Showing papers in "IEEE Transactions on Antennas and Propagation in 1971"
TL;DR: In this article, a theory of characteristic modes for conducting bodies is developed starting from the operator formulation for the current, and the modes are the same ones introduced by Garbacz to diagonalize the scattering matrix of the body.
Abstract: A theory of characteristic modes for conducting bodies is developed starting from the operator formulation for the current. The mode currents form a weighted orthogonal set over the conductor surface, and the mode fields form an orthogonal set over the sphere at infinity. It is shown that the modes are the same ones introduced by Garbacz to diagonalize the scattering matrix of the body. Formulas for the use of these modes in antenna and scatterer problems are given. For electrically small and intermediate size bodies, only a few modes are needed to characterize the electromagnetic behavior of the body.
1,432 citations
TL;DR: In this article, a method is described for determining characteristic mode currents on thin wires of general shape and is applied to several shapes to generate certain backscattering and input admittance data.
Abstract: At a given frequency every perfectly conducting obstacle has associated with it a particular set of surface currents and corresponding radiated fields which are characteristic of the obstacle shape and independent of any specific excitation. These characteristic modes form a useful basis set in which to expand fields radiated or scattered at a great distance from the obstacle. Once these modes are known for a given obstacle, the scattering of plane waves incident from arbitrary source directions into arbitrary receiver directions may be evaluated concisely. To support the theory, a method is described for determining characteristic mode currents on thin wires of general shape and is applied to several shapes to generate certain backscattering and input admittance data. Wherever possible comparison is made with existing data.
625 citations
TL;DR: In this paper, a procedure for computing the characteristic modes for conducting bodies of arbitrary shape is developed, which can be applied to conducting body of revolution and to wire objects, and general computer programs are discussed.
Abstract: A procedure for computing the characteristic modes for conducting bodies of arbitrary shape is developed. The method is applied to conducting bodies of revolution and to wire objects, and general computer programs are discussed. Illustrative examples of the computation of characteristic currents and characteristic fields are given for a cone-sphere, a disk, and a wire arrow. Modal solutions using these modes are computed for representative antenna and scattering problems to illustrate convergence of the solution as the number of modes is increased.
518 citations
TL;DR: In this article, a new recursion relation is derived which reduces the computation effort by several orders of magnitude so that a quantitative analysis for spheres as large as 10 λ in radius at a spacing as small as two spheres in contact becomes feasible.
Abstract: Solution to the multiple scattering of electromagnetic (EM) waves by two arbitrary spheres has been pursued first by the multipole expansion method. Previous attempts at numerical solution have been thwarted by the complexity of the translational addition theorem. A new recursion relation is derived which reduces the computation effort by several orders of magnitude so that a quantitative analysis for spheres as large as 10\lambda in radius at a spacing as small as two spheres in contact becomes feasible. Simplification and approximation for various cases are also given. With the availability of exact solution, the usefulness of various approximate solutions can be determined quantitatively. For high frequencies, the ray-optical solution is given for two conducting spheres. In addition to the geometric and creeping wave rays pertaining to each sphere alone, there are rays that undergo multiple reflections, multiple creeps, and combinations of both, called the hybrid rays. Numerical results show that the ray-optical solution can be accurate for spheres as small as \lambda/4 in radius is some cases. Despite some shortcomings, this approach provides much physical insight into the multiple scattering phenomena.
306 citations
TL;DR: In this article, the backscatter cross section of high-frequency irradiated turbulent dielectric media, many mean free paths L 1/3 wide, was computed for a given medium width.
Abstract: The backscatter cross section Q for high-frequency irradiated turbulent dielectric media, many mean free paths L_{1} wide, is computed. The length L_{1} is the distance into the medium over which the mean electric field decreases in amplitude by a factor e^{-1} . Previous calculations have always been restricted to L \ll L_{1} . It is found that Q increases from the Born approximation Q = Q_{1} for medium width L \ll L_{1} to Q = 2Q_{1} for L \gg L_{1} , and the theory is valid as long as L \ll (kL_{0})^{5/3} L_{1} , a significant improvement over the Born approximation, when the macroscale L_{0} is much larger than the wavelength 2_{\pi}k^{-1} . The improvement is due to incorporation of the dominant effects of cumulative forward scattering in the local electric field in the medium. A rigorous and a heuristic derivation are given. The transitional behavior is discussed and a simple physical interpretation is given.
171 citations
TL;DR: In this paper, a theoretical and experimental investigation of the scattering by a two-dimensional array of loaded dipoles is described, and the scattering through the resonance region shows that a unit reflection coefficient is achieved.
Abstract: Two-dimensional periodic arrays of dipoles or slots act as reflecting or transmitting surfaces, respectively, which have bandpass filter characteristics. The resonant frequency and the bandwidth may be controlled by varying the length, spacing, and load impedance of the dipoles (slots). A theoretical and experimental investigation of the scattering by a two-dimensional array of loaded dipoles is described. The scattering through the resonance region shows that a unit reflection coefficient is achieved. The effect of grating-lobe radiation is included. The scattering properties as a function of the angle of incidence are given for both loaded and unloaded dipoles. The loaded dipole array described in this paper produces a narrower bandwidth than the array of unloaded dipoles, and the resonant frequency is much less dependent on the angle of incidence. The resonant frequency of the array as well as the bandwidth depends strongly on the resonant frequency of the dipole element as would be expected; however, it is also substantially influenced by the interelement spacing and the angle of incidence.
134 citations
TL;DR: In this paper, expressions for the electromagnetic fields transmitted into the time-varying medium when a plane wave is incident upon either a dielectric or dispersive half-space were obtained for the case when the medium is changed in a stepwise fashion, and also for a case when medium varies slowly and continuously.
Abstract: Expressions are obtained for the electromagnetic fields transmitted into the time-varying medium when a plane wave is incident upon either a dielectric or dispersive half-space. Solutions are obtained for the case when the medium is changed in a stepwise fashion, and also for the case when the medium varies slowly and continuously.
133 citations
TL;DR: In this paper, a method for the analysis of scattering from periodic structures based on the numerical solution of the integral equations is further developed using periodicity (Floquet's theorem), where the range of integral equations are reduced to a single period where the kernels are the Green's functions for periodic arrays.
Abstract: A method for the analysis of scattering from periodic structures based on the numerical solution of the integral equations is further developed. Using periodicity (Floquet's theorem), the range of the integral equations is reduced to a single period where the kernels are the Green's functions for periodic arrays. The numerical solution of the integral equations is obtained using the method of moments. Efficient numerical methods for the computation of the periodic Green's functions which allows their rapid evaluation with good accuracy are reported. A new treatment of the singularities which includes the effect of the surface curvature is given. Numerical results for the transverse electric scattering from a conducting surface with a sinusoidal height profile are presented, and several interesting physical phenomena are explored including Brewster angle effects and diffraction grating anomalies.
122 citations
TL;DR: In this article, the authors used spherical-wave expansions as a numerical technique for expressing arbitrary fields specified by analytical, experimental, or numerical data, and found that the generally accepted wave order cutoff value corresponds to 99.9 percent or more of the power in the input pattern.
Abstract: Spherical-wave expansions are a well-known technique of expressing electromagnetic field data. However, most previous work has been restricted to idealized cases in which the expansion coefficients are obtained analytically. In this paper spherical-wave expansions are used as a numerical technique for expressing arbitrary fields specified by analytical, experimental, or numerical data. Numerical results on the maximum wave order needed to expand fields arising from a source of a given size are given for two practical cases, and it is found that the generally accepted wave order cutoff value corresponds to 99.9 percent or more of the power in the input pattern. Near-field patterns computed from far-field data are compared to measured data for the two cases, demonstrating the excellent numerical accuracy of the technique.
116 citations
TL;DR: In this paper, the first appearance of reliable results for the scattered field from two spheres of radii larger than one wavelength and as large as ten or more was presented. But these results were only applied to three collinear spheres of various materials.
Abstract: In [8], both low- and high-frequency solutions to the two-sphere problem were presented in a form suitable for efficient computer solution, Here, numerical results are presented using a method which has enabled the first appearance of reliable results for the scattered field from two spheres of radii larger than one wavelength and as large as ten or more. Radar cross sections (RCS) are computed for numerous configurations of two spheres of various materials. Results for scattering by three collinear spheres are also given. An experimental program was undertaken and is briefly described. Whenever possible, these results are compared with the theory. In all cases the agreement is excellent. Depolarization due to multiple scattering is also investigated, revealing some interesting effects and practical applications to scattering range calibration.
105 citations
TL;DR: In this paper, a numerical solution for the problem of scattering of a plane wave by a dielectric sheet with an imbedded periodic array of conducting strips is presented, and the primary motivation for introducing the strips is to reinforce the mechanical hardness of the sheet in certain radome applications.
Abstract: A numerical solution for the problem of scattering of a plane wave by a dielectric sheet with an imbedded periodic array of conducting strips is presented. The primary motivation for introducing the strips is to reinforce the mechanical hardness of the sheet in certain radome applications. The study shows that with proper design the additional strips can also improve the electric transmission through the composite structure.
TL;DR: In this article, the authors measured the canting angles of freely falling raindrops to determine the magnitude of cross polarization in higher frequency (18-30 GHz) radio relay systems, and the results indicated that a relay system at both 18 and 30 GHz and with a repeater spacing of 3.5 km will experience cross polarization less than -20 dB at rain rates of 150 mm/hr.
Abstract: Analysis indicates that the canting angles of freely falling raindrops are of great importance in determining the magnitude of the cross polarization in higher frequency (18-30 GHz) radio relay systems. Since knowledge of these canting angles is sparse, the images of 463 raindrops obtained with a raindrop camera by personnel at the Illinois State Water Survey have been measured to obtain the distribution of canting angles during two rainstorms. The distributions for both storms are similar, with 40 percent of the drops having positive canting angles exceeding 15\deg with respect to the horizontal, and 25 percent having negative angles of less than -15\deg . Calculations based on the measured distributions and representing upper bounds indicate that a relay system at both 18 and 30 GHz and with a repeater spacing of 3.5 km will experience cross polarization less than -20 dB at rain rates of 150 mm/hr.
TL;DR: The iterative sampling method is introduced for the synthesis of shaped-beam radiation patterns using either line sources or uniformly spaced arrays as discussed by the authors, where a series of correction patterns are added to the original pattern and successive iterations are applied in this manner until the desired performance is achieved.
Abstract: The iterative sampling method is introduced for the synthesis of shaped-beam radiation patterns using either line sources or uniformly spaced arrays. Given an original pattern which is some approximation to the desired pattern, a series of correction patterns is added to it. Successive iterations are applied in this manner until the desired performance is achieved. The current distribution is found by a corresponding series of corrections. Several examples show that patterns with either low main-beam ripple and/or low sidelobe level or sharp cutoff from the main beam can be obtained. Unless there is significant ripple or sidelobe improvement, the complexity of the required source current is usually lower than that of the original pattern. For a ten-element array example with \pm 1 -percent error in the current amplitudes and phases about -40 dB, sidelobe and ripple performance was achieved. Furthermore, the iterative sampling method is simple to apply and converges rapidly.
TL;DR: In this article, the diffraction of a plane electromagnetic wave by a slit in a conducting screen of finite thickness is investigated using the Wiener-Hopf and generalized matrix techniques, and the integral equations occurring in the tandem slit configuration are similar to those given by Jones for the parallelstrip case, they are solved here by a somewhat different method.
Abstract: The diffraction of a plane electromagnetic wave by a slit in a conducting screen of finite thickness is investigated using the Wiener-Hopf and generalized matrix techniques. For purposes of the analysis, the diffraction by two identical semi-infinite parallel-plate waveguides forming a tandem slit configuration is treated first in order to determine the interaction between the open ends of the waveguides. This interaction term is then utilized in solving for the thick slit geometry which is obtained by filling the parallel-plate regions with a dielectric whose relative permittivity is allowed to approach infinity. Although the integral equations occurring in the tandem slit configuration are similar to those given by Jones for the parallel-strip case, they are solved here by a somewhat different method. In contrast to the limitation on the strip-strip separation imposed by Jones, our solution is not restricted to the special case of large separation between the two slits. For an E -polarized incident plane wave, the far field diffracted by each edge of the thick slit is viewed in ray-optical terms as that due to a thin edge centered at the middle of the thick edge modified by a multiplication factor. The thick edge-edge interaction term, on the other hand, is also modified such that each thick edge is viewed by the other as a combination of a line source as well as a line dipole which vanishes when the thickness approaches zero. It is shown that for ratios of screen thickness to slit width below \approx0.5 , the beamwidth is larger than that of the thin slit, while for larger ratios the beamwidth is smaller. Typical diffraction patterns, which are in good agreement with experiment, are presented to illustrate this phenomenon.
TL;DR: It is shown that, with proper constraints on the sidelobes, a given performance index can be optimized to give a radiation pattern with desired sidelobe levels.
Abstract: The solution to the optimization of performance indices of array antennas such as directive gain, efficiency index, and signal-to-noise ratio, do not provide information regarding the sidelobe region of the radiation pattern. It is shown that, with proper constraints on the sidelobes, a given performance index can be optimized to give a radiation pattern with desired sidelobe levels. As most of the performance indices of an array antenna can be expressed as a ratio of two Hermitian quadratic forms, an eigenvalue method is used for the constrained optimization. This method gives explicit expressions for the excitation vector and constrained values of the performance indices. An iterative technique is used to ensure that the specified field values occur at the sidelobe peak positions. The element excitations obtained by this technique for maximum gain and uniform sidelobe level are similar to these obtained by the Dolph-Chebyshev technique.
TL;DR: In this article, a circular-loop antenna composed of N elements with arbitrary circumference arranged parallel in a row is analyzed by Fourier series expansion with emphasis on the existence of finite gaps at the driving points.
Abstract: A circular-loop antenna composed of N elements with arbitrary circumference arranged parallel in a row is analyzed by Fourier series expansion with emphasis on the existence of finite gaps at the driving points. The integral equations at the beginning are reduced to a series of linear simultaneous equations which contain only the Fourier coefficients of the electric currents of the same order. By appraising the current coefficients, the self-admittance is obtained as a sum of two parts: the finite series truncated at the number determined by the ratio of the circular-loop radius to the wire radius and the gap capacitance, and the mutual admittance is obtained as a finite series of fewer terms. Several computed curves concerning a parasitic endfire array of two elements are given, in which the computed values of the input admittance are substantiated by experiments, and radiation characteristics are examined to obtain a desirable configuration.
TL;DR: In this article, the axial currents were obtained as the solution to a pair of coupled integral equations for a top-loaded antenna with one or more cylindrical top-loading elements.
Abstract: The general problem involving the distribution of current and the driving-point impedance of a top-loaded antenna is formulated. Consideration is given to an idealized structure having one or more cylindrical top-loading elements. For the practically important case involving conductors of small radius, the axial currents are obtained as the solution to a pair of coupled integral equations. Approximate solutions obtained by numerical methods for the inverted L -, T -, and four-element top-loaded antennas are compared with measured driving-point impedances. Satisfactory agreement indicates the possibility of utilizing the theory in the analysis of practical configurations involving many top-loading elements.
TL;DR: In this article, the possibilities of an assembly from strips of elliptic shape that are also segments of parabolic dishes are discussed, which can be modified and improved, depending on the type of strip configuration proposed.
Abstract: To produce directional antenna patterns having a shaped beam in one plane such as is required, for instance, in the case of rotating-search radar antennas having a vertical radiation pattern of cosecant-squared shape, doubly curved reflectors are used as a rule. Besides the well-known composition of such reflectors from a stack of strips of parabolic shape, the paper delineates possibilities of an assembly from strips of elliptic shape that are also segments of parabolic dishes. With reflectors assembled in this way certain antenna characteristics such as directivity, sidelobe suppression, etc., can be modified and improved, depending on the type of strip configuration proposed. Experimental results gained with two different reflectors (width 12.5\lambda , height 5.6\lambda ) assembled from strips of elliptic shape are discussed. One of the strip configurations devised turns out particularly favorable for small reflectors.
TL;DR: In this article, a numerical method for predicting the transfer between two receiving sites is outlined and the results are applied to a configuration used in an experimental test over the frequency range from 1 to 10 MHz.
Abstract: The electromagnetic fields of a vertical electric dipole in a conducting half-space are considered. A numerical method for predicting the transfer between two receiving sites is outlined and the results are applied to a configuration used in an experimental test over the frequency range from 1 to 10 MHz.
TL;DR: In this paper, an integral expression for the radiation resistance of a small filamentary loop antenna immersed in a cold collisionless uniform multicomponent magnetoplasma was derived, assuming that the current distribution along the loop is uniform and that the loop axis is parallel to the static magnetic field.
Abstract: A study is made of the radiation resistance R of a small filamentary loop antenna immersed in a cold collisionless uniform multicomponent magnetoplasma. Assuming that the current distribution along the loop is uniform and that the loop axis is parallel to the static magnetic field, an integral expression is derived for R which is valid for arbitrary values of driving frequency, plasma composition and density, and static magnetic field strength. The mathematical properties of this integral are such that R is finite for all values of the driving frequency, including the upper and lower hybrid frequencies as well as the multiple-ion hybrid-resonance frequencies. Application of the integral expression is made to the case of the inner magnetospheric plasma and approximate closed-form expressions are developed for R for the very low-frequency/extremely low-frequency (VLF/ELF) range in the magnetosphere. Numerical results in the VLF/ELF range are also presented. It is found that the inclusion of multiple ions introduces interesting effects: sharp maxima appear at the gyrofrequency and the multipleion hybrid-resonance frequency associated with each ion, while sharp minima occur at the "crossover" frequencies. It is concluded that the presence of these relative extrema in the radiation resistance presents interesting possibilities for the use of a small loop as a diagnostic tool in a multicomponent plasma.
TL;DR: In this article, the scattering of a plane electromagnetic wave, arbitrarily polarized and normally impinging on a wedge-tapered absorbing structure, is theoretically and experimentally studied in two asymptotic cases: spacing between consecutive edges, small and large with respect to the incident wavelength.
Abstract: The scattering of a plane electromagnetic wave, arbitrarily polarized and normally impinging on a wedge-tapered absorbing structure, is theoretically and experimentally studied. The theoretical solution is found in two asymptotic cases: spacing between consecutive edges, small and large with respect to the incident wavelength. In the former case, a transmission line analogy is set up; in the latter, quasi-optical techniques are applied. Numerical and experimental results are presented; the latter are in good agreement with the theory. The possibility of using the studied structure as an absorbing termination is discussed in some detail, and optimizing criteria, as well as the possibility of obtaining polarization-independent performance, are indicated.
TL;DR: In this article, an analysis of multiple interleaved arrays of waveguide radiators operating at different frequencies is presented, which is a generalization of the analysis of an infinite array at a single frequency.
Abstract: An analysis is presented of multiple interleaved arrays of waveguide radiators operating at different frequencies. The approach is a generalization of the analysis of an infinite array at a single frequency. The presence of the low-frequency elements affects the radiation characteristics of the high-frequency elements and generates grating lobes which do not appear in a single-frequency array. Furthermore, power is coupled 'into the low-frequency waveguides when the high-frequency elements are excited. Numerical examples are presented which show that these effects are not severe.
TL;DR: In this paper, the basic relations between mode excitation and the related fields of these multi-arm antennas are reviewed together with some properties that are characteristic of the log-spiral geometry.
Abstract: The n -arm logarithmic spiral antenna having n distinct terminals may be considered as an ( n-1 )-port antenna. It may be operated simultaneously in ( n-1 )independent balanced modes. By varying the relative excitation of these modes it is possible to produce a variety of patterns that have applications to direction finding, tracking, and homing over a broad range of frequencies. It is particularly easy to obtain useful results in this manner because of some unique properties of the logarithmic spiral. The basic relations between mode excitation and the related fields of these multiarm antennas are reviewed together with some properties that are characteristic of the log-spiral geometry. Multimode single-aperture systems, such as those using a relatively simple hybrid matrix to synthesize multiple beams tilted from the axis of the antenna, are discussed. These tilted beams can be conically scanned about the axis of the antenna by a simple phase shift within the excitation matrix.
TL;DR: In this paper, the authors studied the local and sequential propagation characteristics of fields in an inhomogeneous lossy medium, and assertain the significance of the complex rays by studying the shadowing effects produced at an observation point by sampling windows placed in planes crossed by the field.
Abstract: In lossless inhomogeneous media the ray-optical description of the propagation and scattering of electromagnetic waves exhibits the local and sequential properties of these phenomena. The extension of ray optics to lossy inhomogeneous media does not exhibit such properties, in general, since the equations defining the paths of rays connecting real source and observation points yield complex values of the space coordinates, i.e., complex rays. The purpose of this paper is to clarify the local and sequential propagation characteristics of fields in an inhomogeneous lossy medium, and to assertain the significance of the complex rays. The simplest configuration suited to this purpose is a planar interface between homogeneous lossless and lossy half-spaces. By studying the shadowing effects produced at an observation point by sampling windows placed in planes crossed by the field, one finds the region through which the field principally propagates to the observation point, and there-from the local and sequential properties. The results give physical meaning to complex rays and should provide a basis for a description of propagation and scattering in lossy media that avoids the use of complex space.
TL;DR: In this paper, the steepest descent method is shown to be a very powerful tool for pattern synthesis since they take full advantage of all available parameters such as element spacings, current's amplitudes and phases, pattern phase when not specified, and even frequency.
Abstract: Numerical iterative methods such as the steepest descent are shown to be a very powerful tool for pattern synthesis since they take full advantage of all available parameters such as element spacings, current's amplitudes and phases, pattern phase when not specified, and even frequency. Furthermore, the method allows the introduction of linear and nonlinear constraints in all parameters with no special difficulty.
TL;DR: In this article, a simplified solution to the problem of the radio wave diffraction over terrain irregularities is presented, which assumes that each obstacle can be represented by a cylinder with a radius equal to the radius of curvature at the obstacle top.
Abstract: A simplified solution to the problem of the radio wave diffraction over terrain irregularities is presented. The theoretical analysis assumes that each obstacle can be represented by a cylinder with a radius equal to the radius of curvature at the obstacle top. The solution is based on the method proposed by Deygout for the knife-edge case. The experimental results have shown a good agreement with the theoretical calculation.
TL;DR: In this paper, an asymptotic theory for the long distance propagation of FM pulses in dispersive media is presented, which utilizes space-time rays and plane wave dispersion surfaces as well as integral representations.
Abstract: This paper deals with the long distance propagation of FM pulses in dispersive media. The treatment is based on an asymptotic theory which utilizes space-time rays and plane wave dispersion surfaces as well as integral representations. The discussion includes the propagation of prescribed FM signals in homogeneous media as well as synthesis of signals to achieve maximum pulse compression. Special attention is given to the caustics and foci exhibited by the space-time ray system when pulse compression takes place, and to the description of the field in the corresponding space-time transition regions where simple asymptotic constructs are inadequate. While the theory is presented for media with relatively arbitrary spatial and dispersive characteristics, detailed calculations are carried out for a homogeneous isotropic cold plasma for which results can be obtained in explicit form.
TL;DR: In this paper, the problem of diffraction of an electromagnetic wave by a semi-infinite conductor by means of the computer method based on an integral equation formulation was investigated, where the cross section of the conductor can have an arbitrary shape provided the face shined by the incident wave is a uniform plane in the region far from the edge.
Abstract: This paper investigates the problem of diffraction of an electromagnetic wave by a semi-infinite conductor by means of the computer method based on an integral equation formulation. The cross section of the conductor can have an arbitrary shape, provided the face shined by the incident wave is a uniform plane in the region far from the edge. In that plane region, the problem is simply that of reflection from a conductor wall for which a solution is known. This known part of the solution is analytically excluded to derive an integral equation describing the edge effect over a limited region. The limited region is unknown at first and must be determined from the results of some numerical computations. As a numerical example, a thick half-plane conductor is treated in which the electric field polarization is parallel to the conductor, i.e., the case of an incident E wave.
TL;DR: In this paper, a recently distributed research report that presents computer programs suitable for analyzing the electromagnetic behavior of arbitrary configurations of bent and loaded wires is described, and some interesting results already obtained using the programs for analysis of a wire cross scatterer are also pointed out.
Abstract: A recently distributed research report that presents computer programs suitable for analyzing the electromagnetic behavior of arbitrary configurations of bent and loaded wires is described briefly. Some interesting results already obtained using the programs for analysis of a wire cross scatterer are also pointed out.
TL;DR: In this article, a formulation for the electromagnetic fields of finite linear antennas of arbitrary length immersed in a dissipative half-space (such as the ocean or the earth) is presented.
Abstract: A formulation for the electromagnetic fields of finite linear antennas of arbitrary length immersed in a dissipative halfspace (such as the ocean or the earth) is presented. The electric fields in either medium can be readily evaluated once the current distribution is assumed or prescribed. The fields are given in each medium for each of the three major subdivisions of the horizontal range, the near-field range, the intermediate range, and the asymptotic range. Antenna patterns obtained from computer results using formulas derived in this paper are presented for some typical submerged linear antennas. These computer results are compared with experimental measurements performed with linear antennas submerged in the Atlantic Ocean.