Ronald J. Pogorzelski

A continuum model of the dynamics of coupled oscillator arrays for phase-shifterless beam scanning

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.

Continuum modeling of the dynamics of externally injection-locked coupled oscillator arrays

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.

Microstrip reflectarray with elements having variable rotation angles

Two Ka-band, half-meter diameter, circularly polarized microstrip reflectarrays have been developed. One has identical square patches with variable-length phase delay lines. The other uses identical square patches and delay lines with variable element rotation angles. Although both antennas demonstrated excellent efficiencies, adequate bandwidths, and low average sidelobe and cross-pol levels, the one with variable rotation angles achieved superior overall performance. It is believed that these are electrically the largest microstrip reflectarrays (6924 elements with 42 dB gain) ever developed. It is also the first time that circular polarization has been actually demonstrated using microstrip patch elements. It is known that, if a circularly polarized antenna element is rotated from its original position by /spl psi/ degrees, the phase of the element will be either advanced or delayed by the same /spl psi/ degrees. Hence, the technique of rotating circularly polarized elements to achieve the required phases for a conventional array to scan its beam has been previously demonstrated. This technique was also demonstrated for a spiraphase reflectarray where physically large spiral elements with discrete and limited switchable phase states were used to scan the beam. Here small and low-profile printed microstrip elements are used in a reflectarray with continuous variable angular rotations to achieve far-field phase coherence. It has been previously proposed that a controllable miniature or micro-machined motor can be placed under each patch element of a reflectarray to scan the beam to wide angular directions. By doing so, the high-cost/high-loss phase shifters, T/R modules, and beamformer are no longer needed in a beam scanning antenna.

On the dynamics of two-dimensional array beam scanning via perimeter detuning of coupled oscillator arrays

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.

A seven-element S-band coupled-oscillator controlled agile-beam phased array

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.

A two-dimensional coupled oscillator array

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.

A 5-by-5 element coupled oscillator-based phased array

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.

On the design of coupling networks for coupled oscillator arrays

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.

Phased arrays based on oscillators coupled on triangular and hexagonal lattices

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.

Improved computational efficiency via near-field localization

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. >