David K. Cheng

Optimization techniques for antenna arrays

Various techniques for optimizing the performance indices of antenna arrays are discussed. In particular, methods for maximizing array directivity and signal-to-noise power ratio are reviewed. These performance indices are expressible as a ratio of two Hermitian forms, which has a certain special property to enable the facile determination of both its maximum value and the conditions under which this maximum is attained. Special maximization procedures by excitation amplitude and phase adjustments, by spacing perturbation, by phase adjustments only, and by a coordinate transformation with constraints on the array pattern are examined. For wire antennas the method of moments using a subsectioning technique can be applied to obtain numerical answers which include mutual-coupling effects. Methods for considering large arrays and for the maximization of power gain are indicated.

Covariant descriptions of bianisotropic media

It is suggested that a medium it which the field vectors D and H depend on both E and B but are parallel to neither be described as bianisotropic. A moving medium, even if it is isotropic it its rest frame, then appears bianisotropic to the laboratory observer. This paper gives the transformation formulas for the constitutive relations of a bianisotropic medium between inertial frames in relative motion. It circumvents the necessity of knowing the constitutive relations of the medium in its rest frame. As an application of the general formulation, the dispersion relations for plane waves in a bianisotropic medium are derived.

Optimum scannable planar arrays with an invariant sidelobe level

This paper presents two alternative methods for determining the current distribution in the elements of a scanning rectangular array which is optimum in the sense that its radiation pattern has a constant sidelobe level and a narrowest beamwidth in all directions. Exact formulas for both even and odd numbers of elements are given. The dependence of the main-lobe beamwidth on the total number of elements, the element spacing, the sidelobe level, and the scan angle is studied in detail. The minimum required number of controlled elements in a square array with electronic beam scanning over a specified sector for a guaranteed upper limit on beamwidth without grating lobes is determined. Numerical results are included, which illustrate many interesting features of the new design technique.

Gain optimization for Yagi-Uda arrays

The author presents a personal account of the search for a design procedure for Yagi-Uda antenna arrays yielding a maximum gain, or directivity if element losses are neglected. Results on current distributions in the array are briefly reviewed. The analytical approach used to achieve gain optimization by means spacing and length perturbations is sketched. By using both spacing and length perturbations, it was possible to find the optimized array analytically in a systematic way, some examples having gain increases of nearly 80%. The effects of finite dipole radius and mutual coupling were included in the theoretical treatment.<<ETX>>

Electromagnetic fields coupled into a cavity with a slot-aperture under resonant conditions

The electromagnetic coupling of an incident plane wave through a slot-aperture backed by a lossy rectangular cavity is analyzed by using a generalized network formulation based on an application of the equivalence principle. Two types of aperture-cavity resonances manifest themselves. The conditions for the existence and the characteristics of such double aperture-cavity resonances are studied. General expressions for field strength in the aperture, field distributions in the cavity, and maximum power penetration are derived. Appropriate expressions for an equivalent magnetic current to replace the aperture are discussed. A numerical example is given.

Wave Behavior at an Interface of a Semi‐Infinite Moving Anisotropic Medium

The wave behavior at an interface between an isotropic medium and a moving anisotropic medium for an arbitrary plane of incidence is studied. Modified forms of Snells law for refraction are obtained for both the ordinary and the extraordinary waves when the moving medium is uniaxially anisotropic. The critical angle for total reflection is computed for the extraordinary wave as a function of medium velocity and anisotropy. It is found that the reflected and refracted waves behave quite differently, depending on whether the moving medium is a uniaxial crystal or a magneto‐ionic plasma in an infinitely strong magnetic field. Conditions for the existence of the Brewster angle, even for a prependicularly polarized wave incident normal to the direction of medium motion, are examined. Curves for reflection coefficient are plotted vs medium velocity.

A new mathematical approach for linear array analysis

It is well known that linear antenna arrays are representable mathematically by polynomials. However, even for the simplest case of a uniform array, properties of its radiation pattern are conventionally analyzed by examining the transcendental form of the array factor and some of its important characteristics have been determined only approximately. For a more general array, a closed form of the associated polynomial is usually not obtained and the analysis becomes quite difficult. This paper proposes a new approach for linear array analysis. Basically, the current distribution in the discrete elements of a linear array is considered as the sampled values of a continuous function. Known relations in Z , transforms developed for sampled-data systems can then be used to express the array polynomial in a closed form. Mathematical techniques for determining important properties of the array pattern are developed. Typical examples illustrating the applications of this new approach are given.

On the simulation of Fraunhofer radiation patterns in the Fresnel region

Physical limitations on the size of obstacle-free test sites give rise to the need of making radiation-pattern measurements on high-gain antennas at a reduced distance. The general practice is to defocus the primary source along the principal axis of the antenna reflector by a small distance so that Fraunhofer patterns may be simulated in the Fresnel region. This note summarizes and compares three different approaches with which the proper amount of defocus may be determined.

Time‐Harmonic Fields in Source‐Free Bianisotropic Media

A bianisotropic medium is defined as one in which the field vectors D and H depend on both E and B, but may not be parallel to either. A moving medium appears bianisotropic to the laboratory observer, even if it is isotropic in its rest frame. It is shown that, for time‐harmonic fields, a bianisotropic medium can be viewed as one which is electrically and magnetically anisotropic with properly defined dyadic operators. In particular, a moving medium can be characterized by a permittivity tensor and a permeability tensor for plane‐wave propagation. This characterization simplifies the solution of electromagnetic problems in moving media. As illustrated, the dispersion relations in a moving uniaxially anisotropic medium are obtained, and the problem of a plane wave normally incident upon a moving uniaxial medium is solved.

REFLECTION AND REFRACTION OF ELECTROMAGNETIC WAVES BY A MOVING UNIAXIALLY ANISOTROPIC SLAB.

The reflection, refraction, and transmission characteristics of a plane electromagnetic wave incident from an isotropic medium, through a moving uniaxial slab, and into another isotropic medium are studied. The conceptual equivalence of a moving medium and a stationary anisotropic one with suitably defined permittivity and permeability tensors is used for the analysis. Complete field expressions are obtained in all three regions for an arbitrary orientation of the plane of incidence and an arbitrary angle of incidence. Special cases where the plane of incidence is parallel, or perpendicular, to the direction of slab motion are considered for both an incident E wave and an incident H wave. Some interesting numerical results are presented for the transmission coefficient at normal incidence when the moving slab is a magnetoionic plasma subject to a strong magnetic field and when the moving slab is a uniaxial crystal.