Application of Phase-Locked Oscillator for PCM Network Synchronization

In PCM integrated communication systems in which PCM telephone signals are transmitted and switched in an integrated manner, the clock frequency of the PCM signals in the whole network must be synchronized. Mutual synchronization was proposed for this purpose. This is an important application of a phase-locked oscillator. By interconnecting two phase-locked oscillators to control each other, the frequency of the interconnected system will be the average of the free-running frequencies of the two oscillators. By interconnecting a number of multiple input phase-locked oscillators, all the oscinators can be synchronized. The synchronization system based on this principle is called mutual synchronization and various versions of mutually synchronized systems have been proposed. Since the interconnected system of phase-locked oscillators includes many positive and negative feedback loops, to design a system, the dynamic as well as the static behavior of the system should be carefully analyzed. This paper describes the principle of various versions of mutually synchronized systems and the results of analyses on the dynamic and static behavior of mutually synchronized systems.     

Autodyne Effect of the System Involving Two Mutually Synchronized Oscillators under Strong Coupling

The results of research into the autodyne effect of a self-oscillating system subjected to reflected self-radiation and composed of two mutually synchronized partial oscillators with delayed interconnection are presented. The behavioral peculiarities of autodyne changes in the oscillation amplitude of partial oscillators, frequency, phase difference, and the response in the power supply circuit of active components are discussed at different oscillator parameters and various conditions of their mutual coupling. Experimental data are obtained for the flange-type double-diode oscillator built around 8-mm-band Gunn diodes.     

A Note on the Statistical Dynamics of Two Mutually Phase-Locked Oscillators

This note demonstrates that the behavior of two mutually synchronized phase-locked oscillators using delay compensation is equivalent to that of a first-order loop with the loop parameters degraded by the residual uncompensated delays of the system. In particular, the probability density of phase differences between the two oscillators is derived and the numerical results are also presented. The cycle slipping rate is easily obtained from this density.     

N个振荡器相互注入锁定同步振荡系统

本文对Ｎ个振荡器相互注入锁定同步振荡系统提出了一种通用的分析方法。建立了该系统的完整非线性等效模型，导出了系统的状态方程。对于各种不同电路形式的振荡系统，只要将具体的电路参数代入，就可计算其输出功率，功率合成效率及工作频率等参数，从而使这类系统的计算机辅助分析和设计成为可能。     

Phase-noise measurement using two inter-injection-locked microwave oscillators

Phase noise in two mutually coupled oscillators is analyzed by the describing function method, and the after-lock phase noise of the oscillators is calculated in terms of their free-running phase noise. A new phase-noise measurement technique based on inter-injection locking of two similar oscillators is proposed. Experimental results are presented, which confirm the theory. It is shown that in the case of zero phase of coupling coefficient, the system is in the optimum state where the only required parameter for the measurement is the locking bandwidth. In this optimum state, as far as the locking bandwidth is measured correctly, imperfections such as the frequency drift, parameters discrepancy, and nonlinear susceptance of the oscillators have no serious effect on the measurement accuracy. The proposed method is compared to the conventional ones.     

Optically controlled oscillators for millimeter-wave phased-arrayantennas

An approach for the design of optically synchronized millimeter-wave local oscillators based on a subharmonically injection-locked phase-lock-loop technique is introduced. The experimental results support the desired goal of frequency and phase coherency, phase shift control of millimeter-wave oscillators, and self-oscillating mixing to downconvert a millimeter-wave RF signal. Experimental results and theoretical analysis show the advantages of the proposed approach: large locking range of two subharmonically locked oscillators, lower FM noise degradation, and smaller phase error caused by frequency detuning     

Sliding mode based harmonic oscillator synchronization

This paper deals with the synchronization problem of harmonic oscillatory systems, such as two- and three-phase harmonic oscillators. Synchronization between referent and controlled harmonic oscillators, based on amplitude and phase control, is pursued by employing a variable structure control system. Synchronization is achieved by organizing sliding mode along the intersection of two appropriate nonlinear sliding surfaces, individually providing amplitude and phase identity. In case of three-phase harmonic oscillator synchronization an additional symmetry condition arises, which is handled by introduction of another sliding surface. Parameter perturbations and external disturbances are taken into consideration in control system design. Variable structure controllers for two- and three-phase synchronization are designed, which provide sliding mode along the intersection of sliding surfaces in finite time in spite of present disturbances. Ideal sliding dynamics is proved to be insensitive to internal and external disturbances resulting in an ideal harmonic response. Mathematical analysis as well as experimental and simulation results are presented.     

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.     

A high-frequency electronically tunable quadrature oscillator

An architecture composed of mutually regenerative oscillators is introduced. It has been used to design a low-noise high-frequency voltage-controlled oscillator (VCO) capable of producing two output signals in quadrature with essentially identical properties. The phase relation between the quadrature outputs is frequency dependent and extremely stable. A novel way of coupling the regenerative oscillators is suggested in order to improve the frequency stability of the coupled oscillator system. Results obtained from a test chip have verified the viability of the oscillator concept. The oscillator circuit has been realized in a medium-frequency bipolar process. The tuning range extends to 500 MHz. At an oscillation frequency of 200 MHz, measured phase noise was -121 dBc/Hz at 1-MHz distance from the carrier.<>     

A Double-Loop Tracking System

A nonlinear analysis which can be used to assess certain statistical characteristics of double-loop tracking systems is presented. It takes into account the mutual coupling effects of the loops in the system. Two approaches are taken to obtain steady-state probability density functions (pdf's) of the system phase errors, φ1and φ2From these pdf's, important system performance statistics, e.g., the phaseerror variances, can be calculated, thus illustrating the application and usefulness of the analysis. The analysis is applied to a satellite transponder as an example.     

On the dynamics of two-dimensional array beam scanning viaperimeter 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     

Observer-Based Optimal Fault Detection and Diagnosis Using Conditional Probability Distributions

A new optimal fault detection and diagnosis (FDD) scheme is studied in this paper for the continuous-time stochastic dynamic systems with time delays, where the available information for the FDD is the input and the measured output probability density functions (pdf's) of the system. The square-root B-spline functional approximation technique is used to formulate the output pdf's with the dynamic weightings. As a result, the concerned FDD problem can be transformed into a robust FDD problem subjected to a continuous time uncertain nonlinear system with time delays. Feasible criteria to detect and diagnose the system fault are provided by using linear matrix inequality (LMI) techniques. In order to improve FDD performances, two optimization measures, namely guaranteed cost performance and$H_infty$performance, are applied to optimize the observer design. Simulations are given to demonstrate the efficiency of the proposed approach.     

非自治约瑟夫森结阵列的耦合同步研究

针对电阻-电容-电感分路的约瑟夫森结耦合的阵列,当驱动电流的相位差为零时,分析了对称振子之间完全同步流形及其稳定性.当相位差不为零时,计算了误差系统随相位差变化的分岔图和李雅普诺夫指数曲线,发现相位差破坏了振子对之间的完全同步,但却可以抑制系统中的混沌.理论上讨论了约瑟夫森结阵列中延迟同步的存在性,发现距离较远的振子对...     

Analog ALC crystal oscillators for high-temperature applications

Fundamental mode and third-harmonic mode integrated high-performance automatic level controlled (ALC) crystal oscillators for high-temperature applications (up to 250°C), are described in this paper. These oscillators were designed for a pressure measurement system in high-temperature environments, where the output signal is the difference between both generated frequencies. Frequency variations smaller than 0.0001 ppm/s for each oscillator and a frequency drift of about 2.5 ppm/year of the frequency difference are the measured performance concerning, respectively, the short-term (1 s) and long-term frequency stability of these integrated high performance crystal oscillators over the 30°C-225°C temperature range. Other important characteristics are the very stable and constant oscillation levels (~1.1 Vpp), the small second-harmonic distortion (~60 dR), and the phase noise (~95 dB at 50 kHz shift). The characteristics of these oscillators make them also suitable for many other measurement systems (time, temperature, and other physical and chemical quantities), especially if they are constrained to operate under severe temperature conditions     

Pulse avalanche diode oscillators with an injected CW signal

The primary physical parameters affecting the frequency of pulsed avalanche diode oscillators (PAO) are discussed. A simplified equation, describing the interaction of an injected CW signal with the signal generated in the pulsed oscillator, is presented and the results of numerical calculations are plotted. It is shown that the oscillator frequency is merely pulled by the injected CW signal and that neither the output frequency nor the phase are "locked" to the injected signal.     

Pulse-time modulation of mutually coupled arrays of oscillators

This paper specifies the coupling parameters for multioscillator arrays (2" in number) such that nondegenerate symmetric and antisymmetric states may be sequentially accessed by electronic control of the coupling parameters. A requirement of this coupling configuration is that, when mutually locked, the oscillator amplitudes are identical to one another. Thus, when the oscillator signals are combined with a series of magic-T's, the output power is the sum of the oscillator powers in the array minus some small loss in the coupling circuit for the symmetric state and zero for the antisymmetric state. Switching from one state to the other is accomplished by control of the feedback phase delay between oscillators. Ideal oscillator cases are analyzed for two, four, and higher numbers of oscillators by induction. By this electronic-mode control of mutually locked oscillators, we have been able to generate pulse-time modulation (PTM) signals which are useful for communication systems. We describe some results of an X-band PTM signal generator     

PHASE AND FREQUENCY LOCKING OF MICROWAVE AND MILLIMETER WAVE POWER COMBINING

The phase and frequency locking of microwave, millimeter wave power combining were analysed and summarized in an all-round way. The master/slave phase locking of cavity oscillators, the peer phase locking of mutually coupled oscillators, and the peer phase locking of ring-connected multiple oscillators were investigated. The results of numerical calculations, and the relations of phase to phase locking model and oscillator parameters were given. And the cavity and space power combining aspects for microwave and millimeter wave were presented.     

Phase noise in externally injection-locked oscillator arrays

Previous investigations of noise in mutually synchronized coupled-oscillator systems are extended to include the effects of phase noise introduced by externally injected signals. The analysis is developed for arbitrarily coupled arrays and an arbitrary collection of coherent injected signals, and is illustrated with the specific case of linear chains of nearest neighbor coupled oscillators either globally locked (locking signal applied to each array element) or with the locking signal applied to a single-array element. It is shown that the general behavior is qualitatively similar to a single injection-locked oscillator, with the output noise tracking the injected noise near the carrier, and returning to the free-running array noise far from the carrier, with intermediate behavior significantly influenced by the number of array elements and injection strength. The theory is validated using a five-element GaAs MESFET oscillator array operating at S-band     

微波毫米波功率合成中的锁频和锁相

全面分析和评述了微波、毫米波功率合成中的锁频和锁相;研究了不同锁相方式的基本原理和方法;给出了数值计算结果;讨论了相位与锁相方式和振荡器有关参量的关系。简要介绍了微波、毫米波的腔体功率合成和空间功率合成的概念。     

Some aspects of the theory and measurement of frequency fluctuations in frequency standards

Precision quartz oscillators have three main sources of noise contributing to frequency fluctuations: thermal noise in the oscillator, additive noise contributed by auxiliary circuitry such as AGC, etc., and fluctuations in the quartz frequency itself as well as in the reactive elements associated with the crystal, leading to an f^-1type of power spectral density in frequency fluctuations. Masers are influenced by the first two types of noise, and probably also by the third. The influence of these sources of noise on frequency fluctuation vs. averaging time measurements is discussed. The f^-1-spectral density leads to results that depend on the length of time over which the measurements are made. An analysis of the effects of finite observation time is given. The characteristics of both passive and active atomic standards using a servo-controlled oscillator are discussed. The choice of servo time constant influences the frequency fluctuations observed as a function of averaging time and should be chosen for best performance with a given quartz oscillator and atomic reference. The conventional methods of handling random signals, i.e., variances, autocorrelation, and spectral densities, are applied to the special case of frequency and phase fluctuations in oscillators, in order to obtain meaningful criteria for specifying oscillator frequency stability. The interrelations between these specifications are developed in the course of the paper.