Conducting Ground Plane Research Articles

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.

Integrals for the mutual coupling between dipoles or between slots: with or without complex conjugate?

Derivations are given for two integral expressions that give the mutual impedance between dipoles, and a comparison is made. This leads to the conclusion that the expression without the complex conjugate, based on reciprocity, has to be preferred. The expression with complex conjugate, the induced-electromotive-force (EMF) method, is not exact. For practical purposes, however, both are often equivalent. For the mutual admittance between slots in a conducting ground plane, or magnetic currents, the conclusions are reversed: the induced-EMF method is the preferred one, while the reciprocity method is only valid for purely real slot excitations or current distributions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Circular array of outward sloping monopoles for vehicular diversity antennas

A circular array of outward-sloping monopoles is analyzed as a diversity antenna for vehicle rooftop mounting. The monopoles are assumed to approximate minimum scattering antennas, have sinusoidal current distributions, and reside on an infinite, perfectly conducting ground plane. The envelopes of the received signals are considered Rayleigh distributed. The advantage of the array configuration is that the feedpoint spacing can be made almost arbitrarily small, even for a large number of branches. A three-element array with element lengths of 0.6 wavelengths and feedpoint spacing 0.1 wavelengths operating at 463 MHz was field-tested and the results are in good agreement with the analysis.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Surface waves on a lossy planar ferrite slab

The parallel-polarized surface waves which propagate on a planar ferrite slab are considered. The ferrite material is isotropic and homogeneous, the slab rests on a perfectly conducting ground plane, and the ambient medium is free space. Only one mode can propagate on a thin lossless slab, but more and more of the higher order modes begin to propagate when one increases the thickness or the loss tangent of the slab. As the thickness and the loss are increased, the lowest order mode takes on the properties of the Zenneck wave. At the same time, the higher order modes take on the properties of a homogeneous plane wave propagating in the grazing direction in the slab. Among the most interesting properties of a surface wave are the attenuation constant and the phase velocity. Contour maps are included to show how these quantities depend on the thickness, permittivity, permeability and loss tangents of the ferrite slab. Additional insight is provided by graphs showing the root trajectories, cutoff boundaries and field distributions of the four lowest order surface-wave modes.

Radiation resistance of thin antennas of arbitrary elevation and configuration over perfectly conducting ground

Dipole segmentation is used to estimate the radiation resistance of thin antennas of arbitrary elevation and configuration over a perfectly conducting ground plane. Utility of the method for estimating the radiation resistance of VLF/LF trailing wire antennas from aircraft depends upon the extent to which the current distribution deviates from a sinusoid. That deviation is due in part to finite wire thickness as well as the finite conductivity of both wire and ground. The influence of those effects requires further study.

Surface currents induced on a circular strip

The problem of the induced surface currents on a perfectly conducting circular strip mounted on a perfectly conducting ground plane is considered. The induced currents are due to the radiated fields of an electric dipole source on the axis of the circular strip. An electric field integral equation is formulated in terms of the induced surface current and solved in closed form in the quasi‐static limit as an expansion of Chebyshev polynomials. In addition, the integral equation is solved for the general case by the method of moments. Numerical results are given which show the excellent agreement between the quasi‐static and method of moments solutions, and results are given which show the effects of varying the radius and the height of the strip, and the location of the dipole source.

Erratum: Exact image method for field calculation in horizontally layered medium above a conducting ground plane

Erratum: Exact image method for field calculation in horizontally layered medium above a conducting ground plane

Millimeter wave microstrip circulator

A millimeter wave microstrip Y-junction circulator is provided comprising a monolithic, wye-shaped ferrite element disposed on one surface of a section of microstrip dielectric substrate having three, Y-junction oriented sections of microstrip conductor on the same one substrate surface and an electrically conductive ground plane on the opposite substrate surface. The ferrite element has a central right prism-shaped portion with two equilateral triangular-shaped prism bases and three rectangular prism faces and three downwardly-sloping arm portions which extend radially outwardly from the prism faces of the central portion. The top base of the ferrite element central portion and the top surface of the ferrite arm portions which do not rest on the substrate are provided with microstrip conductors which cooperate with the ground plane to convey millimeter wave signals applied to the three Y-junction oriented microstrip sections on the substrate to the ferrite element central portion. A permanent magnet mounted on the ground plane beneath the bottom prism base causes the ferrite element central portion to act as a circulator to selectively couple the three microstrip sections on the substrate.

Exact image method for field calculation in horizontally layered medium above a conducting ground plane

It is shown that the inverse Laplace transform of the Fourier domain reflection coefficient of a layered medium can be easily derived by performing the Mittag-Leffler expansion. Thus exact image theory can be used in field calculations. The radiation pattern is readily deduced from the image functions and the surface wave is also deduced from the field integrals. As applied to microstrip structures, the asymptotic approximations agree with the Sommerfeld formulas.

Circuit-Concept Approach to Externally Excited Transmission Lines

The coupling of external electromagnetic waves to transmission lines is developed using a circuit-analysis concept. The validity of forcing terms of line equations reported in the literature is confirmed by experimental results of a wire model that is installed above a "perfectly" conducting ground plane and excited by plane waves of parallel and perpendicular polarizations. Equivalent-circuit representations are derived from solutions of the equations. These are versatile expressions for prediction of coupling of external waves to various types of lines. Coupling, externally excited transmission line, line equations, forcing terms.

Shielding of Electromagnetic Fields of Current Sources by Hemispherican Enclosures

Presented here is a theory of electromagnetic shielding of fields due to current sources by an imperfectly conducting, hemispherican, open shell with its rim in contact with a perfectly conducting ground plane. Expressions for the shielding effectiveness (SE) of the enclosure excited by Hertzian dipole sources have been derived. Numerican values of SE obtained from these expressions have been compared with those for a similarly excited imperfectly conducting spherical shell [9].

A theoretical study of electrostatic field wave shapes from lightning leaders

Electrostatic dE/dt field wave shapes are calculated for various lightning leader models over a perfectly conducting ground plane. These provide an improved theoretical basis for the characterization and interpretation of observed leader wave shapes for close lightning. Since dE/dt at a particular time is a function of how the leader tip is propagating, whereas the total electric field change at the same time is a function of the aggregate behavior of the leader up to this time, dE/dt is the preferable parameter for leader characterization. In particular, whether or not dE/dt changes polarity in the course of the leader is independent of the channel charge distribution, unlike the polarity of the net field change. The dE/dt wave shape is also more easily interpreted in terms of channel geometry than the electric field wave shape for leader channels that have branches or are not vertical. Features of dE/dt are derived for a vertical, one‐dimensional leader channel assuming an electrostatic relation, and deviations from this model are studied for both inclined channels and three‐dimensional charge distributions. The existence of a turning point (dE/dt = 0) in the electric field wave shape is investigated, and the distance dependence of the leader tip height corresponding to an electric field turning point is presented. For a vertical channel the final leader current IL0 is shown to be related to the final dE/dt, (dE/dt)0, by IL0 = −2πε0[H2 + D2]3/2 (dE/dt)0/H, where H is the height above ground level and D is the horizontal distance for the charge center which is the origin of the leader charge. The physical validity of the leader models used is discussed, and some applications of the derived plots are considered.

Computation of Inductance of Simple Vias Between Two Striplines Above a Ground Plane (Short Papers)

In this paper, an analysis is developed for calculating the lumped inductance of a simple via connecting two infinitely thin striplines, located above a perfectly conducting ground plane. The striplines are oriented in the same direction, and the via is assumed to be in the form of an infinitely thin vertical plate, connecting the two lines. This system is analyzed by a hybrid partial-element and circuit-theory approach. Numerical results are presented to illustrate the application of this technique.

Electromagnetic transmission through mesh covered apertures and arrays of apertures in a conducting screen

The problem of electromagnetic transmission through wire mesh covered arbitrarily shaped aperture or arrays of apertures (possibly covered by a thin lossy dielectric sheet) in a perfectly conducting ground plane is considered. The equivalence principle and image theory are used to derive an integral equation for the equivalent magnetic currents. The method of moments is utilized to solve the integral equation, with the aperture modeled by triangular patches. Numerical results are presented for transmission coefficients and transmission cross-section patterns for electrically small apertures.

Broad-band half-wave dipole

An ultrahigh frequency (UHF) fan-dipole is optimized for wide-band operation near the first resonance in order that the antenna could be used in a planar array of half-wavelength spaced elements operating over a conducting ground plane. The resultant voltage standing-wave ratio (VSWR) of the optimized dipole (with a 50 \Omega coax input) is less than 2:1 over a 37 percent bandwidth.

Analysis of monopole antenna with ground wires

AbstractA monopole antenna with ground wires excited at the terminal between the vertical and several ground wires is analyzed by varying the length of the vertical element, the lengths and numbers of ground wires and their angles of inclination. the characteristics of the structure are analyzed for an antenna with a quarter‐wavelength monopole element on a perfectly conducting ground plane. In the numerical analysis the effect of the feeder is neglected and a Hallen‐type integral equation with a simplified kernel is used. In the experiment the center conductor of the coaxial feeder is connected to the monopole and the outer conductor is connected to the ground wires. the effect of a sperrtopf, which prevents leakage current from flowing on the outer conductor, is studied. From the analytical results it is found that the gain of the monopole antenna with ground wires does not exceed that of a half‐wave dipole even if the length of the monopole is made about a quarter wavelength and the ground wires are directed 60° downward. When the antenna is on a perfect ground plane, the directivity strongly depends on the distance between the feed and the conducting plane and becomes maximum when the distance is about 0.3 wavelength. When the ground wires are 0.2 wavelength long and the angle of inclination is 300 the antenna is matched with a 50‐Ω feed line and the gain becomes 4 dB.

The synthesis of surface reactance using an artificial dielectric

A thin artificial dielectric layer consisting of a rectangular array of closely spaced, thin conductive cylinders (pins), was constructed above a perfectly conducting ground plane. The reactance of the surface was measured at 4.8 GHz for a variety of pin heights and dielectric embedding material by measuring the height-gain profile of a transverse magnetic (TM) surface wave launched across it. Design equations using the theories of artifical dielectrics and propagation in anisotropic media are given. These can be used to predict the surface reactance providing a correction factor accounting for fringing fields at the tops of the pins is included. Using an embedding dielectric tends to reduce this fringing effect.

PERFORMANCE OF AN ARRAY OF VERTICAL DIPOLES OVER AN INHOMOGENEOUS GROUND SYSTEM

The elevation radiation patterns of a stacked array of vertical electric dipoles (VEDs) over several different azimuthally symmetric inhomogeneous ground systems are studied using an integral formulation. As the ground influences the pattern of each VED differently, there is no known optimum array excitation which can be used to achieve desired beam shaping and steering. Patterns in an array of 21 VEDs spaced 0.1 lambda apart are computed and compared to HF (10 MHz) for three excitation functions: (a) conventional linear spacial phasing, (b) phasing according to the complex conjugate of the field produced by each VED in the direction of steering, and (c) spacially sinusoidal excitation with constant phasing. Results are given for grounds consisting of homogeneous earth, a perfectly conducting ground plane, a perfectly conducting disk on homogeneous earth and 2 lambda long radial wire ground systems on well- and poorly-conducting earth. It is found that the radiation pattern cannot be steered below about 9/sup 0/ in elevation for any of the excitation functions or the ground systems used. For low-angle steering conjugate excitation produces a slightly narrower beam with smaller sidelobes. Highly conducting grounds tend to permit steering to slightly higher elevations with narrower beams.

The phase center of a monopole antenna

In Doppler satellite positioning techniques the receiver is often equipped with a monopole antenna. The location of the phase center of this antenna is needed if high accuracy positioning is to be achieved. The phase center, however, changes with the direction of incidence of the received electromagnetic wave. In this paper the phase center is calculated for the idealized model of a monopole antenna with an infinitely large, perfectly conducting ground plane. The analysis is carried out by using the boundary integral equation method for determining the surface current density on the conducting parts of the configuration.

Determination of electric current distributions in animals and humans exposed to a uniform 60-Hz high-intensity electric field.

The thermographic method for determining specific absorption rate (SAR) in animals and models of tissues or bodies exposed to electromagnetic fields was applied to the problem of quantifying the current distribution in homogeneous bodies of arbitrary shape exposed to 60-Hz electric fields. The 60-Hz field exposures were simulated by exposing scale models of high electrical conductivity to 57.3-MHz VHF fields of high strength in a large 3.66 X 3.66 X 2.44-m TE101 mode resonant cavity. After exposure periods of 2-30 s, the models were quickly disassembled so that the temperature distribution (maximum value up to 7 degrees C) along internal cross-sectional planes of the model could be recorded thermographically. The SAR, W', calculated from the temperature changes at any point in the scale model was used to determine the SAR, W, for a full-scale model exposed to a 60-Hz electric field of the same strength by the relation W = (60/f')2 . (sigma'/sigma) . W' where f' is the model exposure frequency, sigma' is the conductivity of the scale model at the VHF exposure frequency, and sigma is the conductivity of the full-scale subject at 60 Hz. The SAR was used to calculate either the electric field strength or the current density for the full-scale subject. The models were used to simulate the exposure of the full-scale subject located either in free space or in contact with a conducting ground plane. Measurements made on a number of spheroidal models with axial ratios from 1 to 10 and conductivity from 1 to 10 s/m agreed well with theoretical predictions. Maximum current densities of 200nA/cm2 predicted in the ankles of man models and 50 nA/cm2 predicted in the legs of pig models exposed to 60-Hz fields at 1kV/m agreed well with independent measurements on full-scale models.