This document summarizes the findings of a report on modeling the propagation of electromagnetic fields over a flat, homogeneous earth. It examines the interaction of fields from vertical and horizontal dipole antennas with the earth's surface. For a vertical dipole, the fields have three transverse magnetic components that are calculated using expressions from a cited source. For a horizontal dipole, the fields have both transverse electric and magnetic components with similar expressions. Comparisons of field strengths are provided for different source and receiver locations at frequencies of interest, with the conclusion that a vertical dipole oriented above the earth can produce significantly stronger fields near the earth than a horizontal dipole from the same location.
The document provides details about the Boeing AH-64 Apache attack helicopter, including:
- It describes the development and selection of the Hughes YAH-64 prototype over the Bell YAH-63 in 1976 for the U.S. Army's Advanced Attack Helicopter program.
- It discusses the key features and capabilities of the Apache, such as its sensors, weapons systems, armor protection, and engines.
- It provides background on the development and production of the Apache helicopter family, including variants for different countries.
What is Path loss?
Indoor Propogation Models?
Multi-floor model?
Partition attenuation model?
Empirical path loss model?
ITU Model for Indoor Attenuation/ Wall and floor factor model?
FRIIS MODEL?
Log-distance path loss model?
This document discusses various topics related to antennas and propagation, including:
- The basic functions of antennas for transmission and reception of signals
- Types of radiation and reception patterns that characterize antenna performance
- Common types of antennas like dipole, vertical, and parabolic reflective antennas
- Factors that influence signal propagation over distance like free space loss, noise, multipath interference, and atmospheric effects
- Techniques to improve reliability like diversity combining, adaptive equalization, and forward error correction coding.
This document is a lecture presentation on electromagnetic wave propagation by Mr. Himanshu Diwakar. It includes:
- An outline discussing Maxwell's equations, the Helmholtz equation, propagation constant, properties of electromagnetic waves, and wave propagation in free space.
- A note emphasizing the need to review electrostatics, magnetostatics, and vector identities to fully understand electromagnetic waves.
- Explanations of the Pointing theorem, which states that the time rate of change of electromagnetic energy within a volume plus the net energy flowing out equals the work done on charges within the volume.
- Definitions of the Poynting vector and its relationship to the electric and magnetic
The document discusses key concepts related to antennas and electromagnetic waves. It defines that radio waves have electric and magnetic fields that are perpendicular to each other and the direction of wave propagation. It also describes how antennas can transmit electromagnetic waves by converting electrical energy to radio waves and receive waves by converting radio waves back to electrical energy. Antenna size is inversely proportional to frequency, with higher frequencies requiring smaller antennas. Antenna radiation patterns and near/far field regions are also discussed.
The document discusses Shannon-Fano encoding, which is an early method for data compression that constructs efficient binary codes for information sources without memory. It works by assigning shorter codes to more frequent messages and longer codes to less frequent messages. The encoding process involves recursively splitting the set of messages in half based on probability until each message has its own unique code. While Shannon-Fano codes are reasonably efficient, they are not always optimal and the codes generated can depend on how the initial splitting of messages is done.
The document provides details about the Boeing AH-64 Apache attack helicopter, including:
- It describes the development and selection of the Hughes YAH-64 prototype over the Bell YAH-63 in 1976 for the U.S. Army's Advanced Attack Helicopter program.
- It discusses the key features and capabilities of the Apache, such as its sensors, weapons systems, armor protection, and engines.
- It provides background on the development and production of the Apache helicopter family, including variants for different countries.
What is Path loss?
Indoor Propogation Models?
Multi-floor model?
Partition attenuation model?
Empirical path loss model?
ITU Model for Indoor Attenuation/ Wall and floor factor model?
FRIIS MODEL?
Log-distance path loss model?
This document discusses various topics related to antennas and propagation, including:
- The basic functions of antennas for transmission and reception of signals
- Types of radiation and reception patterns that characterize antenna performance
- Common types of antennas like dipole, vertical, and parabolic reflective antennas
- Factors that influence signal propagation over distance like free space loss, noise, multipath interference, and atmospheric effects
- Techniques to improve reliability like diversity combining, adaptive equalization, and forward error correction coding.
This document is a lecture presentation on electromagnetic wave propagation by Mr. Himanshu Diwakar. It includes:
- An outline discussing Maxwell's equations, the Helmholtz equation, propagation constant, properties of electromagnetic waves, and wave propagation in free space.
- A note emphasizing the need to review electrostatics, magnetostatics, and vector identities to fully understand electromagnetic waves.
- Explanations of the Pointing theorem, which states that the time rate of change of electromagnetic energy within a volume plus the net energy flowing out equals the work done on charges within the volume.
- Definitions of the Poynting vector and its relationship to the electric and magnetic
The document discusses key concepts related to antennas and electromagnetic waves. It defines that radio waves have electric and magnetic fields that are perpendicular to each other and the direction of wave propagation. It also describes how antennas can transmit electromagnetic waves by converting electrical energy to radio waves and receive waves by converting radio waves back to electrical energy. Antenna size is inversely proportional to frequency, with higher frequencies requiring smaller antennas. Antenna radiation patterns and near/far field regions are also discussed.
The document discusses Shannon-Fano encoding, which is an early method for data compression that constructs efficient binary codes for information sources without memory. It works by assigning shorter codes to more frequent messages and longer codes to less frequent messages. The encoding process involves recursively splitting the set of messages in half based on probability until each message has its own unique code. While Shannon-Fano codes are reasonably efficient, they are not always optimal and the codes generated can depend on how the initial splitting of messages is done.
Numerical studies of the radiation patterns of resistively loaded dipolesLeonid Krinitsky
This document describes a numerical study of the radiation patterns of resistively loaded dipole antennas. It computes the far field radiation patterns as a superposition of transient solutions for infinitesimal dipole elements. The current excitation for each dipole element is modeled as a half cycle of a sine squared waveform that propagates along the antenna at an adjustable speed. The radiation patterns are presented for different dielectric media to model antennas used in ground penetrating radar applications in various materials like water, ice, and soil. Comparisons are made to field observations.
Propagation of ELF Radiation from RS-LC System and Red Sprites in Earth- Iono...degarden
This document compares the propagation of extremely low frequency (ELF) radiation from return stroke-lateral corona (RS-LC) systems and red sprites in the Earth-ionosphere waveguide. It finds that red sprites contribute more greatly to Schumann resonances than RS-LC systems. The document derives mathematical expressions to model the velocity, current, and current moment of RS-LC systems and red sprites. It then uses these expressions to calculate the electric and magnetic fields generated by RS-LC systems and red sprites, finding that red sprites produce fields on the order of 10-5 V/m and 10-8 A/m, peaking at Schumann resonance frequencies.
Propagation of ELF Radiation from RS-LC System and Red Sprites in Earth- Iono...degarden
This document compares the propagation of extremely low frequency (ELF) radiation from return stroke-lateral corona (RS-LC) systems and red sprites in the Earth-ionosphere waveguide. It finds that red sprites contribute more greatly to Schumann resonances than RS-LC systems. The document derives mathematical expressions to model the velocity, current, and current moment of RS-LC systems and red sprites. It then uses these expressions to calculate the electric and magnetic fields generated by RS-LC systems and red sprites and compares their contributions to Schumann resonances.
1. The document discusses key characteristics of antenna radiation patterns including the radiation pattern, which shows the antenna's electric and magnetic fields in 3D space. Common pattern types include omnidirectional, broadside, and endfire.
2. Important parameters that quantify antenna patterns are defined, such as directivity which compares an antenna's power concentration to an isotropic radiator, half-power beamwidth, and maximum sidelobe level.
3. Radiation intensity, which is independent of distance from the antenna, is introduced. It allows defining the total radiated power by integrating over solid angle rather than area.
This document discusses the performance analysis of a microstrip printed antenna conformed on a cylindrical body operating at a resonance frequency of 4.6 GHz for the TM01 mode. It begins with an introduction to microstrip antennas and the effects of curvature. It then presents mathematical models for the electric and magnetic fields, input impedance, return loss, and voltage standing wave ratio for a curved microstrip antenna. Results show the resonance frequency shifts 35 MHz as the radius of curvature changes from 6 mm to a flat antenna. Graphs also show the real and imaginary parts of input impedance vary with frequency for different radii of curvature.
This document discusses plane electromagnetic waves. It defines plane waves as waves whose wavefronts are infinite parallel planes of constant amplitude normal to the phase velocity vector. The electric and magnetic fields of a plane wave are perpendicular to each other and to the direction of propagation. Plane waves can be linearly, circularly, or elliptically polarized depending on the orientation and behavior of the electric field vector over time. Linear polarization occurs when the electric field is oriented along a fixed line. Circular polarization results when the electric field traces out a circle, and elliptical polarization is characterized by an elliptical trace.
Monopole antenna radiation into a parallel plate waveguideYong Heui Cho
This document presents a rigorous solution for analyzing the radiation of a coaxially-fed monopole antenna into a parallel-plate waveguide. Fourier transform representations are used to model the scattered fields. Boundary conditions are enforced to obtain equations for the modal coefficients. A rapidly convergent series solution for the reflection coefficient is obtained and shown to agree well with other results. Input impedance and reflected power characteristics are calculated and presented.
This document describes a new polarimetric ground penetrating radar (GPR) system and algorithms to reduce noise and recognize buried targets. It includes:
1) A clustered planar array of crossed dipole antennas is used to obtain high resolution 2D images from four polarization channels (xx, yy, xy, yx).
2) A granular noise filter and shape smoothing filter are applied to enhance signal-to-noise ratio and extract the buried object shape from the GPR images.
3) A shape recognition algorithm compares the extracted shape to a reference target to determine if there is a match or mismatch for target identification.
4) Finite-difference time-domain simulations demonstrate the effectiveness of the proposed GPR
This standard provides reference solar spectral irradiance distributions for direct normal and hemispherical irradiance on a 37° tilted surface. The distributions are modeled using the SMARTS 2.9.2 radiative transfer code based on an extraterrestrial spectrum, atmospheric properties from the 1976 U.S. Standard Atmosphere, and a rural aerosol profile. The standard extends the spectral range of previous distributions, uses uniform wavelength intervals, and has higher spectral resolution. It is intended for use in evaluating solar-sensitive materials and components, but not as a benchmark for ultraviolet radiation in indoor weathering tests.
The document describes an end-to-end simulator developed to model GNSS reflection signals from bare and vegetated soils. The simulator was validated using experimental data collected during the LEiMON project. The simulator fairly reproduced observed trends in the experimental data for various soil and vegetation conditions. It distinguishes between coherent and incoherent signal components, helping explain saturation effects seen in vegetation measurements. While some discrepancies remain, the simulator provides a useful tool for understanding GNSS reflection signals and predicting capabilities for aerospace applications.
International Journal of Business and Management Invention (IJBMI) is an international journal intended for professionals and researchers in all fields of Business and Management. IJBMI publishes research articles and reviews within the whole field Business and Management, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Radiation Q bounds for small electric dipoles over a conducting ground planeYong Heui Cho
This document discusses theoretical bounds on the quality factor (Q) of small electric dipole antennas placed over a conducting ground plane. It finds that for vertically polarized dipoles, the Q can decrease by approximately a factor of two compared to an antenna of the same size in free space, indicating a doubling of bandwidth. This bandwidth enhancement is validated through simulations and measurements of small spherical helix dipole antennas over a ground plane. For horizontally polarized dipoles, the Q increases significantly compared to free space as the ground separation decreases. The analysis divides space into regions and uses vector spherical wave functions to calculate stored electric and magnetic energies, from which Q is determined following definitions by Chu and Thal.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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) .
Analytic Model of Wind Disturbance Torque on Servo Tracking AntennaIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
High impedance surface_his_ris_amc_nurmerical_analytical_analysis利 金
Features of an AMC such as dispersion diagram and reflection phase are discussed numerically and analytically, along with their experimental set up. Parametric study on polarization (TE and TM,substrate thickness and dielectric constant and unit cell size and spacing is carried out. Their design equations are included from different references.
The document compares the low field electron transport properties in compounds of groups III-V semiconductors by solving the Boltzmann equation using an iterative technique. It calculates the temperature and doping dependencies of electron mobility in InP, InAs, GaP and GaAs. The electron mobility decreases with increasing temperature from 100K to 500K for each material due to increased electron-phonon scattering. Electron mobility also increases significantly with higher doping concentration at low temperatures. The iterative results show good agreement with other calculations and experiments. Electron mobility is highest in InAs and lowest in GaP at 300K, due to differences in their effective masses.
1) This document discusses view factors and shape factors in radiation heat transfer between surfaces. It provides examples of calculating view factors for different geometric configurations using rules like summation, reciprocity, symmetry and superposition.
2) Formulas for net radiation heat transfer between black surfaces are presented. Examples show calculating the net radiation rate between surfaces of enclosures like cubes and cylinders using the view factors and temperatures of the surfaces.
3) Maintaining surfaces at specified temperatures in situations of radiation heat transfer requires supplying or removing heat at rates equal to the calculated net radiation transfer at each surface.
Este manual fornece instruções para a montagem e uso de um kit didático de aquecedor solar de baixo custo, com o objetivo de ensinar conceitos sobre energia solar de forma prática. O manual descreve os componentes do kit, como montá-lo e sugere experimentos a serem realizados na sala de aula.
Este documento fornece instruções para construir e instalar um aquecedor solar de água feito com tubos de PVC, incluindo dimensionamento, montagem do coletor e reservatório, e instalação do sistema. O objetivo é fornecer uma solução barata para aquecer água para banho utilizando energia solar.
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Similar to Miletta joseph r. propagation of electromagnetic fields over flat earth
Numerical studies of the radiation patterns of resistively loaded dipolesLeonid Krinitsky
This document describes a numerical study of the radiation patterns of resistively loaded dipole antennas. It computes the far field radiation patterns as a superposition of transient solutions for infinitesimal dipole elements. The current excitation for each dipole element is modeled as a half cycle of a sine squared waveform that propagates along the antenna at an adjustable speed. The radiation patterns are presented for different dielectric media to model antennas used in ground penetrating radar applications in various materials like water, ice, and soil. Comparisons are made to field observations.
Propagation of ELF Radiation from RS-LC System and Red Sprites in Earth- Iono...degarden
This document compares the propagation of extremely low frequency (ELF) radiation from return stroke-lateral corona (RS-LC) systems and red sprites in the Earth-ionosphere waveguide. It finds that red sprites contribute more greatly to Schumann resonances than RS-LC systems. The document derives mathematical expressions to model the velocity, current, and current moment of RS-LC systems and red sprites. It then uses these expressions to calculate the electric and magnetic fields generated by RS-LC systems and red sprites, finding that red sprites produce fields on the order of 10-5 V/m and 10-8 A/m, peaking at Schumann resonance frequencies.
Propagation of ELF Radiation from RS-LC System and Red Sprites in Earth- Iono...degarden
This document compares the propagation of extremely low frequency (ELF) radiation from return stroke-lateral corona (RS-LC) systems and red sprites in the Earth-ionosphere waveguide. It finds that red sprites contribute more greatly to Schumann resonances than RS-LC systems. The document derives mathematical expressions to model the velocity, current, and current moment of RS-LC systems and red sprites. It then uses these expressions to calculate the electric and magnetic fields generated by RS-LC systems and red sprites and compares their contributions to Schumann resonances.
1. The document discusses key characteristics of antenna radiation patterns including the radiation pattern, which shows the antenna's electric and magnetic fields in 3D space. Common pattern types include omnidirectional, broadside, and endfire.
2. Important parameters that quantify antenna patterns are defined, such as directivity which compares an antenna's power concentration to an isotropic radiator, half-power beamwidth, and maximum sidelobe level.
3. Radiation intensity, which is independent of distance from the antenna, is introduced. It allows defining the total radiated power by integrating over solid angle rather than area.
This document discusses the performance analysis of a microstrip printed antenna conformed on a cylindrical body operating at a resonance frequency of 4.6 GHz for the TM01 mode. It begins with an introduction to microstrip antennas and the effects of curvature. It then presents mathematical models for the electric and magnetic fields, input impedance, return loss, and voltage standing wave ratio for a curved microstrip antenna. Results show the resonance frequency shifts 35 MHz as the radius of curvature changes from 6 mm to a flat antenna. Graphs also show the real and imaginary parts of input impedance vary with frequency for different radii of curvature.
This document discusses plane electromagnetic waves. It defines plane waves as waves whose wavefronts are infinite parallel planes of constant amplitude normal to the phase velocity vector. The electric and magnetic fields of a plane wave are perpendicular to each other and to the direction of propagation. Plane waves can be linearly, circularly, or elliptically polarized depending on the orientation and behavior of the electric field vector over time. Linear polarization occurs when the electric field is oriented along a fixed line. Circular polarization results when the electric field traces out a circle, and elliptical polarization is characterized by an elliptical trace.
Monopole antenna radiation into a parallel plate waveguideYong Heui Cho
This document presents a rigorous solution for analyzing the radiation of a coaxially-fed monopole antenna into a parallel-plate waveguide. Fourier transform representations are used to model the scattered fields. Boundary conditions are enforced to obtain equations for the modal coefficients. A rapidly convergent series solution for the reflection coefficient is obtained and shown to agree well with other results. Input impedance and reflected power characteristics are calculated and presented.
This document describes a new polarimetric ground penetrating radar (GPR) system and algorithms to reduce noise and recognize buried targets. It includes:
1) A clustered planar array of crossed dipole antennas is used to obtain high resolution 2D images from four polarization channels (xx, yy, xy, yx).
2) A granular noise filter and shape smoothing filter are applied to enhance signal-to-noise ratio and extract the buried object shape from the GPR images.
3) A shape recognition algorithm compares the extracted shape to a reference target to determine if there is a match or mismatch for target identification.
4) Finite-difference time-domain simulations demonstrate the effectiveness of the proposed GPR
This standard provides reference solar spectral irradiance distributions for direct normal and hemispherical irradiance on a 37° tilted surface. The distributions are modeled using the SMARTS 2.9.2 radiative transfer code based on an extraterrestrial spectrum, atmospheric properties from the 1976 U.S. Standard Atmosphere, and a rural aerosol profile. The standard extends the spectral range of previous distributions, uses uniform wavelength intervals, and has higher spectral resolution. It is intended for use in evaluating solar-sensitive materials and components, but not as a benchmark for ultraviolet radiation in indoor weathering tests.
The document describes an end-to-end simulator developed to model GNSS reflection signals from bare and vegetated soils. The simulator was validated using experimental data collected during the LEiMON project. The simulator fairly reproduced observed trends in the experimental data for various soil and vegetation conditions. It distinguishes between coherent and incoherent signal components, helping explain saturation effects seen in vegetation measurements. While some discrepancies remain, the simulator provides a useful tool for understanding GNSS reflection signals and predicting capabilities for aerospace applications.
International Journal of Business and Management Invention (IJBMI) is an international journal intended for professionals and researchers in all fields of Business and Management. IJBMI publishes research articles and reviews within the whole field Business and Management, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Radiation Q bounds for small electric dipoles over a conducting ground planeYong Heui Cho
This document discusses theoretical bounds on the quality factor (Q) of small electric dipole antennas placed over a conducting ground plane. It finds that for vertically polarized dipoles, the Q can decrease by approximately a factor of two compared to an antenna of the same size in free space, indicating a doubling of bandwidth. This bandwidth enhancement is validated through simulations and measurements of small spherical helix dipole antennas over a ground plane. For horizontally polarized dipoles, the Q increases significantly compared to free space as the ground separation decreases. The analysis divides space into regions and uses vector spherical wave functions to calculate stored electric and magnetic energies, from which Q is determined following definitions by Chu and Thal.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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) .
Analytic Model of Wind Disturbance Torque on Servo Tracking AntennaIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
High impedance surface_his_ris_amc_nurmerical_analytical_analysis利 金
Features of an AMC such as dispersion diagram and reflection phase are discussed numerically and analytically, along with their experimental set up. Parametric study on polarization (TE and TM,substrate thickness and dielectric constant and unit cell size and spacing is carried out. Their design equations are included from different references.
The document compares the low field electron transport properties in compounds of groups III-V semiconductors by solving the Boltzmann equation using an iterative technique. It calculates the temperature and doping dependencies of electron mobility in InP, InAs, GaP and GaAs. The electron mobility decreases with increasing temperature from 100K to 500K for each material due to increased electron-phonon scattering. Electron mobility also increases significantly with higher doping concentration at low temperatures. The iterative results show good agreement with other calculations and experiments. Electron mobility is highest in InAs and lowest in GaP at 300K, due to differences in their effective masses.
1) This document discusses view factors and shape factors in radiation heat transfer between surfaces. It provides examples of calculating view factors for different geometric configurations using rules like summation, reciprocity, symmetry and superposition.
2) Formulas for net radiation heat transfer between black surfaces are presented. Examples show calculating the net radiation rate between surfaces of enclosures like cubes and cylinders using the view factors and temperatures of the surfaces.
3) Maintaining surfaces at specified temperatures in situations of radiation heat transfer requires supplying or removing heat at rates equal to the calculated net radiation transfer at each surface.
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Increasing urbanization, rural–urban migration, rising standards of living, and rapid development associated with population growth have resulted in increased solid waste generation by industrial, domestic and other activities in Nairobi City. It has been noted in other contexts too that increasing population, changing consumption patterns, economic development, changing income, urbanization and industrialization all contribute to the increased generation of waste.
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Build new environmentally sound infrastructure and systems for safe disposal of residual waste and replacing current dumpsites which should be commissioned.
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The status.
Solid waste generation rate is at 2240 tones / day
collection efficiently is at about 50%.
Actors i.e. city authorities, CBO’s , private firms and self-disposal
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Solid waste generation – collection – dumping
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• Separation – recycling – marketing.
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• Nairobi is one of the C40 cities in this respect , various actors in the solid waste management space have adopted a variety of technologies to reduce short lived climate pollutants including source separation , recycling , marketing of the recycled products.
• Through the network, it should expect to benefit from expertise of the different actors in the network in terms of applicable technologies and practices in reducing the short-lived climate pollutants.
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Despite the dismal collection of solid waste in Nairobi city, there are practices and activities of informal actors (CBOs, CBO-SACCOs and yard shop operators) and other formal industrial actors on solid waste collection, recycling and waste reduction.
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CHALLENGES:
• Resource Allocation.
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Miletta joseph r. propagation of electromagnetic fields over flat earth
1. Propagation of Electromagnetic
Fields Over Flat Earth
ARL-TR-2352 February 2001
Joseph R. Miletta
Approved for public release; distribution unlimited.
2. The findings in this report are not to be construed as an
official Department of the Army position unless so
designated by other authorized documents.
Citation of manufacturer’s or trade names does not
constitute an official endorsement or approval of the use
thereof.
Destroy this report when it is no longer needed. Do not
return it to the originator.
3. ARL-TR-2352 February 2001
Army Research Laboratory
Adelphi, MD 20783-1197
Propagation of Electromagnetic
Fields Over Flat Earth
Joseph R. Miletta
Sensors and Electron Devices Directorate
Approved for public release; distribution unlimited.
4. Abstract
This report looks at the interaction of radiated electromagnetic fields with
earth ground in military or law-enforcement applications of high-power
microwave (HPM) systems. For such systems to be effective, the microwave
power density on target must be maximized. The destructive and construc-
tive scattering of the fields as they propagate to the target will determine
the power density at the target for a given source. The question of field
polarization arises in designing an antenna for an HPM system. Should
the transmitting antenna produce vertically, horizontally, or circularly po-
larized fields? Which polarization maximizes the power density on target?
This report provides a partial answer to these questions. The problems of
calculating the reflection of uniform plane wave fields from a homogeneous
boundary and calculating the fields from a finite source local to a perfectly
conducting boundary are relatively straightforward. However, when the
source is local to a general homogeneous plane boundary, the solution can-
not be expressed in closed form. An approximation usually of the form
of an asymptotic expansion results. Calculations of the fields are provided
for various source and target locations for the frequencies of interest. The
conclusion is drawn that the resultant vertical field from an appropriately
oriented source antenna located near and above the ground can be signif-
icantly larger than a horizontally polarized field radiated from the same
location at a 1.3 GHz frequency at observer locations near and above the
ground.
ii
5. Contents
1 Introduction 1
2 Problem Formulation 2
2.1 Vertical Dipole Over Earth . . . . . . . . . . . . . . . . . . . . 3
2.2 Horizontal Dipole Over Earth . . . . . . . . . . . . . . . . . . 4
2.3 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3.1 Comparison of Field Components Near the Earth . . 6
3 Conclusion 14
References 15
Appendix. MATLAB m-Files 17
Distribution 27
Report Documentation Page 29
Figures
1 Geometry for vertical and horizontal dipole formulations . . . . 2
2 Comparison of main electric field components from a vertical
(Ez) and from a horizontal (Eφ) broadside ideal dipole over a
perfectly conducting ground . . . . . . . . . . . . . . . . . . . . . 7
3 Reflection coefficients for vertically and horizontally polarized
plane waves of 1.3-GHz frequency incident on a flat ground for
five earth-parameter cases listed in table 1 . . . . . . . . . . . . . 8
4 Fresnel reflection coefficient for a vertically polarized plane wave
field compared to “reflection coefficient” as calculated by com-
plete formulation for a vertical dipole over homogeneous earth
as observed at 1-m height 1000 m down range at a frequency of
1.3 GHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
5 Fresnel reflection coefficient for a horizontally polarized plane
wave field compared to “reflection coefficient” as calculated by
complete formulation for a horizontal dipole over homogeneous
earth as observed at 1-m height, broadside 1000 m down range
at a frequency of 1.3 GHz . . . . . . . . . . . . . . . . . . . . . . 10
iii
6. 6 Comparison of principal fields from an ideal dipole oriented
perpendicular and horizontal to a homogeneous flat earth . . . 11
7 Comparison of principal fields from an ideal dipole oriented
perpendicular and horizontal to a homogeneous flat earth . . . 12
8 Effect of ground reflection on primary field components near
ground for typical earth parameters . . . . . . . . . . . . . . . . 13
Tables
1 Earth parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
iv
7. 1. Introduction
Effective military or law-enforcement applications of high-power mi-
crowave (HPM) systems in which the HPM system and the target system
are on or near the ground or water require that the microwave power den-
sity on target be maximized. The power density at the target for a given
source will depend on the destructive and constructive scattering of the
fields as they propagate to the target. Antenna design for an HPM sys-
tem includes addressing the following questions about field polarization:
Should the fields the transmitting antenna produces be vertically, hori-
zontally, or circularly polarized? Which polarization maximizes the power
density on target? (The question of which polarization best couples to the
target is beyond the scope of this report.) While this report does not com-
pletely answer these questions, it addresses the interaction of the radiated
electromagnetic fields with earth ground. It is assumed that the transmit-
ting antenna and the target (or receiver) are located above, but near the
surface of a flat idealized earth (constant permittivity, ε, and conductivity,
σ) ground. First an ideal vertical dipole (oriented along the z-axis perpen-
dicular to the ground plane) is addressed. The horizontal dipole (parallel
to the ground plane) follows.
1
8. 2. Problem Formulation
The problems of calculating the reflection of uniform plane wave fields
from a homogeneous boundary and calculating the fields from a finite
source local to a perfectly conducting boundary are relatively straightfor-
ward. However, when the source is local to a general homogeneous plane
boundary, it is found that the solution cannot be expressed in closed form.
An approximation usually of the form of an asymptotic expansion results.
The problem of an ideal dipole over a homogeneous half-space has been the
topic of a number of studies starting at the turn of the last century with the
solution provided by Sommerfeld (1949) and leading to the more contem-
porary work of Banos (1966) and King et al (1994, 1992). References such
as Maclean and Wu (1993) address in detail the many approaches to solv-
ing the problem. Considerable controversy has surrounded these studies.
We will not attempt to derive the solution or otherwise discuss the solu-
tion of the problem in this report. We will rely on the work of King et al
for a complete and concise formulation of the problem. Figure 1 depicts the
problem geometry. The King expressions have been encoded and solved in
MATLAB (1984–1999). Comparisons of the field structures are provided
for various source and target locations for frequencies of interest.
The expressions that follow are constrained by the magnitude of the wave
numbers (k = ω(µ )1/2, ω = 2π × frequency) in each region:
|k1| ≥ 3 |k2| , (1)
where, after King, the subscript 2 denotes the upper half-space (air) and the
subscript 1 denotes the lower half-space (earth). Also, µ is the permeability
in henries per meter, ε is the permittivity in farads per meter, and σ is the
conductivity in siemens per meter. The subscripts 0 and r represent free
space and relative to free space, respectively.
Figure 1. Geometry for
vertical and horizontal
dipole formulations.
z
z′
0
r0
r1
r2
Region 2
µ0, ε0, σ = 0
Region 1
µ0, ε2 = εr ε0,σ ≠ 0
y
x
Looking down
θd
θ
d
φ
ρ
Ψ
2
9. 2.1 Vertical Dipole Over Earth
The electromagnetic fields from a dipole with dipole moment I oriented
perpendicular to and at a height z = d above the ground plane have three
components in cylindrical coordinates. The magnetic field is symmetric
about the z-axis, perpendicular to the direction of propagation. For that
reason the fields will be termed transverse magnetic (TM) fields. (We will
find that the horizontal dipole has TM and transverse electric (TE) com-
ponents.) The formulation as provided in King et al (1994) is, referring to
figure 1,
Hφ(ρ, z) = −
I
2π
eik2r1
2
ρ
r1
ik2
r1
− 1
r2
1
+ eik2r2
2
ρ
r2
ik2
r2
− 1
r2
2
−eik2r2
k3
2
k1
π
k2r2
1
2
e−iP F(P)
, (2)
Eρ(ρ, z) = −
ωµ0I
2πk2
eik2r1
2
ρ
r1
z−d
r1
ik2
r1
− 3
r2
1
− 3i
k2r3
1
+eik2r2
2
ρ
r2
z+d
r2
ik2
r2
− 3
r2
2
− 3i
k2r3
2
−k2
k1
eik2r2 ρ
r2
ik2
r2
− 1
r2
2
−
k3
2
k1
π
k2r2
1
2
e−iP F(P)
, and (3)
Ez(ρ, z) =
ωµ0I
2πk2
eik2r1
2
ik2
r1
− 1
r2
1
− i
k2r3
1
− z−d
r1
2
ik2
r1
− 3
r2
1
− 3i
k2r3
1
+eik2r2
2
ik2
r2
− 1
r2
2
− i
k2r3
2
− z+d
r2
2
ik2
r2
− 3
r2
2
− 3i
k2r3
2
−eik2r2
k3
2
k1
ρ
r2
π
k2r2
1
2
e−iP F(P)
, (4)
where
r1 = ρ2
+ (z − d)2
1
2
,
r2 = ρ2
+ (z + d)2
1
2
, (5)
P =
k3
2r2
2k2
1
k2r2 + k1 (z + d)
k2ρ
2
, (6)
F(P) =
∞
P
eit
(2πt)
1
2
dt =
1
2
(1 + i) − C2 (P) − iS2 (P) , (7)
and C2(P), S2(P) are the Fresnel integrals as defined in Abramowitz and
Stegun (1970). Since
C2 (P) + iS2 (P) =
1
2
(1 + i) −
i
2
eiP
w
√
iP , (8)
we have
F (P) =
i
2
eiP
w
√
iP , (9)
where w(z), called the plasma dispersion function with complex argument,
is a form of the error function defined in Abramowitz and Stegun (1970). A
3
10. convenient MATLAB m-file is available for solving the function with com-
plex argument (Chase) and is provided in the appendix. Note that
√
i can
be written as (i+1)
2 and that F(P) always appears with e−iP , thus cancel-
ing the exponential term in equation (9). This is reflected in the MATLAB
m-files that calculate the fields (provided in the appendix).
The equations have been written such that the direct and reflected compo-
nents appear first. The last term is referred to as the surface or lateral wave.
Often it is called the Norton surface wave from the engineering models he
developed in the mid-1930s. The equations reduce to the fields above a per-
fectly conducting ground when k1 → ∞; the surface or lateral wave term
then goes to zero.
2.2 Horizontal Dipole Over Earth
The electromagnetic fields produced by an ideal dipole oriented at a height
z = d above and parallel to the ground plane consist in general of both TM
and TE components. The formulation as provided in King et al (1992) for
the TM wave components in cylindrical coordinates, referring to figure 1
and the above definitions, is
Hφ(ρ, φ, z) =
I
4π
cos φ
eik2r1 z−d
r1
ik2
r1
− 1
r2
1
− eik2r2 z+d
r2
ik2
r2
− 1
r2
2
+2k2
k1
eik2r2
ik2
r2
− 1
r2
2
− i
k2r3
2
−
k3
2
k1
r2
ρ
π
k2r2
1
2
e−iP F(P)
, (10)
Eρ(ρ, φ, z) =
ωµ0I
4πk2
cos φ
eik2r1 2
r2
1
+ 2i
k2r3
1
+ z−d
r1
2
ik2
r1
− 3
r2
1
− 3i
k2r3
1
−eik2r2
2
r2
2
+ 2i
k2r3
2
+ z+d
r2
2
ik2
r2
− 3
r2
2
− 3i
k2r3
2
−2k2
k1
z+d
r2
ik2
r2
− 1
r2
2
+
2k2
2
k2
1
ik2
r2
− 1
r2
2
− i
k2r3
2
−
k3
2
k1
r2
ρ
π
k2r2
1
2
e−iP F(P)
, and (11)
Ez(ρ, φ, z) =
ωµ0I
4πk2
cos φ
−eik2r1 ρ
r1
z−d
r1
ik2
r1
− 3
r2
1
− 3i
k2r3
1
+eik2r2 ρ
r2
z+d
r2
ik2
r2
− 3
r2
2
− 3i
k2r3
2
−2k2
k1
eik2r2 ρ
r2
ik2
r2
− 1
r2
2
−
k3
2
k1
π
k2r2
1
2
e−iP F(P)
. (12)
The TM fields are zero broadside to the dipole orientation, φ = π
2 . The TE
components are
4
11. Hρ(ρ, φ, z) =
I
4π
sin φ
eik2r1 z−d
r1
ik2
r1
− 1
r2
1
− eik2r2 z+d
r2
ik2
r2
− 1
r2
2
+2k2
k1
eik2r2
2
r2
2
+ 2i
k2r3
2
+
ik2
2
k1ρ
r2
2
ρ2
π
k2r2
1
2
e−iP F(P)
+ z+d
r2
2
ik2
r2
− 3
r2
2
− 3i
k2r3
2
, (13)
Hz(ρ, φ, z) =
I
4π
sin φ
eik2r1 ρ
r1
ik2
r1
− 1
r2
1
− eik2r2 ρ
r2
ik2
r2
− 1
r2
2
+2 ρ
r2
eik2r2
k2
k1
z+d
r2
ik2
r2
− 3
r2
2
− 3i
k2r3
2
− k2
k1
2
1
r2
2
+ 3i
k2r3
2
− 3
k2
2r4
2
+
z+d
r2
2
ik2
r2
− 6
r2
2
− 15i
k2r3
2
, and (14)
Eφ(ρ, φ, z) = −
ωµ0I
4πk2
sin φ
eik2r1 ik2
r1
+ 1
r2
1
− i
k2r3
1
− eik2r2 ik2
r2
− 1
r2
2
− i
k2r3
2
−eik2r2
−2k2
k1
z+d
r2
ik2
r2
− 1
r2
2
+
2k2
2
k2
1
2
r2
2
+ 2i
k2r3
2
+ z+d
r2
2
ik2
r2
− 3
r2
2
− 3i
k2r3
2
+
2ik4
2
k3
1ρ
r2
ρ
2
π
k2r2
1
2
e−iP F(P)
. (15)
These are the predominant fields broadside to the dipole orientation. Here
Eφ is often termed the horizontal electric field. Again, the equations reduce
to the fields above a perfectly conducting ground when k1 → ∞; the surface
or lateral wave term goes to zero.
2.3 Comparisons
The peak power radiated by a unit dipole is given in Collin and Zucker
(1969):
P =
k2
2ζ0
12π
, (16)
where ζ0 is the free-space impedance µ0
ε0
. The fields and power density
comparisons that follow are normalized to one watt radiated peak power.
To obtain the unnormalized quantities, simply multiply the power results
by P and the field results by P
1
2 . The outward component of the complex
Poynting vector over a closed surface is
1/2
S
E × H ∗
· dS = −Pcomplex , (17)
where the negative sign indicates power flow away from the surface. Our
interest is in the real part of the power density at the observer (or target)
location. In our cylindrical coordinate system for the TM components, this
becomes
1/2 Re (E × H∗
) = 1/2 Re ρ0
EzHφ
∗
+ z0EρHφ
∗
, (18)
5
12. where ρ0
and z0 are the unit vectors in cylindrical coordinates. Near the
ground, the power flow is predominantly radial with a small z component.
And, for the TE components, we have
1/2 Re (E × H∗
) = 1/2 Re ρ0
EφHz
∗
− z0EφHρ
∗
. (19)
For the vertical dipole, the power density at the observer (on target) will be
Pv = 1/2 (Re (EφHz
∗
) + Re (EφHρ
∗
)) . (20)
The horizontal dipole in general will produce a target power density of
Ph = 1/2 ({Re (EφHz
∗
) − Re (EzHφ
∗
)} + {Re (EρHφ
∗
) − Re (EφHρ
∗
)}) . (21)
For broadside calculations this becomes
Ph = 1/2 (Re (EφHz
∗
) + Re (EφHρ
∗
)) . (22)
The calculations that follow are limited to a frequency of 1.3 GHz (wave-
length, λ0, is 0.23 m) and dipole heights of 1 to 3 m. Observer (target)
heights range from 0 to 5 m. The frequency of 1.3 GHz is chosen, since most
of the HPM source and antenna design work at ARL is centered around that
frequency. The height ranges are chosen to be consistent with ground vehi-
cle source and target applications. Five classes of ground parameters that
are representative of distinctly different terrain will be addressed. These
five classes are those discussed in King et al (1994) and are given in table 1.
2.3.1 Comparison of Field Components Near the Earth
When thinking about the interaction of electromagnetic waves with the
earth’s surface, we often view the earth as a perfect conductor. The hori-
zontally polarized field is reflected with the opposite sign of the incident
field, leading to a difference or destructively interfered-with field. The ver-
tically polarized field is reflected with the same sign as the incident field,
leading to a sum or constructively interfered-with field. Figure 2 compares
the resultant primary field components produced from a horizontal and a
vertical ideal dipole located at the same point in space over a perfectly con-
ducting ground plane. From these calculations, one might conclude that
Table 1. Earth
parameters.
Case σ,* S/m εr*
1 Sea water 4 80
2 Wet earth .4 12
3 Dry earth .04 8
4 Lake water .004 80
5 Dry sand .000 2
*The variable name representing σ
in the MATLAB m-files is SIGMA
and for εr it is EPSREL. These vari-
able names appear on many of the
figures.
6
13. Figure 2. Comparison of
main electric field
components from a
vertical (Ez) and from a
horizontal (Eφ)
broadside ideal dipole
over a perfectly
conducting ground. Ez
is a constructively
interfered-with field,
while Eφ is a
destructively
interfered-with field.
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
0
0.5
1
1.5
2
2.5
3
Dipole height = 2 m, frequency = 1.3 GHz,
range = 1000 m
Normalized field magnitude (V/m)
Horizontal E-field, horizontal dipole
z-directed E-field, vertical dipole
Observerheight(m)
an antenna that radiated fields polarized such that the electric field was
essentially perpendicular to the ground plane would produce the largest
fields and, consequently, the greater power densities on a target or near
the ground. This is generally not the case for real earth grounds. While
the perfectly conducting ground plane model may provide some insight
into the interaction with horizontally polarized fields, it clearly is an inad-
equate model for vertical polarization. The complex reflection coefficients
for a plane wave polarized with the electric field in the plane of incidence
(vertical polarization) and with a plane wave polarized with the electric
field perpendicular to the plane of incidence (horizontal polarization) are
given by the following Fresnel expressions. For vertical polarization, it is
(Collin, 1985)
ρcomplex =
εr − i σ
ωε0
sin ψ − εr − i σ
ωε0
− cos2 ψ
εr − i σ
ωε0
sin ψ + εr − i σ
ωε0
− cos2 ψ
, (23)
and for horizontal polarization, it is
ρcomplex =
sin ψ − εr − i σ
ωε0
− cos2 ψ
sin ψ + εr − i σ
ωε0
− cos2 ψ
, (24)
where ψ is the angle of incidence as measured between the ray path and
the surface of the earth (see fig. 1). These reflection coefficients for the five
cases of table 1 are presented in figure 3. One can clearly see that for shal-
low grazing angles, a Brewster angle effect exists (often called a pseudo-
Brewster angle). The result is destructive interference of the vertically po-
larized field for incident angles that are less than this pseudo-Brewster
7
14. Figure 3. Reflection
coefficients for
vertically and
horizontally polarized
plane waves of 1.3-GHz
frequency incident on a
flat ground for five
earth-parameter cases
listed in table 1. Note
that case 5 provides a
true Brewster angle
(since conductivity is
zero) and case 4 is very
near to producing a true
Brewster angle at
1.3-GHz frequency:
(a) vertical polarization
and (b) horizontal
polarization.
0 20 40 60 80
0
0.2
0.4
0.6
0.8
1
Incidence angle (°)
–150
–100
–50
0
170
175
180
185
190
195
200
Case 1
2
5
3
4
4,5
0 20 40 60 80
Incidence angle (°)
0 20 40 60 80
Incidence angle (°)
0 20 40 60 80
Incidence angle (°)
0.5
0.6
0.7
0.8
0.9
1
Reflectioncoefficient
PhasePhase
Reflectioncoefficient
(a)
(b)
Case 1
5
2
4
3
5
3
24
Case 1
3
Case 1
2
angle. This would lead one to conclude that horizontally and vertically po-
larized field levels above a ground would be comparable at shallow angles
of incidence. The Fresnel equations (22) and (23) do not take into account
the surface or lateral wave produced by finite sources above the ground.
They are also not applicable to near-field problems. We can compare the
reflection coefficients as determined from the Fresnel equations with the
results of our complete solution. To do this with the complete equations
(eqs (2) to (4) for the vertical dipole and eqs (10) to (15) for the horizontal
dipole), we fix the radial (or range) distance to 1000 m. The dipole height is
varied to provide a range of incident angles. The observer will be fixed at a
1-m height. The incident and ”reflected” fields are
Evtotal = E2
ρ + E2
z , (25)
for the vertical dipole and
Ehtotal = E2
φ + E2
ρ + E2
z , (26)
for the horizontal dipole. For broadside calculations, this simply becomes
Eφ. The terms involving r1 in equations (2) to (4) and (10) to (15) repre-
sent the incident field and the remaining terms represent the reflected and
surface wave terms. The reflection coefficient will be calculated as the to-
tal incident electric field divided into the total reflected and bound (sur-
face wave) fields. Figures 4 and 5 provide the comparison of the magni-
tude of the reflection coefficient for the five cases of table 1. For the most
part, the Fresnel expressions are a good approximation for the calculation
of horizontally polarized field values (fig. 5) above realistic earth ground at
8
15. Figure 4. Fresnel
reflection coefficient for
a vertically polarized
plane wave field
compared to “reflection
coefficient” as
calculated by complete
formulation for a
vertical dipole over
homogeneous earth as
observed at 1-m height
1000 m down range at a
frequency of 1.3 GHz:
(a) sea water, (b) wet
earth, (c) dry earth,
(d) lake water, and
(e) dry sand.
0 10 20 30 40 50 60 70 80 90
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Incidence angle (°)
Reflectioncoefficient 0 10 20 30 40 50 60 70 80 90
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Incidence angle (°)
Reflectioncoefficient
0 10 20 30 40 50 60 70 80 90
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Incidence angle (°)
Reflectioncoefficient
0 10 20 30 40 50 60 70 80 90
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Incidence angle (°)
Reflectioncoefficient
0 10 20 30 40 50 60 70 80 90
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Incidence angle (°)
Reflectioncoefficient
(a)
(c)
(e)
(d)
(b)
SIGMA = 4 S/m, EPSREL= 80
Fresnel Eq.
Complete Eq.
SIGMA = 0.4 S/m, EPSREL= 12
SIGMA = 0.04 S/m, EPSREL= 8 SIGMA = 0.004 S/m, EPSREL= 80
SIGMA = 0 S/m, EPSREL= 2
Fresnel Eq.
Complete Eq.
Fresnel Eq.
Complete Eq.
Fresnel Eq.
Complete Eq.
Fresnel Eq.
Complete Eq.
1.3 GHz. The horizontally polarized fields diverge from the Fresnel expres-
sions for low conductivities and relative dielectric constants. The resulting
total fields in such cases predicted by the Fresnel expressions will be larger
than the complete solution prediction. The results for vertical polarization
(fig. 4) show significant divergence for shallow incident angles. In this case
the resulting total fields predicted by the complete solution can be signifi-
cantly higher than that predicted from employing the Fresnel expressions.
9
17. Figures 6 and 7 are plots of the fields produced by the two-dipole orien-
tations; these plots compare the predominant field components for each
dipole orientation at 1000 and 100 m, respectively. The plots for the 100-m
case (fig. 7) show the beginning of the lobe effect produced by the phase
difference between the incident and reflected wave. This is shown more
dramatically in figure 8.
Figure 6. Comparison of
principal fields from an
ideal dipole oriented
perpendicular and
horizontal to a
homogeneous flat earth.
In each case, dipole is
placed 2 m above
ground plane and
observer or target is
1000 m down range:
(a) sea water, (b) wet
earth, (c) dry earth,
(d) lake water, and
(e) dry sand.
0 1 2 3 4 5 6 7
× 10–3
0
0.5
1
1.5
2
2.5
3
Normalized field magnitude (V/m)
Observerheight(m)
(a)
0
0
0.5
1
1.5
2
2.5
3
Normalized field magnitude (V/m)
Observerheight(m)
(d)
0
0
0.5
1
1.5
2
2.5
3
Normalized field magnitude (V/m)
Observerheight(m)
(e)
0
0
0.5
1
1.5
2
2.5
3
Normalized field magnitude (V/m)
Observerheight(m)
(c)
0
0
0.5
1
1.5
2
2.5
3
Normalized field magnitude (V/m)
Observerheight(m)
(b)
SIGMA = 4 S/m, EPSREL = 80
dipole height = 2 m, frequency = 1.3 GHz
range = 1000 m
Horizontal E-field, horizontal dipole
z-directed E-field, vertical dipole
SIGMA = 0.4 S/m, EPSREL= 12
dipole height = 2 m, frequency = 1.3 GHz
range = 1000 m
SIGMA = 0.04 S/m, EPSREL= 8
dipole height = 2 m, frequency = 1.3 GHz
range = 1000 m
SIGMA = 0.004 S/m, EPSREL= 80
dipole height = 2 m, frequency = 1.3 GHz
range = 1000 m
SIGMA = 0 S/m, EPSREL= 0.2
dipole height = 2 m, frequency = 1.3 GHz
range = 1000 m
1 2 3 4 5 6 7
× 10–3
1 2 3 4 5 6 7
× 10–3
1 2 3 4 5 6 7
× 10–3
1 2 3 4 5 6
× 10–3
Horizontal E-field, horizontal dipole
z-directed E-field, vertical dipole
Horizontal E-field, horizontal dipole
z-directed E-field, vertical dipole
Horizontal E-field, horizontal dipole
z-directed E-field, vertical dipole
Horizontal E-field, horizontal dipole
z-directed E-field, vertical dipole
11
18. Figure 7. Comparison of
principal fields from an
ideal dipole oriented
perpendicular and
horizontal to a
homogeneous flat earth.
In each case, dipole is
placed 2 m above
ground plane and
observer or target is
100 m down range:
(a) sea water, (b) wet
earth, (c) dry earth,
(d) lake water, and
(e) dry sand.
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.16 0.18 0.2
0
0.5
1
1.5
2
2.5
3
Normalized field magnitude (V/m)
Observerheight(m)
(a)
0
0.5
1
1.5
2
2.5
3
Normalized field magnitude (V/m)
Observerheight(m)
(d)
0
0.5
1
1.5
2
2.5
3
Normalized field magnitude (V/m)
Observerheight(m)
(e)
0
0.5
1
1.5
2
2.5
3
Normalized field magnitude (V/m)
Observerheight(m)
(c)
0
0.5
1
1.5
2
2.5
3
Normalized field magnitude (V/m)
Observerheight(m)
(b)
SIGMA = 4 S/m, EPSREL = 80
dipole height = 2 m, frequency = 1.3 GHz
range = 100 m
Horizontal E-field, horizontal dipole
z-directed E-field, vertical dipole
SIGMA = 0.4 S/m, EPSREL = 12
dipole height = 2 m, frequency = 1.3 GHz
range = 100 m
SIGMA = 0.04 S/m, EPSREL = 8
dipole height = 2 m, frequency = 1.3 GHz
range = 100 m
SIGMA = 0 S/m, EPSREL = 0.2
dipole height = 2 m, frequency = 1.3 GHz
range = 100 m
SIGMA = 0.004 S/m, EPSREL = 80
dipole height = 2 m, frequency = 1.3 GHz
range = 100 m
0.16 0.18 0.2 0.2
Horizontal E-field, horizontal dipole
z-directed E-field, vertical dipole
Horizontal E-field, horizontal dipole
z-directed E-field, vertical dipole
Horizontal E-field, horizontal dipole
z-directed E-field, vertical dipole
Horizontal E-field, horizontal dipole
z-directed E-field, vertical dipole
12
19. Figure 8. Effect of
ground reflection on
primary field
components near
ground for typical earth
parameters. Phase
difference between
incident and reflected
waves results in
development of field
lobes that are more
pronounced as
radiating antenna is
approached: (a) 100 m
down range and (b)
1000 m down range.
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
0
5
10
15
20
25
30
Normalized field magnitude (V/m)
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
0
5
10
15
20
25
30
Normalized field magnitude (V/m)
Observerheight(m)Observerheight(m)
(a)
(b)
SIGMA = 0.4 S/m, EPSREL = 12
dipole height = 2 m, frequency = 1.3 GHz
range = 1000 m
SIGMA = 0.4 S/m, EPSREL = 12
dipole height = 2 m, frequency = 1.3 GHz
range = 100 m
Horizontal E-field, horizontal dipole
z-directed E-field, vertical dipole
Horizontal E-field, horizontal dipole
z-directed E-field, vertical dipole
13
20. 3. Conclusion
A suite of MATLAB m-files have been developed to calculate the electro-
magnetic fields produced by a vertical and a horizontal infinitesimal unit
dipole over a homogeneous flat (ground) plane. Calculations for the fields
above the ground plane have been made for various ground-plane conduc-
tivities and relative dielectric constants. The calculations bound the practi-
cal range of parameters representative of natural earth terrain.
For a frequency of 1.3 GHz, where the dipole and the observer are close to
the ground plane (<3 m), significant difference is seen in the magnitude of
the fields from either dipole orientation. The power density on target will
be much larger for vertical dipole orientation. The effects of rough terrain,
foliage, or scattering from manmade or natural objects in the path from the
dipole to target may alter this conclusion. How these other scatterers might
affect the field structure at a target at 1.3 GHz is not known at this time. If
the effects are random in nature, the present conclusion is most likely still
valid. From the simple, smooth, flat ground model, then, one must con-
clude that vertical polarization (antenna radiating a vertically polarized
field) will deliver the most energy to the target. Unless the target’s pref-
erence for field orientation for maximum pickup is known, a vertically po-
larized antenna may in fact be the best choice for a ground weapon system.
14
21. References
Abramowitz, M., and I. A. Stegun, Handbook of Mathematical Functions, Na-
tional Bureau of Standards, Applied Mathematics Series–55, U.S. Depart-
ment of Commerce (1970).
Banos, A., Dipole Radiation in the Presence of a Conducting Half-Space, Perga-
mon, Oxford (1966).
Chase, R., MATLAB m-file, Plasma Dispersion Function with Complex Argu-
ment (unpublished).
Collin, R. E., Antenna and Radiowave Propagation, McGraw-Hill, New York
(1985).
Collin, R. E., and F. J. Zucker, Antenna Theory, Part 1, McGraw-Hill, New
York (1969).
King, R.W.P., and S. S. Sandler, “The electromagnetic field of a vertical elec-
tric dipole over the earth or sea,” IEEE Trans. Antennas Propag. 42, No. 3
(March 1994), pp 382–389.
King, R.W.P., M. Owens, and T. T. Wu, Lateral Electromagnetic Waves,
Springer-Verlag, New York (1992).
Maclean, T.S.M., and Z. Wu, Radiowave Propagation Over Ground, Chapman
and Hall, London (1993).
MATLAB, release 5.3, The Math Works, Inc., Natick, MA (1984–1999).
Sommerfeld, A., Partial Differential Equations in Physics, Academic Press,
New York (1949).
15
23. Appendix. MATLAB
m-Files
This appendix documents the MATLAB m-files that implemented the field
equations for the vertical and horizontal dipole and array cases. Slight mod-
ification may be required to obtain all the calculations presented.
WERF Function
function w = werf(z,N)
% WERF(Z,N) Plasma Dispersion Function with complex argument.
%
% Computes the function w(z)=exp(-z^2)*erfc(-iz) using a rational
% series with N terms. N should be a power of 2 or it gets SLOW.
% Default value of N is 64. z can be a matrix of values.
% Taken from Siam Journal on Numerical Analysis, Oct 1994, V31,#5.
% Modified by R. Chase to work for all z (4/3/95).
%
% N=32 gives approx 14 place accuracy, N=64 is better and
% it seems as fast.
%
% See wfn.m -- Draws graph in Abramowitz & Stegun,
% Handbook of Mathematical Functions, p. 298
if nargin == 1, N=64 end % Default value for N
M=2*N M2=2*M k= -M+1:1:M-1]' % M2=no. of sampling points
L=sqrt(N/sqrt(2)) % Optimal choice of L
theta=k*pi/M t=L*tan(theta/2) % Variables thetaand t
f=exp(-t.^2).*(L^2+t.^2) f= 0 f] % function to be transformed
a=real(fft(fftshift(f)))/M2 % Coefficients of transform
a=flipud(a(2:N+1)) % Reorder coefficients
nz=imag(z) <= 0 % Find im(z) <=0
z(nz)=conj(z(nz)) % Use conj for above
Z=(L+i*z)./(L-i*z) p=polyval(a,Z) % Polynomial evaluation
w=2*p./(L-i*z).^2+(1/sqrt(pi))./(L-i*z) % Evaluate w(z)
w(nz)=2*exp(-(conj(z(nz)).^2)) - conj(w(nz)) % Handle im(z) <= 0
%if all(imag(z)==0), w=real(w) end % Rtn real if real
17
24. Constants
function w,cv,epso,u0,zo,k0,k1,kappap,lo]=cnstdg(f)
% This m-file contains the basic constants to be used by various
% m-files and functions
%
% f is input in GHz
% global EPSREL SIGMA
w=2*pi*f*1e9
cv=2.99792458e8
epso=(1/(4*pi))*1e7*(1/cv^2)
eps1=EPSREL
u0=4*pi*1e-7
zo=sqrt(u0/epso)
k0=w*sqrt(epso*u0)
epsr=(eps1-j*SIGMA./(w*epso))
k1=k0*sqrt(epsr)
kappap=-k0/sqrt(epsr+1)
lo=cv/(f*1e9)
Vertical Dipole
function ez,er,hp]=dipg(f,d,rho,z)
%
% Electromagnetic fields from a vertical z-directed current element
% at a height, d, over a conducting dielectric plane (ground) calculated
% by the King/Sandler model. This formulation is that developed
% as equations 6, 7, and 8 of "The Electromagnetic Field of a Vertical Electric
% Dipole over the Earth or Sea", IEEE Trans. on Antennas and Propagation,
% March 1994, Vol 42 No. 3, page 383. It is the same as the King/Owens/Wu
% formulation. This formulation is that developed as equations 4.2.30-32 of
% "Lateral Electromagnetic Waves", Springer-Verlag, 1992, pp 293-297.
%
% > f- frequency rho- radial distance from the z-axis
% < z- height of observer above ground plane (input as an array)
% > ez,er,hp- field components at the observer, where the second letter
% < designates the component -- z, r (rho), p (phi)
%
% The formulation is subject to |k1(ground)|>3|k2(air)|
%
w,c,eps0,u0,zo,k2,k1,kappap,lo]=cnstdg(f)
%
18
25. % King, et. al assume an exp(-i*omega*time)dependency thus we convert k1
%
k1=conj(k1)
%N2=(k1/k2)^2
k21=k2/k1
%
% We assume a unit dipole
%
il=1
r1=(rho^2+(z-d).^2).^.5
r2=(rho^2+(z+d).^2).^.5
sd=rho./r1
sr=rho./r2
cd=(z-d)./r1
cr=(d+z)./r2
p=(r2*k2^3/(2*k1^2)).*((k2*r2+k1*(z+d))./(k2*rho)).^2
%
% The attenuation function less the exp(i*p) term - related to the
% error function is
%
Ferf=((1+i)/4)*werf(sqrt(i*p))
%
% Develop the terms for the field expressions
%
t1=w*u0*il/(2*pi*k2)
t11=-il/(2*pi)
t2=exp(i*k2*r1)/2
t3=(i*k2./r1)-(1./r1.^2)-i./(k2*r1.^3)
t31=(i*k2./r1)-(1./r1.^2)
t4=(cd.^2).*((i*k2./r1)-(3./r1.^2)-(3*i)./(k2*r1.^3))
t41=((i*k2./r1)-(3./r1.^2)-(3*i)./(k2*r1.^3))
t5=exp(i*k2*r2)/2
t6=(i*k2./r2)-(1./r2.^2)-i./(k2*r2.^3)
t61=(i*k2./r2)-(1./r2.^2)
t7=(cr.^2).*((i*k2./r2)-(3./r2.^2)-(3*i)./(k2*r2.^3))
t71=((i*k2./r2)-(3./r2.^2)-(3*i)./(k2*r2.^3))
t8=(2*t5*(k2^3)/k1).*((pi./(k2*r2)).^.5).*sr.*Ferf
t81=((k2^3)/k1)*((pi./(k2*r2)).^.5).*Ferf
t82=(2*t5.*(k2^3)/k1).*((pi./(k2*r2)).^.5).*Ferf
%
% Calculate the fields
% ez=t1*(t2.*(t3-t4)+t5.*(t6-t7)-t8)
er=-t1*(t2.*sd.*cd.*t41+t5.*sr.*cr.*t71-k21*2*t5.*(sr.*t61-t81))
hp=t11*(t2.*sd.*t31+t5.*sr.*t61-t82)
19
26. Horizontal Dipole
function ez,ep,er,hz,hp,hr]=dipgh(f,d,phi,rho,z)
%
% Electromagnetic fields from a horizontally directed (perpendicular to z)
% current element located in the phi=0 plane
% at a height, d, over a conducting dielectric plane (ground) calculated
% by the King/Owens/Wu formulation. This formulation is that developed
% as equations 7.10.75, 7.10.80, 7.10.84, 7.10.92, 7.10.93 and 7.10.94 of
% "Lateral Electromagnetic Waves", Springer-Verlag, 1992, pp 293-297.
%
% > f- frequency(GHz) phi- angle about the z-axis, rho- radial distance from
% < the z-axis, z- height of observer above ground plane (input as an array)
% > ez,ep,er,hz,hp,hr- field components at the observer, where the second
% < letter designates the component -- z, r (rho), p (phi)
%
%
% The formulation is subject to |k1(ground)|>3|k2(air)|
%
w,c,eps0,u0,zo,k2,k1,kappap,lo]=cnstdg(f)
%
% King, et. al assume an exp(-i*omega*time)dependency thus we convert k1
%
k1=conj(k1)
%N2=(k1/k2)^2
k21=k2/k1
k2p=k2/rho
%
% We assume a unit dipole
%
il=1
cp=cos(phi)
sp=sin(phi)
r1=(rho^2+(z-d).^2).^.5
r2=(rho^2+(z+d).^2).^.5
sd=r1/rho
sdo=1./sd
sr=r2/rho
sro=1./sr
cd=(z-d)./r1
cr=(d+z)./r2
p=(r2*k2^3/(2*k1^2)).*((k2*r2+k1*(z+d))./(k2*rho)).^2
20
27. %
% The attenuation function less the exp(i*p) term - related to the
% error function is
% Ferf=((1+i)/4)*werf(sqrt(i*p))
%
% Develop the terms for the field expressions
%
t1=w*u0*il*cp/(4*pi*k2)
t11=-w*u0*il*sp/(4*pi*k2)
t12=il*sp/(4*pi)
t13=il*cp/(4*pi)
t2=exp(i*k2*r1)
t32=(i*k2./r1)-(1./r1.^2)-i./(k2*r1.^3)
t3=(2./r1.^2)+2*i./(k2*r1.^3)
t31=(i*k2./r1)-(1./r1.^2)
t4=(cd.^2).*((i*k2./r1)-(3./r1.^2)-(3*i)./(k2*r1.^3))
t41=(cd).*((i*k2./r1)-(3./r1.^2)-(3*i)./(k2*r1.^3))
t5=exp(i*k2*r2)
t62=(i*k2./r2)-(1./r2.^2)-i./(k2*r2.^3)
t6=(2./r2.^2)+2*i./(k2*r2.^3)
t61=(i*k2./r2)-(1./r2.^2)
t7=(cr.^2).*((i*k2./r2)-(3./r2.^2)-(3*i)./(k2*r2.^3))
t71=(cr).*((i*k2./r2)-(3./r2.^2)-(3*i)./(k2*r2.^3))
t72=((1./r2.^2)+(3*i)./(k2*r2.^3)-3./((k2^2)*r2.^4))
t73=(cr.^2).*((i*k2./r2)-(6./r2.^2)-(15*i)./(k2*r2.^3))
t8=((k2^3)/k1)*((pi./(k2*r2)).^.5).*sr.*Ferf
t81=((k2^3)/k1)*((pi./(k2*r2)).^.5).*Ferf
t82=(2*t5*(k2^3)/k1).*((pi./(k2*r2)).^.5).*Ferf
t83=((pi./(k2*r2)).^.5).*Ferf
%
% Calculate the fields
%
ez=t1*(-t2.*sdo.*t41+t5.*sro.*t71-2*k21*t5.*(sro.*t61-t81))
er=t1*(t2.*(t3+t4)-t5.*(t6+t7-2*k21*t61+2*(k21^2)*(t62-t8)))
ep=t11*(t2.*t32-t5.*t62-t5.*(-2*k21*cr.*t61+2*(k21^2)*(t6+t7)...
+2*i*k21^3*k2p*(sr.^2).*t83))
hr=t12*(t2.*cd.*t31-t5.*cr.*t61+2*k21*t5.*(t6+i*k21*k2p*(sr.^2).*t83+t7))
hp=t13*(t2.*cd.*t31-t5.*cr.*t61+2*k21*t5.*(t62-k21*(k2^2)*(sr).*t83))
hz=t12*(t2.*sdo.*t31-t5.*sro.*t61+2*sro.*t5.*(k21*t71(k21^2)*(t72+t73)))
21
28. Plot m-File for Fields
%
% This m-file plots the fields over a conductive flat earth produced by an ideal
% dipole placed a distance d above the earth. It compares the results from
% a vertical and horizontal dipole.
%
%
% Establish the problem conditions
%
%
% EPSREL- Relative dielectric constant SIGMA- Earth conductivity (S/m)
%
EPSREL=80 SIGMA=4
global EPSREL SIGMA
%EPSREL=12 SIGMA=.4
%EPSREL=8 SIGMA=.04
%EPSREL=80 SIGMA=.004
%EPSREL=2 SIGMA=.000
%
% Location of dipole (m)
%
d=2
%
% Location of observer, rho (m) phi (radians) z (m) ---> an array
%
rho=1000
phi=pi/2
z=.1* 1:1:30]
%
% f- frequency in GHz
%
f=1.3
%
% Field normalization factor - one Watt radiated
%
w,c,eps0,u0,zo,k2,k1,kappap,lo]=cnstdg(f)
Fn=sqrt(12*pi/((k2^2)*zo))
%
% Horizontal dipole fields
%
ez,ep,er,hz,hp,hr]=dipgh(f,d,phi,rho,z)
plot(Fn*abs(ep),z,'-b')
hold
22
29. %
% Vertical dipole fields
%
ezv,erv,hpv]=dipg(f,d,rho,z)
plot(Fn*abs(ezv),z,'-.r')
ts=Fn*abs(erv(1))
title('Vertical and Horizontal Ideal Dipole fields over Ground')
text(ts,z(19), 'SIGMA = ',num2str(SIGMA),' S/m EPSREL=
',num2str(EPSREL)])
text(ts,z(18), 'Dipole height = ',num2str(d),' meters Frequency =
',num2str(f),' GHz'])
text(ts,z(17), 'Range = ',num2str(rho),' meters'])
ylabel('Observer height - meters')
xlabel('Normalized field magnitude - V/m')
legend('Horizontal E-field, horizontal dipole','z-directed E-field,
vertical dipole')
hold
Fresnel Reflection Coefficients and Plots
function rcomv,rcomh]=Fresnel1(f,psi)
%
% This routine calculates the Fresnel reflection coefficients for
% vertical and horizontal incident fields
%
% after Collin, "Antenna and Radiowave Propagation", page 345
%
% f-frequency in GHz psi- array of incident angles
%
% Code returns the arrays rcomv and rcomh, the vertical and horizontal
% complex reflection coefficients, respectively.
%
global EPSREL SIGMA
w=2*pi*f*1e9
cv=2.99792458e8
epso=(1/(4*pi))*1e7*(1/cv^2)
epsr=(EPSREL-j*SIGMA./(w*epso))
rcomv=(epsr*sin(psi)-sqrt(epsr-cos(psi).^2))./(epsr*sin(psi)+sqrt(epsr-cos(psi).^2))
rcomh=(sin(psi)-sqrt(epsr-cos(psi).^2))./(sin(psi)+sqrt(epsr-cos(psi).^2))
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%
23
30. % This m-file plots the reflection coefficient for vertical and horizontal
% fields over a homogeneous ground plane
%
%
% EPSREL- Relative dielectric constant SIGMA- Earth conductivity (S/m)
%
EPSREL=80 SIGMA=4
f=1.3
global EPSREL SIGMA
psi= pi/1000:pi/1000:pi/2]
rcomv,rcomh]=Fresnel1(f,psi)
EPSREL=12 SIGMA=.4
rcomv1,rcomh1]=Fresnel1(f,psi)
EPSREL=8 SIGMA=.04
rcomv2,rcomh2]=Fresnel1(f,psi)
EPSREL=80 SIGMA=.004
rcomv3,rcomh3]=Fresnel1(f,psi)
EPSREL=2 SIGMA=.000
rcomv4,rcomh4]=Fresnel1(f,psi)
subplot(2,2,1),plot((180/pi)*psi,abs(rcomv),'k')
hold
axis( 0,90,0,1])
xlabel('Incidence angle (degrees)')
ylabel('Reflection Coefficient')
%text(5,.8, 'SIGMA = ',num2str(SIGMA),' S/m EPSREL= ',num2str(EPSREL)])
subplot(2,2,1),plot((180/pi)*psi,abs(rcomv1),'r')
subplot(2,2,1),plot((180/pi)*psi,abs(rcomv2),'b')
subplot(2,2,1),plot((180/pi)*psi,abs(rcomv3),'g')
subplot(2,2,1),plot((180/pi)*psi,abs(rcomv4),'c')
hold
subplot(2,2,2),plot((180/pi)*psi,(180/pi)*angle(rcomv),'k')
hold
axis( 0,90,-190,5])
xlabel('Incidence angle (degrees)')
ylabel('Phase')
subplot(2,2,2),plot((180/pi)*psi,(180/pi)*angle(rcomv1),'r')
subplot(2,2,2),plot((180/pi)*psi,(180/pi)*angle(rcomv2),'b')
subplot(2,2,2),plot((180/pi)*psi,(180/pi)*angle(rcomv3),'g')
subplot(2,2,2),plot((180/pi)*psi,-(180/pi)*angle(rcomv4),'c')
hold
subplot(2,2,3),plot((180/pi)*psi,abs(rcomh),'k')
24
31. hold
axis( 0,90,.5,1])
xlabel('Incidence angle (degrees)')
ylabel('Reflection Coefficient')
subplot(2,2,3),plot((180/pi)*psi,abs(rcomh1),'r')
subplot(2,2,3),plot((180/pi)*psi,abs(rcomh2),'b')
subplot(2,2,3),plot((180/pi)*psi,abs(rcomh3),'g')
subplot(2,2,3),plot((180/pi)*psi,abs(rcomh4),'c')
hold
subplot(2,2,4),plot((180/pi)*psi,(180/pi)*angle(rcomh),'k')
hold
axis( 0,90,170,200])
xlabel('Incidence angle (degrees)')
ylabel('Phase')
subplot(2,2,4),plot((180/pi)*psi,(180/pi)*angle(rcomh1),'r')
subplot(2,2,4),plot((180/pi)*psi,(180/pi)*angle(rcomh2),'b')
subplot(2,2,4),plot((180/pi)*psi,(180/pi)*angle(rcomh3),'g')
subplot(2,2,4),plot((180/pi)*psi,(180/pi)*angle(rcomh4),'c')
hold
25
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NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)
Prescribed by ANSI Std. Z39-18
298-102
Propagation of Electromagnetic Fields Over Flat Earth
February 2001 Summary, Oct 99 to Sept 00
This report looks at the interaction of radiated electromagnetic fields with earth ground in military or law-
enforcement applications of high-power microwave (HPM) systems. For such systems to be effective, the
microwave power density on target must be maximized. The destructive and constructive scattering of the
fields as they propagate to the target will determine the power density at the target for a given source. The
question of field polarization arises in designing an antenna for an HPM system. Should the transmitting
antenna produce vertically, horizontally, or circularly polarized fields? Which polarization maximizes the
power density on target? This report provides a partial answer to these questions. The problems of calculating
the reflection of uniform plane wave fields from a homogeneous boundary and calculating the fields from
a finite source local to a perfectly conducting boundary are relatively straightforward. However, when the
source is local to a general homogeneous plane boundary, the solution cannot be expressed in closed form. An
approximation usually of the form of an asymptotic expansion results. Calculations of the fields are provided
for various source and target locations for the frequencies of interest. The conclusion is drawn that the resultant
vertical field from an appropriately oriented source antenna located near and above the ground can be
significantly larger than a horizontally polarized field radiated from the same location at a 1.3 GHz frequency
at observer locations near and above the ground.
Antenna, ground interaction
Unclassified
ARL-TR-2352
0NE6YY
622705.H94
AH94
62705A
ARL PR:
AMS code:
DA PR:
PE:
Approved for public release; distribution
unlimited.
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Attn: AMSRL-SE-DS jmiletta@arl.army.mil
U.S. Army Research Laboratory
Joseph R. Miletta
email:
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33
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29