Showing papers in "IEEE Transactions on Antennas and Propagation in 1959"

The equiangular spiral antenna

Abstract: A circularly polarized antenna is described which makes possible bandwidths that a few years ago were considered to be impossible. The design of the antenna is based upon the simple fundamental principle that if the shape of the antenna were such that it could be specified entirely by angles, its performance would be independent of wavelength. Since all such shapes extend to infinity it is necessary to specify at least one length for an antenna of finite size. The one length in this antenna, the arm length, need only be of the order of one wavelength at the lowest frequency of operation to obtain operation essentially independent of frequency, and the geometry of the antenna allows this arm length to be spiraled into a maximum diameter of one half wavelength or less. Antennas have been constructed that have an essentially constant radiation pattern and input impedance over bandwidths greater than 20 to 1.

Guided waves on sinusoidally-modulated reactance surfaces

Abstract: A rigorous solution is derived for the propagation characteristics and field distributions of waves guided by a plane surface which possesses a surface reactance modulated sinusoidally in the propagation direction. The explicit field amplitudes and the determinantal equation for the propagation wavenumber are expressed in a continued fraction form which is rapidly convergent for all values of modulation. Numerical results are obtained for both surface wave (modal) and leaky wave (nonmodal) solutions. The relevance of these studies to high-gain modulated surface-wave antennas is discussed.

Waves on interfaces

Abstract: In wave propagation along plane or cylindrical interfaces a distinction is made between truly guided waves (surface waves) and partially guided waves (radiating waves). When dissipation losses are involved, surface waves no longer represent the asymptotic field near the interfaces at large distances from the source. In order to separate them from the total field it is necessary to have a criterion for radiating waves which are free of any surface wave components. Such a criterion exists in the form of orthogonality relations which are the mathematical formulation of the concept that an ideal antenna which excites only a surface wave should not receive a radiating wave.

Interaction of electromagnetic waves with some natural surfaces

Abstract: The problem of the interaction of electromagnetic radiation with nonuniform surfaces (terrain, roadways, etc.) is of interest for predicting the apparent temperature of radiometers or radio telescopes. In this paper, the interaction is described by the differential scattering coefficients of the surface, in terms of which one may express such parameters of the surface as the radar cross section, the absorption coefficient, the albedo, etc. By making use of the reciprocity properties of the differential scattering coefficients, Kirchhoff's radiation law is derived in its most general form, which takes account of both the angular dependence and the polarization properties of the emitted radiation. Thus, the emissivity of the surface can also be expressed in terms of the scattering coefficients. General formulas for apparent surface temperature are obtained and are used to calculate the apparent temperature of an asphalt roadway and a vegetation-covered surface. The predicted temperatures are found to be in reasonably good agreement with measurements of Britt, Tolbert and Straiton at 4.3 mm wavelength.

Leaky-wave antennas I: Rectangular waveguides

Abstract: A microwave network approach is employed for the description and analysis of leaky-wave antennas. This approach is based on a transverse resonance procedure which yields the complex propagation constants for the leaky waves. A perturbation technique is then applied to the resonance equation to obtain results in simple and practical form. These procedures are illustrated by application to a number of practical leaky rectangular waveguide structures. Very good agreement is obtained between the theoretical results and the measured values.

The unidirectional equiangular spiral antenna

Abstract: Circularly polarized unidirectional radiation, over a bandwidth which is at the discretion of the designer, is obtainable with a single antenna. The antenna is constructed by wrapping balanced equiangular spiral arms on a conical surface. The non-planar structure retains the frequency-independent qualifies of the planar models, and, in addition, provides a single lobe radiation pattern off the apex of the cone. Practical antennas have been constructed with radiation patterns and input impedance essentially constant over bandwidths greater than 12 to 1 and there is no reason to assume that these cannot be readily extended to more than 20 or 30 to 1.

Impedance properties of complementary multiterminal planar structures

Abstract: Booker has shown that Babinet's principle, properly extended to electromagnetic fields, leads to a simple relation between the impedances of two planar complementary structures. A relation, which generalizes this result, is found between the impedance matrices of two complementary n -terminal structures. This relation is applied to the particular n -terminal structures having n -fold symmetry and to those that are also self-complementary. In the latter case the impedance matrix is real and entirely determined by the number of terminals. It is therefore independent of the exact shape of the elements composing the structure and of the frequency. By connecting in groups the terminals of such a structure various impedance levels, all frequency independent and real, may be achieved. Structures having their terminal pairs in different locations in the plane are also considered. A self-complementary two-port structure is found to be equivalent, from the impedance point of view, to a length of lossy transmission line having a characteristic impedance of 60\pi ohms.

A new method for obtaining maximum gain from yagi antennas

Abstract: In conventional Yagi design, optimum performance requires separate adjustments in a number of parameters-the array length and the height, diameter, and spacing of the directors and reflectors. By introducing the notion of a surface wave traveling along the array, it is possible to demonstrate experimentally the interrelationship between these parameters. With this, the gain then depends only on the phase velocity of the surface wave (which is a function of the height, diameter, and spacing of the directors) and on the choice of the reflector. Thus, maximum gain for a given array length, for any director spacing less than 0.5 \lambda , can be obtained by suitable variation of the parameters to yield the desired phase velocity. A design procedure that provides maximum gain for a given array length is presented.

Some new forms of Huygens' principle

Abstract: Several theorems are derived by using the reaction concept. They apply to single frequency sources of finite extent, and to fields which are finite and continuous on a hypothetical closed surface S whose inside or outside is source-free. 1) The field on the source-free side of S is uniquely determined by the normal components E_{n} and H_{n} on S . 2) For measurements on the source-free side of S , the primary source can be replaced by any of the following secondary sources on S : (a) Normal electric and magnetic dipoles in free space. (b) Normal electric and magnetic quadrupoles backed by a medium which makes E_{n} = 0 and H_{n} = 0 . (c) A certain combination of electric and magnetic normal dipoles and quadrupoles which gives zero field on the source side of S . The prescription for (a) requires the solution for the field of the primary source when it is inside a cavity on whose walls E_{n} = 0 and H_{n} = 0 . The surface densities of the various components of secondary sources (b) and (c) are given in terms of the free-space primary field. The formulas are comparatively simple when S is plane. Many applications are cited including a combination of multipoles, consisting of vertical electric and magnetic dipoles, which is equivalent to a horizontal electric dipole.

A flush-mounted leaky-wave antenna with predictable patterns

Abstract: This paper describes the design and the measured performance of a large, flat antenna consisting of an inductive grid spaced over a conducting surface. The analysis employs the transverse-resonance method to determine the radiating properties of the structure. This analytical technique is shown to predict very accurately the amplitude and phase of the illumination along the aperture of the antenna. An antenna was built with an 18- by 24-inch aperture and tested over the frequency band from 7-to-13 kmc. The results of these tests confirm the theoretical predictions in every detail. A pencil beam from the antenna scans in the H-plane (perpendicular to the antenna) from 20\deg to 60\deg from the normal to the aperture as the frequency changes from 7-to-13 kmc. The H-plane beamwidth remains virtually constant over most of this band. The first H-plane sidelobe or shoulder is at least 29 db below the main lobe from 7-to-10 kmc, and at least 23 db below from 10-to-13 kmc. All H-plane sidelobes beyond three or four beamwidths on either side of the main lobe are at least 40 db below the main lobe everywhere in the 7-to-13 kmc band. At the design frequency the measured pattern agrees with the theoretical pattern within a fraction of a db down to 40 db below the peak of the main lobe, even though the gain of the antenna at this frequency is only 33 db.

Scattering of a surface wave by a discontinuity in reactance

Abstract: The following two-dimensional scattering problem is solved exactly by a Wiener-Hopf procedure. The incident field is a TM surface wave traveling in the positive x direction and guided by a reactive surface in the plane z=0 . The surface has normal reactance X_{0} if x , and X_{1} if x>0 . X_{0} and X_{1} are assumed positive and real. The discontinuity produces reflected and transmitted surface waves and a radiated field. Closed form expressions are found for the magnitudes of these fields. The reflected, radiated, and transmitted power flows, relative to that of the incident field, are plotted in universal curves. Conservation of energy is verified exactly.

On the phase velocity of wave propagation along an infinite yagi structure

Abstract: An approximate expression is derived for the phase velocity of wave propagation along an infinite Yagi structure and its dependence on the various parameters of the structure is discussed in detail. The structure is at first studied qualitatively by applying the transmission line analogy. The problem is next treated from the viewpoints of linear antenna and field theories. It is assumed that a traveling wave is propagating along the axial direction and it induces an axially symmetric and sinusoidal current distribution in each element The electric field at any point due to this current distribution is calculated by the Hertz vector method. After applying boundary condition to the electric field, an expression for the propagation constant is derived. The results are compared with existing experimental values. The agreement between theory and experiment is found to be within 5 per cent. The accuracy of the expression given is sufficient for practical purposes.

The synthesis of large radio telescopes by the use of radio interferometers

Abstract: An outline is given of a method of simulating the resolving power of large radio telescopes by a process of synthesis, in which use is made of measurements taken with smaller structures arranged in different configurations. The method has been applied to the construction of some large radio telescopes at Cambridge.

Anatomy of "Surface waves"

Abstract: The triple quotation marks in the title and elsewhere in this paper indicate that the enclosed words are used to denote the wave types enumerated in Table L The purpose of the paper is to call attention to the fact that as a group these wave types have no important physical properties in common. Calling these wave types by the same name, even with qualifying adjectives, encourages one to assume that the most significant physical properties of one wave type are shared by other wave types. This has caused, and will continue to cause, we believe, serious misunderstandings. It is strongly urged that this loose use of words be abandoned. Another solution is possible. We could wait until everyone realizes that the term '"surface waves'" has become devoid of significant meaning and that it is equivalent to just "that thing."

A study of spherical reflectors as wide-angle scanning antennas

Abstract: A study is made of spherical reflectors for use as wide-angle scanning antennas. In order to keep the effects of spherical aberration within tolerable limits, the approach of using a restricted aperture is adopted. This approach is suitable for applications requiring very wide angles of scan. Experimental results show that the phase error over the illuminated aperture of a spherical reflector should not exceed one-sixteenth of a wavelength. This requirement determines the beamwidth of the primary source. A square-aperture horn with diagonal polarization is found to satisfy the requirements of a suitable feed for the reflector. Secondary patterns of a 10-foot-diameter hemispherical reflector illuminated by this horn at 11.2 kmc have a 3-db beamwidth of 1.76\deg and a relative sidelobe level of about -20 db throughout a total useful angle of scan of 140\deg . The measured gain is 39.4 db, which is equivalent to the gain of a uniformly illuminated circular aperture of 31-inch diameter.

A new method of near field analysis

Abstract: The problem of the accurate determination of the total electromagnetic field produced by a current distribution on a circular disc type aperture is examined. For comparison of the near and Fresnel region solutions, an exact Maxwellian integral is used as the starting point. Aperture and space coordinates are separated by the use of Bessel function addition theorems, allowing the field to be expressed as a sum of terms containing radial and angular integrals. The radial integrals involve only the disc (aperture) distribution and coordinates while the angular integrals involve only the elevation angle. The distance from origin appears implicitly in the series coefficients. These integrals are suitable for high speed computations and have been evaluated for a number of cases. The results are compared with the small angle and general Fresnel formula values for various observation angles, distances from the aperture, and aperture distributions.

Linear arrays: Currents, impedances, and fields, I

Abstract: The radiation field of dipoles is usually expressed in the form of a product of a field factor and one or more array factors. Actually, such a formulation depends on the implicit assumption that the distributions of current along all elements are the same regardless of the location in the array or differences in driving conditions. Since this is a satisfactory approximation only when the elements are near a half-wavelength long, a study of the fields of arrays of longer elements in terms of the actual distributions of current is indicated. The available solutions of the simultaneous integral equations for the distributions of current in a circular array of N -parallel elements are adequate in a quantitative sense only for arrays of approximately half-wave elements. Moreover, the form of the solution as a series of complicated terms is quite useless (except in the leading sinusoidal term) when the determination of the radiation field is desired. For this reason, a new solution for the currents, which provides a good approximation for the currents in arrays of elements that may be a full wavelength long or longer, and which is expressed in terms of combinations of simple trigonometric functions, is derived. The new solution is used to determine the currents in and the fields of isolated half-wave and full-wave dipoles more accurately than with the conventional sinusoidal currents. The currents, impedances, and fields of a two-element array of full-wave elements are studied under various driving conditions including the broadside, bilateral end-fire, unilateral end-fire or couplet, and the case when one of the elements is parasitic. It is shown that the null in the conventional pattern for the couplet with identically distributed currents becomes a minor maximum with an amplitude equal to half that of the principal maximum when the more accurate distributions of current are used. The significance of this fact in its application to the minor lobe structure of more general arrays is considered. The usefulness of the new theory in determining the radiation field of parallel arrays, in general and when scanned, is discussed, and plans for further work are outlined.

Closely-spaced transverse slots in rectangular waveguide

Abstract: The traveling-wave modes associated with an infinite, periodic structure are considered. An approximate equation for the propagation constants of these modes is derived through the use of Fourier analysis and an approximate application of the reaction concept. In the homogeneous case considered, it is found that two dominant modes may exist: an attenuated fundamental mode representing a perturbation of the dominant mode of a closed rectangular waveguide, and an unattenuated surface wave, which is similar to the wave associated with a corrugated surface waveguide. By means of the appropriate variation of physical parameters, including the slot length and spacing, essentially independent control of the attenuation constant and phase velocity of the fundamental mode is possible over a wide range. Typical curves of the propagation constant in terms of these parameters are given, and the results of experimental measurements are shown to be in close agreement with the theory.

The inverse scattering problem in geometrical optics and the design of reflectors

Abstract: The inverse scattering problem considered here is that of finding the shape of a reflector which produces a prescribed scattered wave. The scattered wave is characterized by its angular pattern, which determines the differential scattering cross section of the reflector. The problem is solved by means of explicit formulas for cylindrical and for rotationally symmetric objects. Plane, cylindrical, and spherical incident waves are considered. The general three dimensional object is also treated. The method of geometrical optics is used throughout.

The calculated phase velocity of long end-fire uniform dipole arrays

Abstract: Surface waves have been applied recently to the study of end-fire arrays. An important step in the theory of surface-wave antennas is the calculation of the local phase velocity of the surface wave from the antenna geometry. While experimental work has been done along this line, no adequate theoretical solution seems to be available. In this report, a mathematical procedure is presented for obtaining an approximate value of the phase velocity for long end-fire uniform dipole arrays, as a function of the antenna geometry. Results have been reported for a number of geometrical parameters and curves plotted to facilitate the analysis and design of arrays. The results have been compared with experimental measurements and an explanation has been given for the discrepancies found; finally, a criterion for correcting the results has been outlined.

Diffraction by surfaces of variable curvature

Abstract: To investigate the influence of variable curvature on the damping of diffracted waves (creeping waves) the integral equation method has been applied to an arbitrary convex cylinder. In addition to the well-known damping factor, depending on the radius of curvature R , a first-order correction term yields an amplitude factor R^{1/6} while the second-order correction term results in a change in damping depending on the curvature and its first and second derivatives.

Asymmetrical trough waveguide antennas

Abstract: Line source radiators of the leaky wave type may be constructed readily with trough waveguide, which consists of a rectangular trough containing a symmetrically located center fin. Two types of such radiators are investigated: a continuously asymmetrical form suitable for near endfire radiation, and a periodically asymmetrical design permitting radiation through broadside. The propagation characteristics of the leaky wave on the continuously asymmetrical structure are determined theoretically by means of a transverse resonance procedure, and comparison is made with measured values. The influence of finite center fin thickness is also accounted for. Designs and radiation patterns are presented for a typical antenna of each type.

On scattering by large conducting bodies

Abstract: Two sets of sources, equivalent in the sense that they produce the same field as does an illuminated conductor, are discussed. Both representations are suggestive of approximation. Crude approximations are made, yielding what are called "the physical optics solution," and the "image induction solution." It is shown that these two solutions are reciprocal to each other. This means that, given a source and an observer, the solution by one method is equal to the solution by the other method with the source and observe interchanged. Both solutions are amenable to further refinement if more accurate solutions are desired.

The rectangular loop antenna as a dipole

Abstract: An integral equation for the current in a rectangular loop of wire is derived for a loop that is driven by two generators located at the centers of one pair of opposite sides. The EMF's are equal in magnitude and in phase in the sense that they maintain currents in the generators that are in the same direction relative to the coordinate system and, therefore, in opposite directions from the point of view of circulation around the loop. An approximate solution is obtained for the distribution of current around the loop and for the driving-point impedance. It is shown that the solution for the rectangle of wire reduces to that of the symmetrically driven folded dipole when one dimension is made electrically small and to a section of transmission line driven simultaneously at both ends when the other dimension is made small. The loop that is electrically small in both directions is also examined.

Electromagnetic properties of wedge and cone surfaces with a linearly varying surface impedance

Abstract: This paper presents the formal aspects of an analysis of the electromagnetic behavior of wedge and cone surfaces with a linearly varying surface impedance. Alternative field representations are obtained and their utility is described. Special attention is given to reactive surfaces which can support a new type of surface wave. This surface wave is of interest for an analysis of surface wave antennas with a linear reactance taper.

Surface-wave research in Sheffield

Abstract: The paper is divided into four sections, each dealing with a specific aspect of the current research program in the Department of Electrical Engineering at Sheffield University. Section I deals with the radiation from a cylindrical surface-wave resonator. Section II presents some numerical results obtained by an electronic computer of the guide-wavelength/dielectric constant relationship for the EH_{11} mode on a dielectric rod. Section III deals with the coupling between two adjacent surface waveguides. Parallel dielectric sheets and parallel rods are both discussed theoretically. Section IV presents the theory of a new form of surface-wave launching antenna, including an evaluation of its hunching efficiency.

Decay exponents and diffraction coefficients for surface waves on surfaces of nonconstant curvature

Abstract: The decay exponents and diffraction coefficients for a cylindrical surface of nonconstant curvature are computed by two methods which yield the same results. The results consist of leading terms which depend upon the curvature of the surface and corrections which depend upon the derivative of the curvature. The leading terms coincide with those found previously. With these corrections, the geometric theory of diffraction can be used at longer wavelengths than before. In the first method the solution for diffraction by an elliptic cylinder is expanded asymptotically for wavelengths small compared to the cylinder dimensions. From the expansion the decay exponents and diffraction coefficients are determined. They are then expressed in terms of the curvature and its derivative, and in this form they are assumed to apply to a cylinder of arbitrary convex cross section. This assumption is verified by comparison with the corresponding results for a parabolic cylinder. Then the same results are obtained by asymptotically solving the integral equation for the field on a cylinder of arbitrary convex cross section.

The launching of surface waves by a parallel plate waveguide

Abstract: The excitation of the lowest TM surface wave in grounded dielectric slab by a terminated parallel plate waveguide is discussed. The ground plane is the continuation of the lower plate of the waveguide and the infinite dielectric slab is partially filling the waveguide. The thickness of the slab, the height of the parallel plate waveguide, and the frequency are such that only the lowest slow wave can propagate in the partially filled waveguide and the grounded dielectric slab. The Fourier transform of the field scattered by the termination of the upper plate of the waveguide is found by means of the Wiener-Hopf technique and the far fields obtained by the method of steepest descents. The percentage of power reflected back into the waveguide, of power transmitted to the surface wave in the slab, and of power radiated into the open space are plotted vs the thickness of the slab for different heights of the waveguide and \epsilon=2.49 . This method of excitation is found to be very efficient. If the dimensions of the waveguide and the slab remain within a considerably wide range, the efficiency obtained for a given frequency is very close to the optimum. Therefore, the adjustments for maximum efficiency are not critical.