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A simple geometrical estimate resulting from rigorous asymptotic evaluation of the Fourier transform integral leads one to conclude that the angular range of the far-field obtainable using planar near-field measurement techniques is limited by the extent of the scan plane and the separation of this plane from the antenna under test. Here, it is shown that this angular range can be extended to a full hemisphere through proper selection of the measurement parameters and careful treatment of the transform integral. In particular, it is noted that the transverse spectrum of the field can possess singularities. These singularities are spectrally filtered by the finite size of the scan plane resulting in a “muting” effect that must be accounted for in the data processing. This is accomplished through the analytic approximation of the bandlimited singularities. Three hardware examples are shown that demonstrate this more detailed approach comparing the results with corresponding patterns obtained using spherical near-field measurement.

The measured radiation field of an antenna may be expanded in a series of vector spherical modes in a specified spherical coordinate system. Such an expansion may be resolved, by means of an iterative algorithm, into two constituent vector spherical mode expansions in two other specified spherical coordinate systems. The sum of these constituent expansions is equal to the original total radiation field. The purpose of such a resolution is to separate the radiation fields due to two identified parts of the original antenna which together constitute the entire radiating structure. Once the resolution has been accomplished, one may study the radiation from the currents on the two parts of the antenna individually including mutual interaction to all orders. This is to be distinguished from measurement of the radiation fields of the two parts individually because that measurement does not include the mutual interaction. A demonstration measurement of a two antenna system is described and iterative postmeasurement processing is employed to identify the radiation from currents on the two constituent antennas of the overall radiating structure. The results are compared with those of an earlier approximate noniterative algorithm developed for the same purpose and the differences are discussed.

An iterative post-measurement data-processing procedure is proposed that effectively separates the field radiated by a selected part of a radiating system from the total radiated field. No additional measurement is required, and the processing involves only the usual expansion and summation procedures normally used in near-field data processing. The accuracy of the result far exceeds that of the conventional filtering technique. Applications include elimination of the effects of certain types of fixtures, and enhancement of certain chamber artifact-removal techniques. The example of separating the feed pattern from a simulated measurement of a reflector antenna's radiation field is presented in both a spherical near-field scenario and a single-cut far-field scenario.

A chamber calibration technique for spherical near-field antenna measurements proposed by Pogorzelski is experimentally demonstrated. The chamber was purposely degraded by introducing a metal plate situated so as to produce a strong specular reflection from the antenna under test to the chamber probe. The effects of this artifact were easily observed in the raw data. The chamber with the artifact was calibrated using an open ended waveguide calibration antenna and the resulting calibration coefficients were used to correct the raw measurement producing a result very similar to the measurement carried out in the undegraded chamber over about 30 to 35 dB of dynamic range.

The distribution of the phase of the oscillations of a set of mutually injection locked electronic oscillators is investigated for the case of a hexagonal nearest neighbor coupling topology. It is shown that planar distributions are not, in general, steady-state solutions of the system of nonlinear differential equations governing the system. An exact steady-state solution of the equations is obtained and shown to be planar only for six discrete azimuth angles. The degree of deviation from a planar distribution is determined and its impact on the directivity of a phased array excited by the oscillator output signals is estimated.

Design, fabrication, and test of a 25-element planar coupled oscillator based phased array is described. The array operates at S-band and is shown to produce an agile beam which is steerable via adjustment of the perimeter oscillator tuning biases only. A phase diagnostic system is described which displays the aperture phase distribution during the far field measurements of the radiated beam. Measured results are presented both with and without the diagnostic system present. Without the diagnostic system, the beam pointing was achieved by setting the perimeter oscillator biases to be values previously used in the measurements with the diagnostic system present. The far field was then measured without the benefit of a knowledge of the aperture phase distribution. Finally, the results of far field measurements are described in which the beam position was incremented from a position previously measured with the diagnostic system in place to a new position by incrementing the perimeter oscillator biases by a fixed amount.

Neutron radiography has been used to study the wetting of construction porous materials by water. The wetting front was found to propagate proportionally to the square root of time. The observed changes in water profiles were interpreted in terms of capillary flow in ensemble of tubes of various diameters. The tube radii distribution function was determined within the Washburn approximation.

A previously reported two-dimensional (2-D) coupled oscillator array is fitted with an array of frequency triplers and a radiating aperture comprising nine patch elements to create an agile beam transmitter with aperture phase excursion consistent with /spl plusmn/90/spl deg/ of scan. Results of measurements of the aperture phase distribution and the far zone field of this transmitter under both unscanned and scanned conditions are reported.

Phased arrays have been proposed in which a two-dimensional array of voltage-controlled oscillators coupled to nearest neighbors provides excitations for the radiating elements which are properly phased to result in a steerable radiated beam. These arrays have been arranged on a rectangular lattice and the beam is steered by tuning the oscillators along the four edges of the array. Proposed here are similar arrays in which the oscillators are coupled on a triangular lattice or a hexagonal lattice and provide excitations for radiating elements similarly disposed in a planar triangular array. Beam steering is accomplished by tuning the oscillators along the three edges of the array. The dynamic behavior of the arrays is studied via a continuum model and the results compared with those of a full nonlinear discrete analysis and a linearized discrete model.

Arrays of voltage-controlled oscillators can be coupled by means of a network so as to be mutually injection locked and thus oscillate as an ensemble. This ensemble may be used to excite the elements of a phased array antenna in such a manner as to radiate an agile beam. Design of the coupling network requires attention to three key parameters: the inter-oscillator coupling strength, the network bandwidth, and the oscillator loading. These parameters can be related to the network admittance matrix elements, which, in turn, are related to the lumped element values. This provides convenient formulas for use in designing networks, which provide the necessary values of the above three key design parameters.

This paper describes a set of experimental measurements designed to test the predictions of the continuum theoretical model concerning the dynamics of a linear array of mutually injection-locked voltage-controlled oscillators. The model indicates that the phase distribution evolves according to a diffusion process, the diffusion rate being determined by the inter-oscillator locking range. The theoretical predictions are confirmed by the experimental results. In addition, a discussion of computational predictions of the characteristics of the signal received in the far zone when such an oscillator array excites a linear array of radiating elements is included.

Arrays of voltage-controlled oscillators coupled to nearest neighbors have been proposed as a means of controlling the aperture phase of one-dimensional (1-D) and two-dimensional (2-D) array antennas. It has been demonstrated, both theoretically and experimentally, that one may achieve linear distributions of phase across a linear array aperture by tuning the end oscillators of the array away from the ensemble frequency of a mutually injection-locked array of oscillators. These linear distributions result in steering of the radiated beam. It is demonstrated theoretically that one may achieve similar beamsteering in two dimensions by appropriately tuning the perimeter oscillators of a 2-D array. The analysis is based on a continuum representation of the phase in which a continuous function satisfying a partial differential equation of diffusion type passes through the phase of each oscillator as its independent variables pass through integer values indexing the oscillators. Solutions of the partial differential equation for the phase function exhibit the dynamic behavior of the array during the beamsteering transient.

This paper describes the design, fabrication, and testing of a seven-element S-band phased array, in which the beam is steered by means of a coupled-oscillator technique. Seven monolithic-microwave integrated-circuit-based voltage-controlled oscillators were coupled via microstrip transmission lines in such a manner that they mutually injection locked and, thus, oscillated as an ensemble. The output of each oscillator was connected to a microstrip patch array element and the seven elements were disposed in a line on a Duroid substrate. The resulting antenna was characterized in benchtop tests, revealing the relative phase behavior of the oscillators, and in range tests, producing far-field pattern cuts. Patterns showing beams steered to several angles were obtained by applying appropriate tuning voltages to the end oscillators of the array.

The behavior of arrays of coupled oscillators has been previously studied by computational solution of a set of nonlinear differential equations describing the time dependence of each oscillator in the presence of signals coupled from neighboring oscillators. The equations are sufficiently complicated in that intuitive understanding of the phenomena which arise is exceedingly difficult. We propose a simplified theory of such arrays in which the relative phases of the oscillator signals are represented by a continuous function defined over the array. This function satisfies a linear partial differential equation of diffusion type, which may be solved via the Laplace transform. This theory is used to study the dynamic behavior of a linear array of oscillators, which results when the end oscillators are detuned to achieve the phase distribution required for steering a beam radiated by such an array.

Mutually injection-locked arrays of electronic oscillators provide a novel means of controlling the aperture phase of a phased-array antenna, thus achieving the advantages of spatial power combining while retaining the ability to steer the radiated beam. In a number of design concepts, one or more of the oscillators are injection locked to a signal from an external master oscillator. The behavior of such a system has been analyzed by numerical solution of a system of nonlinear differential equations which, due to its complexity, yields limited insight into the relationship between the injection signals and the aperture phase. In this paper, we develop a continuum model, which results in a single partial differential equation for the aperture phase as a function of time. Solution of the equation is effected by means of the Laplace transform and yields detailed information concerning the dynamics of the array under the influence of the external injection signals.

This paper demonstrates a novel means of achieving cophasal far-field radiation for a circularly polarized microstrip reflectarray with elements having variable rotation angles. Two Ka-band half-meter microstrip reflectarrays have been fabricated and tested. Both are believed to be the electrically largest reflectarrays ever developed using microstrip patches. One, a conventional design, has identical square patches with variable-length microstrip phase-delay lines attached. The other has identical square patches with identical microstrip phase-delay lines but different element rotation angles. Both antennas demonstrated excellent performance with more than 55% aperture efficiencies, but the one with variable rotation angles resulted in better overall performance. A brief mathematical analysis is presented to validate this "rotational element" approach. With this approach, a means of scanning the main beam of the reflectarray over a wide angular region without any RF beamformer by using miniature or micromachined motors is viable.

The coefficient matrix which results when one applies the method of moments to the solution of the electric field integral equation is rendered sparse by appropriate selection of basis functions. These new basis functions arise when equivalent sources are arranged in such a manner as to produce a field focused on the bounding surface. The local nature of the focused fields reduces to a negligible level the interactions represented by many of the off-diagonal elements of the coefficients matrix. Moreover, the resulting basis appears to represent the surface fields more efficiently than many of the commonly used bases. The technique is currently limited to closed structures. Its application is demonstrated in two dimensions by computing the scattering of a plane wave by circular and square perfectly conducting cylinders. As the electrical size of the structure is increased and the number of unknowns is correspondingly increased, that the number of significant matrix elements per row is shown to remain approximately constant. >

Design, fabrication, and test of a two-dimensional (2-D) coupled oscillator array is described. The array consists of nine voltage-controlled oscillators in a 3/spl times/3 configuration and operates at S-band. It is demonstrated experimentally that the array can generate planar phase distributions suitable for producing a radiated beam which is agile in two dimensions via tuning of the perimeter oscillators only. This is believed to be the first implementation of such an array.

In the above-named article [ibid., vol. 51, no. 4, pp. 794-801, Apr. 2003], the line below (8), Y should be Y0. Also, (18) is incorrect. The correct equation is provided. These changes decrease the computed numerical values of for Qnet the presented examples thus supporting the conclusion that is small even more strongly than the values in the original article.