65. Network Toplogy Terms & Deļ¬nitions
Summary and a Question:
Q. Does the following graph with branches a and e form a tree?
1
2
3
4
a
b c
fed
14 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
66. Network Toplogy Terms & Deļ¬nitions
Summary and a Question:
Q. Does the following graph with branches a and e form a tree?
1
2
3
4
a
b c
fed
67. The number of nodes in this subgraph is
equal to that of the given graph.
14 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
68. Network Toplogy Terms & Deļ¬nitions
Summary and a Question:
Q. Does the following graph with branches a and e form a tree?
1
2
3
4
a
b c
fed
69. The number of nodes in this subgraph is
equal to that of the given graph.
70. But it has unconnected subgraphs and
moreover total number branches
= n ā 1(= 3). Therefore, it is not a tree.
14 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
71. Network Toplogy References
Text Books & References
M. E. Van Valkenburg
Network Analysis, 3/e.
PHI, 2005.
W.H. Hayt, J.E. Kemmerly, S.M. Durbin
Engineering Circuit Analysis, 8/e.
MH, 2012.
15 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
72. Network Toplogy References
Text Books & References
M. E. Van Valkenburg
Network Analysis, 3/e.
PHI, 2005.
W.H. Hayt, J.E. Kemmerly, S.M. Durbin
Engineering Circuit Analysis, 8/e.
MH, 2012.
M. Nahvi, J.A. Edminister
SchuamĆ¢ÄŹs Outline Electric Circuits, 4/e.
TMH, SIE, 2007.
A. Sudhakar, S.S. Palli
Circuits and Networks: Analysis and Synthesis, 2/e.
TMH, 2002.
15 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
73. Network Toplogy Khublei Shibun!
Thank You!
Any Question?
16 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
74. Home Assignment Graph and Incidence Matrix
Problems for Practice: Graph and Incidence Matrix
1. Classify whether each of the following graphs as planar or
nonplanar.
2. Find the number of possible trees for each graph and draw all
possible trees.
1
2
3
4
(a)
a
b c
d
(b)
1 2
3
4
5
(c)
17 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
75. Home Assignment Graph and Incidence Matrix
Problems for Practice - II
Note: While replacing all elements of the network with lines to form a
graph, we replace active elements by their internal resistances
to simplify analysis and computation.
For example - 1:
1
2
3 4
5
+
āVs
R1
Is
R2
I1
R3
I2
R4
I3
C
IC
L
IL
Is
(a)
18 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
76. Home Assignment Graph and Incidence Matrix
Problems for Practice - II
Note: While replacing all elements of the network with lines to form a
graph, we replace active elements by their internal resistances
to simplify analysis and computation.
For example - 1:
1
2
3 4
5
+
āVs
R1
Is
R2
I1
R3
I2
R4
I3
C
IC
L
IL
Is
(a)
2
3
4
1, 5
(b)
18 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
77. Home Assignment Graph and Incidence Matrix
Problems for Practice - II
Note: Transformer gives a unconnected graph!
For example - 2:
1
2 3 4
56
+
āVs
R1
I1
R2
I2
K
C
IC
R3
I3
I
(a)
19 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
78. Home Assignment Graph and Incidence Matrix
Problems for Practice - II
Note: Transformer gives a unconnected graph!
For example - 2:
1
2 3 4
56
+
āVs
R1
I1
R2
I2
K
C
IC
R3
I3
I
(a)
1
2
6
3
4
5
(b)
19 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
79. Home Assignment Graph and Incidence Matrix
Few non-planar Graphs
1
2
3
4
(a)
1 2
3
45
6
(b)
20 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph