Showing papers in "IEEE Transactions on Antennas and Propagation in 1956"

Partially reflecting sheet arrays

Abstract: Multiple reflections of electromagnetic waves between two planes are studied, and the increase in directivity that results by placing a partially reflecting sheet in front of an antenna with a reflecting screen is investigated at a wavelength of 3.2 cm. The construction and performance of various models of such arrays is discussed. Thus, for example, a "reflex-cavity antenna" with an outer diameter of 1.88 \lambda and an over-all length of only 0.65 \lambda is described which has half-power beamwidths of 34\deg and 41\deg in the E and H planes, respectively, and a gain of approximately 14 db. It is shown that larger systems produce considerably greater directivity but that their efficiency is poor.

Variational principles for electromagnetic resonators and waveguides

Abstract: Variational expressions are presented for the propagation constants of a waveguide and for the resonant frequencies of a cavity directly in terms of the field vectors for situations not covered in the literature. These situations occur when the electromagnetic problem is not susceptible of a scalar formulation and are typified by the presence of inhomogeneous or anisotropic matter. The variational expressions are applied to several illustrative examples and the results are compared to known exact solutions. The variational expressions are also applied to the derivation of certain perturbation formulas, some of which were previously obtained by different methods.

Diffraction of a convex cylinder

Abstract: The leading term in the asymptotic expansion for large k = 2 \pi/\lambda , of the fields reflected and diffracted by any convex cylinder are constructed. The cross section of the cylinder is assumed to be a smooth curve which may be either closed or open and extending to infinity. The method employed is an extension of geometrical optics in two respects. First, diffracted rays are introduced. Secondly, fields are associated with the rays in a simple way. The results are applicable when the wavelength is small compared to the cylinder dimensions.

On field representations in terms of leaky modes or Eigenmodes

Abstract: Solutions to source-excited field problems are frequently represented as superpositions of source-free field solutions. The latter are in general of two types: eigenmodes and noneigenmodes which are related to the zeros of the total impedance or alternatively the poles of the scattering coefficient of a system. The eigenmodes are everywhere finite and comprise a complete orthogonal set. The noneigenmodes become infinite in the infitely remote spatial limits of a region and are not in general members of a complete orthogonal set; examples are "radio-active states," "damped resonances," and "leaky waves." Despite their physically singular behavior, the nonmodal solutions can be employed to represent field solutions in certain ranges.

On the scatttering of waves by an infinite grating

Abstract: Using Green's function methods, we express the field of a grating of cylinders excited by a plane wave as certain sets of plane waves: a transmitted set, a reflected set, and essentially the sum of the two "inside" the grating. The transmitted set is given by \psi_{o} + 2\SigmaC_{\upsilon}G(\theta_{\upsilon}, \theta_{o})\psi_{\upsilon} , where the \psi 's are the usual infinite number of plane wave (propagating and surface) modes; G(\theta_{\upsilon}, \theta_{o}) is the "multiple scattered amplitude of a cylinder in the grating" for direction of incidence \theta_{o} and observation \theta_{\upsilon} ; and the C's are known constants. (For a propagating mode, C_{\upsilon} is proportional to the number of cylinders in the first Fresnel zone corresponding to the direction of mode v .) We show (for cylinders symmetrical to the plane of the grating) that G(\theta,\theta_{o})= g(\theta,\theta_{o}) +(\Sigma_{\upsilon} - \int dv)C_{\upsilon}[g(\theta,\theta_{\upsilon} + g (\theta,\pi - \theta_{\upsilon})G(\pi-\theta_{\upsilon},\theta_{o})] , where g is the scattering amplitude of an isolated cylinder. This inhomogeneous "sum-integral" equation for G is applied to the "Wood anomalies" of the analogous reflection grating; we derive a simple approximation indicating extrema in the intensity at wavelengths slightly longer than those having a grazing mode. These extrema suggest the use of gratings as microwave filters, polarizers, etc.

On discontinuous electromagnetic waves and the occurrence of a surface wave

Abstract: Two problems are considered: (1) The field around a dipole free in space. Contrary to the usual treatment, where the moment of the dipole is considered to vary harmonically in time, here the moment is assumed initially to be zero but at the instant t = 0 to jump to a constant value, which it further maintains. (2) The same dipole is placed vertically on a horizontal plane separating two media of different refractive index. It is shown that the resulting disturbance on the plane is composed of two space waves and one surface wave. First the Hertzian vector at a distance \rho from the dipole is zero. At t = t_{1} the disturbance arrives there through the less dense medium, and slowly begins to rise till, at the moment t = t_{2} , when the disturbance has had time to reach the same distance through the second (denser) medium it reaches its final static value and further stays constant. During the transitory interval t_{1} the disturbance is found to be representable, apart from a constant, by a pure surface wave. The two problems are solved with the help of the modern form of the operational calculus based on the two-sided Laplace transform. The analytical tools of the operational calculus needed are explained in a separate paragraph.

Plasma oscillations

Abstract: This paper is a report on the investigations by the author and collaborators F. Berz, E. A. Ash, and D. Dracott at Imperial College. F. Berz has theoretically investigated wave propagation in a uniform plasma and found that even in the absence of collisions only damped waves can arise, because the fluctuating velocity distribution contains a term, overlooked by previous authors, which represents a flowing-apart of the electron density. The cutoff due to this effect alone is at about 1.15 of the Langmuir frequency, and the shortest wavelength at about 20 Debye lengths. Experimental investigations by E. A. Ash and D. Dracott extending over 5 years have at last elucidated the paradox of the existence of Maxwellian electron distributions in the positive column of arcs at low pressures. The interaction is not between electrons and electrons but between these and an oscillating boundary sheath. The sheath was explored by an electron beam probe and oscillations of about 100 mc observed under conditions when the plasma frequency in the arc was about 500 mc. Electrons diving into the boundary sheath spend about one cycle in it, during which time they can gain or lose energies of the order of several volts. Possible applications to radio astronomy are briefly suggested.

Microwave lens matching by simulated quarter-wave transformers

Abstract: The reflections from the surface of a dielectric lens may be cancelled by a quarter-wavelength layer of refractive index intermediate between that of air and the lens medium. The possibility of simulating a quarter-wave matching section by perturbing the boundary of the lens is described in this paper. Some of the configurations considered are corrugated surfaces, arrays of dielectric cylinders, and arrays of holes in the dielectric surface. In each case, a match may be obtained at a given frequency and angle of incidence by the proper adjustment of the depth of the perturbation, and of one other parameter such as the width of a groove.

Exterior electromagnetic boundary value problems for spheres and cones

Abstract: The problem of determining a harmonic time-varying electromagnetic field where the electric vector assumes prescribed values for its tangential components over given spherical or conical boundaries and which has proper radiation characteristics at infinity is considered by a procedure very much like that used in the theory of slots in waveguide walls. The technique used in solving this type of boundary value problem is to establish, by an application of the Lorentz Reciprocity Theorem, a Green's function which represents the electric and magnetic fields of a point generator (infinitesimal dipole) applied at an arbitrary position on the conducting surface where the fields satisfy homogeneous boundary conditions. The total fields for an arbitrary source are then obtained by superposition; i.e., direct integration over the aperture. Since detailed results for the case of a sphere have been obtained by many authors, we confine the details of the technique to the infinite cone. It is assumed that in each case the tangential components of the electric vector are given functions over the entire boundary surface. The results apply directly to the theory of radiating apertures in a perfectly conducting spherical wall or a cone, since the tangential components of the electric vector are different from zero only in the area of the aperture, where it is presumed they are known. The results are also applicable to scattering by conducting spheres and cones, since the tangential electric field components over the boundary surfaces are the negative of those of the incident field. To illustrate the applicability and the limitations of the results, we shall present the formal solutions for arbitrarily shaped apertures on cones and apply them to the several types of delta slots which are usually discussed in connection with other radiating structures.

Nonreflecting absorbers for microwave radiation

Abstract: The absorption of very short electromagnetic waves by absorbing systems, which avoid reflection of the incident wave is a problem of practical interest. Three different methods are applicable: 1. Complete absorption of the incident energy can be obtained for one wavelength by using resonance systems of relatively small thickness; e.g., a resistance card having a surface resistivity equal to the wave impedance of free space and placed a quarter of the wavelength in front of a metal sheet; a dielectric layer of lossy material on a metal sheet, with the thickness of the layer equal to about a quarter of the wavelength in the material; a two-dimensional periodic structure of concentric resonant circuits arranged within the metal sheet itself. 2. The reflecting object can be covered by a thick layer of absorbing material, so that in a wide wavelength range most energy of the incident wave will be absorbed before reaching the reflecting surface. To avoid reflection, the absorption material can be tapered or arranged in different layers in such a manner that the loss tangent steadily increases towards the base plate. 3. The bandwidth of resonance absorbers can be widened without an increase of its thickness by combination of two specially dimensioned resonant circuits.

The theoretical and numerical determination of the radar cross section of a prolate spheroid

Abstract: The exact curve is found for the nose-on radar cross section of a perfectly conducting prolate spheroid whose ratio of major to minor axis is 10:1, for values of \pi times the major axis divided by the wavelength less than three. The exact acoustical cross section is also found. The mathematical solution is obtained by setting up a series expansion for the scattered wave in terms of two sets of solutions of the vector Helmholtz equation and evaluating the undetermined coefficients in this series by applying the boundary conditions on the surface of the spheroid.

Theory of ferrites in rectangular waveguides

Abstract: Reciprocal and nonreciprocal propagation of electromagnetic energy in an infinitely long rectangular waveguide partially filled with one or two ferrite slabs is described.Methods for obtaining exact solutions of the transcendental equations usually encountered in these boundary value problems are demonstrated for several structures. Calculations are carried out for a lossless ferrite and the phase constant is plotted as a function of the ferrite slab thickness. The cutoff conditions for the lowest TE mode are evaluated in terms of the ferrite slab thickness. New modes, not associated with the empty waveguide modes, are analyzed as ferrite dielectric modes, their propagation characteristics are discussed and the rf electric and magnetic field patterns are plotted. The rf electric fields are plotted for all reciprocal and nonreciprocal modes and the appropriate field configurations are used to explain the operation of ferrite cutoff isolators, the field-displacement isolator, the field-displacement circulator, and the nonreciprocal phase shifter. Solutions above ferromagnetic resonance are shown and the E -fields are plotted. A brief comparison of the operation of dispersive devices at high and low frequencies is made. The calculations are extended to include absorption loss, and nonreciprocal attenuation is plotted as a function of slab position near resonance.

Creeping waves for objects of finite conductivity

Abstract: It is shown that it is not necessary to apply the van der Pol-Bremmer expansion in order to obtain the Watson residue series without remainder integral. There appear two kinds of residual waves. Those of the first kind do not enter the object and correspond to the usual creeping waves for objects of infinite conductivity. They arise from poles in the vicinity of the zeros of H\upsilon(ka) . Residual waves of the second kind correspond to waves transversing the object and arise from poles in the vicinity of the zeros of J\upsilon(nka) . They are of no importance in the case of strongly absorbing materials. Waves which are expected according to geometrical optics are obtained-as in the case of infinite conductivity-by splitting off an integral. Primary and reflected waves arise from two different saddle points of the same integrand which was thought of till now as only yielding the reflected waves. On the other hand the terms corresponding to the ingoing part of the primary wave give no contribution at all, but must be kept in order to assure the convergence of the integrals when shifting the path of integration.

Phenomenological vector model of microwave reflection from the ocean

Abstract: A model of one-way transmission of microwave electromagnetic signals over the ocean surface is developed from experiment. The received signal is described as a vector sum of a constant direct signal, a coherent reflected signal, whose amplitude and phase are fixed by geometry and sea state, and a fluctuating reflected component of random amplitude and phase. By interpreting experimental data in the light of this phenomenological model it has been possible to relate, quantitatively, the coherent and incoherent reflected signal and total signal to geometry and sea state. The results give support to the theoretical expression previously derived by Ament and others relating the coherent reflected signal to "apparent ocean roughness." In addition, the general shape of the curve relating the incoherent scattering to "apparent ocean roughness" has been established and its asymptotic value found.

Radiation from ring quasi-arrays

Abstract: The present paper constitutes a summary of investigations of certain antenna systems with rotational symmetry, so-called ring arrays and ring quasi-arrays, which have turned out to be or can be supposed to become of practical importance. Particular stress has been laid on an investigation of the field radiated from homogenous ring arrays of axial dipoles and homogeneous ring quasi-arrays of tangential and radial dipoles; i.e., systems of respectively axial, tangential, and radial dipoles placed equidistantly along a circle and carrying currents of the same numerical value but with a phase that increases uniformly along the circle. At first a calculation has been made of the radiated field in the case where the number of elements in the antenna system is infinitely large. After that the influence of the finite number of elements is accounted for by the introduction of correction terms. Subsequently, the radiation resistance and the gain have been calculated in a few simple cases. The antenna systems described above may display super-gain. On the basis of the theory of super-gain an estimate is made of the smallest permissible radius of these antenna systems. Further an investigation is made of the field from a directional ring array with a finite number of elements to ascertain in particular the influence on the field of the finite number of elements.

Phase centers of microwave antennas

Abstract: This paper is concerned with the location of the phase centers of microwave antennas. The inadequacy of conventional aperture theory for the accurate description of phase centers is discussed. Formulas are developed and, for numerical indications, calculations are made for paraboloidal reflectors of different f/D ratios and a class of primary patterns which provide an approximate representation of a great many common feeds. The results are presented in graphical form to provide useful design information and show the dependence of principal E- and H- plane phase center location on feed and dish parameters. Contrary to the prediction of aperture theory, it is shown that the phase centers of axially symmetric antennas are not in the aperture plane, but they are dispersed about it.

Edge currents in diffraction theory

Abstract: A comparatively simple method for obtaining an asymptotic approximation to the electromagnetic field diffracted by a large aperture in a perfectly conducting, infinitely thin, plane screen is suggested. The method is based on two assumptions: first, that in some regions the scattered field is nearly the same as the field that would be generated by certain currents located on the edge of the aperture; secondly, that at any point on the edge of the aperture these currents are nearly the same as the corresponding currents for a half-plane lying in the plane of the diffracting screen, the straight edge of which is locally coincident with the edge of the aperture. In the crudest approximation the calculation is made on the basis that the half-planes are excited by the incident field alone; higher order approximations arise from a consideration of the interaction between the different parts of the edge of the aperture. Applications of the method to the cases of a plane wave normally incident on (1) a slit of infinite length with parallel straight edges, and (2) a circular aperture are considered. In the former case several terms of the asymptotic development of the transmission cross section in inverse powers of the slit width are given; in the latter case the aperture and axial fields based on the zero-order approximation which neglects interaction are compared with experimental data published by various authors and with some rigorous calculations of Andrejewski.

Directivity, super-gain and information

Abstract: In this paper some analogies between antenna theory and the theory of optical resolving power are analyzed. The effect of the finite size of a rotating antenna on the informational content of the echo is discussed, without taking into account noise. From this point of view, the most important feature of the aerial is the highest angular frequency which is contained in its radiation pattern. Supergain is possible because no upper limit exists for this frequency. A simple method is pointed out for synthesizing a radiation pattern containing any prescribed set of finite angular frequencies. A numerical example is worked out.

An experimental study of the disk-loaded folded monopole

Abstract: Data is presented to show the reduction in size and increase in radiation resistance and bandwidth of the disk-loaded folded monopole as compared with a disk-loaded monopole of the same electrical length. The ratio of diameters of the folded part to the diameter of the driven part was varied for one series of impedance measurements and the axial spacing between the driven part and folded part was varied for another series. The resonant radiation resistance and resonant length may be varied almost independently. The radiation resistance depends upon the ratio of diameter of the folded part to the diameter of the driven part, and the resonant length depends upon axial spacing. The radiation resistance multiplication factor relative to a disk-loaded monopole of the same electrical length is approximately the same as the multiplication factor of a folded dipole relative to a dipole. The disk-loaded folded monopole has a greater bandwidth than an unloaded monopole of the same wavelength-to-diameter ratio. Where the effective diameter1 of the folded antenna is ?2DdS, its radiation pattern is essentially that of an unloaded monopole.

Loop antenna measurements

Abstract: Experimental measurements on three loop antenna configurations are presented. The technique for obtaining impedance and current distributions using a single-wire transmission line over an image plane is described with particular attention given to the difficulties encountered. The results are reproduced in graphical form, and for loops where theoretical results are available, curves comparing theory and experiment are presented.

The low-frequency problem in the design of microwave gyrators and associated elements

Abstract: The introduction of ferrite microwave circuit elements has allowed considerable simplification in the realization of many system functions. However, to date practical low loss ferrite devices have not been built to operate at frequencies below 3,000 mc. Many problems arise when one attempts to build devices to operate below this frequency. Some of these problems arise from the fact that mechanisms of loss occur in the ferrites at lower frequencies which are negligible at the higher microwave frequencies. In addition, at frequencies below 1,000 mc, one can seldom neglect the existence of internal anisotropy fields in the ferrite materials. The most fundamental limitation to the operation of ferrite devices at very low microwave frequencies, however, is that one is approaching the relaxation frequency for ferromagnetic resonance, and as a result the performance of all ferrite microwave devices must deteriorate at sufficiently low frequencies, regardless of whether one assumes a ferrite whose other properties are ideal. All these problems are discussed and quantitative expressions are obtained for the ultimate low-frequency limitation of ferrite isolators, circulators, and microwave gyrators.

Exact treatment of antenna current wave reflection at the end of a tube-shaped cylindrical antenna

Abstract: of the auth0r.l-3 In this equation the distance between two points on the antenna is normally represented by the distance between the corresponding points on some central line. Only when the distance is small this is not permitted and from such regions arises the only term which contains the dimension of the cross section, which is a parameter mainly consisting of a logarithm. The equation therefore has a certain limited degree of accuracy which is such that the ratio of the radius of cross section to the length of the antenna or to the wavelength is neglected compared with unity. The results which can be drawn from the linearized integral equation thus also should have this limited accuracy which is a normal one in electrotechnics in all kinds of devices, where wires are involved. Nevertheless much discussion has gone on about this accuracy. The only way of finding definite numerical answers to this question is to solve exactly the antenna integral equations, both the linearized one and the exact one, for some special case. Nowadays this can be done for a straight cylindrical tube-shaped antenna. (R. Gans has recently expressed the opinion that Hallen’s linearized integral equation should not have any exact sol~tion.~~ This is a mistake made by Gans because he apparently has never seen my original papers. What he studies and criticizes is the coarser form of the equation given in many American papers and books as “Hall6n’s integral equation.” Gans in reality criticizes the deviation that is made in those papers from my own form, which is not subject to any criticism of the kind expressed by Gans.6.7

On the electromagnetic characterization of ferromagnetic media: Permeability tensors and spin wave equations

Abstract: Various constitutive equations applicable to ferromagnetic and ferrimagnetic media are discussed systematically, the emphasis being on a formulation and analysis of the underlying assumptions. A distinction is made between the "ordinary" (Maxwellian) and certain "average" field vectors. The latter are useful in the presence of domain structure; they include appropriately defined spatial averages, \langle\overrightarrow{b}\rangle and \langle\overrightarrow{h}\rangle , of the time-dependent components of the ordinary \overrightarrow{B} and \overrightarrow{H} , respectively. In cases where \langle\overrightarrow{b}\rangle and \langle\overrightarrow{h}\rangle are connected by a "point relation", the general form of Polder's permeability tensor is extended to nonsaturated media; the special tensors due to Polder, the writer, and Wangsness, are then reviewed. In cases where \langle\overrightarrow{b}\rangle and \langle\overrightarrow{h}\rangle are not so connected, the "exchange effect" and the "spin wave equation" are discussed. Following Ament and Rado, three consequences of this equation are treated: the new boundary conditions, and the triple refraction and "equivalent isotropic permeability" in metals.

Optical Fresnel-Zone gain of a rectangular aperture

Abstract: An equation for the on-axis gain of a uniformly illuminated rectangular aperture is derived which is valid in the "Optical Fresnel Zone." This equation is formulated in terms of the ordinary radiation field gain multiplied by a correction factor which depends upon the aperture dimensions and the distance, R, from the aperture at which the gain is measured. A table of the function [C2(v)+S(v)]/v2 is given; C(v) and S(v) being the Fresnel integrals. The gain of a square aperture (LXL meters) in the Fresnel-zone region is compared with the gain of a circular aperture and it is shown that for apertures of equal Gsquare < Gcircle when (L2/?)

Spherical surface-wave antennas

Abstract: Solutions of Maxwell's equations are presented which approximately satisfy the boundary conditions for corrugated and dielectric-clad conducting spheres. These solutions have the physical interpretation of leaky latitudinal surface waves. Values of the complex propagation constant are given as functions of the geometry. For large spheres the leakage is small and the transmission properties approach those of a trapped cylindrical wave on a flat surface. A corrugated spherical cap, used to support surface waves, has been found to have interesting possibilities as a low-drag omnidirectional antenna. Preliminary experimental results are offered as an illustration of the theory.

Some data for the design of electromagnetic horns

Abstract: Using an idea recently suggested by the author,1 a table is presented from which the gain of all electromagnetic horns may be calculated with substantially the same accuracy obtainable using the gain formula. The exact parameters of an optimum horn are given, and a simple procedure for the design of optimum horns with a specified gain and other desirable properties is described.

Forward- and back-scattering from certain rough surfaces

Abstract: Heuristic relations are derived between the specular reflection coefficient, R , and the radar echoing power of rough surfaces in which induced current elements are constrained to radiate equal powers in the reflected ray's direction and back toward the radar. To the extent that currents in the surface and fields scattered by it are calculable through a self-consistent formulation, a simple Fresnel-zone computation of R shows that \sigma_{o} , the radar area per unit area of mean plane, is proportional to | R^{2} | \sin^{2} \theta , where \theta is the angle incident rays make with the mean plane. It is plausibly assumed that large scatterers on the surface cast shadows with "beamwidth" proportional to radar wavelength \lambda ; here the argument leads to \sigma_{o} \propto ( |R^{2}| \sin^{2} \theta)/\lambda . In two appendices the law \sigma_{o} = 4 \sin^{2} \theta is derived for a lossless surface obeying Lambert's law, and a known self-consistent "solution" of a rough surface problem is examined by three generally applicable criteria.

Slot admittance data at K a band

Abstract: Admittance data on transverse edge slots in RG-96/U waveguide can be obtained by a technique called the moving lossy short technique. By this technique the radiation attenuation of a test section of identical slots can be determined. It is then possible to specify both the slot inclination angle and the slot depth of cut required to yield any conductance with in the range of measurements. These data were used to design an experimental 30-slot array with a 25-db Taylor aperture distribution. This array was successful, yielding sidelobes near -23 db. Subsequently, the same data were used in designing an 8-foot array with 432 edge slots having the same aperture distribution. This array had a half-power beamwidth of 14 minutes and sidelobes of the order of -24 db. These results compared favorably with design objectives.