Here we look at how to create a projection Matrix for orthogonal projection or transformation and projection onto a Line under Numerical Linear Algebra.
Efficient Finite Element Computation of Circulating Currents in Thin Parallel...Antti Lehikoinen
My poster for the International Conference on the Computation of Electromagnetic Fields (Compumag 2015).
I developed a non-conforming meshing approach for stranded conductors, resulting in a significant reduction on the degrees-of-freedom and computation times in loss calculation.
Seismic presentation for Dip correction for convolution modellingHarshal Pende
This document discusses dip correction for convolution modelling and elastic inversion in seismic reservoir characterization. It presents the mathematical concepts of convolution and how it can be used to model seismic reflection data. Specifically, it proposes adding a dip-dependent stretch to the standard 1D convolution model to account for dipping structures. It demonstrates this dip-corrected convolution modelling on synthetic fault and injectite models, and shows how relative elastic inversion can further improve lateral resolution. The document concludes the dip correction provides a simple first-order method to include dip effects and benefits from elastic inversion techniques.
The document discusses convolution and its applications in imaging. Convolution describes how one function is modified by another function. In imaging, the point spread function (PSF) describes how a point object is blurred by the imaging system. The image formation process can be described as the convolution of the object with the PSF plus noise. Fourier analysis is useful because convolution in the spatial domain is equivalent to multiplication in the frequency domain. This allows filtering techniques to be used to modify images. Examples are provided of using Fourier analysis to determine the PSF and modulation transfer function of an imaging system.
Optimal Budget Allocation: Theoretical Guarantee and Efficient AlgorithmTasuku Soma
The document presents two main results:
1. A general framework for submodular function maximization over integer lattices with a (1-1/e)-approximation algorithm that runs in pseudo polynomial time. This extends budget allocation to more complex scenarios.
2. A faster algorithm for budget allocation when influence probabilities are non-increasing, running in almost linear time compared to previous polynomial time algorithms. Experiments on real and large synthetic graphs show it outperforms heuristics by up to 15%.
The document discusses spin models on networks. It provides background on spin models in statistical physics, traditionally using lattices as the underlying graph. It explores reasons for studying spin models on networks and describes several specific models. The XY model is described, where spins are angles and the Hamiltonian favors alignment between connected spins. Results are presented for the XY model on Watts-Strogatz networks and a dynamic XY model. The YX model is introduced where spins are fixed but links can change. Analysis of the largest components and their behavior at the magnetic transition temperature is shown for the YX model. The free XY model is also analyzed, looking at magnetization, largest component size, and number of components for varying average degrees.
This document summarizes the Metropolis Light Transport (MLT) algorithm for Monte Carlo ray tracing. MLT improves upon previous algorithms by using Metropolis sampling to focus samples in areas where the function f is large, leading to faster convergence. The basic MLT algorithm starts with an initial random path, then iteratively mutates the path and accepts or rejects the mutation based on an acceptance probability to ensure detailed balance. This allows MLT to efficiently simulate difficult lighting effects like caustics and indirect lighting.
The document discusses the Fourier transform, which relates a signal sampled in time or space to the same signal sampled in frequency. It explains the mathematical definition and provides an example of using a Fourier transform to convert time domain data to the frequency domain. Specifically, it uses a cosine wave as input data and calculates the Fourier transform to reveal a strong amplitude at the expected frequency component.
Here we look at how to create a projection Matrix for orthogonal projection or transformation and projection onto a Line under Numerical Linear Algebra.
Efficient Finite Element Computation of Circulating Currents in Thin Parallel...Antti Lehikoinen
My poster for the International Conference on the Computation of Electromagnetic Fields (Compumag 2015).
I developed a non-conforming meshing approach for stranded conductors, resulting in a significant reduction on the degrees-of-freedom and computation times in loss calculation.
Seismic presentation for Dip correction for convolution modellingHarshal Pende
This document discusses dip correction for convolution modelling and elastic inversion in seismic reservoir characterization. It presents the mathematical concepts of convolution and how it can be used to model seismic reflection data. Specifically, it proposes adding a dip-dependent stretch to the standard 1D convolution model to account for dipping structures. It demonstrates this dip-corrected convolution modelling on synthetic fault and injectite models, and shows how relative elastic inversion can further improve lateral resolution. The document concludes the dip correction provides a simple first-order method to include dip effects and benefits from elastic inversion techniques.
The document discusses convolution and its applications in imaging. Convolution describes how one function is modified by another function. In imaging, the point spread function (PSF) describes how a point object is blurred by the imaging system. The image formation process can be described as the convolution of the object with the PSF plus noise. Fourier analysis is useful because convolution in the spatial domain is equivalent to multiplication in the frequency domain. This allows filtering techniques to be used to modify images. Examples are provided of using Fourier analysis to determine the PSF and modulation transfer function of an imaging system.
Optimal Budget Allocation: Theoretical Guarantee and Efficient AlgorithmTasuku Soma
The document presents two main results:
1. A general framework for submodular function maximization over integer lattices with a (1-1/e)-approximation algorithm that runs in pseudo polynomial time. This extends budget allocation to more complex scenarios.
2. A faster algorithm for budget allocation when influence probabilities are non-increasing, running in almost linear time compared to previous polynomial time algorithms. Experiments on real and large synthetic graphs show it outperforms heuristics by up to 15%.
The document discusses spin models on networks. It provides background on spin models in statistical physics, traditionally using lattices as the underlying graph. It explores reasons for studying spin models on networks and describes several specific models. The XY model is described, where spins are angles and the Hamiltonian favors alignment between connected spins. Results are presented for the XY model on Watts-Strogatz networks and a dynamic XY model. The YX model is introduced where spins are fixed but links can change. Analysis of the largest components and their behavior at the magnetic transition temperature is shown for the YX model. The free XY model is also analyzed, looking at magnetization, largest component size, and number of components for varying average degrees.
This document summarizes the Metropolis Light Transport (MLT) algorithm for Monte Carlo ray tracing. MLT improves upon previous algorithms by using Metropolis sampling to focus samples in areas where the function f is large, leading to faster convergence. The basic MLT algorithm starts with an initial random path, then iteratively mutates the path and accepts or rejects the mutation based on an acceptance probability to ensure detailed balance. This allows MLT to efficiently simulate difficult lighting effects like caustics and indirect lighting.
The document discusses the Fourier transform, which relates a signal sampled in time or space to the same signal sampled in frequency. It explains the mathematical definition and provides an example of using a Fourier transform to convert time domain data to the frequency domain. Specifically, it uses a cosine wave as input data and calculates the Fourier transform to reveal a strong amplitude at the expected frequency component.
Maximizing Submodular Function over the Integer LatticeTasuku Soma
The document describes generalizations of submodular function maximization and submodular cover problems from sets to integer lattices. It presents polynomial-time approximation algorithms for maximizing monotone diminishing return (DR) submodular functions subject to constraints like cardinality, polymatroid and knapsack on the integer lattice. It also presents an algorithm for the DR-submodular cover problem of minimizing cost subject to achieving a quality threshold. The results provide useful extensions of submodular optimization to settings that cannot be modeled as set functions.
This document summarizes a majorization-minimization approach to designing power transmission networks. It models power flow as current flow in a resistive network. It formulates the problem of designing the network topology and line sizes to minimize power loss as a convex optimization problem. To impose sparsity, it introduces a non-convex penalty term and solves the problem using a majorization-minimization algorithm that solves a sequence of convex subproblems. The approach can also design robust networks that are resilient to failures by optimizing for the worst-case power loss after failures.
This document proposes applying ΣΔ quantization to fusion frames for efficient analog-to-digital and digital-to-analog conversion in wireless sensor networks. It develops 1st-order and high-order ΣΔ quantization algorithms for fusion frame projections that use a minimal number of bits per subspace. It proves the canonical left inverse minimizes operator norms and introduces Sobolev left inverses, which minimize reconstruction error. Numerical experiments show the reconstruction error from high-order ΣΔ quantization decays as O(N-r).
Accelerated reconstruction of a compressively sampled data streamPantelis Sopasakis
Recursive compressed sensing on a stream of data: The traditional compressed sensing approach is naturally offline, in that it amounts to sparsely sampling and reconstructing a given dataset. Recently, an online algorithm for performing compressed sensing on streaming data was proposed: the scheme uses recursive sampling of the input stream and recursive decompression to accurately estimate stream entries from the acquired noisy measurements.
In this paper, we develop a novel Newton-type forward-backward proximal method to recursively solve the regularized Least-Squares problem (LASSO) online. We establish global convergence of our method as well as a local quadratic convergence rate. Our simulations show a substantial speed-up over the state of the art which may render the proposed method suitable for applications with stringent real-time constraints.
Camera calibration from a single image based on coupled line cameras and rect...Joo-Haeng Lee
(1) The document proposes a method for camera calibration from a single image based on modeling the image as two coupled line cameras and applying rectangle constraints.
(2) It presents an analytic solution for estimating the pose of a 2D line camera and models a rectangle constraint using two coupled line cameras.
(3) Based on this, the method derives an analytic solution for projective reconstruction that allows reconstructing the scene rectangle in a metric sense without full camera calibration.
11903 Electromagnetic Waves And Transmission Linesguestd436758
This document contains information about an electromagnetic waves and transmission lines exam for a fourth semester engineering course. It includes 8 questions covering topics like Maxwell's equations, electric and magnetic fields, wave propagation, transmission lines, and waveguides. Students were instructed to answer any 5 of the 8 questions in the exam, which would be graded out of 80 total marks. The questions involve both theoretical concepts and calculations.
This document discusses Bode plots, which are used to analyze the stability of linear time-invariant control systems. Bode plots graphically represent a system's transfer function and consist of a magnitude plot and a phase plot versus frequency. The magnitude plot shows the gain in decibels and the phase plot shows the phase angle. Together these plots can determine the gain and phase margins of a system, which indicate its stability. Examples are provided to demonstrate how to construct Bode plots from transfer functions and analyze system stability.
This document provides an overview of chapters 6 through 10 of the Computer Graphics and Animation course taught by Dr. Sumanta Guha. Chapter 6 covers figures and book figures. Chapter 7 discusses an unspecified topic. Chapter 8 introduces Bezier curves and their mathematical properties. Chapter 9 covers an unknown subject. Chapter 10 is the final chapter summarized.
This document provides an overview of parallel coordinate descent algorithms. It discusses how naive parallelization of sequential coordinate descent will not always converge due to coordinate interactions. Two approaches for parallel coordinate descent are presented: Expected Separable Over-approximation (ESO) and Shotgun. ESO minimizes an overapproximated quadratic function to determine step sizes. Shotgun randomly selects coordinates to update in parallel each iteration. The document also notes limitations such as large communication overhead and inability to prove convergence without knowing the separability and smoothness of the objective function.
This document presents an efficient convex hull algorithm for finding the convex hull of a planar set of points. The algorithm partitions the set of points into four regions based on the minimum and maximum x and y coordinates. It then finds the convex hull parts belonging to each region in parallel. Those parts are merged to derive the full convex hull. For each region, the algorithm uses a modified gradient concept to efficiently process the points and find the boundary points of the convex hull part. The algorithm achieves parallelism, data reduction, and has lower computational cost compared to traditional interior points algorithms. However, its drawbacks include difficulty extending it to higher dimensions and its static nature which requires the entire dataset from the beginning.
This document discusses using coordinate descent optimization in recommendation systems. It begins with an introduction to coordinate descent, explaining that it optimizes dimensions sequentially to minimize an objective function. It then provides a case study on applying coordinate descent to linear regression, collaborative filtering, and weighted regularized matrix factorization models. Specific algorithms for coordinate descent in linear regression and collaborative filtering are presented.
This document contains a mathematics project with multiple parts and questions.
1) Part 1 involves solving simultaneous equations to find the maximum area of a fence given certain constraints. The maximum area is 1250 square meters.
2) Part 2 involves using a volume equation and given values to find the largest possible volume, which is 2000 cubic centimeters.
3) Part 3 involves solving word problems related to time, population, and trigonometric functions.
This document discusses convex hull algorithms. It defines a convex set as one where any line segment between two points in the set is also contained in the set. The convex hull of a set of points is the smallest convex set containing those points. Intuitively, in 2D the convex hull is the shape formed by stretching a rubber band around nails at each point, and in 3D it is the shape formed by stretching plastic wrap tightly around the points. The document then lists and describes several existing convex hull algorithms and provides an overview of an interior points algorithm that identifies non-extreme points based on whether they lie within triangles formed by other points.
The document discusses the conjugate-beam method for analyzing structural beams. It involves using a mathematical analogy where:
- The actual beam is represented by a conjugate beam with the same slope-deflection, load-shear-moment relationships.
- At any point along the beams, the deflection (y), slope (θ), shear (V), and bending moment (M) of the actual beam equals the corresponding values of the conjugate beam.
- The conjugate beam has a simplified loading (e.g. a single point load P) which allows the bending moment and shear to be easily calculated using beam equations. This then provides the bending moment and shear distributions for the actual beam.
New geometric interpretation and analytic solution for quadrilateral reconstr...Joo-Haeng Lee
Poster presentation for ICPR 2014 paper.
Title: New geometric interpretation and analytic solution for quadrilateral reconstruction
Author: Joo-Haeng Lee (ETRI)
This document contains tutorial problems on vector transformations between Cartesian, cylindrical, and spherical coordinate systems. It provides the steps to:
1) Express points and vectors in different coordinate systems, such as transforming between Cartesian and cylindrical coordinates.
2) Derive transformation matrices for changing between coordinate systems.
3) Write out the differential elements of length, area, and volume for each coordinate system.
This presentation on Pseudo Random Number Generator enlists the different generators, their mechanisms and the various applications of random numbers and pseudo random numbers in different arenas.
Projectors and Projection Onto SubspacesIsaac Yowetu
The document discusses projections onto subspaces. It provides examples of projecting vectors onto lines and subspaces. For projecting a vector v onto a line defined by a vector u, it shows that the projection matrix is P=uuT/uTu. It also shows how to project vectors onto subspaces defined by matrices and how to decompose a vector into components within and orthogonal to a subspace.
We solve elliptic PDE with uncertain coefficients. We apply Karhunen-Loeve expansion to separate stochastic part from spatial part. The corresponding eigenvalue problem with covariance function is solved via the Hierarchical Matrix technique. We also demonstrate how low-rank tensor method can be applied for high-dimensional problems (e.g., to compute higher order statistical moments) . We provide explicit formulas to compute statistical moments of order k with linear complexity.
This document contains a mid-term examination on microwave engineering with 5 questions. Question 1 asks to show that a sinusoidal wave function represents a wave and find the direction of propagation. Question 2 calculates the reflection and transmission coefficients and powers for a coaxial line with a resistor attached. Question 3 calculates the reflection coefficient for a coaxial line with an inductor attached. Question 4 calculates the reflection coefficient for a coaxial line with a real inductor and resistor attached. Question 5 calculates the VSWR for the system in question 4.
1) The reflection coefficient Γ is calculated for a coaxial line with resistors R=12Ω and R=213Ω attached. The VSWR is also calculated for each case.
2) The reflection coefficient Γ is calculated for a coaxial line with a capacitor C=12pF attached.
3) Parameters of a Hertzian dipole antenna are calculated including the E-field and H-field at a distance of 1km from the antenna oriented at 90° and 90°, and the phase at the end of the dipole.
Maximizing Submodular Function over the Integer LatticeTasuku Soma
The document describes generalizations of submodular function maximization and submodular cover problems from sets to integer lattices. It presents polynomial-time approximation algorithms for maximizing monotone diminishing return (DR) submodular functions subject to constraints like cardinality, polymatroid and knapsack on the integer lattice. It also presents an algorithm for the DR-submodular cover problem of minimizing cost subject to achieving a quality threshold. The results provide useful extensions of submodular optimization to settings that cannot be modeled as set functions.
This document summarizes a majorization-minimization approach to designing power transmission networks. It models power flow as current flow in a resistive network. It formulates the problem of designing the network topology and line sizes to minimize power loss as a convex optimization problem. To impose sparsity, it introduces a non-convex penalty term and solves the problem using a majorization-minimization algorithm that solves a sequence of convex subproblems. The approach can also design robust networks that are resilient to failures by optimizing for the worst-case power loss after failures.
This document proposes applying ΣΔ quantization to fusion frames for efficient analog-to-digital and digital-to-analog conversion in wireless sensor networks. It develops 1st-order and high-order ΣΔ quantization algorithms for fusion frame projections that use a minimal number of bits per subspace. It proves the canonical left inverse minimizes operator norms and introduces Sobolev left inverses, which minimize reconstruction error. Numerical experiments show the reconstruction error from high-order ΣΔ quantization decays as O(N-r).
Accelerated reconstruction of a compressively sampled data streamPantelis Sopasakis
Recursive compressed sensing on a stream of data: The traditional compressed sensing approach is naturally offline, in that it amounts to sparsely sampling and reconstructing a given dataset. Recently, an online algorithm for performing compressed sensing on streaming data was proposed: the scheme uses recursive sampling of the input stream and recursive decompression to accurately estimate stream entries from the acquired noisy measurements.
In this paper, we develop a novel Newton-type forward-backward proximal method to recursively solve the regularized Least-Squares problem (LASSO) online. We establish global convergence of our method as well as a local quadratic convergence rate. Our simulations show a substantial speed-up over the state of the art which may render the proposed method suitable for applications with stringent real-time constraints.
Camera calibration from a single image based on coupled line cameras and rect...Joo-Haeng Lee
(1) The document proposes a method for camera calibration from a single image based on modeling the image as two coupled line cameras and applying rectangle constraints.
(2) It presents an analytic solution for estimating the pose of a 2D line camera and models a rectangle constraint using two coupled line cameras.
(3) Based on this, the method derives an analytic solution for projective reconstruction that allows reconstructing the scene rectangle in a metric sense without full camera calibration.
11903 Electromagnetic Waves And Transmission Linesguestd436758
This document contains information about an electromagnetic waves and transmission lines exam for a fourth semester engineering course. It includes 8 questions covering topics like Maxwell's equations, electric and magnetic fields, wave propagation, transmission lines, and waveguides. Students were instructed to answer any 5 of the 8 questions in the exam, which would be graded out of 80 total marks. The questions involve both theoretical concepts and calculations.
This document discusses Bode plots, which are used to analyze the stability of linear time-invariant control systems. Bode plots graphically represent a system's transfer function and consist of a magnitude plot and a phase plot versus frequency. The magnitude plot shows the gain in decibels and the phase plot shows the phase angle. Together these plots can determine the gain and phase margins of a system, which indicate its stability. Examples are provided to demonstrate how to construct Bode plots from transfer functions and analyze system stability.
This document provides an overview of chapters 6 through 10 of the Computer Graphics and Animation course taught by Dr. Sumanta Guha. Chapter 6 covers figures and book figures. Chapter 7 discusses an unspecified topic. Chapter 8 introduces Bezier curves and their mathematical properties. Chapter 9 covers an unknown subject. Chapter 10 is the final chapter summarized.
This document provides an overview of parallel coordinate descent algorithms. It discusses how naive parallelization of sequential coordinate descent will not always converge due to coordinate interactions. Two approaches for parallel coordinate descent are presented: Expected Separable Over-approximation (ESO) and Shotgun. ESO minimizes an overapproximated quadratic function to determine step sizes. Shotgun randomly selects coordinates to update in parallel each iteration. The document also notes limitations such as large communication overhead and inability to prove convergence without knowing the separability and smoothness of the objective function.
This document presents an efficient convex hull algorithm for finding the convex hull of a planar set of points. The algorithm partitions the set of points into four regions based on the minimum and maximum x and y coordinates. It then finds the convex hull parts belonging to each region in parallel. Those parts are merged to derive the full convex hull. For each region, the algorithm uses a modified gradient concept to efficiently process the points and find the boundary points of the convex hull part. The algorithm achieves parallelism, data reduction, and has lower computational cost compared to traditional interior points algorithms. However, its drawbacks include difficulty extending it to higher dimensions and its static nature which requires the entire dataset from the beginning.
This document discusses using coordinate descent optimization in recommendation systems. It begins with an introduction to coordinate descent, explaining that it optimizes dimensions sequentially to minimize an objective function. It then provides a case study on applying coordinate descent to linear regression, collaborative filtering, and weighted regularized matrix factorization models. Specific algorithms for coordinate descent in linear regression and collaborative filtering are presented.
This document contains a mathematics project with multiple parts and questions.
1) Part 1 involves solving simultaneous equations to find the maximum area of a fence given certain constraints. The maximum area is 1250 square meters.
2) Part 2 involves using a volume equation and given values to find the largest possible volume, which is 2000 cubic centimeters.
3) Part 3 involves solving word problems related to time, population, and trigonometric functions.
This document discusses convex hull algorithms. It defines a convex set as one where any line segment between two points in the set is also contained in the set. The convex hull of a set of points is the smallest convex set containing those points. Intuitively, in 2D the convex hull is the shape formed by stretching a rubber band around nails at each point, and in 3D it is the shape formed by stretching plastic wrap tightly around the points. The document then lists and describes several existing convex hull algorithms and provides an overview of an interior points algorithm that identifies non-extreme points based on whether they lie within triangles formed by other points.
The document discusses the conjugate-beam method for analyzing structural beams. It involves using a mathematical analogy where:
- The actual beam is represented by a conjugate beam with the same slope-deflection, load-shear-moment relationships.
- At any point along the beams, the deflection (y), slope (θ), shear (V), and bending moment (M) of the actual beam equals the corresponding values of the conjugate beam.
- The conjugate beam has a simplified loading (e.g. a single point load P) which allows the bending moment and shear to be easily calculated using beam equations. This then provides the bending moment and shear distributions for the actual beam.
New geometric interpretation and analytic solution for quadrilateral reconstr...Joo-Haeng Lee
Poster presentation for ICPR 2014 paper.
Title: New geometric interpretation and analytic solution for quadrilateral reconstruction
Author: Joo-Haeng Lee (ETRI)
This document contains tutorial problems on vector transformations between Cartesian, cylindrical, and spherical coordinate systems. It provides the steps to:
1) Express points and vectors in different coordinate systems, such as transforming between Cartesian and cylindrical coordinates.
2) Derive transformation matrices for changing between coordinate systems.
3) Write out the differential elements of length, area, and volume for each coordinate system.
This presentation on Pseudo Random Number Generator enlists the different generators, their mechanisms and the various applications of random numbers and pseudo random numbers in different arenas.
Projectors and Projection Onto SubspacesIsaac Yowetu
The document discusses projections onto subspaces. It provides examples of projecting vectors onto lines and subspaces. For projecting a vector v onto a line defined by a vector u, it shows that the projection matrix is P=uuT/uTu. It also shows how to project vectors onto subspaces defined by matrices and how to decompose a vector into components within and orthogonal to a subspace.
We solve elliptic PDE with uncertain coefficients. We apply Karhunen-Loeve expansion to separate stochastic part from spatial part. The corresponding eigenvalue problem with covariance function is solved via the Hierarchical Matrix technique. We also demonstrate how low-rank tensor method can be applied for high-dimensional problems (e.g., to compute higher order statistical moments) . We provide explicit formulas to compute statistical moments of order k with linear complexity.
This document contains a mid-term examination on microwave engineering with 5 questions. Question 1 asks to show that a sinusoidal wave function represents a wave and find the direction of propagation. Question 2 calculates the reflection and transmission coefficients and powers for a coaxial line with a resistor attached. Question 3 calculates the reflection coefficient for a coaxial line with an inductor attached. Question 4 calculates the reflection coefficient for a coaxial line with a real inductor and resistor attached. Question 5 calculates the VSWR for the system in question 4.
1) The reflection coefficient Γ is calculated for a coaxial line with resistors R=12Ω and R=213Ω attached. The VSWR is also calculated for each case.
2) The reflection coefficient Γ is calculated for a coaxial line with a capacitor C=12pF attached.
3) Parameters of a Hertzian dipole antenna are calculated including the E-field and H-field at a distance of 1km from the antenna oriented at 90° and 90°, and the phase at the end of the dipole.
This document contains exam questions about antenna engineering parameters for a Hertzian dipole antenna operating at 13 GHz. The questions ask the examinee to: (1) calculate the E-field, H-field, radiation power, resistance, and input impedance at given distances and angles from the antenna; (2) draw the input impedance on a Smith chart; and (3) compare resonance characteristics of Hertzian and half-wave dipole antennas without using formulas. An additional question asks the examinee to explain electromagnetic wave radiation by a antenna in terms of current density and vector potential without using textbook formulas.
The document contains questions about designing antennas for WiFi applications. For a dipole antenna operating at 2.4 GHz, it asks to calculate the antenna length, reflection coefficient and VSWR when the input impedance is 73 ohms and the transmission line impedance is 50 ohms. It also asks how to reduce the antenna length while keeping the resonant frequency fixed. For a microstrip patch antenna at 3.7 GHz, it asks to determine the antenna dimensions, calculate the reflection coefficient and VSWR when the input impedance is 200 ohms and transmission line impedance is 50 ohms, and design a quarter-wave transformer.
The document describes two microwave engineering problems involving the design of power dividers and a quadrature hybrid. The first problem involves designing a T-junction power divider with a quarter-wave transformer with specified impedances and calculating the impedance and length of the transformer. The second problem involves calculating the scattered voltage waves at the ports of a quadrature hybrid when one port is excited, given the scattering matrix and specifications.
1) Design a microstrip patch antenna for 5 GHz with dimensions l x w for dielectric constant εr = 2.2. Perform impedance matching with transfer impedance ZT and length lT when Zin = 250Ω and Z0 = 50Ω. Draw the antenna design.
2) Explain the design procedures for microstrip patch antennas and that a good substrate provides a balance of bandwidth, small size, and efficiency for antenna applications.
3) Array antennas are designed even when a single antenna is sufficient because an array provides directivity and gain through constructive and destructive interference from an array factor and element patterns.
This document discusses transmission lines and their characteristics. It covers:
1) The advantages of transmission lines including less distortion, radiation and cross-talk compared to point-to-point wiring. Transmission lines can handle signals traveling over long distances.
2) Reflections that can occur on transmission lines when there is a mismatch in impedances. Methods to reduce reflections include source and load termination techniques.
3) The mathematics and modeling of transmission lines, including their characteristic impedance, propagation constant, and behavior as either infinite lines, matched lines or unmatched lines based on the source and load impedances. Key formulas are derived for voltage, current, input acceptance, output transmission and reflective coefficients.
This document contains engineering equations related to radio frequency transmission and antennas. It includes equations for reflection coefficient, voltage standing wave ratio, characteristic impedance of transmission lines, Friis transmission equation, antenna gain, noise factor, free space path loss, radio horizon, gain of parabolic antennas, beamwidth of parabolic antennas, and beam broadening versus sidelobe ratio. The document is a reference sheet from Kathrein Inc. providing essential equations for RF engineering.
This document contains engineering equations related to radio frequency transmission and antennas. It includes equations for reflection coefficient, voltage standing wave ratio, characteristic impedance of transmission lines, Friis transmission equation, antenna gain, noise factor, free space path loss, radio horizon, gain of parabolic antennas, beamwidth of parabolic antennas, and beam broadening versus sidelobe ratio. The document is a reference sheet from Kathrein Inc. providing essential equations for RF engineering.
1. The document discusses transmission line theory and parameters. Key topics covered include:
- Telegrapher's equation and circuit model for transmission lines
- Wave propagation and characteristic impedance calculations
- Reflection coefficient and standing wave ratio definitions
- Comparisons of transmission line, circuit, and field theories
2. Specific transmission line types are analyzed, including planar lines, coaxial cables. Equations are given for calculating the capacitance, conductance, inductance, resistance, and characteristic impedance of these common line configurations.
3. Simulation and modeling techniques for transmission lines are briefly mentioned, such as the transmission line matrix method for modeling microstrip lines in antennas and circuits.
The document contains 10 problems involving electromagnetic induction and Maxwell's equations. Problem 10.1 involves calculating the voltage and current in a circuit with a changing magnetic flux. Problem 10.2 replaces a voltmeter with a resistor and calculates the resulting current. Problem 10.3 calculates the emf induced in closed paths with changing magnetic fluxes.
The document contains 10 problems involving electromagnetic induction and Maxwell's equations. Problem 10.1 involves calculating the voltage and current in a circuit with a changing magnetic flux. Problem 10.2 replaces a voltmeter with a resistor and calculates the resulting current. Problem 10.3 calculates the emf induced in two different rectangular paths with a given magnetic field.
This document contains a 10 question test on electronics topics like amplifiers, diodes, transistors, and feedback. It includes multiple choice and open response questions requiring calculations of voltages, currents, gains, frequencies, and impedances for various circuit configurations. The test covers both conceptual questions, such as types of feedback, as well as numerical problems involving circuit analysis, equivalent impedances, and amplifier specifications.
This document contains a set of practice problems related to sinusoidal signals, phasors, and AC power analysis. It begins with definitions of terms like sinusoids, phasors, resistance, inductance, capacitance, and impedance. It then presents 35 problems involving concepts like phasor representations of signals, phase relationships between voltage and current in different circuit elements, power calculations, RMS values, and power factors. The document spans 24 pages and provides the questions, blank spaces for solutions, and sometimes diagrams related to circuit analysis.
The document contains a past exam for a Microwave Engineering course. It includes 3 questions:
1) A design procedure question for a microstrip line power divider in 1-2 sentences.
2) A question involving the design and analysis of a quadrature hybrid circuit, including calculating scattered voltage waves from port excitations.
3) A brief explanation of the usage of scattering matrices in electromagnetic problems.
This document contains a sample MCAT exam with 220 multiple choice questions covering physics, chemistry and biology. Some example questions are provided on topics like logic diagrams, stress-strain graphs, gas laws, radioactivity, optics and chemical reactions. The exam is designed for students completing their F.Sc. or non-F.Sc. degrees, with a maximum time of 150 minutes and total marks of 1100.
The document discusses inertial algorithms for minimizing convex functions. It begins by introducing the gradient method and accelerated/inertial gradient method. It then reviews several classic approaches for analyzing the convergence of inertial algorithms, such as algebraic proofs, estimate sequences, and viewing the algorithm as a discretization of an ordinary differential equation (ODE). More recent approaches discussed include analyzing inertial algorithms as a combination of primal and mirror descent steps or using Bregman estimate sequences. The document raises questions about interpreting the difference between inertial algorithms and the heavy ball method from an ODE perspective. It also discusses a new direction of analyzing inertial algorithms by viewing them as numerical integration schemes approximating the solution to an ODE.
1) An AC generator with an RMS voltage of 110 V is connected in series with a 35-Ω resistor and 1-μF capacitor. To maintain a current of 1.2 A, the generator must operate at a frequency of 1.9 kHz.
2) An AC generator with an emf of 22.8 V at 353 rad/s is connected to a 17.3 H inductor. When the current is maximum, the emf is 22.8 V. When the emf is -11.4 V and increasing, the current is 4.11 A.
3) A series RLC circuit with a 148-Ω resistor, 1.50-μF capacitor
This document provides instructions for candidates taking the Oxford Colleges Physics Aptitude Test (PAT). It includes boxes for candidates to fill in identifying information. The test has two parts (A and B) with equal weight, focusing on mathematics and physics respectively. Part A contains 12 math problems worth a total of 50 marks. Part B contains multiple choice and written answer physics questions worth a total of 50 marks. Calculators and formulas are not permitted. Answers should be shown on the question sheet. The test is 2 hours long and candidates are advised to divide their time evenly between the two parts.
11903 Electromagnetic Waves And Transmission Linesguestac67362
This document contains an exam for the subject Electromagnetic Waves and Transmission Lines. It consists of 8 questions, each with 2 parts, and students must answer 5 questions. The questions cover topics like Maxwell's equations, wave equations, transmission lines, waveguides, and electric and magnetic fields. The exam is worth a total of 80 marks and students have 3 hours to complete it.
The document discusses Android's Sensor Manager and how it works with sensors. It covers the SensorManager class, which allows apps to access sensor data, and the SensorEventListener interface that apps must implement to receive sensor updates. It also lists some of the different types of sensors available on Android devices like accelerometers, gyroscopes, and light sensors.
This document discusses BroadcastReceivers in Android. A BroadcastReceiver is an intent-based publish-subscribe system that allows apps to receive system events like SMS messages. BroadcastReceivers can receive and react to system broadcasts, broadcasts from other apps, and initiate broadcasts to other apps. They are registered either dynamically in code or statically in the AndroidManifest.xml file. Broadcasts are sent using the sendBroadcast or sendOrderedBroadcast methods and an Intent. Ordered broadcasts are executed in a defined order while normal broadcasts run asynchronously. The BroadcastReceiver object is only valid during the onReceive method call.
1. The document discusses the Android application lifecycle and how activities can transition between different states like onCreate, onStart, onResume, onPause, onStop, and onDestroy.
2. It also covers the activity lifecycle methods and how they relate to different states, as well as how to save and restore activity instance states.
3. Additionally, it provides comparisons between the Android and Windows lifecycles and messaging systems, and introduces concepts like handlers, loopers, threads, and the context class in Android.
This document provides an overview of cloud computing fundamentals. It defines cloud computing as on-demand access to configurable computing resources over the internet. The document discusses key cloud concepts like deployment models (private, public, hybrid, community clouds), service models (IaaS, PaaS, SaaS), and requirements for cloud services. Popular cloud providers like AWS, Azure, Google Cloud are presented for each service model. Benefits of cloud computing are also highlighted such as reduced costs, flexibility, and global access to resources.
This document summarizes the analysis of bias for a BJT (bipolar junction transistor) circuit. It includes:
1. An overview of different BJT amplifier configurations - common emitter (CE), common base (CB), and common collector (CC).
2. A description of the bias point as the quiescent operating point in the active mode.
3. An analysis of the bias for a CE amplifier using a Thevenin equivalent circuit and equations for the base-emitter loop and collector-emitter loop to solve for collector current and CE voltage.
4. Guidelines for selecting resistor values in the bias network, including RB being greater than 10kΩ, RE being
This document discusses the different cloud service models of Infrastructure as a Service (IaaS), Platform as a Service (PaaS), and Software as a Service (SaaS). IaaS provides basic computing resources like servers and storage. PaaS provides development tools and platforms for building applications. SaaS provides complete software solutions that are accessed via the internet. Popular providers for each service model are also mentioned.
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...Diana Rendina
Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
Your Skill Boost Masterclass: Strategies for Effective Upskilling
2010-1 중간고사문제(초고주파공학)
1. 2010 mid-term examination (100)
Microwave Engineering
Date: October 20, 2010.
Z − Z0
Z = 50Ω, f = 5.3 [GHz], Γ = L
1. Consider a coaxial line with 0 Z L + Z 0 (80)
1)Calculate the reflection coefficient, Γ in terms of the magnitude (in dB) and
phase when resistors, R = 23 [Ω] and R = 374 [Ω] are attached. (10) Hint:)
Γ(dB) = 20 log10 Γ
2)Calculate the reflected and transmitted powers for problem 1) when
Pi = 1 [mW ] . Hint:) PR =| Γ | 2 Pi , PT = (1− | Γ | 2 ) Pi (20)
3)Calculate the VSWR (Voltage Standing Wave Ratio) for problem 1). Hint:)
1+ Γ
VSWR =
1 − Γ (10)
4)Calculate the reflection coefficient, Γ in terms of the magnitude and phase
when an inductor, L = 3[ nH ] is attached. Hint:) Z L = jωL (20)
5)Calculate the transmitted power to the inductor in problem 4) when
Pi = 1 [mW ] . (10)
6)Calculate the VSWR (Voltage Standing Wave Ratio) for problem 4). (10)
2. 2. Compare the voltage in circuit theory and the voltage wave in transmission line
theory (10)