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Showing papers in "IEEE Transactions on Antennas and Propagation in 1958"


Journal ArticleDOI
TL;DR: In this paper, the maximum gain of a class of antennas having fields expressible as a finite number of spherical wave functions is given for arbitrarily polarized radiation fields, and it can be related to antenna size by requiring the near fields to be small in magnitude.
Abstract: A formula is given for the maximum gain of a class of antennas having fields expressible as a finite number of spherical wave functions. This maximum gain can be achieved for arbitrarily polarized radiation fields, and it can be related to antenna size by requiring the near fields to be small in magnitude. Also, the radiation field is in the form of a polynomial, so that patterns optimum in the Tchebycheff sense can be defined. Formulas for the relationship of beamwidth to sidelobe level are given.

215 citations


Journal ArticleDOI
TL;DR: In this paper, a theoretical method of finding the characteristic impedance of two infinite cones of arbitrary cross section is presented, which reduces the problem to finding the solution of Laplace's equation by using conformal mapping techniques.
Abstract: A theoretical method of finding the characteristic impedance of two infinite cones of arbitrary cross section is presented. In this problem, the spherical geometry can be mapped on a plane, thus reducing the problem to finding the solution of Laplace's equation by using conformal mapping techniques. This method is applied to the inclined biconical antenna and several types of fin antennas. The solution for the biconical antenna is Z_{0}=\eta/2\pi \cosh ^{-1}F , where F is a function of the geometry of the antenna. For the fin, the solution takes the form Z_{0} =\etaK(k)/K'(k) where K and K' are complete elliptic integrals of the first kind and k depends on the geometry.

97 citations


Journal ArticleDOI
TL;DR: In this article, an investigation was made of stepped-index lenses in which the desired continuous variation of index with radius was approximated by a number of constant-index spherical shells.
Abstract: Since materials with a continuous variation of index of refraction were unavailable for the construction of spherical Luneberg lenses, an investigation was made of stepped-index lenses in which the desired continuous variation of index with radius was approximated by a number of constant-index spherical shells. Experimental data on two-dimensional, TE_{10} mode, stepped-index Luneberg lenses indicated that 10 shells were sufficient for 18-inch diameter lenses for use at X band. Expanded polystyrene materials, developed with dielectric constants ranging from 1.1 to 2.0 in increments of 0.1, were used to construct 10-step, 18-inch diameter, spherical Luneberg lenses. Performance data for these lenses are given at wavelengths of 3.2, 1.8, and 0.8 centimeters.

88 citations


Journal ArticleDOI
TL;DR: In this paper, an analysis of the effect on radiation pattern of random errors in the construction of a two-dimensional scanning array is presented, where translational and rotational errors are assumed to cause the dominant effect.
Abstract: An analysis is presented of the effect on radiation pattern of random errors in the construction of a two-dimensional scanning array. Translational and rotational errors in the positions of all elements are assumed together with errors in the electrical excitations themselves. Translational errors are found to cause the dominant effect. A formula connecting side lobe level and errors is derived and representative curves are shown. For a given tolerance, pattern deterioration is found to decrease as the array is enlarged. For the same tolerance, pattern deterioration is less for a planar array of size L^{2} - than it is for a linear array of length L . Side lobe increase due to random errors does not depend on scan angle.

84 citations


Journal ArticleDOI
Yueh-Ying Hu1
TL;DR: In this article, a variational method for the broadside backscattering cross section of a center-loaded cylindrical antenna with any load impedance, Z, was proposed.
Abstract: A solution of the broadside back-scattering cross section, \sigma , of a center-loaded cylindrical antenna with any load impedance, Z_{L} , is obtained by a variational method through a four-terminal network approach. A simple formula for \sigma , in terms of Z_{L} and the parameters Z_{11}, Z_{12} , and Z_{22} associated with the antenna has been derived. The impedances Z_{11}, Z_{12} , and Z_{22} are independent of the load and they are determined by using the variational principle. Numerical results of the first order approximation are presented, and they are in good agreement with some measured results available in the literature.

70 citations


Journal ArticleDOI
TL;DR: The double-layer pillbox as mentioned in this paper is a microwave parallel-plate system in which the image space and the object space relative to a two-dimensional internal reflector are electrically separated by a metal septum.
Abstract: The double-layer pillbox is a microwave parallel-plate system in which the image space and the object space relative to a two-dimensional internal reflector are electrically separated by a metal septum. The double-layer prevents the shadowing effects and impedance mismatch that result in a single-layer pillbox when energy from the reflector reenters the primary feed. It also allows correction of the optical aberrations of the system in the image space, the object space, or both. The pillbox with semicircular reflector has wide-angle scanning properties. Its inherent spherical aberration can be reduced by such elements as dielectric lenses, geodesic contours, quasi point-source feeds, and auxiliary reflectors. These techniques have been applied to the construction of pillboxes whose wide-angle scanning properties and improved radiation characteristics substantiate the theory.

61 citations


Journal ArticleDOI
TL;DR: In this paper, the results of the approximative diffraction theory dealing with the propagation of radio waves around a smooth spherical earth (surrounded by a homogeneous atmosphere) can be derived from a one-dimensional integral equation originally discussed by Hufford.
Abstract: All results of the approximative diffraction theory dealing with the propagation of radio waves around a smooth spherical earth (surrounded by a homogeneous atmosphere) can be derived from a one-dimensional integral equation originally discussed by Hufford. This equation can be solved in terms of operational calculus which leads, first of all, to the well-known residue series. In this treatment the Sommerfeld theory for a fiat earth appears at once as a limiting case; moreover, analytic expressions for correction terms accounting for the finite value of the earth's radius are easily determined. Finally, the equation in question can also be used for the extension to inhomogeneous soil conditions, without neglecting the earth's curvature.

54 citations


Journal ArticleDOI
TL;DR: In this paper, the echo area resulting from traveling waves excited on the surface of long, thin bodies is considered and a means of predicting this echo area on the basis of antenna theory is derived.
Abstract: The echo area resulting from traveling waves excited on the surface of long, thin bodies is considered. A means of predicting this echo area on the basis of antenna theory is derived. Computed and measured values are compared for a long wire, an ogive, and a shorted polyrod.

45 citations


Journal ArticleDOI
TL;DR: In this paper, the radiation fields of electric and magnetic type antennas mounted on smooth curved surfaces of finite conductivity have been analyzed using a circular cylinder whose surface impedance is specified. But the model chosen is a circular cylindrical cylinder and the results are also applicable to other smoothly varying curved surfaces such as spheres, parabolic cylinders, and paraboloids.
Abstract: Extensive numerical results are presented for the radiation fields of electric and magnetic type antennas mounted on smooth curved surfaces of finite conductivity. The model chosen is a circular cylinder whose surface impedance is specified. A residue series representation is employed for the portion of space deep in the shadow while a geometrical-optical representation is used in the "lit" region. In the penumbra, the fields are expressed in terms of the "Fock functions." The results are also applicable to other smoothly varying curved surfaces such as spheres, parabolic cylinders, and paraboloids. As an application, the E -plane patterns are computed for a small loop antenna on a spherical earth for both sea and land illustrating the so-called cut-back effect.

45 citations


Journal ArticleDOI
G. Owyang1, T. Wu
TL;DR: In this article, an approximate attenuation coefficient due to ohmic loss was derived for both parallel slots and parallel strip lines, and the capacitance per unit length, as well as the inductance per unit-length of the lines were also obtained.
Abstract: An approximate attenuation coefficient due to ohmic loss is derived for both parallel slots and parallel strip lines. The capacitance per unit length, as well as the inductance per unit length of the lines are also obtained. The properties of a transmission line immersed in a lossless dielectric are thus completely determined. The attenuation coefficient due to lossy dielectric may be approximated by similar procedure.

42 citations


Journal ArticleDOI
TL;DR: The existence of a surface wave which propagates across a corrugated metallic surface at an oblique angle with the teeth is investigated both experimentally and theoretically in this article, where expressions are derived which give the variation of the wave velocity and amplitude with the change of wave direction.
Abstract: The existence of a surface wave which propagates across a corrugated metallic surface at an oblique angle with the teeth is investigated both experimentally and theoretically in this paper. Expressions are derived which give the variation of the wave velocity and amplitude with the change of wave direction. Experimentally measured values of the surface velocity compare favorably with the theory. The radiation pattern of an experimental antenna is given which demonstrates that a low sidelobe, narrow azimuth beam scannable to \pm30 degrees with a cosecant-squared elevation pattern is attainable. A method of feeding this antenna to give a low silhouette, making the corrugated scanner antenna suitable for flush mounted applications is illustrated.

Journal ArticleDOI
TL;DR: In this article, the magnetic interception area is determined by the size of the radome and by the radianlength or skin depth in sea water (2 meters at 15 kc).
Abstract: A submarine requires a small VLF antenna for reception while submerged. Since the propagation in sea water is nearly vertical (downward from the surface), the only operative types are horizontal dipoles, electric and magnetic. The electric dipole is coupled by conduction and the magnetic dipole by induction in a loop. The former has no resonance and nearly unlimited bandwidth, but fails when not submerged. The latter, by resonance, is able to present much greater interception area and available power. The magnetic interception area is determined by the size of the radome and by the radianlength or skin depth in sea water (2 meters at 15 kc). The radiation power factor, which is essential to bandwidth and efficiency, is influenced also by the size of the inductor and by the magnetic permeability of an iron core. Simple formulas illustrate these relations for the idealized spherical shape of radome, coil and core. Omnidirectivity in azimuth requires crossed coils in a two-phase circuit.

Journal ArticleDOI
TL;DR: In this article, the distribution of slot conductance of nonresonant arrays is obtained by considering the array as a continuous line source, and the performance of an experimental array is described.
Abstract: The distribution of slot conductance of nonresonant arrays is obtained by considering the array as a continuous line source. Distributions of conductance per unit length for three Taylor aperture distributions are thus obtained. However, the discreteness of the array is retained for a discussion of second-order beams and for the development of a method leading to their suppression. The performance of an experimental array is described.

Journal ArticleDOI
TL;DR: In this paper, a broadside phased array (SFA) was used to swing a 0.49-degree beam in azimuth through a 4.2-degree sector each tenth of a second.
Abstract: By using a broadside phased array for an antenna, a narrow beam can be swung rapidly and in quick succession through a limited sector by fast control of the phasing, rather than by movement of the entire antenna structure. This technique is used at the receiving end of a 101-mile beyond-the-horizon transmission path in order to probe the portion of the troposphere through which the signal is propagated. At the frequency employed of 3.12 kmc, a 0.49- degree beam is swung in azimuth through a 4.2-degree sector each tenth of a second. A variety of phenomena are observed with this technique which have not been directly apparent in slower beam-swinging experiments. The beam-broadening effect attributed to atmospheric scattering is not always evident on any one sector scan. However, the change from scan to scan is frequently rapid enough so that a time average would show the broadening. At times the scan-to-scan changes are systematic and show a continuity indicative of a motion of the scattering or reflecting regions; in some cases this motion is too rapid to be accounted for by transport of air, thus implying a wave motion rippling through the atmosphere. At other times the atmospheric structure is too fine to be resolved by the beamwidth employed, and the time variations are too rapid to reveal a continuity from one scan to the next.


Journal ArticleDOI
TL;DR: In this paper, the applicability of the four electrode methods of measuring ground conductivity at very low radio frequencies is discussed and the general theory is extended to include anisotropy in the substrata.
Abstract: The applicability of the four electrode methods of measuring ground conductivity at very low radio frequencies is discussed. The general theory is extended to include anisotropy in the substrata. In view of the spurious coupling between the current and potential line in conventional configurations, an alternative array is proposed which is arranged so that the inductive coupling is zero. A number of charts are computed which facilitate the interpretation of the measured or apparent conductivity in terms of a two-layer earth.

Journal ArticleDOI
TL;DR: In this paper, the U.S. Navy's high-power transmitter to be located in Maine, was the first to radiate 1 megawatt continuously at 15 kc.
Abstract: For a VLF flat-top antenna much smaller than the radian sphere (a sphere whose radius is one radianlength), the effective height, effective area, and effective volume are defined. The required power factor of radiation proportionately determines the effective volume. For a specified power to be radiated, the effective height inversely determines the current and the effective area inversely determines the voltage. For a limited electric gradient on the overhead wires, the current requires a proportionate area of conductor surface. A corresponding total length of wire in the flat top is adequate if disposed for uniform distribution of charge and if spread out to realize the required effective area. These objectives are obtained more readily by some configurations, such as long parallel wires or concentric circles of wire. This study has been made for the U. S. Navy's high-power transmitter to be located in Maine, the first to radiate 1 megawatt continuously at 15 kc.

Journal ArticleDOI
TL;DR: In this paper, the problem of finding the maximum attainable gain is solved through the introduction of n dimensional vectors and tensors and the result is obtained in closed form for the case of two harmonics, and it is concluded that a small improvement in the specific gain is accompanied by a large change in the super gain ratio.
Abstract: If the highest permitted harmonics of the distribution function (this is the quantity of interest in practical application) and the supergain ratio are given, what is the maximum attainable gain? In this paper this optimum problem is solved through the introduction of n dimensional vectors and tensors and the result is obtained in closed form. For the case of two harmonics, numerical results are given. It is concluded that a small improvement in the specific gain is accompanied by a large change in the supergain ratio. The examination of the maximum of the specific gain, without auxiliary condition, leads to the conclusion that the addition of every harmonic increases the value of specific gain, but that the improvement is negligibly small until the number of harmonics becomes greater than the size of the aperture in wavelength. Using the method developed in this paper it is possible for any finite number of harmonics to calculate the optimum distribution function, but the computations become very lengthy as the number of harmonics increases.

Journal ArticleDOI
TL;DR: In this article, a simplified method of computing knife edge diffraction in the shadow region is presented which is applicable to most obstacle gain paths, that is, paths with a dominant mountain obstacle.
Abstract: A simplified method of computing knife edge diffraction in the shadow region is presented which is applicable to most obstacle gain paths, that is, paths with a dominant mountain obstacle. The method has been worked out for 1) the four-ray model-specular reflection on each side of the obstacle, 2) the two-ray model-reflection on one side only, and 3) the single-ray model-no reflection on either side. The obstacle can be at any location along the path. The accuracy is within 2 db for path geometries such that the usual diffraction parameter u is greater than 1 and the two terminal heights are less than the obstacle height. Curves which further simplify the computation procedure are presented.

Journal ArticleDOI
TL;DR: In this article, it was shown that mixing-ingradient cannot explain the wavelength dependence characteristic of much of the radio data, and experimentally determined spectra of refractive index fluctuations lend strong support to the mixing theory.
Abstract: The Villars-Weisskopf-Wheelon theory describing turbulent mixing of an established gradient is shown to contain a contradiction which necessitates its being discarded. To fill the gap thus created, the theory of isotropic mixing is extended to account for the presence of a gradient. The results indicate that "mixing-ingradient" cannot be employed to explain the wavelength dependence characteristic of much of the radio data. On the other hand, it is shown that experimentally determined spectra of refractive index fluctuations lend strong support to the mixing theory herein set forth. Hence, the conclusion is reached that scatter theory, as it is currently based on atmospheric turbulence, can provide, at best, an incomplete description of transhorizon propagation.

Journal ArticleDOI
R. Tanner1
TL;DR: It is shown that shunt and notch antennas are most effective when located in a region of high current concentration, and that the current concentration which occurs in the fillet area of swept-wing aircraft makes this area particularly favorable for their installation.
Abstract: In the hf range radiation from aircraft must be accomplished by exciting radiating currents on the airframe itself. One method of exciting such currents is by shunts or notches which electrically penetrate the airframe. The strength of coupling of such devices is analyzed and shown to be proportional to the square of the normal mode current which they interrupt. A theory is developed and substantiated by experimental data, which enables the prediction of the impedance characteristics of such antennas. It is shown that these antennas are most effective when located in a region of high current concentration, and that the current concentration which occurs in the fillet area of swept-wing aircraft makes this area particularly favorable for their installation. Shunt and notch antennas, when they can be used, have a number of structural advantages over cap-type antennas, and certain electrical advantages also. They require no special lightning protection and eliminate the need for special isolating devices. In general, they are capable of handling higher powers before encountering high-altitude voltage breakdown.

Journal ArticleDOI
TL;DR: In this paper, the radiation properties of a single Zig-zag antenna are reported, which is a special type of broad-band traveling-wave antenna which, when properly designed, produces a strong axial beam of radiation.
Abstract: The radiation properties of a single zig-zag antenna are reported. This is a special type of broad-band traveling-wave antenna which, when properly designed, produces a strong axial beam of radiation. The radiation pattern has a half-power beamwidth of 22\deg in the E plane and 28\deg in the H plane; the corresponding sidelobe ratios are 10.5 db and 17.5 db down, respectively, in the two planes. Approximate expressions for the radiation fields are also given and compared with the experimental values. The broad-band property of the antenna is studied by measuring the radiation patterns over a range of frequencies. The performance of the antenna is compared with the Yagi antenna. The high directivity of the antenna can be utilized advantageously in the vhf and uhf ranges. The results of impedance measurement also are reported.

Journal ArticleDOI
TL;DR: In this paper, the exact fields generated by transient electric and magnetic dipoles in an infinite conducting medium were derived and a specialization to brief, approximately triangular pulses was made to bring out the salient practical features of such signals.
Abstract: The exact fields generated by transient electric and magnetic dipoles in an infinite conducting medium are derived. Specialization to brief, approximately triangular pulses then brings out the salient practical features of such signals. The peak signals are attenuated as r^{-3} or r^{-4} rather than exponentially, and, in a practical sense, they travel very slowly (mean effective velocity about equal to sonic speed for a range of 1 km in sea water).

Journal ArticleDOI
TL;DR: In this article, an experimental comer reflector was erected at the Table Mesa antenna range near Boulder, and the aperture angle of this antenna was made adjustable to any value between 20 and 180 degrees.
Abstract: An experimental comer reflector was erected at the Table Mesa antenna range near Boulder. The aperture angle of this antenna was made adjustable to any value between 20 and 180 degrees. The widths and lengths of the reflecting surfaces were each adjustable from 0.4 to 5.0 wavelengths. Measurements of gain were made for numerous combinations of lengths and widths of reflecting surfaces. These measurements were made with a half-wave dipole in the first, second and third maximum positions. The aperture angle was adjusted to maximize the gain. The principal results are presented in the form of contours of constant gain plotted for a range of widths and lengths of reflecting surfaces from 0.4 to 5.0 wavelengths. These graphs should be useful to a designer of corner-reflector antennas.

Journal ArticleDOI
TL;DR: In this article, the influence on field strength from ground moisture and temperature, snow, topography, and vegetation, and also field strength variations along mixed land-water paths have been studied.
Abstract: Results are given from a general investigation regarding the different factors that govern vhf ground wave propagation at low heights and short distances, i.e., mainly in the Sommerfeld region. In this work the influence on field strength from ground moisture and temperature, snow, topography, and vegetation, and also field strength variations along mixed land-water paths have been studied. The measurements refer to terrain typical for middle Sweden. Suitable formulas for field strength calculations over smooth ground are developed. The moisture in the ground is found to play a principal role and a method is shown for calculation of changes in the path attenuation caused by known or predicted changes in the water content of ground. The influence of temperature is found to be smalls even when the ground freezes, but a covering of snow may be of greater consequence. Characteristics of local variations and exponential attenuation of the field in a forest is demonstrated, the fluctuations being very large and the average exponential attenuation factor mostly very small. Measurements along a mixed land to fresh-water path verifies Millington's recovery effect. The field over a hill is found to have a maximum value a certain distance below the top towards the transmitter.

Journal ArticleDOI
TL;DR: In this paper, high-frequency radio echoes from ionization associated with the Aurora Borealis have been identified at Stanford University (geomagnetic latitude 43.75°75°deg ).
Abstract: High-frequency radio echoes from ionization associated with the Aurora Borealis have been identified at Stanford University (geomagnetic latitude 43.75\deg ). The echoes occur at ranges between 1400 km and 4700 km corresponding to reflection from ionization in the zone of maximum auroral occurrence located far to the north of Stanford. The formation of the ionization is attributed to the bombardment of the upper atmosphere by high-speed charged particles emitted from the sun. The echoes have great amplitudes with duration times between one second and one hour. Their appearance and disappearance is quite similar to the behavior of visual auroras; the occurrence of the echoes has been found to be related to geomagnetic disturbances. The heights of reflection appear to be between 100 km and 1200 km above the surface of the earth. The paths which the auroral signals travel over the relatively enormous distance from Stanford to the auroral zone (and back) are greatly influenced by the presence of the normal ionospheric layers. The echoes have been observed at ranges and bearings which indicate reflection from ionization at points along the auroral zone all the way from eastern Canada to Alaska.

Journal ArticleDOI
TL;DR: In this article, the authors give susceptance data for practical configurations having electrical diameters of from 0.2 to 0.6 wavelength, and describe the theory of operation of the annular slot radiator.
Abstract: While several excellent papers have been published describing the theory of operation of the annular slot radiator, certain design parameters have not been too readily available. This note gives susceptance data for practical configurations having electrical diameters of from 0.2 to 0.6 wavelength.

Journal ArticleDOI
TL;DR: In this article, the power of the Sommerfeld expansion in computing Fresnel and near fields of antennas has been shown, a matter which has become of increasing importance in high resolution antennas.
Abstract: The purpose of this paper is to show the power of the Sommerfeld expansion in computing Fresnel and near fields of antennas, a matter which has become of increasing importance in high resolution antennas. A connection is shown between the Fresnel and Fraunhofer approximations for radiation fields which is derived by using Sommerfeld's expansion of the field in inverse powers of radial distance. This expansion permits an estimate of the error incurred in using the Fresnel approximation. Higher-order corrections to the phase and amplitude portion of the Fresnel approximation are also exhibited. By way of illustrating the power of the Sommerfeld expansion of the fields in the Fresnel (intermediate) region of a radiation source, numerical calculations of amplitude, phase, and power patterns have been made for a finite line source of length D with an equiphase cosine-on-a-pedestal current distribution. It is found that the first five terms of the series are sufficient to obtain accurate results when r\geqD^{2}/2\lambda , as compared with the Fraunhofer approximation which is usually considered valid for r\geq2D^{2}/\lambda . Non-Fraunhofer zone effects on the power pattern and phase front are discussed as a function of distance r and the type of current distribution.

Journal ArticleDOI
TL;DR: In this article, a microwave device is described which collimates the radiation from a point feed into a parallel beam using reflection and diffraction, and the expressions of the aberrations are worked out and a graph is given where one can read the maximum values of the aperture and field for a given tolerance.
Abstract: A microwave device is described which collimates the radiation from a point feed into a parallel beam. The instrument operates by both reflection and diffraction. The offense against the sine condition is corrected perfectly, so that no monochromatic aberration is present for a moderate field even at very high apertures. The expressions of the aberrations are worked out and a graph is given where one can read the maximum values of the aperture and field for a given tolerance. It seems that the device described may be useful for radio astronomy and for rapid scanning.

Journal ArticleDOI
R. Bickmore1
TL;DR: In this paper, an exact effective aperture based on half-power beamwidth is derived and compared with the approximate solution for various aperture lengths as a function of scan angle, where the end-fire effect is negligible.
Abstract: Since the size of current radar antennas must be increased in order to detect aircraft and missiles flying at supersonic speeds, it is no longer possible to use rapid mechanical scanning. Therefore this type of scanning is being gradually replaced by electrical scanning. The popular approximation which states that the effective aperture length is proportional to cos \theta_{0} , where \theta_{0} is the scan angle from broadside, is examined and shown to be adequate in many cases where the end-fire effect is negligible. An exact effective aperture based on half-power beamwidth is derived and compared with the approximate solution for various aperture lengths as a function of scan angle.