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NASA NTRS2000

Two-Dimensional Array Beam Scanning Via Externally and Mutually Injection Locked Coupled Oscillators

Some years ago, Stephan proposed an approach to one dimensional (linear) phased array beam steering which requires only a single phase shifter. This involves the use of a linear array of voltage-controlled electronic oscillators coupled to nearest neighbors. The oscillators are mutually injection locked by controlling their coupling and tuning appropriately. Stephan's approach consists of deriving two signals from a master oscillator, one signal phase shifted with respect to the other by means of a single phase shifter. These two signals are injected into the end oscillators of the array. The result is a linear phase progression across the oscillator array. Thus, if radiating elements are connected to each oscillator and spaced uniformly along a line, they will radiate a beam at an angle to that line determined by the phase gradient which is, in turn, determined by the phase difference between the injection signals.The beam direction is therefore controlled by adjusting this phase difference. Recently, Pogorzelski and York presented a formulation which facilitates theoretical analysis of the above beam steering technique. This was subsequently applied by Pogorzelski in analysis of two dimensional beam steering using perimeter detuning of a coupled oscillator array. The formulation is based on a continuum model in which the oscillator phases are represented by a continuous function satisfying a partial differential equation of diffusion type. This equation can be solved via the Laplace transform and the resulting solution exhibits the dynamic behavior of the array as the beam is steered. Stephan's beam steering technique can be similarly generalized to two-dimensional arrays in which the beam control signals are applied to the oscillators on the perimeter of the array. In this paper the continuum model for this two-dimensional case is developed and the dynamic solution for the corresponding aperture phase function is obtained. The corresponding behavior of the resulting far-zone radiation pattern is displayed as well.

Pogorzelski, Ronald J.↗
NASA NTRS1999

Two-dimensional Array Beam Scanning via Externally and Mutually Injection Locked Coupled Oscillators

Some years ago, Stephan proposed an approach to one dimensional (linear) phased array beam steering which requires only a single phase shifter. This involves the use of a linear array of voltage-controlled electronic oscillators coupled to nearest neighbors. The oscillators are mutually injection locked by controlling their coupling and tuning appropriately.Stephan's approach consists of deriving two signals from a master oscillator, one signal phase shined with respect to the other by means of a single phase shifter. These two signals are injected into the end oscillators of the array as shown in Figure 1. The result is a linear phase progression across the oscillator array. Thus, if radiating elements are connected to each oscillator and spaced uniformly along a line, they will radiate a beam at an angle to that line determined by the phase gradient which is, in turn, determined by the phase difference between the injection signals. The beam direction is therefore controlled by adjusting this phase difference.

Pogorzelski, Ronald J.↗
NASA NTRS2000

Recent Developments in the Analysis of Couple Oscillator Arrays

This presentation considers linear arrays of coupled oscillators. Our purpose in coupling oscillators together is to achieve high radiated power through the spatial power combining which results when the oscillators are injection locked to each other. York, et. al. have shown that, left to themselves, the ensemble of injection locked oscillators oscillate at the average of the tuning frequencies of all the oscillators. Coupling these arrays achieves high radiated power through coherent spatial power combining. The coupled oscillators are usually designed to produce constant aperture phase. Oscillators are injection locked to each other or to a master oscillator to produce coherent radiation. Oscillators do not necessarily oscillate at their tuning frequency.

Pogorzelski, Ronald J.↗
NASA NTRS1998

The Dynamics of Coupled Oscillator Phase Control

Arrays of coupled oscillators have been proposed as means of realizing high power rf sources via coherent spatial power combining. In such applications, a uniform phase distribution over the aperture is usually desired. However, it has been shown that by detuning some of the oscillators away from the oscillation frequency of the ensemble of oscillators, one may achieve other useful aperture phase distributions. Of particular interest among those achievable are linear phase distributions because these result in steering of the output rf beam away from the broadside direction. The theory describing the behavior of such arrays of coupled oscillators is quite complicated since the phenomena involved are inherently nonlinear. However, a simplified theory has been developed which facilitates intuitive understanding. This simplified theory is based on a "continuum model" in which the aperture phase is represented by a continuous function of the aperture coordinates. A challenging aspect of the development of this theory is the derivation of appropriate boundary conditions at the edges or ends of the array.

Pogorzelski, R. J.↗
NASA NTRS1993

An Agile Beam Transmit Array Using Coupled Oscillator Phase Control

A few years ago York and colleagues suggested that injection locking of voltage controlled oscillators could be used to implement beam steering in a phased array [I]. The scheme makes use of the fact that when an oscillator is injection locked to an external signal, the phase difference between the output of the oscillator and the injection signal is governed by the difference between the injection frequency and the free running frequency of the oscillator (the frequency to which the oscillator is tuned). Thus, if voltage controlled oscillators (VCOs) are used, this phase difference is controlled by an applied voltage. Now, if a set of such oscillators are coupled to nearest neighbors, they can be made to mutually injection lock and oscillate as an ensemble. If they are all tuned to the same frequency, they will all oscillate in phase. Thus, if the outputs are connected to radiating elements forming a linear array, the antenna will radiate normal to the line of elements. Scanning is accomplished by antisymmetrically detuning the end oscillators in the array by application of a pair of appropriate voltages to their tuning ports. This results in a linear phase progression across the array which is just the phasing required to scan the beam. The scan angle is determined by the degree of detuning. We have constructed a seven element one dimensional agile beam array at S-band based on the above principle. Although, a few such arrays have been built in the past, this array possesses two unique features. First, the VCO MMICs have buffer amplifiers which isolate the output from the tuning circuit, and second, the oscillators are weakly coupled to each other at their resonant circuits rather than their outputs. This results in a convenient isolation between the oscillator array design and the radiating aperture design. An important parameter in the design is the so called coupling phase which determines the phase shift of the signals passing from one oscillator to its neighbors. Using this array, we have been able to verify the theoretical predictions concerning the effect of this phase on both the locking range and ensemble frequency of the array. However, the scan range achieved fell somewhat short of the theoretical value because of the amplitude variation of the oscillator outputs with tuning.

Pogorzelski, Ronald S.↗
NASA NTRS1998

A Fresh Look at Coupled-Oscillator Spatial Power Combining

Quasi-optical oscillators were proposed a little more than ten years ago as a means of developing the power levels needed for applications at millimeter frequencies using large numbers of individual semiconductor devices each of which produces only a modest amount of power [J.W. Mink, IEEE Trans. MTT., vol. 34, p. 273, 19861. An operating system was demonstrated soon after [Z.B. Popovic et. al, Int. J. Infrared and Millimeter Waves, v. 9, p. 647, 1988] in the form of a so-called grid oscillator. This device constituted a rectangular array of oscillating devices that are mutually coupled so that they oscillator coherently. The interconnecting lines in one direction serve as radiators so that the oscillators radiate directly, and the radiated fields add. Subsequently, coupled oscillators using resonant transmission line lengths was demonstrated by Mortazawi and Itoh [IEEE Trans. MTT., vol. 38, p. 86,1990). In recent work, coupled-oscillator power combiners have received less attention, with amplifier/combiners receiving more attention. Specific weaknesses of spatial-combining oscillators have motivated this transition. Namely, the oscillators employ low-Q resonators (resulting in low signal quality) and no clear means of modulation has been identified until recently. In this presentation, we review coupled-oscillator combiners in broad terms, indicating the features that make particular systems viable. We indicate how these features can be reconciled to functional requirements for system applications. Comparisons are drawn between two approaches to obtain mutual coupling: One employs low-Q oscillator circuits at each site, with concomitantly high propensity for the oscillators to couple. The other approach employs moderate-Q oscillators at each site with the concomitant requirement to tune the oscillators so that they share a range of frequencies over which they can couple and lock. In either case, precise frequency control and modulation can be achieved through locking to an external frequency source that ensures high quality signals. A recent development in coupled-oscillator arrays provides a means for beam-steering the radiation field of coupled oscillators through de-tuning of the edge elements in the array. This detuning introduces a progressive phase shift across the oscillator array. This 0 suggests architectures that can replace the functionality of a phased array without the cost 0 incurred by phase shifters. A comprehensive theory of the phase interactions among devices in such arrays is under development [e.g., Pogorzelski, York, and Maccarini, 1998 AP-S International Symposium, Atlanta, GA. June, 19981.

Pearson, L.W.↗
NASA NTRS1997

A Simplified Theory of Coupled Oscillator Array Phase Control

Linear and planar arrays of coupled oscillators have been proposed as means of achieving high power rf sources through coherent spatial power combining. In such - applications, a uniform phase distribution over the aperture is desired. However, it has been shown that by detuning some of the oscillators away from the oscillation frequency of the ensemble of oscillators, one may achieve other useful aperture phase distributions. Notable among these are linear phase distributions resulting in steering of the output rf beam away from the broadside direction. The theory describing the operation of such arrays of coupled oscillators is quite complicated since the phenomena involved are inherently nonlinear. This has made it difficult to develop an intuitive understanding of the impact of oscillator tuning on phase control and has thus impeded practical application. In this work a simpl!fied theory is developed which facilitates intuitive understanding by establishing an analog of the phase control problem in terms of electrostatics.

Pogorzelski, R. J.↗
NASA NTRS1997

A Simplified Theory of Coupled Oscillator Phase Control

York and Liao have shown both theoretically and experimentally that one can control the phases of an array of coupled oscillators by tuning the oscillators on the perimeter of the array.

coupled oscillators continuum limit↗