This document discusses various methods for calculating radar cross section (RCS), including the finite difference time domain method, method of moments, geometrical optics, physical optics, geometrical theory of diffraction, and physical theory of diffraction. It provides overviews and comparisons of each method, explaining their approaches, assumptions, accuracy, and applicability to different target sizes and frequencies.
This document provides an introduction and outline for a course on radar systems engineering given by Dr. Robert O'Donnell of the IEEE New Hampshire Section. The course covers the history of radar development including pre-radar detection methods, the early pioneers of radar technology, and key radar systems used in World War II such as the Chain Home radar network and SCR-584 fire control radar. It also summarizes how radar contributed to British victories during the Battle of Britain and in defending against German V-1 buzz bomb attacks. The document outlines topics to be covered on radar basics, principles of operation, and classifications of military, civilian and other radar systems.
This document provides an overview of radar cross section (RCS) and techniques for predicting a target's RCS through both measurement and theoretical calculation. It begins with definitions of RCS and factors affecting it. Examples of typical RCS values for different targets are given. Physical scattering mechanisms and contributors to a target's RCS are described. Both full-scale and scale model target measurement techniques are outlined. Theoretical prediction methods including geometrical optics, physical optics, and diffraction theories are introduced. Scaling laws for applying results from scale models to full-scale targets are also covered.
Radar 2009 a 16 parameter estimation and tracking part2Forward2025
This document summarizes a lecture on parameter estimation and tracking. It discusses tracking processes like track association, initiation, maintenance through prediction and updating, and termination. Filtering techniques like the Kalman filter are presented as ways to estimate target position and velocity while accounting for noise and maneuvers. Examples of civilian and military target maneuvers are provided to illustrate the challenges of tracking.
This document provides an overview of radar antennas and scanning techniques. It begins with introductions to basic antenna concepts such as near and far field regions, electromagnetic field equations, polarization, and antenna gain. It then discusses reflector antennas, which use mechanical scanning to direct the antenna beam. The document outlines additional topics that will be covered, including phased array antennas, frequency scanning, and hybrid scanning methods. The goal is to provide an introduction to different types of radar antennas and how they are used to direct electromagnetic energy.
This document summarizes a lecture on radar clutter. It discusses different types of clutter sources including ground, sea, rain, and birds. It provides details on the attributes of rain clutter such as how it is affected by wavelength and circular polarization. Graphs are presented showing reflectivity of rain and its Doppler spectrum. Bird clutter properties around radar cross-section, velocity, and density are also covered. The document aims to explain the impact of various clutter sources on radar performance.
The document discusses various topics related to naval stealth technology including radar cross section (RCS) reduction techniques. It provides information on radar frequencies and functions, radar working principles, RCS prediction methods, and examples of stealth ships. Key points covered include how shaping, radar absorbing materials, and passive/active cancellation can be used to reduce the RCS and vulnerability of detection of naval vessels. Prediction software, instrumentation systems, and examples of reduced RCS for components like gun barrels are also summarized.
Tutorial Content
This tutorial provides a broad-based discussion of radar system, covering the following topics:
-Introduction to Radars in Military and Commercial Applications
-Radar System Block Diagram
-Radar Antennas (slotted waveguide array, planar array), Transmitter (magnetron, solid-state), Receiver, Pedestal and Radome
-Plot Extraction, Tracking Algorithms and Display
-Radar Range Equation, Detection Performance
-Wave Propagation and Radar Cross Section
-Emerging and Advanced Radar Systems (phased-array, multi-beam, multi-mode, FMCW, solid-state)
In the discussion, practical systems, technical specifications and data will be used to enhance learning.In addition, simulation results will also be used to present findings.
The objective of the tutorial session is to equip participants with solid understanding of radar systems for system level applications and prepare them for advanced and professional radar courses, projects and research.
This tutorial is designed and developed based on the following references:
[1] G. W. Stimson, Introduction to Airborne Radar Second Edition, Scitech Publishing, 1998.
[2] L. V. Blake, A Guide to Basic Pulse-Radar Maximum-Range Calculation, NRL Report 6930, 1969.
[3] K. H. Lee, Radar Systems for Nanyang Technological University, TBSS, 2014.
This document contains lecture slides about radar signal propagation through the atmosphere. It discusses various propagation effects including reflection from the Earth's surface, atmospheric refraction, multipath interference, and attenuation. It provides equations for calculating propagation losses and phase differences between direct and reflected signals. Examples are given of how propagation affects radar coverage and detection range for a shipborne surveillance radar system.
This document provides an introduction and outline for a course on radar systems engineering given by Dr. Robert O'Donnell of the IEEE New Hampshire Section. The course covers the history of radar development including pre-radar detection methods, the early pioneers of radar technology, and key radar systems used in World War II such as the Chain Home radar network and SCR-584 fire control radar. It also summarizes how radar contributed to British victories during the Battle of Britain and in defending against German V-1 buzz bomb attacks. The document outlines topics to be covered on radar basics, principles of operation, and classifications of military, civilian and other radar systems.
This document provides an overview of radar cross section (RCS) and techniques for predicting a target's RCS through both measurement and theoretical calculation. It begins with definitions of RCS and factors affecting it. Examples of typical RCS values for different targets are given. Physical scattering mechanisms and contributors to a target's RCS are described. Both full-scale and scale model target measurement techniques are outlined. Theoretical prediction methods including geometrical optics, physical optics, and diffraction theories are introduced. Scaling laws for applying results from scale models to full-scale targets are also covered.
Radar 2009 a 16 parameter estimation and tracking part2Forward2025
This document summarizes a lecture on parameter estimation and tracking. It discusses tracking processes like track association, initiation, maintenance through prediction and updating, and termination. Filtering techniques like the Kalman filter are presented as ways to estimate target position and velocity while accounting for noise and maneuvers. Examples of civilian and military target maneuvers are provided to illustrate the challenges of tracking.
This document provides an overview of radar antennas and scanning techniques. It begins with introductions to basic antenna concepts such as near and far field regions, electromagnetic field equations, polarization, and antenna gain. It then discusses reflector antennas, which use mechanical scanning to direct the antenna beam. The document outlines additional topics that will be covered, including phased array antennas, frequency scanning, and hybrid scanning methods. The goal is to provide an introduction to different types of radar antennas and how they are used to direct electromagnetic energy.
This document summarizes a lecture on radar clutter. It discusses different types of clutter sources including ground, sea, rain, and birds. It provides details on the attributes of rain clutter such as how it is affected by wavelength and circular polarization. Graphs are presented showing reflectivity of rain and its Doppler spectrum. Bird clutter properties around radar cross-section, velocity, and density are also covered. The document aims to explain the impact of various clutter sources on radar performance.
The document discusses various topics related to naval stealth technology including radar cross section (RCS) reduction techniques. It provides information on radar frequencies and functions, radar working principles, RCS prediction methods, and examples of stealth ships. Key points covered include how shaping, radar absorbing materials, and passive/active cancellation can be used to reduce the RCS and vulnerability of detection of naval vessels. Prediction software, instrumentation systems, and examples of reduced RCS for components like gun barrels are also summarized.
Tutorial Content
This tutorial provides a broad-based discussion of radar system, covering the following topics:
-Introduction to Radars in Military and Commercial Applications
-Radar System Block Diagram
-Radar Antennas (slotted waveguide array, planar array), Transmitter (magnetron, solid-state), Receiver, Pedestal and Radome
-Plot Extraction, Tracking Algorithms and Display
-Radar Range Equation, Detection Performance
-Wave Propagation and Radar Cross Section
-Emerging and Advanced Radar Systems (phased-array, multi-beam, multi-mode, FMCW, solid-state)
In the discussion, practical systems, technical specifications and data will be used to enhance learning.In addition, simulation results will also be used to present findings.
The objective of the tutorial session is to equip participants with solid understanding of radar systems for system level applications and prepare them for advanced and professional radar courses, projects and research.
This tutorial is designed and developed based on the following references:
[1] G. W. Stimson, Introduction to Airborne Radar Second Edition, Scitech Publishing, 1998.
[2] L. V. Blake, A Guide to Basic Pulse-Radar Maximum-Range Calculation, NRL Report 6930, 1969.
[3] K. H. Lee, Radar Systems for Nanyang Technological University, TBSS, 2014.
This document contains lecture slides about radar signal propagation through the atmosphere. It discusses various propagation effects including reflection from the Earth's surface, atmospheric refraction, multipath interference, and attenuation. It provides equations for calculating propagation losses and phase differences between direct and reflected signals. Examples are given of how propagation affects radar coverage and detection range for a shipborne surveillance radar system.
This document contains 23 slides from a course on radar systems and the radar equation. It begins with an overview of key radar functions like detection, measurement, tracking and identification. It then provides details on the development of the radar range equation, covering topics like radar cross section, noise sources, system noise temperature and the effects of factors like target properties, radar characteristics, propagation medium and range. Examples are provided to demonstrate how modifying parameters like transmitter power, antenna diameter or range can impact radar performance. Charts show specifications for different types of search radars.
Radar 2009 a 17 transmitters and receiversForward2025
This document provides an overview of radar transmitter and receiver systems. It begins with an introduction and block diagram of radar transmitters and receivers. The bulk of the document then focuses on different types of high power tube amplifiers used in radar transmitters, including klystrons, traveling wave tubes, crossed field amplifiers, and magnetrons. It also briefly discusses solid state RF power amplifiers. The document concludes with an outline of topics to be covered, including receivers and waveform generators, other transmitter and receiver subsystems, and radar receiver-transmitter architectures.
This document provides a summary of key components and operating principles of radar transmitters. It discusses the transmitter components including magnetrons, klystrons and traveling wave tubes that are used as microwave oscillators and amplifiers. It describes the use of waveguides and other components to transmit and manipulate microwave signals. Circulators and duplexers are discussed which allow transmit and receive signals to share an antenna. Operation and limitations of magnetron-based transmitters commonly used in radars are summarized. Factors affecting transmitter design such as output power, frequency stability and coherence are also highlighted at a high level.
Marine radars use radio waves to measure the bearing and distance of ships to prevent collisions at sea. They can detect ships within range of shore references like islands and buoys to aid navigation and position fixing. Radar works by transmitting radio wave pulses that bounce off objects and return to the radar antenna. The travel time is used to calculate distances to objects like other ships. Modern radar has diverse uses including air traffic control, weather monitoring, and target detection for military systems.
Radar 2009 a 12 clutter rejection basics and mtiForward2025
This document contains lecture slides about radar clutter rejection techniques. It discusses the history of moving target indication (MTI) and how digital technology has enabled more advanced processing. MTI uses Doppler filtering to suppress stationary clutter and detect moving targets. Early MTI employed crude subtraction of stored pulses. Modern digital implementations allow complex signal processing over many pulses for improved clutter cancellation.
- Antennas are devices used for radiating and receiving electromagnetic waves and are essential for wireless communication technologies like mobile phones, WiFi, and satellite communications.
- The radiation pattern of an antenna shows its radiation properties as a function of position and is usually represented by the electric field magnitude over a spherical surface. Common patterns include isotropic, directional, and omnidirectional.
- Key antenna parameters include the main beam direction, half power beamwidth (-3dB beamwidth), beamwidth between first nulls, and side lobe level. These characteristics help describe the antenna's radiation properties.
Radar 2009 a 19 electronic counter measuresForward2025
This document contains slides from a lecture on electronic countermeasures (ECM) against radar systems. It discusses how ECM techniques like chaff, noise jamming and random pulses can be used to mask targets from radar detection by increasing clutter. It provides details on how chaff works, including its reflectivity properties and how it is dispensed. Examples are given of chaff masking an aircraft and deceiving trackers. The presentation also introduces how electronic counter-countermeasures (ECCM) can be used to counter ECM techniques.
In radio and electronics, an antenna (plural antennae or antennas), or aerial, is an electrical device which converts electric power into radio waves, and vice versa.[1] It is usually used with a radio transmitter or radio receiver. In transmission, a radio transmitter supplies an electric current oscillating at radio frequency (i.e. a high frequency alternating current (AC)) to the antenna's terminals, and the antenna radiates the energy from the current as electromagnetic waves (radio waves). In reception, an antenna intercepts some of the power of an electromagnetic wave in order to produce a tiny voltage at its terminals, that is applied to a receiver to be amplified.
Radar was originally developed for military purposes during World War 2 to detect ships and airplanes. Scientists later discovered that radar could also detect precipitation, making it an essential tool for weather prediction. There are two main types of radar: pulse radar which uses pulse transmission to determine range and continuous wave radar which relies on the Doppler effect. Key radar components include the transmitter, receiver, antenna, and display unit. Radar systems can be classified by their primary mission as search, tracking, or weather surveillance radars. Common examples include air search radars, long range surveillance radars, and tracking radars used in aircraft.
RADAR - RAdio Detection And Ranging
This is the Part 1 of 2 of RADAR Introduction.
For comments please contact me at solo.hermelin@gmail.com.
For more presentation on different subjects visit my website at http://www.solohermelin.com.
Part of the Figures were not properly downloaded. I recommend viewing the presentation on my website under RADAR Folder.
This document provides an overview of microstrip antennas and techniques for improving their bandwidth and miniaturization. It begins with an introduction to microstrip antennas, including their history, advantages, disadvantages, and applications. It then discusses various feeding methods, the basic cavity model principles of operation, and general characteristics such as bandwidth, resonance frequencies, and radiation efficiency. The document focuses on improving bandwidth through techniques such as changing the substrate thickness and permittivity or using special feeding methods. It also covers miniaturization methods such as modifying the patch shape or using stacked patches.
Radar was invented in the early 1900s and applied during World War II to detect aircraft. The basic principles of radar involve transmitting electromagnetic signals that are reflected off targets and detected. A typical radar system includes a transmitter, antenna, receiver, and display. The radar range equation relates key variables such as transmitted power, wavelength, target radar cross-section, and system losses to the maximum detectable range. Integration of multiple radar returns can improve the signal-to-noise ratio and increase detection range.
This document provides an overview of two basic radar types: pulse transmission radar and continuous wave radar. It describes the key components and operating principles of each. Pulse radar relies on pulse width and repetition frequency to determine range, while continuous wave radar uses the Doppler effect of the frequency shift in returned echoes to deduce information about targets. The document also discusses radar modulation techniques, antenna design and beamforming, and other major components like transmitters, receivers, and waveguides.
1. The document discusses fundamentals of electromagnetic radiation and antennas. It describes how accelerated charges radiate electromagnetic waves according to Poynting's theorem.
2. It then analyzes the radiation pattern and fields of an infinitesimal electric dipole antenna. The electric and magnetic fields are derived in the far-field region and shown to depend on angle with maxima at 90 degrees to the dipole axis.
3. Properties of a finite electric dipole antenna with a sinusoidally driven current are also examined, with the current assumed to have a sinusoidal distribution along the antenna rods.
This document summarizes Atul Sharma's training report on studying radar systems during an internship from June 16th to July 26th 2014. It introduces radar technology, explaining that radar uses radio waves to detect objects and determine their location, distance and direction. It then describes the basic principles of how radar works, including the radar range equation. It also outlines the main components of a radar system, such as the antenna, transmitter, receiver and display, and different types of radars like primary and secondary radar. Finally, it provides examples of specific radar sets used in India.
The document discusses different types of radar systems and their components and principles of operation. It covers topics like pulse radar vs continuous wave radar, components of each type of system like transmitter, receiver, antennas, and how factors like pulse width, repetition frequency and power affect radar performance and capabilities. It also discusses modulation techniques, antenna beam formation, and different types of radar displays.
This document provides an introduction to pulse repetition interval (PRI) analysis and deinterleaving from an electronic intelligence (ELINT) perspective. It discusses key concepts such as PRI, unambiguous range and velocity, range-velocity ambiguity, optimum PRI for medium PRF radars, and PRI stagger. The document explains how understanding radar constraints such as range resolution, integration time limits, Doppler resolution, and frequency agility can help an ELINT analyst correctly interpret radar signals and anticipate signal characteristics.
This document discusses various methods for calculating radar cross section (RCS), including the finite difference time domain method, method of moments, geometrical optics, physical optics, geometrical theory of diffraction, and physical theory of diffraction. It provides overviews and comparisons of each method, explaining their approaches and areas of applicability. The document also includes examples of RCS calculations and summaries of key points about specific methods.
Este documento presenta la posición oficial de Ciudadanos Partido de la Ciudadanía sobre las prospecciones petrolíferas cerca de las costas de Canarias. Se oponen a las prospecciones debido al alto riesgo de accidentes que podrían dañar gravemente la economía basada en el turismo y el suministro de agua de Canarias, así como por la falta de beneficios económicos para Canarias y España. Argumentan que el sector del turismo y el medio ambiente son más importantes para Canarias que los posibles ingresos de
This document contains 23 slides from a course on radar systems and the radar equation. It begins with an overview of key radar functions like detection, measurement, tracking and identification. It then provides details on the development of the radar range equation, covering topics like radar cross section, noise sources, system noise temperature and the effects of factors like target properties, radar characteristics, propagation medium and range. Examples are provided to demonstrate how modifying parameters like transmitter power, antenna diameter or range can impact radar performance. Charts show specifications for different types of search radars.
Radar 2009 a 17 transmitters and receiversForward2025
This document provides an overview of radar transmitter and receiver systems. It begins with an introduction and block diagram of radar transmitters and receivers. The bulk of the document then focuses on different types of high power tube amplifiers used in radar transmitters, including klystrons, traveling wave tubes, crossed field amplifiers, and magnetrons. It also briefly discusses solid state RF power amplifiers. The document concludes with an outline of topics to be covered, including receivers and waveform generators, other transmitter and receiver subsystems, and radar receiver-transmitter architectures.
This document provides a summary of key components and operating principles of radar transmitters. It discusses the transmitter components including magnetrons, klystrons and traveling wave tubes that are used as microwave oscillators and amplifiers. It describes the use of waveguides and other components to transmit and manipulate microwave signals. Circulators and duplexers are discussed which allow transmit and receive signals to share an antenna. Operation and limitations of magnetron-based transmitters commonly used in radars are summarized. Factors affecting transmitter design such as output power, frequency stability and coherence are also highlighted at a high level.
Marine radars use radio waves to measure the bearing and distance of ships to prevent collisions at sea. They can detect ships within range of shore references like islands and buoys to aid navigation and position fixing. Radar works by transmitting radio wave pulses that bounce off objects and return to the radar antenna. The travel time is used to calculate distances to objects like other ships. Modern radar has diverse uses including air traffic control, weather monitoring, and target detection for military systems.
Radar 2009 a 12 clutter rejection basics and mtiForward2025
This document contains lecture slides about radar clutter rejection techniques. It discusses the history of moving target indication (MTI) and how digital technology has enabled more advanced processing. MTI uses Doppler filtering to suppress stationary clutter and detect moving targets. Early MTI employed crude subtraction of stored pulses. Modern digital implementations allow complex signal processing over many pulses for improved clutter cancellation.
- Antennas are devices used for radiating and receiving electromagnetic waves and are essential for wireless communication technologies like mobile phones, WiFi, and satellite communications.
- The radiation pattern of an antenna shows its radiation properties as a function of position and is usually represented by the electric field magnitude over a spherical surface. Common patterns include isotropic, directional, and omnidirectional.
- Key antenna parameters include the main beam direction, half power beamwidth (-3dB beamwidth), beamwidth between first nulls, and side lobe level. These characteristics help describe the antenna's radiation properties.
Radar 2009 a 19 electronic counter measuresForward2025
This document contains slides from a lecture on electronic countermeasures (ECM) against radar systems. It discusses how ECM techniques like chaff, noise jamming and random pulses can be used to mask targets from radar detection by increasing clutter. It provides details on how chaff works, including its reflectivity properties and how it is dispensed. Examples are given of chaff masking an aircraft and deceiving trackers. The presentation also introduces how electronic counter-countermeasures (ECCM) can be used to counter ECM techniques.
In radio and electronics, an antenna (plural antennae or antennas), or aerial, is an electrical device which converts electric power into radio waves, and vice versa.[1] It is usually used with a radio transmitter or radio receiver. In transmission, a radio transmitter supplies an electric current oscillating at radio frequency (i.e. a high frequency alternating current (AC)) to the antenna's terminals, and the antenna radiates the energy from the current as electromagnetic waves (radio waves). In reception, an antenna intercepts some of the power of an electromagnetic wave in order to produce a tiny voltage at its terminals, that is applied to a receiver to be amplified.
Radar was originally developed for military purposes during World War 2 to detect ships and airplanes. Scientists later discovered that radar could also detect precipitation, making it an essential tool for weather prediction. There are two main types of radar: pulse radar which uses pulse transmission to determine range and continuous wave radar which relies on the Doppler effect. Key radar components include the transmitter, receiver, antenna, and display unit. Radar systems can be classified by their primary mission as search, tracking, or weather surveillance radars. Common examples include air search radars, long range surveillance radars, and tracking radars used in aircraft.
RADAR - RAdio Detection And Ranging
This is the Part 1 of 2 of RADAR Introduction.
For comments please contact me at solo.hermelin@gmail.com.
For more presentation on different subjects visit my website at http://www.solohermelin.com.
Part of the Figures were not properly downloaded. I recommend viewing the presentation on my website under RADAR Folder.
This document provides an overview of microstrip antennas and techniques for improving their bandwidth and miniaturization. It begins with an introduction to microstrip antennas, including their history, advantages, disadvantages, and applications. It then discusses various feeding methods, the basic cavity model principles of operation, and general characteristics such as bandwidth, resonance frequencies, and radiation efficiency. The document focuses on improving bandwidth through techniques such as changing the substrate thickness and permittivity or using special feeding methods. It also covers miniaturization methods such as modifying the patch shape or using stacked patches.
Radar was invented in the early 1900s and applied during World War II to detect aircraft. The basic principles of radar involve transmitting electromagnetic signals that are reflected off targets and detected. A typical radar system includes a transmitter, antenna, receiver, and display. The radar range equation relates key variables such as transmitted power, wavelength, target radar cross-section, and system losses to the maximum detectable range. Integration of multiple radar returns can improve the signal-to-noise ratio and increase detection range.
This document provides an overview of two basic radar types: pulse transmission radar and continuous wave radar. It describes the key components and operating principles of each. Pulse radar relies on pulse width and repetition frequency to determine range, while continuous wave radar uses the Doppler effect of the frequency shift in returned echoes to deduce information about targets. The document also discusses radar modulation techniques, antenna design and beamforming, and other major components like transmitters, receivers, and waveguides.
1. The document discusses fundamentals of electromagnetic radiation and antennas. It describes how accelerated charges radiate electromagnetic waves according to Poynting's theorem.
2. It then analyzes the radiation pattern and fields of an infinitesimal electric dipole antenna. The electric and magnetic fields are derived in the far-field region and shown to depend on angle with maxima at 90 degrees to the dipole axis.
3. Properties of a finite electric dipole antenna with a sinusoidally driven current are also examined, with the current assumed to have a sinusoidal distribution along the antenna rods.
This document summarizes Atul Sharma's training report on studying radar systems during an internship from June 16th to July 26th 2014. It introduces radar technology, explaining that radar uses radio waves to detect objects and determine their location, distance and direction. It then describes the basic principles of how radar works, including the radar range equation. It also outlines the main components of a radar system, such as the antenna, transmitter, receiver and display, and different types of radars like primary and secondary radar. Finally, it provides examples of specific radar sets used in India.
The document discusses different types of radar systems and their components and principles of operation. It covers topics like pulse radar vs continuous wave radar, components of each type of system like transmitter, receiver, antennas, and how factors like pulse width, repetition frequency and power affect radar performance and capabilities. It also discusses modulation techniques, antenna beam formation, and different types of radar displays.
This document provides an introduction to pulse repetition interval (PRI) analysis and deinterleaving from an electronic intelligence (ELINT) perspective. It discusses key concepts such as PRI, unambiguous range and velocity, range-velocity ambiguity, optimum PRI for medium PRF radars, and PRI stagger. The document explains how understanding radar constraints such as range resolution, integration time limits, Doppler resolution, and frequency agility can help an ELINT analyst correctly interpret radar signals and anticipate signal characteristics.
This document discusses various methods for calculating radar cross section (RCS), including the finite difference time domain method, method of moments, geometrical optics, physical optics, geometrical theory of diffraction, and physical theory of diffraction. It provides overviews and comparisons of each method, explaining their approaches and areas of applicability. The document also includes examples of RCS calculations and summaries of key points about specific methods.
Este documento presenta la posición oficial de Ciudadanos Partido de la Ciudadanía sobre las prospecciones petrolíferas cerca de las costas de Canarias. Se oponen a las prospecciones debido al alto riesgo de accidentes que podrían dañar gravemente la economía basada en el turismo y el suministro de agua de Canarias, así como por la falta de beneficios económicos para Canarias y España. Argumentan que el sector del turismo y el medio ambiente son más importantes para Canarias que los posibles ingresos de
Víctor Maestre Ramírez successfully completed the online course "BrainX: Cellular Mechanisms of Brain Function" offered by École Polytechnique Fédérale de Lausanne through edX. The certificate verifies that he received a passing grade in the course taught by Professor Carl Petersen and certified by Pierre Dillenbourg, Director of the Center for Digital Education at École Polytechnique Fédérale de Lausanne.
This certificate verifies that Víctor Maestre Ramírez successfully completed and passed the course DAT201x: Querying with Transact-SQL offered by Microsoft through edX. The certificate is signed by Satya Nadella, CEO of Microsoft Corporation, and Björn Rettig, Senior Director of Technical Content at Microsoft Corporation, and includes a link to verify its authenticity.
Exposición de la necesidad de cambiar la mentalidad actual, y aplicar enfoques y ejercicios que permitan prever y protegerse frente a amenazas dirigidas.
Para dar solución a dicho problema se presenta el concepto de Red Team, sus beneficios, equipo, metodología y enfoque aportado desde el proyecto RedTeaming.es.
Para finalizar se exponen una serie de casos de éxito de ejercicios realizados por los integrantes del proyecto RedTeaming.es.
Víctor Maestre Ramírez completed the System Center Advisor course on February 10, 2017. The document certifies that Víctor Maestre Ramírez successfully finished the System Center Advisor training. This record shows that Víctor achieved the goals of the System Center Advisor course.
This certificate confirms that Victor Maestre Ramírez completed a 7 CEU/CPE, 7.5 hour incident response and advanced forensics training course provided by Cybrary on November 10, 2016. The certificate is signed by Ralph P. Sita, CEO of Cybrary and includes the certificate number C-05235cb1c-efc0bb.
El documento es un diploma emitido por el Instituto Nacional de Ciberseguridad acreditando que Víctor Maestre Ramírez completó con éxito un curso de 50 horas sobre Seguridad en Sistemas de Control y Automatización Industrial del 12 de diciembre al 13 de febrero, cubriendo temas como dispositivos de control, comunicaciones industriales, amenazas a redes SCADA y buenas prácticas de seguridad para entornos industriales.
Keeping a car looking like new requires regular cleaning of both the interior and exterior. Exterior cleaning through weekly car washes or spot cleaning bird droppings and sap is important. Interior cleaning should occur monthly or more for vehicles with children and pets. Using the proper cleaning products and protecting the vehicle from elements in a garage can help maintain a like-new appearance and increase resale value.
The document discusses opportunities for growth at the Seminole Community Library through increasing children's programming. It notes that peer libraries have higher percentages of residents with library cards than Seminole's current rate. The proposed approach is to give youth services full control over programming and make adult programs subordinate. This could increase attendance, new registrations, and publicity if implemented successfully. Potential risks include increased costs and staffing issues. In conclusion, children's programming represents an opportunity for library growth if properly supported and monitored.
The document is a lecture on radar antennas and discusses various antenna scanning techniques. It begins with an overview of radar systems and the radar equation. It then covers antenna fundamentals and different types of mechanical, electronic and hybrid scanning antennas used in radar systems. The lecture outlines electronic scanning with phased arrays, including linear and planar array beamforming. It discusses controlling the array pattern through element excitation phases and amplitudes. Properties of linear arrays like beamwidth and sidelobes are also covered. The document provides examples of increasing array gain by adding more elements.
This document contains 20 slides from a lecture on radar systems and the radar equation. The slides cover topics such as the basic components of a radar system, definitions of terms like radar cross section, development of the radar range equation, sources of noise, and examples of how radar performance scales with different design parameters. Key aspects of the radar equation like transmitter power, antenna size, range, losses, and noise temperature are discussed across the slides.
This document discusses different techniques for modelling optical properties of nanostructures, including frequency domain and time domain methods. It provides examples of the rigorous coupled wave analysis (RCWA) frequency domain method and finite difference time domain (FDTD) time domain method. RCWA is suitable for periodic gratings and involves representing fields with Fourier expansions. FDTD discretizes Maxwell's equations in time and space using Yee's algorithm and is applicable to arbitrary structures but time consuming. Examples show using these methods to design tunable photonic crystal cavities.
CEM Workshop Lectures (4/11): CEM of High Frequency MethodsAbhishek Jain
Above lecture can be downloaded from www.zeusnumerix.com
Computational Electromagnetics Workshop Lecture 4 of 11. The lecture focuses on the CEM methods used for high-frequency incident radiation. The methods explained are Geometric Optics and Physical Optics. PO-PTD and GO-GTD methods are mainly used for large objects where time-domain methods will be very expensive. Mathematical modeling, pitfalls and modifications to these methods are discussed.
Radar Cross Section reduction in antennas.pptxjosephine167719
This document discusses reducing radar cross section (RCS) in microstrip patch antennas. It begins by introducing RCS and how it is measured, then discusses how the RCS of antennas is influenced by their structure and feed network. Artificial magnetic conductors (AMCs) are proposed for RCS reduction, as they can prevent reflection of energy back to the antenna for low RCS while maintaining radiation characteristics. A split ring polarization rotation reflective surface (PRRS) based on AMC is designed, simulated, and analyzed. Results show the PRRS provides RCS reduction of up to 9.35 dB at various resonant frequencies, with angular stability up to 45 degrees. Finally, integrating the PRRS with a microstrip patch
Radar 2009 a 15 parameter estimation and tracking part 1Forward2025
The document discusses a lecture on parameter estimation and tracking in radar systems. It covers topics like observable estimation including range, angle, Doppler, and amplitude measurement accuracy. It also discusses single target tracking techniques such as amplitude monopulse, phase comparison monopulse, sequential lobing, and conical scanning. The outline indicates it will cover multiple target tracking and provide a summary. Diagrams are included to illustrate concepts like angular tracking error sources and Doppler estimation.
This document discusses the electromagnetic modeling of large planar arrays using the Scale Changing Technique (SCT). SCT decomposes planar structures into hierarchical scales to reduce computational requirements. It expresses fields on orthogonal modes and computes scale-changing networks between domains to model coupling. The document presents applications of SCT to modeling infinite and finite reflectarrays, characterizing coupling in non-uniform arrays, and simulating 2D arrays under plane wave and horn excitation. SCT was shown to efficiently model multiscale arrays and characterize coupling while avoiding issues of conventional full-wave solvers.
Initial study and implementation of the convolutional Perfectly Matched Layer...Arthur Weglein
In this report, first steps and results of the implementation of the Convolutional Perfectly
Matched Layer (CPML), for the modeling of the 2D acoustic heterogeneous wave equation
are presented. We also compare the conditions to set to zero, for all angles of incidence, the
reflection coefficient at the interface between two PML media, with the analogous conditions
for the reflection coefficient at an interface between two acoustic media. A side product of the
present work for the M-OSRP is a code to create synthetic data, using Finite-Difference (FD)
methods with PML BCs.
We also provide a short description of the main stages involved in the original Reverse Time
Migration (RTM) algorithm, with focus on the 2D acoustic heterogeneous wave equation. We
include a derivation of the equations of the CPML for the backward propagation of the data,
which is part of the RTM. As far as the authors knowledge, these equations and derivations
have not been reported in the literature. The reason we include the RTM is because the present
report can be considered part of a broader research project whose objective is to compare the
RTM with PML BCs with the Green’s theorem based RTM, developed within the M-OSRP.
Initial study and implementation of the convolutional Perfectly Matched Layer...Arthur Weglein
In this report, first steps and results of the implementation of the Convolutional Perfectly
Matched Layer (CPML), for the modeling of the 2D acoustic heterogeneous wave equation
are presented. We also compare the conditions to set to zero, for all angles of incidence, the
reflection coefficient at the interface between two PML media, with the analogous conditions
for the reflection coefficient at an interface between two acoustic media. A side product of the
present work for the M-OSRP is a code to create synthetic data, using Finite-Difference (FD)
methods with PML BCs.
We also provide a short description of the main stages involved in the original Reverse Time
Migration (RTM) algorithm, with focus on the 2D acoustic heterogeneous wave equation. We
include a derivation of the equations of the CPML for the backward propagation of the data,
which is part of the RTM. As far as the authors knowledge, these equations and derivations
have not been reported in the literature. The reason we include the RTM is because the present
report can be considered part of a broader research project whose objective is to compare the
RTM with PML BCs with the Green’s theorem based RTM, developed within the M-OSRP.
This document discusses the potential for x-ray interferometry and the Maxim Pathfinder mission concept. It describes how an x-ray interferometer could achieve much higher resolution than current x-ray telescopes by using multiple collector spacecraft separated by long distances. The Maxim Pathfinder would demonstrate 100 microarcsecond resolution using two spacecraft separated by 450 km. System modeling tools would be crucial for development and optimization of the interferometer design.
Radiation patterns account of a circular microstrip antenna loaded two annularwailGodaymi1
In this paper, theoretical study of circular microstrip antenna loaded two annular (CMSAL2AR) and calculation
of the radiation pattern using principle equivalence with moment of method formulation of electromagnetic
radiation in this these based on the bodies of revolution (BoR), which are generated by revolution a planar curve
about an axis called axis of symmetry to solving the electric fields integral equation (EFIE) and magnetic field
integral equation (MFIE). To find an unknown electric current density on the conductor surface ,and both
unknowns electric and magnetic density current on the dielectric surface which are responsible for the
generation of far fields radiation in the space for the components (Eθ ,Eφ) ,the surface currents was represented
by a set of basis functions that give the Fourier series because the body has a circular symmetry property and
then select a set of weighted functions to find a linear system by using Galerkin method which requires that the
weighted functions are equal to the complex conjugate of the current ( ) * W = J .from radiation pattern
calculated the Directive gain can be utilized to the directive gain increased to (G= 21.30 dB) when
( 0.015λ 1 = g R ) for the ratio of (Rab= 5.5), and bandwidth has been better (BW%= 19.9%) when
( 0.01λ 1 = g R ) for the ratio (Rab= 6.5) .
The document describes the principles of operation and first results of SMOS, a satellite mission to measure soil moisture and ocean salinity. It discusses the basic principles of synthetic aperture radiometry used by SMOS and describes the MIRAS instrument, including its array topology, receivers, digital correlator system, and calibration system. It also addresses instrument performance metrics like angular resolution and radiometric sensitivity. Lastly, it discusses image reconstruction algorithms and geolocalization of retrieval products.
Investigation of repeated blasts at Aitik mine using waveform cross correlationIvan Kitov
We present results of signal detection from repeated events at the Aitik and Kiruna mines in Sweden as based on waveform cross correlation. Several advanced methods based on tensor Singular Value Decomposition is applied to waveforms measured at seismic array ARCES, which consists of three-component sensors.
Integral Equation Formulation of Electromagnetic Scattering from Small ParticlesHo Yin Tam
1) The document discusses various methods for modeling electromagnetic scattering from small particles, including integral equation formulations, the T-matrix method, and finite-difference time-domain (FDTD) simulations.
2) It finds that the T-matrix method most accurately calculates internal fields, while FDTD has significant errors near particle surfaces.
3) An analytic approximation (AA) approach is presented that separates shape and frequency dependencies for simple calculations of internal fields in small particles.
The document describes a method for retrieving column water vapor at night using mid-wave infrared bands from sensors like MODIS. It adapts an existing algorithm used to retrieve sea surface temperature that relies on the "same temperature criterion" - if the atmosphere is correctly characterized, surface temperatures derived from multiple bands should be the same. The algorithm uses a lookup table approach and can retrieve column water vapor, atmospheric temperature offset, and surface temperature using multiple pixels to reduce ambiguity. It is shown to work well when applied to MODIS data.
Night Water Vapor Borel Spie 8 12 08 Whiteguest0030172
The document describes a method for retrieving column water vapor at night using mid-wave infrared bands from sensors like MODIS. It adapts an existing algorithm used to retrieve sea surface temperature that relies on the "same temperature criterion" - if the atmosphere is correctly characterized, surface temperatures derived from multiple bands should be the same. The algorithm uses a lookup table approach and can retrieve column water vapor, atmospheric temperature offset, and surface temperature using multiple pixels to avoid ambiguities. It is shown to work well when applied to MODIS data.
Distributed Data Processing using Spark by Panos Labropoulos_and Sarod Yataw...Spark Summit
Spark can help with distributed data processing for radio astronomy in three key ways:
1. It allows for in-memory distributed processing of very large datasets across clusters in a fault-tolerant manner, avoiding unnecessary data movement. This is crucial for processing the exabytes of data expected from projects like the Square Kilometer Array.
2. Spark supports iterative algorithms well through its Resilient Distributed Datasets (RDDs) abstraction, which is important for techniques like calibration and deconvolution.
3. Spark can implement consensus-based distributed optimization algorithms to help with calibration, allowing information to be collectively optimized from data distributed across a network.
Time Domain Modelling of Optical Add-drop filter based on Microcavity Ring Re...iosrjce
IOSR Journal of Electronics and Communication Engineering(IOSR-JECE) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of electronics and communication engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in electronics and communication engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
This document summarizes the time domain modeling of an optical add-drop filter based on microcavity ring resonators. It uses the Multiresolution Time Domain (MRTD) technique to analyze the transmission characteristics of single and double ring configurations. The MRTD method provides high numerical accuracy while reducing computational burden compared to FDTD. The analysis investigates parameters like gap size, distance between rings, and ring/waveguide width to understand their effects on transmitted power and quality factors. Studies of a 3.4 μm diameter ring show quality factors of several thousand and a free spectral range of 9 THz can be achieved in the 1.55 μm wavelength range.
1. IEEE New Hampshire Section
Radar Systems Course 1
Radar Cross Section 1/1/2010 IEEE AES Society
Radar Systems Engineering
Lecture 7 Part 2
Radar Cross Section
Dr. Robert M. O’Donnell
IEEE New Hampshire Section
Guest Lecturer
2. Radar Systems Course 2
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Methods of Radar Cross Section
Calculation
RCS Method
Approach to Determine
Surface Currents
Finite Difference-
Time Domain (FD-TD)
Solve Differential Form of Maxwell’s
Equation’s for Exact Fields
Method of Moments
(MoM)
Solve Integral Form of Maxwell’s
Equation’s for Exact Currents
Physical Optics
(PO)
Currents Approximated by Tangent
Plane Method
Physical Theory of
Diffraction (PTD)
Physical Optics with Added Edge
Current Contribution
Geometrical Optics
(GO)
Current Contribution Assumed to Vanish
Except at Isolated Specular Points
Geometrical Theory of
Diffraction (GTD)
Geometrical Optics with Added Edge
Current Contribution
3. Radar Systems Course 3
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Electromagnetic Scattering
Incident
Plane Wave
Scattered Field
(Radiated by Induced Currents)
• Two step process to determine scattered fields
– Determine induced surface currents
– Calculate field radiated by currents
Induced
Surface
Currents
Courtesy of MIT Lincoln Laboratory
Used with permission
4. Radar Systems Course 4
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Method of Moments (MoM) Overview
• The Method of Moments calculations predict the exact
solution for the target RCS
• Method – Solve integral form of Maxwell’s Equations
– Generate a surface patch model for the target
– Transform the integral equation form of Maxwell’s equations into a
set of homogeneous linear equations
– The solution gives the surface current densities on the target
– The scattered electric field can then be calculated in a straight
forward manner from these current densities
– Knowledge of the scattered electric field then allows one to readily
calculate the radar cross section
• Significant limitations of this method
– Inversion of the matrix to solve the homogeneous linear
equations
– Matrix size can be very large at high frequencies
Patch size typically ~λ/10
Surface Patch
Model
For a Sphere
5. Radar Systems Course 5
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Standard Spherical Coordinate System
x
y
z
θ
φ
)z,y,x(
r
6. Radar Systems Course 6
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Spherical Coordinate System for MOM
Calculations
• Source currents distributed over surface
• Field observation point located at
• Point on surface is
S′
x
y
z
θ
θ′
φ
φ′
)z,y,x( ′′′
)z,y,x(
Target Surface S′
r′
R
r
rrR
rrr
′−=
S′ )z,y,x( ′′′
)z,y,x(
7. Radar Systems Course 7
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Method of Moments
• Maxwell’s Equations transform to the Stratton and Chu
Equations using the vector Green’s Theorem and yield:
• Free space Green’s function is an spherical wave falling of
as:
• Also, note:
( ) ( ) ( )[ ]
( ) ( ) ( )[ ]
rrR
R4
e
SdHnˆxHxnˆExnˆiH
SdEnˆxExnˆHxnˆiE
ikR
'S
S
'S
S
′−==⎥
⎦
⎤
⎢
⎣
⎡
π
=ψ
′ψ∇⋅−ψ∇−ψεω+=
′ψ∇⋅+ψ∇+ψμω+=
+
∫∫
∫∫
rrrrrr
rrrrrr
Free Space
Green’s Function
SI
SI
HHH
EEE
rrr
rrr
+=
+=
R/1
8. Radar Systems Course 8
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Method of Moments (continued once)
• On the surface of the perfectly conducting target these
equations become:
– Total tangential electric field zero at surface
– No magnetic sources of currents or charges as source of
scattered fields
• Electric Field Integral Equation (EFIE)
• Magnetic Field Integral Equation (MFIE)
• Causes of scattered fields
– Scattered electric field – electric currents and charges
– Scattered magnetic field – electric currents
∫∫∫∫ ′′
′ψ∇=′ψ∇=
SS
S SdxJSdx)Hxnˆ(H
rrr
[ ] Sd
1
JiSd)Enˆ()Hxnˆ(iE
SS
S
′⎥
⎦
⎤
⎢
⎣
⎡
ψ∇ρ
ε
+ψμω+=′ψ∇⋅+ψμω+= ∫∫∫∫ ′′
rrr
9. Radar Systems Course 9
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Method of Moments (continued twice)
• Applying the boundary conditions for Maxwell’s Equations
and the Continuity Equation to free space yields:
• Procedure to calculate the scattered electric field:
– Convert the integral equation into a set of algebraic equations
– Solve for induced current density using matrix algebra
– With the current density known, the calculation of the
scattered electric field, , is reasonably straightforward and
the cross section can be calculated:
SdxJxnˆ
2
J
Hxnˆ
SdJ
i
JixnˆExnˆExnˆ
S
I
S
SI
′ψ∇−=
′⎥
⎦
⎤
⎢
⎣
⎡
ψ∇⋅∇
εω
+
+ψμω+=−=
∫∫
∫∫
′
′
r
r
r
rrrr
S
E
r
2I
2S
2
E
E
R4 π=σ
10. Radar Systems Course 10
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Method of Moments (continued again)
• Break up the target into a set of N discrete patches
– 7 to 10 patches per wavelength
• Expand the surface current density as a set of known
basis functions
• Define the “Magnetic Field Operator”, , as
• Insert the series expansion of currents and bringing
the sum out of the operator, we get:
Surface Patch Model
For Sphere∑=
=
N
1n
nn )r(BI)r(J
rrrr
∑=
==
N
1n
I
nHnH Hxnˆ))r(B(LI)J(L
rrrr
∫∫′
′ψ∇−≡
S
H SdxJxnˆ
2
J
)J(L
r
r
r
)J(LH
r
11. Radar Systems Course 11
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Method of Moments (one last time)
• Multiply by the weighting vector, , and integrating over
the surface:
– Point Testing
– Galerkin’s Method
• This is a set of N equations in N unknowns (current
coefficients, ) of the form:
• The only difficulty is inversion of a very large matrix
( )[ ] 0dSSd))r(B(LWiIdSHxnˆ)r(W n
S
m
'S
N
1n
n
S
I
=′⋅μω−⋅ ∫∫∫∫∑∫∫ =
rrrrr
mW
r
VIZ
vrrr
=
)r(BW mm
rrr
=
)rr(W mm
rrr
−δ=
mI
VZI 1
vrrr −
=
N...,3,2,1m =
12. Radar Systems Course 12
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Monostatic RCS of a Square Plate
• 15 cm x 15 cm Plate 6.0 GHz HH Polarization
Aspect Angle (degrees)
-90 -60 -30 0 30 60 90
RadarCrossSection(dBsm)
-30
-20
-10
0
10
20
Measurement
13. Radar Systems Course 13
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Monostatic RCS of a Square Plate
• 15 cm x 15 cm Plate 6.0 GHz HH Polarization
Aspect Angle (degrees)
-90 -60 -30 0 30 60 90
RadarCrossSection(dBsm)
-30
-20
-10
0
10
20
Measurement
Method of Moments
Patch
Size
λ/4
N = 12
14. Radar Systems Course 14
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Surface Patch Model of JGAM for
Method of Moments RCS Calculation
• 1.0 GHz 1350 unknowns
Top View
Side View
Photo of JGAM on Pylon
Courtesy of MIT Lincoln Laboratory
Used with Permission
15. Radar Systems Course 15
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Summary - Method of Moments
• Method of moments solution is exact
– Patch size must be small enough
– 7 to 10 samples per wavelength
• Well suited for small targets at long wavelengths
– Example - Artillery shell at L-Band (23 cm)
• Aircraft size targets result in extremely large matrices to be
inverted
– JGAM (~ 5m length)
1350 unknowns at 1.0 GHz
– Typical Fighter aircraft (~ 5m length)
A very difficult computation problem at S-Band (10 cm
wavelength)
16. Radar Systems Course 16
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Comparison of MoM and FD-TD Techniques
• For Single Frequency RCS Predictions (perfect conductors)
• 2-Dimensional Calculation
• 3-Dimensional Calculation
Method of Moments
(MoM)
Finite Difference-
Time Domain (FD-TD)
Method of
Calculation
Integral Equation
Frequency Domain
Differential Equation
Time Domain
No. of
Unknowns
N (2-D) N2
(3-D) N2
(2-D) N3
(3-D)
Memory
Requirement
Matrix Decomposition
N3
(2-D) N6
(3-D)
Time Steps
N3
(2-D) N4
(3-D)
Computer
Time
N2
(2-D) N4
(3-D) N2
(2-D) N3
(3-D)
Accuracy Exact Exact
17. Radar Systems Course 17
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Methods of Radar Cross Section
Calculation
RCS Method
Approach to Determine
Surface Currents
Finite Difference-
Time Domain (FD-TD)
Solve Differential Form of Maxwell’s
Equation’s for Exact Fields
Method of Moments
(MoM)
Solve Integral Form of Maxwell’s
Equation’s for Exact Currents
Geometrical Optics
(GO)
Current Contribution Assumed to Vanish
Except at Isolated Specular Points
Physical Optics
(PO)
Currents Approximated by Tangent
Plane Method
Geometrical Theory of
Diffraction (GTD)
Geometrical Optics with Added Edge
Current Contribution
Physical Theory of
Diffraction (PTD)
Physical Optics with Added Edge
Current Contribution
18. Radar Systems Course 18
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Geometrical Optics (GO) - Overview
• Geometrical Optics (GO) is an approximate method for RCS
calculation
– Valid in the “optical” region (target size >> λ)
• Based upon ray tracing from the radar to “specular points” on the
surface of the target
– “Specular points” are those points, whose normal vector points back to
the radar.
• The amount of reflected energy depends on the principal radii of
curvature at the surface reflection point
1ρ
2ρ
21 ρρπ=σ
nˆ
• Geometrical optics (GO) RCS calculations
are reasonably accurate to 10 – 15% for
radii of curvature of 2 λ to 3λ
• The GO approximation breaks down for
flat plates, cylinders and other objects
that have infinite radii of curvature; and at
edges of these targets
19. Radar Systems Course 19
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Geometric Optics
• Power Density Ratio =
• Radar Cross Section of Sphere =
• Radar Cross Section of an Arbitrary Specular Point =
– Where radii of curvature at specular point =
Ω
Ω
===
dR
d
4
a
A
A
A
1
A
1
S
S
2
2
S
I
I
S
INC
SCAT
r
r
2
2
2
2
INC
SCAT2
a
R4
a
R4
S
S
R4 π=π=π
21 ρρπ
2,1 ρρ
a2/aΩd
Image
Point
Incident Rays
Incident
Rays
Specular
Point
20. Radar Systems Course 20
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Single and Double Reflections
• RCS Calculation for Single Reflection
– Identify all specular points and add contributions
– Phase calculated from distance to and from specular point
– Local radii of curvature used to determine amplitude of
backscatter
• RCS Calculation for Double Reflection
– Identify all pairs of specular points
– At each reflection use single reflection methodology to
calculate amplitude and phase
(Geometrical Optics Method)
Perfectly
Conducting
Sphere
Perfectly
Conducting
Sphere
Two Modes of Double Reflection
Single Reflection
Single Reflection
21. Radar Systems Course 21
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Methods of Radar Cross Section
Calculation
RCS Method
Approach to Determine
Surface Currents
Finite Difference-
Time Domain (FD-TD)
Solve Differential Form of Maxwell’s
Equation’s for Exact Fields
Method of Moments
(MoM)
Solve Integral Form of Maxwell’s
Equation’s for Exact Currents
Geometrical Optics
(GO)
Current Contribution Assumed to Vanish
Except at Isolated Specular Points
Physical Optics
(PO)
Currents Approximated by Tangent
Plane Method
Geometrical Theory of
Diffraction (GTD)
Geometrical Optics with Added Edge
Current Contribution
Physical Theory of
Diffraction (PTD)
Physical Optics with Added Edge
Current Contribution
22. Radar Systems Course 22
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Physical Optics (PO) Overview
• Physical Optics (PO) is an approximate method for RCS
calculation
– Valid in the “optical” region (target size >> λ)
• Method - Physical Optics (PO) calculation
– Modify the Stratton-Chu integral equation form of Maxwell’s Equations,
assuming that the target is in the far field
– Assume that the total fields, at any point, on the surface of the target are
those that would be there if the target were flat
Called “Tangent plane approximation”
– Assume perfectly conducting target
– Resulting equation for the scattered electric field may be readily calculated
– RCS is easily calculated from the scattered electric field
• Physical Optics RCS calculations:
– Give excellent results for normal (or nearly normal) incidence (< 30°)
– Poor results for shallow grazing angles and near surface edges
e.g. leading and trailing edges of wings or edges of flat plates
23. Radar Systems Course 23
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Physical Optics
• For an incident plane wave :
• Substituting this surface current yields (for the monostatic case)
Tangent Plane Approximation
( ) ( ) rdeHxnˆxrˆxrˆ
r4
e
i2rE rrˆki2
o
ikr
S
′
π
ωμ−= ′⋅−
∫
rrrr r
( ) rrˆki
oS eHxnˆ2rJ
rrrr ′⋅−
=′
· · ·· ·· ·· ·
··
Infinite Perfectly Conducting Plane
(Exact Solution)
Arbitrary Conducting Surface
(Approximate Solution)
·
·
·
Tangent Plane
oE
r oE
r
oH
r
oH
r
24. Radar Systems Course 24
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Normal and Oblique Incidence
• Physical Optics
contribution adds
constructively (in phase)
• For large plates, the edge
contribution is a small
part of the total current
• Except near the edges,
Physical Optics gives
accurate results
Normally Incident
Plane Wave
Obliquely Incident
Plane Wave
Edge
Current
Physical Optics
Current
Physical Optics Valid Perfectly Conducting
Plate
• Except near the edges, Physical
Optics gives accurate results
• Fresnel Zones of alternating
phase caused by phase delay
across plate
• In the backscatter direction, the
Physical Optics contribution is
predominantly cancelled
• The most significant part of total
current due to edge effects
Perfectly Conducting
Plate
Specular Scattering
Direction
Edge
Current
Physical Optics
Current
Fresnel
Zones
25. Radar Systems Course 25
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Monostatic RCS of a Square Plate
• 15 cm x 15 cm Plate 10.0 GHz HH Polarization
Aspect Angle (degrees)
-90 -60 -30 0 30 60 90
RadarCrossSection(dBsm)
-30
-20
-10
0
10
20
Measurement
Physical Optics (PO)
Approximation
2
2
MAX
A
4
λ
π=σ
26. Radar Systems Course 26
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Methods of Radar Cross Section
Calculation
RCS Method
Approach to Determine
Surface Currents
Finite Difference-
Time Domain (FD-TD)
Solve Differential Form of Maxwell’s
Equation’s for Exact Fields
Method of Moments
(MoM)
Solve Integral Form of Maxwell’s
Equation’s for Exact Currents
Geometrical Optics
(GO)
Current Contribution Assumed to Vanish
Except at Isolated Specular Points
Physical Optics
(PO)
Currents Approximated by Tangent
Plane Method
Geometrical Theory of
Diffraction (GTD)
Geometrical Optics with Added Edge
Current Contribution
Physical Theory of
Diffraction (PTD)
Physical Optics with Added Edge
Current Contribution
27. Radar Systems Course 27
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Geometrical Theory of Diffraction (GTD)
Overview
• Geometrical Theory of Diffraction (GTD) a ray tracing method of
calculating the diffracted fields at surface edges / discontinuities
– Assumption: When ray impinges on an edge, a cone (see Keller (1957)
Cone below) of diffracted rays are generated
– Half angle of cone is equal to the angle, , between the edge and the
incident ray.
In backscatter case the cone becomes a disk
– Diffracted electric field proportional to “diffraction coefficients”, and
and a “divergence factor, , and given by:
• Diffraction coefficients
– – when parallel to edge
– + when parallel to edge
• Divergence factor reduces amplitude
as rays diverge from scattering point
and accounts for curves edges
Conducting
Wedge
Edge Diffracted Rays
On
Keller Cone
IE
r
( )YX
ks2sin
ee
E
4/iiks
DIF m
r
πβ
Γ
=
π
YX
Γ
β
IE
r
IH
r
28. Radar Systems Course 28
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Geometrical Theory of Diffraction (GTD)
Ray Tracing (With Creeping Waves and Diffraction)
• Advantages
– Easy to Understand
– Multiple Interactions
• Disadvantages
– Implementation difficult for complex targets
– Requires more accurate description than PTD
COREDGEREFLSCAT EEEE
rrrr
++=CWDIFFSRERSCAT EEEEE
rrrrr
+++=
Cylinder Plate
Creeping Wave
Side Reflection
Endcap ReflectionDiffraction
Edge
Diffraction
Corner
Diffraction
Reflection
29. Radar Systems Course 29
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Methods of Radar Cross Section
Calculation
RCS Method
Approach to Determine
Surface Currents
Finite Difference-
Time Domain (FD-TD)
Solve Differential Form of Maxwell’s
Equation’s for Exact Fields
Method of Moments
(MoM)
Solve Integral Form of Maxwell’s
Equation’s for Exact Currents
Geometrical Optics
(GO)
Current Contribution Assumed to Vanish
Except at Isolated Specular Points
Physical Optics
(PO)
Currents Approximated by Tangent
Plane Method
Geometrical Theory of
Diffraction (GTD)
Geometrical Optics with Added Edge
Current Contribution
Physical Theory of
Diffraction (PTD)
Physical Optics with Added Edge
Current Contribution
30. Radar Systems Course 30
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Physical Theory of Diffraction (PTD)
Overview
• Approach: Integrate surface current obtained from local tangent
plane approximation (plus edge current)
• Advantages: Reduced computational requirements and applicable
to arbitrary complex geometries
• Disadvantages: Neglects multiple interactions or shadowing
IE
r
IE
r
IE
r
Diffraction
Specular
Reflection
POJ
r
nˆ
DIFPO JJJ
rr
+=
Edge Current
Tangent
Plane
Courtesy of MIT Lincoln Laboratory
Used with permission
31. Radar Systems Course 31
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Physical Theory of Diffraction (PTD)
• In 1896, Sommerfeld developed a method to find the total
scattered field for an the infinite, perfectly conducting wedge.
• In 1957, Ufimtsev obtained the edge current contributions by
subtracting the physical optics contributions from the total
scattered field.
• The current for finite length structures may be obtained by
truncating the edge current from that of the infinite structure
Uniform Current
(Physical Optics)
Infinite Perfectly
Conducting
Wedge
Non-Uniform
Edge Current
Incident Plane WaveScattered
Field
Scattered
Field
32. Radar Systems Course 32
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Normal and Oblique Diffraction
Diffraction
Perpendicular to Edge
Oblique Diffraction
Keller Cone
Incident
Ray
Perfectly Conducting
Wedge
Perfectly Conducting
Wedge
Scattering
Perpendicular
to Edge
• Constructive addition from edge
current contribution along entire
edge results in strong
perpendicular backscatter
• Small contribution from corner
edge current
• Perpendicular to edge, scattering
is strong in all directions
• Edge current contribution
interferes destructively in direction
of backscatter
• For near grazing angles, corner
current may be significant
• Strong scattering along “Keller
Cone”
Edge CurrentEdge Current
Corner
Current
Corner
Current
Incident
Ray
33. Radar Systems Course 33
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Trailing / Leading Edge Diffraction
• Tangential component of
electric field equals zero
along the conductor.
• Diffracted electric field is
produced by current
induced to cancel
incident electric field.
• No diffraction at back
edge because electric
field is close to zero.
• Negligible scattering at
front edge – Electric field
normal and continuous
• Traveling waves; above
and below plate develop
a relative phase delay.
• Required continuity of
electric field at back edge
causes induced edge
current, and thus a
diffracted electric field.
Trailing Edge Diffraction
Leading Edge Diffraction
0Exn =
r
Incident
Electric
Field
iE
r
Diffracted Field
Induced
Edge
Current
0E ≈
r
iE
r
Induced Edge
Current
Diffracted
Field
Surface Field
Out of Phase
34. Radar Systems Course 34
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
FD-TD Simulation of Scattering by Strip
0.5 m
Ey
4 m
• Gaussian pulse plane wave incidence
• E-field polarization (Ey plotted)
15 deg
• Phenomena: leading edge diffraction
Case 2
Courtesy of MIT Lincoln Laboratory
Used with permission
35. Radar Systems Course 35
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
FD-TD Simulation of Scattering by Strip
Case 2
Courtesy of MIT Lincoln Laboratory
Used with permission
36. Radar Systems Course 36
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
FD-TD Simulation of Scattering by Strip
0.5 m
Hy
4 m
• Gaussian pulse plane wave incidence
• H-field polarization (Hy plotted)
15 deg
• Phenomena: trailing edge diffractionCase 3
Courtesy of MIT Lincoln Laboratory
Used with permission
37. Radar Systems Course 37
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
FD-TD Simulation of Scattering by Strip
Case 3
Courtesy of MIT Lincoln Laboratory
Used with permission
38. Radar Systems Course 38
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Monostatic RCS of a Square Plate
• 15 cm x 15 cm Plate 10.0 GHz HH Polarization
Aspect Angle (degrees)
-90 -60 -30 0 30 60 90
RadarCrossSection(dBsm)
-30
-20
-10
0
10
20
Measurement
Physical Optics (PO)
Approximation
Physical Theory
Of Diffraction (PTD)
Courtesy of MIT Lincoln Laboratory
Used with permission
39. Radar Systems Course 39
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Measured and Predicted RCS of JGAM
–180 –150 –120 –90 –60 –30 0 30 60 90 120 150 180
Target Aspect Angle (deg)
RCS(dBsm)
30
20
10
0
–10
–20
–30
–40
End Cap
Fuselage Specular
Cone Specular
Wing Leading Edge
Wing Trailing Edge
Tail TailNose BroadsideBroadside
• VV polarization
• Elevation = 7°
• 9.67 GHz
RATSCAT Measurement
PTD Prediction
Johnson Generic Aircraft Model (JGAM) at
RATSCAT Outdoor Measurement Facility
Courtesy of MIT Lincoln Laboratory
Used with permission
40. Radar Systems Course 40
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Radar Cross Section Calculation Methods
• Introduction
– A look at the few simple problems
• RCS prediction
– Exact Techniques
Finite Difference- Finite Time Technique (FD-FT)
Method of Moments (MOM)
– Approximate Techniques
Geometrical Optics (GO)
Physical Optics (PO)
Geometrical Theory of Diffraction (GTD)
Physical Theory of Diffraction (PTD)
• Comparison of different methodologies
41. Radar Systems Course 41
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
RCS Prediction Techniques Family Tree
Exact Techniques Approximate Techniques
• Limited Geometry
• All Phenomena
• Limited Phenomena
• Computationally Speedy
• Valid for High Frequencies
Classical
Solutions
Hybrid
Methods
Numerical
Methods•Few Geometries
•Rigorous, Exact •Computationally Slow
•Low Frequency
Surface
Integral
Techniques
Ray
Tracing
Techniques
•Computationally Slow
•All Geometries
•Computationally Slow
•All Geometries
Differential
Equation
Solutions
Hybrid
Methods
Integral Equation
Techniques
Series Solutions
MoM / UTD
MoM / PO
MoM / GO
Physical Optics (PO)
Physical Theory
of Diffraction (PTD)
Geometrical Optics (GO)
Geometrical Theory
of Diffraction (GTD)
Universal Theory
of Diffraction (UTD)
Shooting and Bouncing
Rays (SBR)
Finite Element
Finite Difference-Time Domain (FT-TD)
Finite Difference-Frequency Domain (FD-FD)
Method of Moments (MoM)
Other Integral Techniques
42. Radar Systems Course 42
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Comparison of Different RCS
Calculation Techniques
Methods of Calculation
FT-TD MOM GO - GTD PO-PTD
Calculation
Of
Current
Exact
Solve Partial
Differential
Equation
Exact
(Solve Integral
Equation)
Specular Point
Reflections
(Edge Currents)
Tangent Plane
Approximation
(Edge Currents)
Physical
Phenomena
Considered
All All Ray Tracing
Reflections
(Single & Double)
Diffraction
Main
Computational
Requirement
Time
Stepping
Matrix
Inversion
Multiple
Reflection
Diffraction
Surface Integration
-
Shadowing
Advantages
Exact
Visualization Aids
Physical Insight
Exact
- Simple
Formulation
- Good Insight
into Physical
Phenomena
Easiest Computationally
- Good Insight into Physical
Phenomena
Limitations
And/or
Disadvantages
- Low Frequency
Only
- Complex
Geometries Difficult
- Single Incident
Angle
- Low Frequency
Only
- Formulation
Difficult
(Materials)
- Single Frequency
- High Frequency
Only
- Canonical
Geometries Only
- Caustics
- High Frequency Only
- Many
Phenomena Neglected
43. Radar Systems Course 43
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Corner Reflectors
• Give a large reflection, , over a wide range of angles
– Used as test targets and for radar calibration
• Different shapes
– Dihedral
– Trihedral
Square, triangular, and circular
σ
Ray Trace for a
Dihedral Corner Reflector
(Side view)
=EFA Area of projected aperture
On the incident ray
2
2
EFA4
λ
π
=σ
RCS of Dihedral Corner Reflector
(Broadside Incidence)
Physical Optics Model
Sailboat Based
Circular Trihedral Corner Reflector
Courtesy of dalydaly
44. Radar Systems Course 44
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Summary
• Target RCS depends on its characteristics and the radar
parameters
– Target : size, shape, material, orientation
– Radar : frequency, polarization, range, viewing angles, etc
• The target RCS is due to many different scattering centers
– Structural, Propulsion, and Avionics
• Many RCS calculation tools are available
– Take into account the many different electromagnetic scattering
mechanisms present
• Measurements and predictions are synergistic
– Measurements anchor predictions
– Predictions validate measurements
45. Radar Systems Course 45
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
References
1. Atkins, R., Radar Cross Section Tutorial, 1999 IEEE National
Radar Conference, 22 April 1999.
2. Skolnik, M., Introduction to Radar Systems, New York,
McGraw-Hill, 3rd Edition, 2001.
3. Skolnik, M., Radar Handbook, New York, NY, McGraw-Hill,
3rd Edition, 2008 (Chapter 14 authored by E. Knott)
4. Ruck, et al., Radar Cross Section Handbook, Plenum Press,
New York, 1970, 2 vols.
5. Knott et al., Radar Cross Section, Massachusetts, Artech
House, Norwood, MA, 1993.
6. Bhattacharyya, A. K. and Sengupta, D. L., Radar Cross
Section Analysis and Control, Artech House, Norwood, MA,
1991.
7. Levanon, N., Radar Principles, Wiley, New York, 1988
46. Radar Systems Course 46
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Acknowledgement
• Dr. Robert T-I. Shin
• Dr. Robert K. Atkins
• Dr. Hsiu C. Han
• Dr. Audrey J. Dumanian
• Dr. Seth D. Kosowsky
47. Radar Systems Course 47
Radar Cross Section 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Homework Problems
• From Skolnik (Reference 2)
– Problems 2-10, 2-11, 2-12, and 2-13
• From Levanon (Reference 6)
– Problems 2-1 and 2-5
• For an ellipsoid of revolution, (semi major axis, a ,aligned
with the x-axis, semi minor axis, b, aligned with the y axis,
and axis of rotation is the x-axis; what are the radar cross
sections (far field) looking down the x, y, and z axes, if the
radar has wavelength λ and a >> λ and b >> λ?
• Extra credit: Solve the last problem assuming a << λ and b
<< λ.