A study of steering capability of a microstrip phased array using inter-injection locked oscillators

An innovative, phase coherent, power combining method, known as inter-injection locking applied to linear limited scan phased arrays is investigated. In this novel method, each antenna element in the array is supplied by power from a separate oscillator. However, the oscillator phases are allowed to be synthesized coherently by means of a coupling network and injection currents, being the input controls to the system of coupled phases oscillators. The inter-injection-locked phased arrays studied in this paper provide more design freedom than conventional phased arrays. They also result in systems more adapted to solid state monolithic integration technology.     

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.     

Inter-Injection-Locked Oscillators for Power Combining and Phased Arrays

This paper presents a novel approach to synchronizing the phases of several oscillators for coherent power combining either in a conventional power-combining circuit or in free space as each oscillator drives an antenna element in a phased array. A set of nonlinear differential equations is derived to predict the system's behavior. These equations are used in the computer-aided design and construction of a demonstration three-oscillator inter-injection-locked system at VHF. Good qualitative agreement between initial experimental results and theoretical predictions is observed, and applications of the inter-injection-locking concept to systems are discussed.     

On the steady-state phase distribution in a hexagonally coupled oscillator array

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.     

Phase and Amplitude Noise Analysis in Microwave Oscillators Using Nodal Harmonic Balance

In this paper, a nodal harmonic balance (HB) formulation is presented for the phase and amplitude noise analysis of free-running oscillators. The implications of using different constraints in the resolution of the perturbed-oscillator equations are studied. The obtained formulation allows the prediction of the possible spectrum resonances without ill conditioning at low frequency offset from the carrier. The noise spectrum is meaningfully expressed in terms of the eigenvalues of a newly defined matrix, obtained from the linearization of the nodal HB system about the steady-state solution. The cases of real or complex-conjugate dominant eigenvalues are distinguished. The developed phase-noise formulation is extended to a system of two coupled oscillators. The phase and amplitude noise analyses have been applied to a push-push oscillator at 18 GHz, a bipolar oscillator at 1 GHz, and a coupled system of two field-effect transistor oscillators at 6 GHz.     

Pulse Synchronization of Intestinal Myoelectrical Models

Electrical stimulation of the stomach and small intestine in animals has been shown to give a "pacing" effect, whereby the normal frequency of the myoelectrical slow-waves can be altered to that of the pulse stimulus if it has a frequency close to that of the natural rhythm. In this paper the effect of pulse stimulation on three different types of models used for gastrointestinal studies is investigated. Each of the models is an electronic implementation comprising coupled oscillators, where the unit oscillators are either based on van der Pol's equation, Hodgkin-Huxley type equations, or a relaxation switching circuit. The synchronization range is investigated for each model for variations in stimulus pulse height and width. The effect of the number of oscillators in a chain, the waveshape of the individual oscillators, and the coupling between oscillators are also studied. It is shown that the relaxation model has different synchronization characteristics than the other two models. These differences are that a weakly coupled system is easier to synchronize than a strongly coupled system, that increasing pulsewidth does not always increase the pacing band, phase lead cannot be induced, and the synchronization-band can be entirely above the unpaced system frequency.     

Synchronization of oscillators coupled through narrow-band networks

The ability of two coupled oscillators to synchronize depends critically on the coupling network. Previous analyses have accurately predicted the performance of quasi-optical microwave oscillator arrays for both weak and strong coupling, but have been limited to coupling networks with bandwidths considerably larger than the locking bandwidths of the oscillators. In this paper, the authors develop a method for deriving a suitable system of nonlinear differential equations describing the oscillator amplitude and phase dynamics using a generalization of Kurokawa's method. The method is applied to the case of two Van der Pol oscillators coupled through a resonant network for a wide range of coupling strengths and bandwidths. Simple approximate formulas are developed for the size of the frequency locking region as functions of the basic circuit parameters     

A continuum model of the dynamics of coupled oscillator arrays forphase-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     

Coupling phenomena in concentric multi-applicator phased arrayhyperthermia systems

The coupling between the waveguide applicators of a four-element phased array hyperthermia system irradiating a three-layered cylindrical tissue model of circular cross section is analyzed theoretically. The fields inside the tissue layers are expressed in terms of cylindrical vector wave functions satisfying the corresponding wave equations, while the fields inside each waveguide are expanded in terms of guided and evanescent normal modes. Then, by implementing the appropriate boundary conditions, a system of four coupled integral equations is derived in terms of the unknown electric field distributions on the open waveguide apertures. This system is solved by expanding the unknown electric field on each aperture into waveguide normal modes and by applying a Galerkin's procedure. The self reflection coefficient and the mutual coupling coefficients are then determined and numerical results for a four-element phased array hyperthermia system are computed and presented for different waveguide applicator sizes and settings     

Two-dimensional array beam scanning via externally and mutuallyinjection-locked coupled oscillators

The use of arrays of injection-locked voltage-controlled oscillators coupled to nearest neighbors has been proposed as a means of controlling the aperture phase of one and two-dimensional (2-D) phased-array antennas. It has been demonstrated both theoretically and experimentally that one may achieve linear distributions of phase across a linear array aperture by injection locking to an external oscillator the end oscillators of an array of a mutually injection-locked oscillators. These linear distributions cause steering of the radiated beam. It is demonstrated theoretically here that one may achieve beamsteering in a similar manner in two dimensions by injecting appropriately phased signals into the perimeter oscillators of a 2-D array. The analysis is based on a continuum representation of the phase previously developed in the context of beamsteering via tuning of the perimeter oscillators     

A seven-element S-band coupled-oscillator controlled agile-beamphased 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     

Effects of changes in operating conditions on the phase of a frequency-locked Gunn oscillator in X band

The frequency and phase-locking properties of solid-state microwave oscillators are of current interest in the contexts of phase control of oscillators, and the combining of a number of oscillators to achieve improved output power. A particular case of interest is that of the phased array antenna, in which the dual functions of power combination and beam steering are needed. In the latter case, it may be necessary to have control over the relative phases of a large number of oscillators locked to a common frequency. In a phased array, there is a special need to set the relative phases of the oscillators accurately, and to maintain the accuracy of the settings as parameters such as ambient temperature vary. A number of workers have investigated the frequency-locking properties of negative-resistance oscillators, but no comprehensive study of their phase-locking properties has been reported.     

一种实用的相控阵近场诊断新方法

提出了一种相控阵天线近场诊断的新方法.传统的方法要诊断出相控阵天线单元的激励,必须已知阵列单元的方向图和探头的方向图.文中基于相控阵天线的激励、单元方向图、探头方向图和近场测量数据之间的关系,得到了相控阵天线的激励和近场测量数据之间的耦合方程.利用多项式插值,在不必已知单元方向图和探头方向图的情况下,求解出相控阵天线的单元激励.     

Active antenna array lumped ring configuration

Coupled active antenna oscillator arrays are used for power-combining at microwave and millimeter-wave frequencies. It is known that the relative phase determined by the element separation distance ultimately determines the array operational mode and, hence, far-field radiation characteristics. Separately, it is known that coupled oscillator modal stability is achieved by coupling oscillators through lumped capacitive elements. In this paper, an arrangement whereby lumped capacitive elements (placed across the oscillator loads) and radiative coupling are employed concurrently is investigated. The arrangement takes the form of a ring of coupled oscillators used to excite a 2×2 antenna array. The effect that these couplings have on array behavior are evaluated using time-domain analysis and analytically derived equations. Experimental results for far-field radiation patterns are discussed in relation to coupled oscillator dynamical behavior. These suggest that the theoretical predictions are valid, offering a robust design tool for studies of larger power-combining arrays     

Transient processes under stochastic synchronization of oscillators in colored-noise medium

Equations that describe mutual and induced chaotic synchronization of n (n = 2, 3, 4,...) autooscillation systems in colored-noise medium are derived. It is demonstrated that external colored noise acting upon a system of coupled oscillators and a chain of unidirectionally coupled oscillators causes a decrease in the duration of transient processes that lead to the chaotic synchronization (both mutual and induced) of nonidentical oscillators and a decrease in the time needed for stabilization of the symmetric state of the system when the parameters of oscillators are identical.     

Canonic coupling of sinusoidal oscillators

The problem of coupling between oscillators is usually tackled by employing the Van der Pol equation for representing the oscillators and solving the equations approximately. The present communication suggests another well-known oscillator and simple coupling factors for modeling the system. As a result, the system equations become directly integrable without approximations. The problem of the coupling of two oscillators is solved comprehensively and several regions of distinct dynamic behavior of the system and bifurcation points are identified.     

Effect of Process Mismatches on Integrated CMOS Phased Arrays Based on Multiphase Tuned Ring Oscillators

Tuned ring oscillators are used to generate multiple phases of a sinusoid for a variety of applications including phased- array transceivers and clock and data recovery circuits. A variable-phase ring oscillator (VPRO) is presented that generates outputs with a controllable phase progression, enabling its use in a compact low-power single-chip phased-array transceiver architecture. The VPRO functionality is shown to be robust with respect to process and layout mismatches. This enables the implementation of integrated phased arrays with acceptable array performance even in the absence of mismatch calibration circuitry, which are essential in other phase-shifterless schemes such as coupled oscillator arrays. A prototype 24-GHz four-channel single-chip phased-array transceiver implemented in a 0.13-mum CMOS process is presented to validate these claims.     

A network of electronic neural oscillators reproduces the dynamics of the periodically forced pyloric pacemaker group

Low-dimensional oscillators are a valuable model for the neuronal activity of isolated neurons. When coupled, the self-sustained oscillations of individual free oscillators are replaced by a collective network dynamics. Here, dynamical features of such a network, consisting of three electronic implementations of the Hindmarsh-Rose mathematical model of bursting neurons, are compared to those of a biological neural motor system, specifically the pyloric CPG of the crustacean stomatogastric nervous system. We demonstrate that the network of electronic neurons exhibits realistic synchronized bursting behavior comparable to the biological system. Dynamical properties were analyzed by injecting sinusoidal currents into one of the oscillators. The temporal bursting structure of the electronic neurons in response to periodic stimulation is shown to bear a remarkable resemblance to that observed in the corresponding biological network. These findings provide strong evidence that coupled nonlinear oscillators realistically reproduce the network dynamics experimentally observed in assemblies of several neurons.     

A NOVEL PHASE CONTROL TECHNIQUE FOR INJECTION LOCKED OSCILLATORS

A novel technique to obtain injection locked oscillators phase tuning beyond 180° is demonstrated. The idea is to cascade injection locked oscillators together for phase change accumulation. A two stage injection locked oscillators can theoretically provide a maximum of 360?phase change within the locking range. This is particularly useful for phased array antenna applications.     

Coupled oscillators at a distance: applications to coupledsemiconductor lasers

A theory for coupled oscillators is developed and applied to data for coupled semiconductor lasers. The theory generalizes much of the early work on this subject, as it includes the effects of time delays along the coupling path. By allowing for these time delays, additional degrees of freedom, or longitudinal modes are introduced in the coupled oscillator system. It is shown that quality phase locking requires that only one coupled-cavity mode be excited in the system, and that this limits the allowable levels of coupling to a range that extends from the minimum at which locking first occurs (the Adler condition) to a maximum coupling at which the lock begins to degrade; this latter level occurs only in oscillators coupled at a distance