1. An antenna acts as a transducer that converts electromagnetic waves between free space and a transmission line. It is an integral part of any radio communication system.
2. Maxwell's equations relate the electric and magnetic fields through vector and scalar potentials. For time-varying electromagnetic waves, the vector potential A and scalar potential φ are defined in terms of the current and charge densities using retarded potentials.
3. Radiation from an infinitesimal current element called a Hertzian dipole is analyzed. The vector potential at a point due to a constant current element of length dl is derived in terms of the current moment dlI0.
This chapter provides complete solution of of first, Second order differential equations of series & parallel R-L, R-C, R-L-C circuits, bu using different methods.
This document discusses electromagnetic field theory and computational electromagnetics. It introduces electromagnetic theory, which is divided into electrostatics, magnetostatics, and time-varying fields. Computational electromagnetics is presented as a way to numerically solve electromagnetic problems using computers. Different types of equation solvers are described, including integral equation solvers and differential equation solvers. General coordinate systems and transformations between coordinate systems are also covered.
This first lecture describes what EMT is. Its history of evolution. Main personalities how discovered theories relating to this theory. Applications of EMT . Scalars and vectors and there algebra. Coordinate systems. Field, Coulombs law and electric field intensity.volume charge distribution, electric flux density, gauss's law and divergence
1. Light interference occurs when two light waves overlap and their amplitudes combine according to the principle of superposition.
2. Constructive interference occurs when the light waves are in phase, resulting in enhanced intensity. Destructive interference occurs when light waves are out of phase, cancelling each other out.
3. Interference patterns from thin films can be observed by overlapping the light waves that are reflected or transmitted through the film. The optical path difference between the waves determines whether constructive or destructive interference occurs.
1. Alternating current is an electric current whose magnitude and direction periodically revers. It can be expressed by the equation I = I0 sinωt, where I0 is the peak value and ω is the angular frequency.
2. When alternating current flows through a pure resistor, the current is in phase with the applied voltage. There is no phase difference. However, when it flows through a pure inductor, the current lags the applied voltage by 90 degrees.
3. Root mean square (RMS) value is a useful parameter for alternating current and voltage. It is defined as the square root of mean of the squares of instantaneous values over one complete cycle. The RMS value of a sinusoidal current
The document discusses transmission line analysis and the telegrapher's equations. It introduces transmission lines as two-conductor structures that can guide electrical energy from one point to another. At microwave frequencies, transmission lines must be analyzed using distributed element models rather than lumped element models due to effects like phase variation, radiation, and causality. The telegrapher's equations describe voltage and current propagation on a transmission line as a function of both space and time. They take the form of wave equations that can be solved for traveling wave solutions on the line.
- Any steady state voltage or current in a linear circuit with a sinusoidal source is a sinusoid with the same frequency as the source. Phasors and complex impedances allow conversion of differential equations to circuit analysis by representing magnitude and phase of sinusoids.
- For a resistor, the voltage and current are in phase. In the phasor domain, the resistor phasor relationship is V=IR. In the time domain, the average power dissipated is proportional to the product of RMS current and voltage.
The document discusses the method of moments (MoM) technique for solving electromagnetic problems. It begins by introducing MoM and its application to electrostatic problems. The basic steps in MoM are then outlined, which involve transforming integro-differential equations into a matrix system of linear equations using a basis function approximation. Weighting functions are used to enforce boundary conditions and eliminate error, resulting in a matrix equation that can be solved for the unknown coefficients. An example problem applying Galerkin's MoM to a 1D differential equation is presented to illustrate the method.
This chapter provides complete solution of of first, Second order differential equations of series & parallel R-L, R-C, R-L-C circuits, bu using different methods.
This document discusses electromagnetic field theory and computational electromagnetics. It introduces electromagnetic theory, which is divided into electrostatics, magnetostatics, and time-varying fields. Computational electromagnetics is presented as a way to numerically solve electromagnetic problems using computers. Different types of equation solvers are described, including integral equation solvers and differential equation solvers. General coordinate systems and transformations between coordinate systems are also covered.
This first lecture describes what EMT is. Its history of evolution. Main personalities how discovered theories relating to this theory. Applications of EMT . Scalars and vectors and there algebra. Coordinate systems. Field, Coulombs law and electric field intensity.volume charge distribution, electric flux density, gauss's law and divergence
1. Light interference occurs when two light waves overlap and their amplitudes combine according to the principle of superposition.
2. Constructive interference occurs when the light waves are in phase, resulting in enhanced intensity. Destructive interference occurs when light waves are out of phase, cancelling each other out.
3. Interference patterns from thin films can be observed by overlapping the light waves that are reflected or transmitted through the film. The optical path difference between the waves determines whether constructive or destructive interference occurs.
1. Alternating current is an electric current whose magnitude and direction periodically revers. It can be expressed by the equation I = I0 sinωt, where I0 is the peak value and ω is the angular frequency.
2. When alternating current flows through a pure resistor, the current is in phase with the applied voltage. There is no phase difference. However, when it flows through a pure inductor, the current lags the applied voltage by 90 degrees.
3. Root mean square (RMS) value is a useful parameter for alternating current and voltage. It is defined as the square root of mean of the squares of instantaneous values over one complete cycle. The RMS value of a sinusoidal current
The document discusses transmission line analysis and the telegrapher's equations. It introduces transmission lines as two-conductor structures that can guide electrical energy from one point to another. At microwave frequencies, transmission lines must be analyzed using distributed element models rather than lumped element models due to effects like phase variation, radiation, and causality. The telegrapher's equations describe voltage and current propagation on a transmission line as a function of both space and time. They take the form of wave equations that can be solved for traveling wave solutions on the line.
- Any steady state voltage or current in a linear circuit with a sinusoidal source is a sinusoid with the same frequency as the source. Phasors and complex impedances allow conversion of differential equations to circuit analysis by representing magnitude and phase of sinusoids.
- For a resistor, the voltage and current are in phase. In the phasor domain, the resistor phasor relationship is V=IR. In the time domain, the average power dissipated is proportional to the product of RMS current and voltage.
The document discusses the method of moments (MoM) technique for solving electromagnetic problems. It begins by introducing MoM and its application to electrostatic problems. The basic steps in MoM are then outlined, which involve transforming integro-differential equations into a matrix system of linear equations using a basis function approximation. Weighting functions are used to enforce boundary conditions and eliminate error, resulting in a matrix equation that can be solved for the unknown coefficients. An example problem applying Galerkin's MoM to a 1D differential equation is presented to illustrate the method.
Here are the steps to solve this example:
1) Find the moment of inertia, I, of the composite section about the neutral axis:
I = I1 + I2 + A1*d1^2 + A2*d2^2
Where:
I1 = moment of inertia of rectangular section 1 = b1*h1^3/12 = 4*6^3/12 = 144 in^4
I2 = moment of inertia of rectangular section 2 = b2*h2^3/12 = 2*4^3/12 = 32 in^4
A1 = area of section 1 = b1*h1 = 4*6 = 24 in^2
A
This document discusses electromagnetic transmission lines and the Smith chart. It introduces equivalent electrical circuit models for coaxial cables, microstrip lines, and twin lead transmission lines using distributed inductors and capacitors. The telegrapher's equations are derived from Kirchhoff's laws. For sinusoidal waves on the transmission lines, phasor analysis is used. Key concepts covered include characteristic impedance, propagation velocity, wavelength, and modeling forward and backward traveling waves.
This document provides an overview of alternating current (AC) circuits. It begins by introducing AC voltage sources and defining key concepts like frequency, period, and angular frequency. It then analyzes simple circuits with a single circuit element - resistor, inductor, or capacitor - connected to an AC source. The behavior of current and voltage in each case is examined. Finally, the document considers the driven RLC series circuit, deriving the differential equation that governs it. Key circuit concepts like impedance and resonance are also introduced.
1) Secondary arcs on transmission lines can be modeled as a time-varying resistance using an arc conductance equation that represents the energy balance in the arc column.
2) Field tests on transmission lines are useful for verifying numerical arc simulations and understanding arc behavior. Tests showed secondary arcs excite traveling waves that influence the arc current waveform.
3) Arc parameters like the time constant are represented as functions of random arc length variations. This allows simulations to reproduce the random secondary arc behavior observed in tests.
1. The document discusses single phase AC circuits including definitions of terms like amplitude, time period, frequency, instantaneous value. It also discusses generation of sinusoidal AC voltage using a rotating coil.
2. Key concepts discussed include phasor representation, RMS and average values, form factor, phase difference, AC circuits with pure resistance and inductance. Instantaneous and average power calculations for resistive and inductive circuits are also presented.
3. Various waveforms, equations and phasor representations are used to explain these concepts for sinusoidal quantities in AC circuits.
This document discusses transmission lines and their parameters. It begins by introducing transmission lines as guided structures that direct the propagation of energy from a source to a load. It then discusses the key parameters used to describe transmission lines - resistance, inductance, conductance and capacitance per unit length. It provides examples of how electromagnetic waves propagate through transmission lines and derives the transmission line equations. It also covers input impedance, standing wave ratio, power, and gives examples of calculating transmission line properties. The document concludes by discussing microstrip transmission lines.
- describes how different magnetic materials behave in the presence of external magnetic field
- presents the difference between electric circuit analysis and magnetic circuit analysis.
- Basic overview of transmission line analysis
-How transmission line analysis differs from basic circuit analysis
- How distributed circuit element differs from Lumped elements
-Links to be referred for Smith Chart
This document contains a set of multiple choice questions and answers related to circuit theory and design. There are 42 questions in total, each with 4 answer options and the correct answer indicated. The questions cover topics such as network analysis techniques, network functions, network parameters, network theorems, transient analysis, filters, and more.
This document discusses mathematical modeling of electrical circuits. It covers passive networks using components like resistors, capacitors and inductors with no internal energy source. Analysis methods for passive networks include mesh analysis, nodal analysis and voltage division. Operational amplifiers are also covered, noting their differential input, high input/low output impedance, and high constant gain characteristics. Types of operational amplifiers include inverting and non-inverting configurations.
519 transmission line theory by vishnu (1)udaykumar1106
This document discusses transmission line theory for microwave frequencies. It begins by explaining how power is delivered through electric and magnetic fields along transmission lines at microwave frequencies rather than through wires. It then lists common types of transmission lines and discusses how circuit elements are analyzed as lumped units at microwave frequencies. Key transmission line concepts are also summarized such as characteristic impedance, velocity factor, standing waves, and using transmission lines as filters. The document concludes by discussing the Smith chart and how it can be used to solve problems involving transmission line matching and impedance transformations.
1) The document discusses transmission lines and their characteristics. It describes different types of transmission lines including coaxial lines, two-wire lines, and microstrip lines.
2) It presents the telegrapher's equations which model voltage and current on a transmission line as a function of position and time. These equations include parameters like inductance and capacitance per unit length.
3) Waves can propagate down transmission lines, maintaining their shape as they travel at a characteristic velocity. The wavelength depends on the wave velocity and frequency. Phasors are used to represent sinusoidal waves independent of time.
This document discusses transmission lines and the Telegrapher's equation. It begins by introducing transmission lines and their parameters such as resistance, inductance, conductance and capacitance per unit length. It then derives the Telegrapher's equation that describes voltage and current on a transmission line. It shows how the equation can be used to find the propagation constant and solve for voltage and current as a function of position and time. It also discusses phase velocity and provides examples of calculating attenuation constant, phase constant, and phase velocity for different transmission line scenarios.
This document provides an overview of transmission line basics and concepts. It discusses key transmission line parameters like characteristic impedance, propagation delay, per-unit-length capacitance and inductance. It covers transmission line equivalent circuit models and relevant equations. It also discusses transmission line structures, parallel plate approximations, reflection coefficients, and discontinuities. The goal is to understand transmission line behavior and analysis techniques.
This document provides an introduction to three-phase circuits and power. It defines key concepts like real power, reactive power, and power factor for sinusoidal voltages and currents. It describes how to calculate real and reactive power from rms voltage, current, and phase angle. Balanced three-phase systems are introduced, and how they allow more efficient power transmission compared to single-phase systems. Equations for solving problems involving three-phase circuits are also presented.
This document discusses plane wave reflection from a media interface. It begins by introducing the concepts of reflection and transmission coefficients which describe how much of an incident wave is reflected or transmitted at a boundary. It then examines plane wave reflection at normal incidence, deriving expressions for the reflected and transmitted electric and magnetic fields in two lossy media. Boundary conditions requiring the tangential field components to be continuous are applied to obtain equations relating the reflection and transmission coefficients to the material properties on either side of the interface.
1) The document discusses thin linear wire antennas and their properties like radiation from small electric dipoles, quarter wave monopoles and half wave dipoles.
2) It describes the calculation of electromagnetic fields using retarded potentials for time-varying sources like electric and magnetic dipoles.
3) Key concepts discussed include the vector and scalar potentials, derivation of wave equations from Maxwell's equations, and calculation of power radiated from a current element.
The document discusses magnetic fields produced by electric currents. It begins by introducing the Biot-Savart law, which describes the magnetic field generated by a straight wire carrying a current. It then examines the magnetic field of a circular current loop, noting that the field depends on the current I, distance R from the loop, and radius a. At large distances R compared to the radius a, the field approximates that of a magnetic dipole with a magnetic dipole moment m proportional to the current I and area A of the loop.
This document discusses electromagnetic radiation and antenna fundamentals. It begins by defining an antenna as a transducer between transmission lines and the surrounding medium that allows efficient launching of electromagnetic waves. The key characteristics of antennas like frequency, mounting location, gain, polarization, and efficiency are discussed. The document then covers topics such as radiation patterns, directivity, power gain, near fields, far fields, and polarization. Dipole antennas and the Friis transmission equation are also summarized.
This document provides an overview of electromagnetic radiation, antenna fundamentals, and wave propagation. It discusses antennas as the linkage between circuits and electromagnetic fields. Key concepts covered include the electromagnetic spectrum, frequency-wavelength relationships, antenna radiation patterns, gain, directivity, polarization, and near, intermediate, and far field regions. Common antenna types for mobile communication like dipoles, monopoles, and arrays are also mentioned. Baluns are described as devices that convert between balanced and unbalanced signals.
1. Magnetostatics describes the magnetic forces and fields that result from stationary electric charges and currents. The magnetic force on a moving charge in the presence of both electric and magnetic fields is given by the Lorentz force equation.
2. The two fundamental postulates of magnetostatics specify that the divergence of the magnetic flux density B is zero, and the curl of B is equal to the magnetic permeability times the current density.
3. Ampere's circuital law states that the circulation of the magnetic flux density around any closed path is equal to the total current flowing through the surface bounded by that path, according to the integral form of the curl relation.
Here are the steps to solve this example:
1) Find the moment of inertia, I, of the composite section about the neutral axis:
I = I1 + I2 + A1*d1^2 + A2*d2^2
Where:
I1 = moment of inertia of rectangular section 1 = b1*h1^3/12 = 4*6^3/12 = 144 in^4
I2 = moment of inertia of rectangular section 2 = b2*h2^3/12 = 2*4^3/12 = 32 in^4
A1 = area of section 1 = b1*h1 = 4*6 = 24 in^2
A
This document discusses electromagnetic transmission lines and the Smith chart. It introduces equivalent electrical circuit models for coaxial cables, microstrip lines, and twin lead transmission lines using distributed inductors and capacitors. The telegrapher's equations are derived from Kirchhoff's laws. For sinusoidal waves on the transmission lines, phasor analysis is used. Key concepts covered include characteristic impedance, propagation velocity, wavelength, and modeling forward and backward traveling waves.
This document provides an overview of alternating current (AC) circuits. It begins by introducing AC voltage sources and defining key concepts like frequency, period, and angular frequency. It then analyzes simple circuits with a single circuit element - resistor, inductor, or capacitor - connected to an AC source. The behavior of current and voltage in each case is examined. Finally, the document considers the driven RLC series circuit, deriving the differential equation that governs it. Key circuit concepts like impedance and resonance are also introduced.
1) Secondary arcs on transmission lines can be modeled as a time-varying resistance using an arc conductance equation that represents the energy balance in the arc column.
2) Field tests on transmission lines are useful for verifying numerical arc simulations and understanding arc behavior. Tests showed secondary arcs excite traveling waves that influence the arc current waveform.
3) Arc parameters like the time constant are represented as functions of random arc length variations. This allows simulations to reproduce the random secondary arc behavior observed in tests.
1. The document discusses single phase AC circuits including definitions of terms like amplitude, time period, frequency, instantaneous value. It also discusses generation of sinusoidal AC voltage using a rotating coil.
2. Key concepts discussed include phasor representation, RMS and average values, form factor, phase difference, AC circuits with pure resistance and inductance. Instantaneous and average power calculations for resistive and inductive circuits are also presented.
3. Various waveforms, equations and phasor representations are used to explain these concepts for sinusoidal quantities in AC circuits.
This document discusses transmission lines and their parameters. It begins by introducing transmission lines as guided structures that direct the propagation of energy from a source to a load. It then discusses the key parameters used to describe transmission lines - resistance, inductance, conductance and capacitance per unit length. It provides examples of how electromagnetic waves propagate through transmission lines and derives the transmission line equations. It also covers input impedance, standing wave ratio, power, and gives examples of calculating transmission line properties. The document concludes by discussing microstrip transmission lines.
- describes how different magnetic materials behave in the presence of external magnetic field
- presents the difference between electric circuit analysis and magnetic circuit analysis.
- Basic overview of transmission line analysis
-How transmission line analysis differs from basic circuit analysis
- How distributed circuit element differs from Lumped elements
-Links to be referred for Smith Chart
This document contains a set of multiple choice questions and answers related to circuit theory and design. There are 42 questions in total, each with 4 answer options and the correct answer indicated. The questions cover topics such as network analysis techniques, network functions, network parameters, network theorems, transient analysis, filters, and more.
This document discusses mathematical modeling of electrical circuits. It covers passive networks using components like resistors, capacitors and inductors with no internal energy source. Analysis methods for passive networks include mesh analysis, nodal analysis and voltage division. Operational amplifiers are also covered, noting their differential input, high input/low output impedance, and high constant gain characteristics. Types of operational amplifiers include inverting and non-inverting configurations.
519 transmission line theory by vishnu (1)udaykumar1106
This document discusses transmission line theory for microwave frequencies. It begins by explaining how power is delivered through electric and magnetic fields along transmission lines at microwave frequencies rather than through wires. It then lists common types of transmission lines and discusses how circuit elements are analyzed as lumped units at microwave frequencies. Key transmission line concepts are also summarized such as characteristic impedance, velocity factor, standing waves, and using transmission lines as filters. The document concludes by discussing the Smith chart and how it can be used to solve problems involving transmission line matching and impedance transformations.
1) The document discusses transmission lines and their characteristics. It describes different types of transmission lines including coaxial lines, two-wire lines, and microstrip lines.
2) It presents the telegrapher's equations which model voltage and current on a transmission line as a function of position and time. These equations include parameters like inductance and capacitance per unit length.
3) Waves can propagate down transmission lines, maintaining their shape as they travel at a characteristic velocity. The wavelength depends on the wave velocity and frequency. Phasors are used to represent sinusoidal waves independent of time.
This document discusses transmission lines and the Telegrapher's equation. It begins by introducing transmission lines and their parameters such as resistance, inductance, conductance and capacitance per unit length. It then derives the Telegrapher's equation that describes voltage and current on a transmission line. It shows how the equation can be used to find the propagation constant and solve for voltage and current as a function of position and time. It also discusses phase velocity and provides examples of calculating attenuation constant, phase constant, and phase velocity for different transmission line scenarios.
This document provides an overview of transmission line basics and concepts. It discusses key transmission line parameters like characteristic impedance, propagation delay, per-unit-length capacitance and inductance. It covers transmission line equivalent circuit models and relevant equations. It also discusses transmission line structures, parallel plate approximations, reflection coefficients, and discontinuities. The goal is to understand transmission line behavior and analysis techniques.
This document provides an introduction to three-phase circuits and power. It defines key concepts like real power, reactive power, and power factor for sinusoidal voltages and currents. It describes how to calculate real and reactive power from rms voltage, current, and phase angle. Balanced three-phase systems are introduced, and how they allow more efficient power transmission compared to single-phase systems. Equations for solving problems involving three-phase circuits are also presented.
This document discusses plane wave reflection from a media interface. It begins by introducing the concepts of reflection and transmission coefficients which describe how much of an incident wave is reflected or transmitted at a boundary. It then examines plane wave reflection at normal incidence, deriving expressions for the reflected and transmitted electric and magnetic fields in two lossy media. Boundary conditions requiring the tangential field components to be continuous are applied to obtain equations relating the reflection and transmission coefficients to the material properties on either side of the interface.
1) The document discusses thin linear wire antennas and their properties like radiation from small electric dipoles, quarter wave monopoles and half wave dipoles.
2) It describes the calculation of electromagnetic fields using retarded potentials for time-varying sources like electric and magnetic dipoles.
3) Key concepts discussed include the vector and scalar potentials, derivation of wave equations from Maxwell's equations, and calculation of power radiated from a current element.
The document discusses magnetic fields produced by electric currents. It begins by introducing the Biot-Savart law, which describes the magnetic field generated by a straight wire carrying a current. It then examines the magnetic field of a circular current loop, noting that the field depends on the current I, distance R from the loop, and radius a. At large distances R compared to the radius a, the field approximates that of a magnetic dipole with a magnetic dipole moment m proportional to the current I and area A of the loop.
This document discusses electromagnetic radiation and antenna fundamentals. It begins by defining an antenna as a transducer between transmission lines and the surrounding medium that allows efficient launching of electromagnetic waves. The key characteristics of antennas like frequency, mounting location, gain, polarization, and efficiency are discussed. The document then covers topics such as radiation patterns, directivity, power gain, near fields, far fields, and polarization. Dipole antennas and the Friis transmission equation are also summarized.
This document provides an overview of electromagnetic radiation, antenna fundamentals, and wave propagation. It discusses antennas as the linkage between circuits and electromagnetic fields. Key concepts covered include the electromagnetic spectrum, frequency-wavelength relationships, antenna radiation patterns, gain, directivity, polarization, and near, intermediate, and far field regions. Common antenna types for mobile communication like dipoles, monopoles, and arrays are also mentioned. Baluns are described as devices that convert between balanced and unbalanced signals.
1. Magnetostatics describes the magnetic forces and fields that result from stationary electric charges and currents. The magnetic force on a moving charge in the presence of both electric and magnetic fields is given by the Lorentz force equation.
2. The two fundamental postulates of magnetostatics specify that the divergence of the magnetic flux density B is zero, and the curl of B is equal to the magnetic permeability times the current density.
3. Ampere's circuital law states that the circulation of the magnetic flux density around any closed path is equal to the total current flowing through the surface bounded by that path, according to the integral form of the curl relation.
This document discusses plane electromagnetic waves. It defines plane waves as waves whose wavefronts are infinite parallel planes of constant amplitude normal to the phase velocity vector. The electric and magnetic fields of a plane wave are perpendicular to each other and to the direction of propagation. Plane waves can be linearly, circularly, or elliptically polarized depending on the orientation and behavior of the electric field vector over time. Linear polarization occurs when the electric field is oriented along a fixed line. Circular polarization results when the electric field traces out a circle, and elliptical polarization is characterized by an elliptical trace.
This document provides preparatory notes and examples for an exam on electromagnetic theory. It covers key concepts like the Lorentz force equation, Biot-Savart law, Ampere's circuital law, Gauss's law for magnetism, and magnetic boundary conditions. Examples calculate the magnetic field and force on charges in various configurations like an infinite line current, parallel wires, and a ring of current. The document is a useful study guide summarizing the essential electromagnetic concepts and formulas tested on the exam.
This document contains 29 multi-part physics problems related to electric fields, electric potential, and capacitance. The problems cover a range of concepts including Gauss's law, electric fields due to various charge distributions, capacitors in series and parallel, energy stored in capacitors, and more. Detailed calculations and explanations are required to fully solve each problem.
Electromagnetic fields of time-dependent magnetic monopoleIOSR Journals
Dirac-Maxwell’s equations, retained for magnetic monopoles, are generalized by introducing
magnetic scale field. It allows the magnetic monopoles to be time-dependent and the potentials to be Lorentz
gauge free. The non-conserved part or the time-dependent part of the magnetic charge density is responsible to
produce the magnetic scalar field which further contributes to the magnetic and electric vector fields. This
contribution makes possible to create an ideal square wave magnetic field from an exponentially rising and
decaying magnetic charge.
This document contains lecture notes on microwave techniques and transmission line theory. It discusses TEM, TE, and TM waves that can propagate in transmission lines and waveguides. It also covers the TEM mode in coaxial cables, deriving the electric and magnetic fields using Maxwell's equations and separating variables. The document emphasizes that the TEM mode is desirable because it has zero cutoff frequency, no dispersion, and solutions to Laplace's equation are relatively easy.
Method of Moment analysis of a printed Archimedian Spiral antenna Piyush Kashyap
A single arm Archimedean spiral printed on a grounded dielectric substrate is analyzed using the method of moments. Piecewise sinusoidal subdomain basis and test functions are used over curved segments that exactly follow the spiral curvature. Results for the input impedance obtained using the curved segmentation approach on MATLAB are compared with those obtained after simulating the model on FEKO. A comparison with published results shows that the curved segment model requires fewer segments and is therefore significantly more computationally efficient than the linear segmentation model.
This document presents a theoretical treatment of charge exchange processes that can occur during the scattering of positively charged lithium ions (Li+) from the surface of a narrow band insulator (KF) in the presence of a laser field. Equations are derived to describe the dynamics and describe how the laser field can be incorporated into the system Hamiltonian. The treatment is then applied to model charge exchange during the scattering of Li+ from KF surfaces. The key conclusions are that the charge state of the scattering species can be controlled by adjusting parameters of the applied laser field, such as frequency and intensity.
The cascade equivalent A-H-circuit of the salient-pole generator on the base ...IJECEIAES
This document presents the cascade equivalent A-H circuit model of a salient-pole synchronous generator. It begins by reviewing previous laminated models used to model electric machine fields and discusses their limitations for salient-pole machines. It then presents a new approximate method using one piecewise continuous function to model the pole field and sinusoidal functions for the airgap field, allowing the creation of a cascade equivalent circuit. The document derives the impedances for the rotor circuit based on the field solution and boundary conditions. It then combines the rotor and airgap circuits into a two-cell cascade model and validates it with control calculations showing matching results with numerical simulation. In summary, the document presents a new cascade equivalent circuit modeling approach for salient-pole
Nonlinear Electromagnetic Response in Quark-Gluon PlasmaDaisuke Satow
The document discusses nonlinear electromagnetic response in quark-gluon plasma, specifically focusing on quadratic induced currents. It first outlines collision-dominant and collisionless cases. For the collision-dominant case, it lists possible forms of quadratic currents using CP symmetry properties and derives the Boltzmann equation in relaxation time approximation to calculate induced currents order-by-order in electromagnetic fields. The linear terms reproduce known results while quadratic terms are most sensitive to quark chemical potential at high temperature.
- The document discusses magnetic fields created by electric currents. It covers the magnetic field of a moving point charge, the Biot-Savart law for calculating the magnetic field from a current-carrying wire, and an example calculation of the magnetic field from a long straight wire.
- The right hand rule is introduced for determining the direction of magnetic fields.
- Maxwell's equations for static magnetic fields in integral and differential form are presented.
- The document discusses magnetic fields created by electric currents. It covers the magnetic field of a moving point charge, the Biot-Savart law for calculating the magnetic field from a current-carrying wire, and an example calculation of the magnetic field from a long straight wire.
- The right hand rule is introduced for determining the direction of magnetic fields.
- Maxwell's equations for static magnetic fields in integral and differential form are presented.
The Biot-Savart law describes the magnetic field generated by electric currents. It states that the magnetic field at a point P is proportional to the current I and inversely proportional to the distance r from the current element ds. Specifically, the field is given by the equation dB = (μ0I/4πr2)ds x r̂, where μ0 is the permeability of free space. This law can be used to calculate the magnetic fields generated by various current distributions like long straight wires, circular loops, and coils.
This document discusses circuit and network theory. It covers topics such as circuit elements and laws, magnetic circuits, network analysis, network theorems, AC circuits and resonance, coupled circuits, transients, two-port networks, and filters. Mesh analysis is introduced as a technique for network analysis that is applicable to planar networks containing voltage sources. The key steps are selecting mesh currents, then writing and solving KVL equations in terms of the unknown currents.
This document discusses Maxwell's equations and electromagnetic waves through conceptual problems and examples.
Some key points:
1) Maxwell's equations apply to both time-independent and time-dependent electric and magnetic fields. The electromagnetic wave equation can be derived from Maxwell's equations.
2) Electromagnetic waves are transverse waves where the electric and magnetic fields oscillate perpendicular to the direction of propagation.
3) The momentum of an electromagnetic wave depends on its intensity, so waves of equal intensity have equal momentum regardless of frequency.
4) Radiation pressure from sunlight was determined to be causing changes to the orbit of one of the first U.S. satellites, something not accounted for in its design. Estimates
1. The document discusses transmission lines, which guide electromagnetic wave propagation between a source and load through parallel conductors.
2. Transmission lines have distributed parameters including resistance, inductance, capacitance, and conductance per unit length. These parameters determine the line's characteristic impedance and propagation properties.
3. Lossless transmission lines have no resistance or conductance, so waves propagate without attenuation. Distortionless lines minimize signal distortion during propagation by making the attenuation and phase constants independent of frequency.
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
Null Bangalore | Pentesters Approach to AWS IAMDivyanshu
#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
- An overly permissive IAM role configuration can lead to privilege escalation by creating a role with administrative privileges and allow a user to assume this role.
- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
- Steps:
- Create role with administrative privileges.
- Allow user to assume the role.
- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
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Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
radio propagation
1. 1
CHAPTER FOUR: ELECTROMAGNETIC RADIATION
A system of conductors/material media which is connected to a power source so as to produce a
time varying electromagnetic field in an external region will radiate energy. When this system is
arranged so as to optimize the radiation of energy from some portion of the system while at the
same time minimizing/suppressing radiation from the rest of the system, that portion of the
system is called an antenna.
Antenna Fundamentals
An antenna acts as a transducer for converting a movement of charge on a conductor into
electromagnetic waves propagating in free space (transmitter function) and the reverse process
(receiver function). It is assumed that the antenna is connected to a known power source by
means of a transmission line/wave guide. Reception and transmission antennas have similar
characteristics and therefore the two words will be used synonymously and sometimes the same
antenna is often used for both purposes. The antenna is an integral part of any radio
communication system and thus its design is of paramount importance to a radio engineer.
Vector ( A ) and Scalar ( ) Potentials
The electric and magnetic fields are so closely inter-related that one can never be defined without
the other unlike in electrostatics and magnetostatics. This relationship is shown in Maxwell’s
equations of electromagnetics.
t
B
E
(1)
J
t
D
H
(2)
D (3)
0 B (4)
Note: In a material media with electrical properties r and r , the constitutive electric and
magnetic field equations are re-written as:
ED r 0 (5a)
HB r 0 (5b)
In electromagnetic waves, the magnetic and electric are related to the vector ( A ) and scalar ( )
potentials. These are in turn also related to their sources which are: current density (J) and charge
2. 2
density ( ). Consider the distribution of charge density, tr, which varies with space and
time. The relationship between charge density and current density is manifested in the continuity
equation.
t
tr
trJ
,
,
(6)
We wish to relate the magnetic and electric fields to their sources, i.e. current density, J and
charge density, .However, equations 1 and 2 are coupled in a complex fashion, with the result
that it is difficult to relate H and E to J and directly.
Taking the curl of 1 and 2 with substitutions of Maxwell’s equations yields;
t
J
t
E
E
2
2
(7)
J
t
J
J
2
2
(8)
Using the vector identity: FFF 2
and equation 3 in equation 7 and 8:
t
J
t
E
E
2
2
2
(9)
J
t
H
H
2
2
2
(10)
The LHS of equation 9 and 10 are travelling wave equations.
In order to relate the vector ( A ) and the scalar potentials to the sources J and , it is
necessary to make use of supporting functions, i.e. 0 F and 0 V .
Therefore the vector potential A is defined as:
AB (11)
Thus from equation 1 and 11,
t
A
E
(12)
3. 3
0
t
A
E (13)
Hence:
t
A
E (14)
Equations 2,3 and 14 are used to show how A and are related to their respective sources, J and
. Using equations 2 and 11, we obtain:
J
t
E
A
1
(15)
Note: All the vectors have space and time functional relationships, i.e. tr, .
Using 14 and 15 together with the above vector identity gives:
J
tt
A
AA
2
2
21
(16)
Using 3 and 14 also gives:
2
t
A
(17)
The partial differential equations 16 and 17 are coupled since each of them contains A and .
Since A is already known, it is also necessary to determine A in order to define A
completely. A vector field is completely specified only if its curl and divergence are defined.
The Lorentz gauge condition (equation 18) defines A completely and is used to decouple A and
.
0
t
A
(18)
Substituting 18 in 16 gives:
J
t
A
A
2
2
2
(19)
Substituting 18 in 17 gives:
4. 4
2
2
2
t
(20)
Consider the following cases:
Case 1: is independent of time, then:
2
, such that
r
dr
r
4
1
Case 2: 0 , then
02
2
2
t
, such that vtrgvtrftr ,
Where f and g are arbitrary functions.
The solutions of equation 19 and 20 are given as:
r rr
v
rr
trJ
trA
,
4
, (21)
r rr
v
rr
tr
tr
,
4
1
, (22)
where
v
rr
tt
Equation 21 and 22 say that sources which had the configurations J and at a t (previous time
instant) produce a potential A and at a point P at a time t which is later than the time t by an
amount that takes into account the finite velocity of propagation of waves in the medium.
Because of this time delay aspect of solutions, the potentials A and are known as retarded
5. 5
potentials and the phenomenon itself is known as retardation. These retarded potentials give rise
to fields only after their sources are brought into existence.
The solutions to 19 and 20 remain unchanged if we change v to –v, i.e.
r rr
v
rr
trJ
trA
,
4
, (23)
r rr
v
rr
tr
tr
,
4
1
, (24)
This shows that the solutions to 19 and 20 have two parts, i.e. two waves travelling in opposite
directions. The potentials in 23 and 24 are called advanced potentials and they give rise to fields
only before the current and charge distributions are brought into existence. However, in all
physical phenomena, effects should occur after their cause. Consequently Advanced potentials
are outside the scope of this work.
For time harmonic variation of current and charge density, the expressions for the retarded
potentials are given as:
r
rrj
rr
erJ
rA
4
(25)
r
rrj
rr
er
r
4
(26)
where
2
v
is the wave number.
Once the retarded vector and scalar potentials are obtained, then the magnetic and electric fields
at a point away from the sources J and can also be obtained using equations 11 and 14.
6. 6
Radiation from a Current Element
Characteristics of a current element
It should be of negligible thickness and if its length is dl , then dl
The current in the element should vary harmonically with time and have a constant
amplitude along the length of the element.
A constant current element of infinitesimal length cannot be realized practically but it is however
important to study s radiation characteristics as a foundation to understand how antennas work.
This infinitensimal length current element is called a Hertzian dipole. The dipole we consider
is a cylindrical tube of length dl and we wish to find the vector potential at a point ,,rP .
Assuming the current density on the cylindrical tube to be only in the z-direction, then the
resultant vector potential at P is also in the z-direction and is given by the equation 25 i.e
rr
erJ
rA
rrj
z
z
4
(27)
The position vector to any point on the cylindrical tube is denoted as r . If the radius a , of the
tube is very small in comparison to the wave length , such that 1a and also the length of
the element is infinitensimally small, then it is proper to omit r in equation 27. Thus:
r
rJe
rA z
rj
4
(28)
The current density integrated over the cross section of the cylindrical tube gives the total current
0I which we assumed to be constant along the length of the current element. Thus:
dlIrJ
r
z 0
(29)
Hence
z
y
x
I
7. 7
rj
z e
r
dlI
rA
4
0
(30)
dlI0 is called the moment of current (current moment).
Expressing the vector potential at P in spherical coordinates we obtain:
cos
4
cos 0 rj
zr e
r
dlI
rArA
(31a)
sin
4
sin 0 rj
z e
r
dlI
rArA
(31b)
0rA (31c)
Thus:
aae
r
dlI
rA r
rj
sincos
4
0
(32)
The scalar potential can now be easily obtained from the vector potential by considering the
harmonic time variation equation of the Lorentz gauge condition, i.e.:
rA
j
r
1
(33)
Hence,
2
0 1
4
cos
rr
j
j
edlI
r
rj
(34)
Magnetic and Electric fields from a Current Element
The magnetic and electric fields due to the current element can now be easily obtained from the
vector and scalar potentials obtained above, i.e.
rA
r
rH
1
(35)
Thus:
a
rr
jedlI
rH
rj
2
0 1
sin
4
(36)
Also:
8. 8
rH
j
rE
1
(37)
Thus:
a
rjrr
jedlI
a
rjr
edlI
rE
rj
r
rj
32
0
32
0 11
sin
4
11
cos
2
(38)
Where
is the intrinsic impedance of the media between the source and observation
points.
It is recognized that the magnetic and electric field components involve inverse terms of 32
,, rrr .
Since the antenna’s primary function is to radiate energy to distant points, it is possible and valid
most of the time to ignore the components that do not contribute to energy radiation. In this case,
we can neglect the higher order terms for large distances, and thus call these fields (that are
reverse functions of r) radiation fields. These are given as:
a
r
edlI
jrH
rj
sin
4
0
(39)
a
r
edlI
jrE
rj
sin
4
0
(40)
The inverse 2
r term is called the induction field and this term dominates at short distances (i.e.
r ). Essentially it is the field you find near the source (current element). At r , the
radiation field dominates. It is possible to determine the induction field from the Biot-Savart law.
In the case of the electric field, the inverse 2
r term represents the electric field intensity of an
electric dipole. The inverse 3
r term is called the electrostatic field term. Since we are dealing
with antennas, both the induction and electrostatic field terms will be dropped.
On close examination of rH and rE , the inverse r and 2
r terms are equal in magnitude
when:
rv
1
(41)
Therefore:
62
v
r (42)
9. 9
Far-zone and Near-zone Fields
The far zone and near zone are defined respectively by the inequalities 1r and 1r . The
terms of the fields whose amplitudes vary as the inverse of r are called the far zone fields, i.e.
a
r
eH
rH
rj
0
(43)
a
r
eE
rE
rj
0
(44)
Where
sin
4
0
0
dlI
jEHo (45)
It’s observed that the ratio of the magnitude of the far-zone electric field to the magnitude of the
far-zone magnetic field is equal to the intrinsic impedance, of the medium i.e.
rH
rE
For a lossless medium, the intrinsic impedance is real. The electric and magnetic vectors are thus
both in time and space phase. The electric field, magnetic field and the direction of propagation
form a triad of mutually perpendicular right handed system of vectors; thus in the far-zone, the
fields due to a current element constitute a plane transverse electromagnetic wave (TEM mode).
In the near-zone, the exponential rj
e
is expanded into a power series in r and since 1r ;
sin
4 2
0
r
dlI
rH (47)
cos
2 3
0
r
dlI
rEr (48)
sin
4 3
0
r
dlI
rE (49)
Therefore the fields in the near-zone are equivalent to the field obtained due to a current element
by application of the laws of magnetostatics.
10. 10
Power Radiated by a Current Element & Radiation Resistance
The power flow per unit area (power density) at the point P due to a current element will be
given by Poynting’s vector at that point.
2
/ mWHEP (50)
The time-averaged power density is then obtained from;
2
/
2
1
2
1
mWHEPPav (51)
Since the far zone fields of the current element are perpendicular to each other, then;
2
0 sin
322
1
r
dlI
HEPav
(52)
Hence,
rav a
r
dlI
P
2
0 sin
32
(53)
Then the total power radiated, )(WPav by the current element is obtained by carrying out the
integration of the time-averaged power density over the closed spherical shell surrounding the
element, i.e.
v
ravavrad addrPdsPP sin2
(54)
Making the necessary substitutions, the total power is given as;
2
02
0
312
dlI
dlIPrad (55)
radP is observed to be a real quantity which shows that the far zone fields of the current element
give rise to transport of time-averaged power only. 0I in (55) is the peak value (amplitude) of the
current, which can be expressed in terms of the r.m.s (root mean square)value of current, smrI .. ,
i.e.
smrII ..0 2 (56)
Thus:
11. 11
22
..
3
2
dlI
P smr
rad (57)
The coefficient of 2
.. smrI in (57) has the dimensions of resistance and is called the radiation
resistance, Rrad of the current element (antenna), i.e.
2
.. smrradrad IRP (58)
Where:
2
3
2
dl
Rrad (59)
In free space, :asgivenissoand120 radR
2
2
80
dl
Rrad (60)
Antenna properties
There are several properties/characteristics that determine the operation of all antennas in any
wireless communication network. The following are some of these properties:
Antenna Power Gain, g
Antenna gain, g is the measure of the antenna’s ability to radiate the power that has been input
into its terminals into the media surrounding it (i.e. free space). It is defined as a ratio of the
radiated power density at a given point, P distant r from the test antenna, to the radiated power
density at the same point due to an isotropic antenna, both antennas having the same input
power.
G (61)
Where and represent the radiated power densities at a distance r from the test and isotropic
antennas respectively.
Antenna Directive Gain, gd
Antenna directive gain, gd is the measure of the antenna’s ability to concentrate the radiated
power/energy in a particular direction ,r . It is defined as the power density at a point P in a
12. 12
given direction, distant r from the test antenna, to the power density at the same point due to an
isotropic antenna radiating the same power.
The maximum value of the directive gain of an antenna is commonly referred to as the antenna
directivity, D.
Antenna gain and directive gain seem quite similar but they slightly differ and are related to each
other through equation (62) where k is the efficiency factor. Antenna gain is usually less than
directive gain because of the losses that occur within the antenna.
dkgg (62)
Radiation pattern
The radiation pattern from an antenna is a three dimensional plot of the radiated power density
from an antenna (at a given distance r) as the directional parameters ( and in spherical
coordinates) are varied. The radiation pattern will always give an indication of the direction in
which the maximum power is radiated from an antenna.
The radiation patterns of an antenna can either be field or power patterns and their shapes vary
with the different antenna types. The figure below shows the power pattern for the Hertzian
dipole antenna (current element).
Polarization
This is the orientation of the far zone electric field vector within the radiated electromagnetic
wave from an antenna. It describes the locus of the tip of the electric field vector. If this locus is
a straight line constantly parallel to a constant direction, then the polarization is linear. Circular
or elliptical polarization are obtained when the loci are either circular or elliptical respectively.
Depending on the antenna design, different antenna polarisations can be achieved with each
having its merits and demerits. However, it’s important to note that in any wireless system
design, the transmitting and receiving antennas should always have the same polarization.
Antenna bandwidth, BW
This is the range of frequencies (centred about the resonant/design frequency, fc) that can be used
by antennas to radiate electromagnetic waves. At resonant frequencies, the antenna has zero
input reactance and will radiate/deliver maximum power due to the fact that the matching has
been achieved at this frequency. Depending on the application, some antennas are designed with
narrowband (i.e. narrowband antennas)while others may have wider bandwidth (i.e. broad band
antennas). The percentage band width of an antenna can be obtained using equation 63 below:
13. 13
100%
C
LH
f
ff
BW (63)
Where fH and fL are determined by 2VSWR511 dbS th which accounts for approximately
88.9% of the power being radiated (transmitted/received) by the antenna.
Effective Area, Aeff
This is the area of an antenna on to which the power density of a radiated electromagnetic
wave is incident. Equation 64 gives the relationship between the effective area of an antenna effA ,
and the antenna’s gain, G.
4
2
g
Aeff (64)
where is the operating centre wavelength of the antenna.
The product of this area with the power density , gives the power received Pr, by an antenna
from a passing wave. The effective area therefore measures the antenna’s ability to extract
electromagnetic energy from an incident/radiated electromagnetic wave.