Showing papers in "IEEE Transactions on Antennas and Propagation in 1967"

Geometrical shadowing of a random rough surface

Abstract: In the context of the backscattering of waves from a random rough surface, a theoretical model is used to investigate the geometrical self-shadowing of a surface described by Gaussian statistics. Expressions are derived for various shadowing probabilities as functions of the parameter characterizing surface roughness and of the angle of incidence of the illuminating beam. The theoretical shadowing functions compare closely with those obtained experimentally from a recent computer simulation of a Gaussian surface.

Depolarization of EM waves by slightly rough surfaces

Abstract: Depolarization is obtained for the scattering of electromagnetic waves from a slightly rough surface using Rice's theory. In the plane of incidence, depolarization is a second-order effect. The results are applied to backscattering from a slightly rough sea using the Neumann spectrum for a fully developed sea. The expression for the depolarized scattered power is of the form obtained in multiple scattering investigations. Therefore, it can be inferred that depolarization from slightly rough surfaces is due to multiple scattering. For the sea, depolarization increases with wind speed and with the magnitude of the complex dielectric constant of the surface.

On radio-wave propagation in forest environments

Abstract: Propagation of electromagnetic waves in forest environments at medium and high (1-100 MHz) frequencies is examined for the case where both the transmitting and receiving points are situated within the vegetation. A dissipative slab in the presence of a reflecting ionosphere is employed to describe the forest configuration. If the effect of the ground-forest interface is disregarded, the radiated field of an arbitrarily oriented, small dipole is found to consist primarily of two separate waves: a lateral wave which skims along the tree tops, and a sky wave which is produced by a single-hop reflection at the ionospheric layer. These two field constituents are compared and their domains of preponderance are calculated for a large range of the pertinent parameters; it is then found that the lateral wave plays the major role since the sky wave is restricted to a narrow frequency band and its amplitude is appreciable only at large distances. The lateral-wave field is examined in detail and is shown to yield a simple physical picture for the propagation mechanism in forests. Its features are found to be qualitatively consistent with the field behavior reported in the literature and the quantitative aspects agree well with the available experimental data. The observed variation of the field with distance, the height-gain effect, the vegetation factor, the basic path loss, and depolarization effects are separately examined and are all shown to express merely one or another of the intrinsic properties of a lateral wave. The ground-proximity effect produced by the presence of a planar-conducting ground is also estimated and shown to be of minor importance in most cases.

The apparent temperature of the sea at microwave frequencies

Abstract: A discussion of the apparent temperature of the sea at microwave frequencies is presented using a theory based on the Kirchhoff approximation for scattering from rough, finitely conducting surfaces. Detailed numerical results on the variation of the temperature with wind speed are discussed for a frequency of 19.4 GHz. The dependence of the rms slope of the sea on wind speed, which is needed in the theory, is based on experimental measurements. It is found that significant temperature changes occur with increasing wind speed for horizontally polarized radiation. The temperature of vertically polarized radiation is much less affected by the wind and, at an angle of 50\deg (at 19.4 GHz), is almost independent of the state of the sea.

Polarization and angle-of-arrival fluctuations for a plane wave propagated through a turbulent medium

Abstract: The correlation function of the fluctuations of the depolarized component of a plane wave as a function of the distance between two parallel line-of-sight paths is derived in terms of the index of refraction variations. A first-order solution to the wave equation is found using spectral analysis techniques. The mean square polarization fluctuation is predicted to have a \lambda^{2} dependence, in contrast to the work of another author which showed no wavelength dependence. Some numerical values are calculated and the restrictions on the solutions are discussed. At optical wavelengths the depolarized component is extremely small. From the point of view of minimizing the noise introduced by a turbulent atmosphere, polarization modulation seems attractive compared to amplitude or angle modulation. The problem of determining the angle-of-arrival fluctuations when using a wave optics formulation is discussed. If one accepts the statement that the angle-of-arrival is the normal to the wave front at any point, then the correlation function of the angle-of-arrival is simply related to the correlation function of the phase fluctuations and agrees with the ray optics results.

A note on reflector arrays

Abstract: A Van Atta antenna array, which has a major lobe of the reradiated field in a direction retrograde to that of the incident wave for arbitrary directions of incidence, is analyzed in terms of the scattering matrix of the network interconnecting the antennas.

Transient signal propagation in lossless, isotropic plasmas

Abstract: The asymptotic behavior of transient signal propagation in lossless, isotropic plasmas is discussed for a typical input signal of a step modulated sine wave. A generalized saddlepoint integration is carried out which gives a continuous solution for the dispersed signal everywhere except at the signal wavefront. The solution which is valid at the signal wavefront is obtained by using a high-frequency expansion technique. Universal curves are presented for the behavior of the distorted signal as a function of the plasma frequency, signal frequency, and propagation distance. The solution is a good approximation for the case of plasma propagation lengths which are long compared to a free space wavelength and for the operating frequency near the plasma frequency. This solution is useful since the available exact solutions for this case converge too slowly to be practically computed.

Theory of conical equiangular-spiral antennas--Part I--Numerical technique

Abstract: The integral equation method is applied to find the rigorous solutions of the current distributions on conical, eqaiangular-spiral antennas of arbitrary spiral parameter and cone angle. With a transcendental interpolation function, antennas up to 10\lambda in armlength can be calculated. Comparisons of calculated and experimental results are presented, indicating excellent agreement. The computer programming resulting from this investigation thus replaces painstaking procedures of design, experimentation, and optimization of equiangular-spiral antennas by a few minutes of computer calculations.

Flush mounted rectangular cavity slot antennas--Theory and design

Abstract: The loaded rectangular cavity slot antenna is analyzed using variational methods in conjunction with simplified equivalent circuit techniques to derive accurate design guides for efficiency, bandwidth, and resonant frequency. The aperture admittance is computed and the effects of a compound aperture plane iris and of material loading are analyzed. The aperture admittance of all such loaded cavity antennas is proportional to \mu_{r} , \sqrt{\mu_{r}/\epsilon_{r}} , or 1/\epsilon_{r} , which characteristic lends to a common method of optimization of |T|^{2} (transmission cofficient). Experimental results include: 1) measurements of aperture field; 2) a comparison of theoretical and experimental value of bandwidth, efficiency, resonant frequency, and beam pattern for several experimental models; and 3) the measurement of the effect of applied dc magnetic field.

Straight wires with arbitrary excitation and loading

Abstract: A general analysis of straight wire antennas and scatterers, with arbitrary excitation and loading, is given. The resulting formulas are in matrix notation, in a form suitable for programming on a digital computer. Many numerical results for input admittances, current distributions, radiation patterns, and scattering cross sections of various antennas and scatterers are included.

The admittance of a rectangular waveguide radiating into a dielectric slab

Abstract: The variational analysis of Compton is modified to account for the surface-wave pole contribution to the admittance of a waveguide-fed slot on a ground plane covered with a low-loss dielectric slab. The results of an extensive experimental study to determine the effects of ground-plane and dielectric slab size upon waveguide admittance are compared with calculations using the dominant waveguide mode field as a trial solution. It is found that a waveguide terminated in a flat flange is of sufficient size to approximate the infinite ground plane assumed in the theory. A disagreement of 20 percent was noted for some thin sheet cases. Based upon a thorough theoretical and experimental investigation, it was concluded that tolerances do not explain the error; however, a measurement of the aperture field for cases where maximum error occurs reveals significant distortions. Hence, it is concluded that induced higher-order modes are the probable cause of disagreement.

Path diversity in propagation of millimeter waves through rain

Abstract: Cumulative distributions of attenuation due to rain are computed for the frequencies 11,18.5, and 30 GHz. The results are derived from a four-year sample of rainfall data obtained on a highly resolving areal rain gauge network in Bedfordshire, England. Lack of correlation of attenuation on both orthogonal and parallel paths is discussed and the effect of path diversity is demonstrated for the frequency 30 GHz. Examples of computer-generated maps of intense rain showers at the earth's surface are given.

Propagation in random media--Cumulative effect of weak inhomogeneities

Abstract: The effect of weak, random inhomogeneities on wave propagation is studied. Of particular concern is the case of long distance propagation where the nature of the wave is significanfly affected by the inhomogeneities. Conventional perturbation techniques such as geometrical optics and the Born and Rytov approximations cannot be applied in this realm. The approximation technique employed is basically a selective summation technique of the type utilized in other areas of physics such as quantum electrodynamics and the theory of many-body interactions. Results are obtained for the average value and two-point correlation function of an arbitrary, initial wave. A physical interpretation of the results in terms of coherent and incoherent scattering and the classical theory of dielectrics is given. Wave statistics and the application of the results to the problem of determining the effect of the atmosphere on coherent optical communication are discussed.

An experimental investigation of dielectric-coated antennas

Abstract: The characteristics of a monopole antenna embedded in a cylinder of low-loss dielectric have been measured. A cylinder of infinite length was approximated by extending the length of a finite cylinder until the admittance did not change. Admittance and current distribution data are represented as a function of antenna length for various diameters and dielectric constants of the cylinders. The results compare well with a theoretical analysis by Ting. The effect of the cylinder is to increase the electrical length of the antenna and decrease the bandwidth.

Application of spherical wave theory to cassegrainian-fed paraboloids

Abstract: In this paper the spherical wave expansion technique is used to analyze the general properties of paraboloidal antenna feed systems. As a result, fundamental aperture efficiency and noise temperature limitations are established as quantitative functions of antenna wavelength size. A boundary-value solution is found for synthesis of ideal subreflector shapes in a Cassegrain-type feed system. The resulting surface is found to reduce the classical hyperboloid in the limit of zero wavelength. Applications of this synthesis technique to high performance feed systems and subreflector matching are discussed. Finally, an interesting quantitative cross-check between vector spherical wave and vector diffraction theories is obtained.

An experimental study of the antenna with nonreflecting resistive loading

Abstract: The current amplitude, input admittance, and radiation field pattern of a dipole antenna with a step-function internal impedance were measured in the UHF range and compared with theory. The zero-order theory gives accurate descriptions of the current distribution, the field pattern, the wide bandwidth property, and the existence of the traveling wave on the antenna. The agreement in the input admittance is not good, but it can be improved with the help of the variational principle. The field pattern of this resistive antenna when displayed as a 90\deg V antenna was found to be directional and insensitive to changes in frequency.

Asymptotic theory for dipole radiation in the presence of a lossy slab lying on a conducting half-space

Abstract: The basic theory for dipole radiation in the presence of a two-layer half-space is outlined with special reference to its use as a model for studying radio propagation through and over heavily vegetated terrain. The source dipole may be located above or below the top surface of the slab. The dipole orientation is either vertical or horizontal. The asymptotic derivations for the field expressions are carried out without making the usual assumption that the refractive index of the uppermost layer is large compared with unity. The final results exhibit the expected inverse square dependence of the field on horizontal range.

Resolution limitations of a finite aperture

Abstract: Methods of increasing antenna resolution by data processing are of interest in radio astronomy and radiometric mapping applications. This paper deals with the fundamental limitations of such operations. Communication theory techniques using prolate spheroidal wave functions have already been applied to antenna pattern synthesis. These techniques are applied to the problem of reconstituting an observed temperature distribution. The manner in which noise limits this reconstitution process is clearly shown. A least expected mean square error reconstitution process is also detailed. An interesting analogy between data processing and supergaining is noted. Finally, the limitation set by noise on the resolution of a data processed finite aperture is concluded.

Coherence theory of radio-astronomical measurements

Abstract: A unified theory of radio-astronomical measurements is presented within the framework of the theory of partial coherence. It is shown how different coherence functions are related to the spectrum, the brightness distribution, and the polarization of statistical electromagnetic fields, and to their measurement. These coherence functions can be derived from the space-time coherence tensor. Various radio-astronomical techniques for measuring the spectrum, the brightness distribution, and the polarization are discussed with special reference to correlation techniques. The connection between the theory of antennas and that of optical systems is discussed. In both cases the theory of partial coherence provides a unified theoretical foundation and an important framework for future research and development.

The quasi-near fields of dipole antennas

Abstract: The electric- and magnetic-field components produced by vertical and horizontal dipole antennas (both electric and magnetic types) located over, on, or below the surface of a semi-infinite conducting medium are derived and presented for the quasi-near range. (The measurement distance is much greater than an earth skin depth, but much less than a free-space wavelength.) Previously derived results are briefly summarized. The horizontal separation \rho between the transmitting and the receiving dipole antennas is comparable to their heights. The derivations are the result of applying the quasi-near approximations to the basic Sommerfeld integrals and, in some cases, utilizing the reciprocity theorem. When \rho is much greater than the antenna heights, the formulas for the field-component expressions reduce to previously derived results. It is observed that some of the field-component expressions are characterized by unusual height gain (or loss) functions. Some numerical values for these functions are provided.

Gain optimization for arbitrary antenna arrays subject to random fluctuations

Abstract: A general procedure is formulated for the maximization of the expected directive gain for arbitrary antenna arrays whose excitation amplitudes and phases as well as element positions are subject to random errors. Correlations are allowed to exist between the random fluctuations, and the general formulation imposes no restrictions on either the magnitude or the probability distribution of the fluctuations. Numerical examples are given which illustrate the dependence of the expected gain, the main-beam radiation efficiency, the radiation pattern, and the optimum element excitations on the standard deviation and correlation distance of the parameter errors. It is shown that, in typical cases, the properly optimized array yields not only a higher directive gain and a higher mainbeam radiation efficiency but also a better radiation pattern than an array which is "optimized" under the assumption of no random errors.

Guided waves in bounded media with random gross inhomogeneities

Abstract: A formalism to deal with propagation in waveguides containing media with statistically inhomogeneous, random, gross inhomogeneities over a finite axial range is proposed. Statistics of the propagating fields are obtained in terms of those of the medium through an iterative perturbation technique which does not use expansion in a small parameter. A modal expansion, with a nonlinear phase progression term in the exponent of the axial dependence of the incident mode, is utilized and permits the direct calculation of all desired field statistics from the formal perturbation expressions for the modal amplitudes and phase progression. Examples are presented to show that many quantities of interest, involving mode coupling and transmission and reflection parameter., may straightforwardly be determined through this procedure. Some prevalent notions concerning the significance of the mean wave are discussed.

A study of the sheath helix with a conducting core and its application to the helical antenna

Abstract: A theoretical study of the sheath helix antenna with a conducting core is made via the complex solutions of an associated determinantal equation. The variation of the characteristics of operation with respect to core size and pitch angle is established. A comparison of the complex solutions for the sheath helix and tape helix indicates that a good understanding of the helical antenna can be gained from the sheath model. In particular, explaining broadside radiation in terms of complex solutions is shown to give results in agreement with previously reported empirical data. However, this comparison also points out the limitations of the sheath model in predicting the operational parameters accurately.

An analytical approach to the coverage of a hemisphere by n planar phased arrays

Abstract: The coverage of a hemisphere by N planar phased arrays arranged in pyramids or pyramidal frustra is discussed. Transformations between the spherical coordinates of individual arrays and of the hemisphere of coverage are derived. These results are then used to determine the minimum value of the maximum scan angle required of each array and the positioning of the arrays. Numerical results are given. These transformations are also used to minimize the number of elements needed in a given array aperture. This is shown for an example with both equilateral triangular and rectangular element spacing. It is further demonstrated how the use of an isosceles triangular element spacing affords additional reduction of the number of elements needed.

Scattering by random distribution of spheres vs. concentration

Abstract: We give data and theory for scattering of 5-mm waves by Styrofoam spheres moving randomly within a slab region Styrofoam container. The results summarize two systematic programs of measurements for the forward scattered coherent phase, the average intensities (coherent, incoherent, and total), and for the variances and covariance of phase-quadrature components of the instantaneous field. These were obtained separately and simultaneously vs. the number ( N ) of spheres in the container for concentrations corresponding to sparse gases through dense gases, on to the limiting case of an amorphous solid. Two relatively distinct "compression processes" for which the coherent phase increased linearly with increasing N were studied: the amplitude of the covariance was either as large or as small as we could obtain. The data records for the small case are in relatively good accord with computations; those for the large show departures in the direction indicated by qualitative considerations of the effects of clumping.

Waveguide admittance for radiation into plasma layers--Theory and experiment

Abstract: Measured admittance of an X -band waveguide radiating into dielectric and plasma layers is compared with variationally computed admittance figures. The waveguide admittance measurements for polystyrene sheets of varying thicknesses compared closely with calculations. The admittance is computed first by assuming the principal waveguide mode, and second by using a superposition of sine and shifted cosine waves as trial functions for aperture fields. Although the aperture fields are shown to differ significantly in the two cases, the computed admittance data are nearly the same because of the stationary character of the admittance expression. The admittance measurements for plasma layers are made during the diffusion controlled afterglow of a pulsed discharge contained in a bell-shaped vessel. Thin Teflon sheets are used to confine the plasma layers to an approximate size of 5 \times 5 \times \frac{3}{4} inches. The electron density of the plasma profile is measured by Langmuir probes at various times during the afterglow. The plasma density was measured over approximately 70 percent of the thickness of the plasma layers, and was found to be nearly constant in this range which excluded regions near the boundary. Numerical solutions of the equations for ambipolar diffusion during the afterglow in a rectangular geometry show that the lateral plasma density variations are negligible in the vicinity of the waveguide. The measured admittance and plasma density data are shown to agree with calculations made for homogeneous plasma layers, if a correction is made for elevated ion temperatures for times of approximately 10 to 20 \mu s following the discharge. Several computational models consider plasma stratifications near the boundary of the plasma layer but they do not improve the agreement between measurement and calculations.

On antenna tolerance theory

Abstract: To predict the loss of gain of antennas due to surface deviations which are not distributed uniformly over the aperture, an extension of Ruze's theory is presented. It is found that the assumption of uniform error distribution, in general, underestimates the axial gain of an antenna whose surface deviations have regional variations over the aperture. This effect becomes significant only when the surface deviations cannot be considered small as compared to the wavelength. Furthermore, it is found that the assumption of a uniform distribution of error may have a significant effect on the predicted scatter even when surface deviations are not large. Assuming that the deviations from uniform distribution are also random, a correction term to the theory is also presented.