A class of antennas that utilizes arrays of elementary antennas as reflecting surfaces has been investigated. An antenna of this type is here called a Reflectarray. It has been found that the Reflectarray combines much of the simplicity of the reflector-type antenna with the performance versatility of the array type. The reflecting surfaces employed in these antennas are characterized by a surface impedance that can be synthesized to produce a variety of radiation patterns. The equations of the surface impedance as a function of the desired reflected phase front is derived for the lossless case and methods of realizing this surface impedance are presented. Experimental results of a waveguide array type Reflectarray are given including pencil beam, broad beam and scanning modes. Data on the effects of specific phase errors are presented.

The reflectarray antenna

An overview of electronically scanned array technology with a brief introduction of the basic theory and array architectures are presented. Implementations, current state-of-the-art, and future trends are briefly reviewed in Part II of this paper.

Phased arrays - part 1: theory and architectures

The differences in mutual coupling for a central slot and a peripheral slot cannot be ignored in small arrays if good patterns and impedance are to be obtained. A theory has been developed whereby the length and offset of every slot in the array can be determined, in the presence of mutual coupling, for a specified aperture distribution and impedance match. The theory enlarges on Stevenson's method, and uses a modified form of Booker's relation based on Babinet's principle to treat nonresonant longitudinal shunt slots in the broad wall of a rectangular waveguide. A general relation between slot voltage and mode voltage is developed, and then formulas are derived for the active, self-, and mutual admittances among slots. These formulas result in a design procedure. Analogous treatments of inclined series slots in rectangular guide and of strip-line-fed slots are possible. Comparison between various experiments and the theory is presented. Tests of the theory include the resonant length of a zero offset slot, resonant conductance versus offset and resonant conductance versus frequency for a single slot, and self- and mutual admittances for two staggered slots. The design and performance of a two-by-four longitudinal shunt slot array is also described.

The design of small slot arrays

This paper discusses in some detail the scanning properties of planar and linear phased arrays consisting of a large number of equispaced radiators, either omnidirectional or directive. Assuming that a suitable beam shape and sidelobe level in the broadside direction have been attained, it is shown how scanning of the array through introduction of a phase delay into the wave front distorts this pattern and introduces new sidelobes. The study uses contour maps of the antenna pattern in "sin ?-space," which is a projection of the unit sphere on the plane of the array. In this space the antenna pattem remains invariant with scan angle and merely undergoes a translation proportional to the phase delay between adjacent radiators. Using a parallel projection of the unit sphere onto the plane of the array, the actual antenna pattems are then readily obtained in conventional spherical coordinates. This method also permits ready evaluation of the influence of the directivity of the radiating elements, including a slight shift of the beam maximum with respect to that of an array of isotropic radiators. Furthermore, a pictorial representation of the coverage of a tilted planar array of given scanning properties can be obtained in terms of an earth-fixed coordinate systerr. Finally, it is shown how the beam-pointing error in a phased array is related to systematic errors in the phase delay.

Properties of Phased Arrays

An analytical method based on Interval Analysis (IA) is proposed to predict the impact of the manufacturing tolerances of the excitation amplitudes on the radiated array pattern. By expressing the array factor according to the rules of the Interval Arithmetic, the radiation features of the linear array are described in terms of intervals whose bounds are analytically determined as functions of the nominal value and the tolerances of the array amplitudes. A set of representative numerical experiments dealing with different radiated beams and linear array sizes is reported and discussed to point out the features and potentials of the proposed approach.

Tolerance Analysis of Antenna Arrays Through Interval Arithmetic

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.

R. Elliott

Papers

Mechanical and electrical tolerances for two-dimensional scanning antenna arrays