Determining the strength and orientation of an elevated dipole

The electromagnetic field expressions of an elevated electric dipole above a flat perfectly conducting ground plane are presented. It is shown that surface-based measurements at a specified location, of the vertical electric field and the horizontal magnetic fields permit a unique determination of the strength and orientation of the dipole     

ELF and VLF fields of a horizontal electric dipole

The waves in the spherical guide between the earth and ionosphere are excited by a horizontal electric dipole. The guide boundaries are characterized by surface impedances and the resulting waves are expressed as a superposition of TM and TE modes. The wavenumbers, excitation factors, height-gain functions, and height-dependent impedances are examined for both types of modes. A thin-shell approximation of the radial wave functions is shown to be adequate for phase velocity estimates; but other propagation parameters are of restricted validity in the VLF range where Airy integral approximations provide more reliable data. A horizontal electric dipole is shown to provide a nearly omnidirectional coverage of horizontal field components in the frequency range of the lower Schumann resonances. For an elevated source the horizontal fields are essentially omnidirectional also in the VLF range. Near fields are expressed as a summation of waveguide modes. The vertical field components vanish at the antipode, but the horizontal components remain of finite magnitude.     

Analysis of Airborne VHF Incidental Noise over Metropolitan Areas-Part II: Horizontal Dipole Antenna

Computation of the incidental, quasi-peak electric field intensity detected by an airborne, tuned, horizontal dipole antenna has been performed using a symmetrical representation of measured, surface man-made incidental radio noise data and the radiation field integral for the observed power at a height, h, above the surface. The derived electric field intensity as a function of observer altitude is compared with the results of four sets of measurements obtained over central Tokyo by Ishida for heights lying between 0.3 and 3 km. The comparisons reveal that the dependence upon altitude of the predicted quasi-peak electric field strength agrees with the observed trends and, further, that the measured and predicted field intensities display an average difference of less than 0.7 dB. These results and experimental comparisons for a tuned, airborne, horizontal dipole antenna complement the experimental confirmations of a comparable analysis previously reported for vertical, tuned, airborne dipole and monopole antennas.     

地下SLF/ELF水平电偶极子在球形地-电离层中产生的场

在非理想导电地面与电离层条件下,导出了地下SLF/ELF水平电偶极子在地上、地下及电离层中产生的电磁场的球谐级数表达式.并提出了一种加速收敛算法,算出了大气层及电离层中的电磁场分布.计算结果表明:地下几十公里的水平电偶极子产生的场除了增加了一个固定衰减外,与地面上的水平电偶极子产生的场分布完全相似,它产生的电磁场可理解为电波首先垂直地透过土壤,然后在地一电离层腔体中传播.在SLF频段,地一电离层空腔中的电磁场可理解为两个"行波"的叠加.在ELF频段,空腔中的电磁场是驻波,其频率变化规律能正确反映出"舒曼"谐振现象.     

The excitation of current on an infinite horizontal wire above earth by a vertical electric dipole

The formal solution to the problem of finding the current induced on a horizontal wire above earth by a vertical electric dipole is given. A simple solution for the case where the dipole is electrically distant from the wire is developed. The interpretation and restrictions of this solution are discussed.     

Radiation fields from an electric dipole antenna in homogeneous Antarctic terrain

The radiation fields from an electric dipole antenna in homogeneous Antarctic terrain are analyzed. The terrain is represented as a semi-infinite ice medium with a complex dielectric constant dependent upon temperature and frequency. The space and ground waves from a horizontal dipole are evaluated initially for different ice conditions. Similar evaluations arc extended to a vertical dipole to apply superposition to the general case of an inclined dipole in Antarctic ice.     

On the input impedance of a Hertzian dipole over a flat surface

An explicit formula is derived for the change of input impedance of a vertical electric dipole as a function of the distance of the dipole to a horizontal boundary with a prescribed surface impedancen. It is shown that, ifn ll 120pi, the result is consistent with the formula obtained by the compensation-theorem approach.     

Exact image theory for the Sommerfeld half-space problem, part III: General formulation

The general Sommerfeld problem with bothepsilonandmudiscontinuous and a source consisting of arbitrarily oriented electric and/or magnetic dipoles at the same location is considered in terms of image theory. The problem is formulated with electric and magnetic fields instead of potential quantities resulting in a vector transmission-line interpretation of the Fourier transformed problem. The image sources are seen to be located in complex space expressable in terms of a certain basic image current function, which was encountered in part II of this paper on the vertical electric dipole problem. The horizontal electric/magnetic dipole image is solved and found to consist of both vertical and horizontal current components. The image concept is generalized to the most general three-dimensional sources. As a check, the well-known reflection coefficient method is obtained as the far-field approximation of the present theory.     

Electromagnetic fields due to dipole antennas embedded in stratified anisotropic media

A method is presented for calculating the electric and magnetic fields from dipoles embedded in anisotropic stratified media. By decomposing the fields into transverse electric (TE) and transverse magnetic (TM) modes, the results are obtained more directly and are more computationally efficient than methods using the Hertz potential. The electromagnetic fields are obtained for four types of dipole sources: horizontal electric, horizontal magnetic, vertical electric, and vertical magnetic. The source is embedded within one of several anistropic layers, which are further sandwiched between two semi-infinite media.     

Image theory for electric dipoles above a conducting anisotropic earth

New image representations for vertical electric dipoles (VED) above an imperfectly conducting and axially anisotropic earth are developed. These include multidiscrete images at different depths below the air-earth interface and multipole image sources. It is shown that, in contrast with the available image representations in the literature, the developed ones predict the correct behavior of the fields in the far zone along the earth's surface. Extension to a layered earth's model is made. The theory is also extended to the horizontal electric dipole with similar conclusions to the case of the vertical dipole.     

Air to undersea communication with magnetic dipoles

Simplified expressions are derived for the electromagnetic fields produced by a vertical or horizontal magnetic dipole (loop antenna) located in air above the sea. The expressions hold over the quasi-near range in both media subject to certain mild restrictions. The solutions are obtained by first applying the boundary conditions to determine the magnetic Hertz potentialbar{pi}^{ast}in the form of Sommerfeld integrals, and then relating these to two auxiliary integralsU, Vand their derivatives, asymptotic series for which are obtained by extending the work of Baños and Wesley. The horizontal magnetic dipole (loop in the vertical plane) is found to be superior to the vertically-oriented dipole of the same size and excitation from the point of view of field strength induced in the sea at large distances from the source. A comparison with previously published results for the electric dipole shows the magnetic dipole to be better, provided the number of turns in the loop exceeds a certain minimum. An approximate analysis on the basis of equal powers also shows the magnetic dipole to be better except for points near the outer rim of the quasi-near range, where the two types of dipoles are equivalent.     

水平电偶极子在负折射媒质半空间激励的场

讨论了水平电偶极子在由介电常数和磁导率都为负数的媒质和普通媒质构成的均匀半空间中激励的电磁场,并得出了远区场的解析表达式.理论分析和数值计算结果表明:位于普通介质中的水平电偶极子在普通媒质和负折射媒质分界面能够有效激励表面波.该表面渡是一种"慢波",沿分界面传播的波数小于波在两种均匀媒质中传播的波数.当两种介质均无损耗时,沿径向传播的幅度按波的几何扩散衰减.由于存在三种传播波数,表面波、侧面波、直达波和反射波共同作用形成的总场将发生复杂的干涉现象.     

Analysis of an infinite phased array of dipole elements with RAMcoating on ground plane and covered with layered radome

An analysis of an infinite array of dipole elements over a radar absorbing material (RAM) coated ground plane and covered with a radome is presented. The radiation impedance of the dipole element is obtained when the array is in transmitting mode, and a scattering analysis is carried out when the array is excited by an incoming plane wave and the dipole elements are terminated in loads. The electric field Green's function in terms of Floquet mode expansion due to a periodic δ-function horizontal dipole source is derived to satisfy the layered boundary conditions. The method of moments is used to solve the current distribution on the dipole. Numerical calculation of the radiation impedance of a dipole array covered with a radome has been verified with results from waveguide simulator measurements. Numerical examples are given to show the effect of the RAM coated ground plane on the radiation impedance and the scattering characteristics     

位于介质覆盖的导电基底中水平电偶极子的场

讨论了位于有介质层覆盖的非理想导电基底中的水平电偶极子激励起的电磁场,获得了方便于计算的解析表达式,并进行了数值计算和讨论。     

Electromagnetic fields due to a horizontal electric dipole antenna laid on the surface of a two-layer medium

With applications to geophysical subsurface probings, electromagnetic fields due to a horizontal electric dipole laid on the surface of a two-layer medium are solved by a combination of analytical and numerical methods. Interference patterns are calculated for various layer thickness. The results are interpreted in terms of normal modes and the accuracies of the methods are discussed.     

Modeling of simple antennas near to and penetrating an interface

Some results are presented for horizontal and vertical electric dipole antennas as they are brought close to, or penetrate, the interface between two half-spaces. The model used is an electric-field integral equation together with the Sommerfeld solution for the fields caused by the interface.     

地下水平电偶极子在均匀球形地面产生的侧面波

讨论了位于地下的水平电偶极子在均匀球形地面上产生的侧面波（Lateral wave)。从位于球形地面场的垂直电偶极子和磁偶极子在地面上建立的电磁场出发，利用互易定理，获得了地下水平电偶极子在地面上和地面下产生的既方便于数值计算又具有足够精度的电磁场的解析表达式。计算结果表明，由于地球曲率的影响，沿球形地面传播的侧面波比沿平行地面传播的侧面波衰减的快，当收发地点的距离超过40km后，地球曲率对传播的影响就不能被忽视，对地下通信以及潜艇通信有一定指导意义。     

Optimization of radio communication in media with three layers

The electromagnetic radiation of an electric dipole in a medium with three layers is examined using dyadic Green's functions. The far zone field for problems of this nature is primarily determined from the lateral wave. It is shown that the excitation of this wave may be reinforced through a dipole inclination and an optimum position may be determined. The radio losses for typical forests were calculated for vertical and horizontal dipoles and for dipoles with an optimum inclination. The theoretical results are in good agreement with the available experimental data.     

Geophysical subsurface probing with a horizontal magnetic dipole

The use of a horizontal magnetic dipole in geophysical subsurface probing with the electromagnetic fringes method is investigated. It is found that when placed on the surface of a half-space medium, angles of maximum power coupling into the medium occur atsin^{-1} ((1 + n^{2})/2n^{2})^{1/2}in the endfire direction andsin^{-1} (1/n)in the broadside direction, wherenis the refractive index of the half-space medium. Also the broadside radiation pattern exhibits a sharper maximum as compared with that of a horizontal electric dipole, which provides a clearer indication of the depth of a subsurface layer.