Phase-locked Oscillator Research Articles

Noise induces synchronous and phase-locked oscillations in a cortical model

We analyze effects of noise on the dynamics of a excitatory–inhibitory (EI) cortical model with finite range connections. The dynamics is studied both analytically and with numerical simulations. Both the case of periodic boundary conditions and the more plausible case of open boundary conditions are considered. In a proper parameter regime, noise induces synchronous and phase-locked oscillations.

Noise induces synchronous and phase-locked oscillations in a cortical model

We analyze effects of noise on the dynamics of a excitatory–inhibitory (EI) cortical model with finite range connections. The dynamics is studied both analytically and with numerical simulations. Both the case of periodic boundary conditions and the more plausible case of open boundary conditions are considered. In a proper parameter regime, noise induces synchronous and phase-locked oscillations.

A superconducting phase-locked local oscillator for a submillimetre integratedreceiver

Comprehensive measurements of the flux flow oscillator (FFO) radiation linewidthare performed using an integrated harmonic SIS mixer; the FFO linewidth andspectral line profile are compared to a theory. An essential dependence of the FFOlinewidth on frequency is found; a possible explanation is proposed. The results of thenumerical solution of the perturbed sine–Gordon equation qualitatively confirm thisassumption. To optimize the FFO design, the influence of the FFO parameters on theradiation linewidth is studied. A novel FFO design at a moderate current density hasresulted in a free-running FFO linewidth of about 10 MHz in the flux flow regimeup to 712 GHz, limited only by the gap frequency of Nb. This relatively narrowfree-running linewidth (along with implementation of a wide-band phase locking loopsystem) allows continuous phase locking of the FFO in the wide frequency range of500–710 GHz. These results are the basis for the development of a 550–650 GHz integratedreceiver for the terahertz limb sounder (TELIS) intended for atmosphere study andscheduled to fly on a balloon in 2005. We report here also on the design of the secondgeneration of the phase-locked superconducting integrated receiver chip for TELIS.

Multiple slowly oscillating periodic solutions in coupled lossless transmission lines

We study the coexistence and global continuation of several slowly oscillating periodic solutions for some systems of neutral FDEs due to the interaction of temporal delay and spatial dihedral symmetries. By using the equivariant degree theory we establish general results on the existence of multiple branches of nonconstant periodic solutions, classify their symmetries, and describe their maximal continuations. As an application, we study in detail a ring of identical oscillators with identical coupling between adjacent cells and prove the existence of large amplitude phase-locked and synchronous oscillations in these ring-structured systems. We also give an example to illustrate the possibility of the coexistence of several slowly oscillatory periodic solutions when the bifurcation parameter is far away from the bifurcation point. The key in our argument is the spectral theory for circulant matrices and the construction of a Liapunov function to exclude periodic solutions of a certain integer multiple of the delay.

Externally phase-locked flux flow oscillator for submm integrated receivers: achievements and limitations

A Josephson flux flow oscillator (FFO) is the most developed superconducting local oscillator for integration with an SIS mixer in a single-chip submm-wave receiver. Recently, using a new FFO design, a free-running linewidth /spl les/10 MHz has been measured in the frequency range up to 712 GHz, limited only by the gap frequency of Nb. This enabled us to phase lock the FFO in the frequency range 500-712 GHz where continuous frequency tuning is possible; resulting in an absolute FFO phase noise as low as -80 dBc at 707 GHz. Comprehensive measurements of the FFO radiation linewidth have been performed using an integrated SIS harmonic mixer. The influence of FFO parameters on radiation linewidth, particularly the effect of the differential resistances associated both with the bias current and the applied magnetic field has been studied in order to further optimize the FFO design. A new approach with a self-shielded FFO has been developed and experimentally tested.

First harmonic injection locking of 24-GHz-oscillators

Abstract. An increasing number of applications is proposed for the 24 GHz ISM-band, like automotive radar systems and short-range communication links. These applications demand for oscillators providing moderate output power of a few mW and moderate frequency stability of about 0.5%. The maximum oscillation frequency of low-cost off-theshelf transistors is too low for stable operation of a fundamental 24GHz oscillator. Thus, we designed a 24 GHz first harmonic oscillator, where the power generated at the fundamental frequency (12 GHz) is reflected resulting in effective generation of output power at the first harmonic. We measured a radiated power from an integrated planar antenna of more than 1mW. Though this oscillator provides superior frequency stability compared to fundamental oscillators, for some applications additional stabilization is required. As a low-cost measure, injection locking can be used to phase lock oscillators that provide sufficient stability in free running mode. Due to our harmonic oscillator concept injection locking has to be achieved at the first harmonic, since only the antenna is accessible for signal injection. We designed, fabricated and characterized a harmonic oscillator using the antenna as a port for injection locking. The locking range was measured versus various parameters. In addition, phase-noise improvement was investigated. A theoretical approach for the mechanism of first harmonic injection locking is presented.

Noise-induced critical breakdown of phase lockings in a forced van der Pol oscillator

The effect of noise on the period of the van der Pol oscillator forced by a sinusoidal signal is analyzed in detail. The dynamics of the forced nonlinear oscillator with noise is described by the evolution of probability densities by a Markov operator. The oscillator shows a 1 : 1 phase-locked oscillation whose period is equal to the period of the sinusoidal forcing when the forcing is sufficiently strong. Noise modulates the oscillator's period as expected, but we show that this modulation is not uniform; the period of the oscillator changes drastically at a certain strength of noise. Thus this noise-induced breakdown of the phase locking can be considered as a stochastic bifurcation. The breakdown of stochastic phase-locking or the stochastic bifurcation is also analyzed from the viewpoint of the spectra of the Markov operator.

Oscillatory modes in a neuronal network model with transmission latency

We analyzed the oscillatory activities in a neuronal network model as the basis of synchrony of the activities in the brain. The model consists of two groups of neurons that are interconnected. One group is composed of an excitatory and an inhibitory neuron which are expressed by Hodgkin–Huxley equations. The network shows different phase-locked oscillations and other activities depending on the structure and intensity of interconnection between groups or coupling of neurons in the group, or the value of transmission latency. In the present paper we show the oscillatory modes in symmetrical and asymmetrical networks with the mutual coupling from the inhibitory neuron in each group to the excitatory neuron in the other group.

Phase-locked Josephson flux flow local oscillator for sub-mm integrated receivers

The Josephson flux flow oscillator (FFO) has proven to be one of the best on-chip local oscillators for heterodyne detection in integrated sub-mm receivers based on SIS mixers. Nb–AlOx–Nb FFOs have been successfully tested from about 120 to 700 GHz (gap frequency of Nb) providing enough power to pump an SIS mixer (about 1 μW at 450 GHz). Both the frequency and the power of the FFO can be dc-tuned. Extensive measurements of the dependence of the free-running FFO linewidth on the differential resistances associated with both the bias current and the control-line current (applied magnetic field) have been performed. The FFO line is Lorentzian both in the resonant regime, on Fiske steps (FSs), and on the flux flow step (FFS). This indicates that internal wide-band noise is dominant. A phenomenological noise model can account for the FFO linewidth dependence on experimental parameters. The narrow free-running FFO linewidth achieved, in combination with the construction of a wide-band phase-locked loop (PLL) system, enable us to phase lock the FFO in the frequency range 490–712 GHz where continuous frequency tuning is possible.

Phase-locked oscillations in a neuronal network model

We analyzed the oscillatory activities in a neuronal network model as the basis of synchrony of the activities in the brain. The model consists of two groups of neurons that are interconnected. One group is composed of an excitatory and an inhibitory neuron which are expressed by Hodgkin–Huxley equations. The network shows different phase-locked oscillations depending on the structure and intensity of interconnection between groups or coupling of neurons in the group, or the value of synaptic latency. The oscillations include various periodic solutions in which the two groups oscillate not only in in-phase or anti-phase but also in continuously changing phase difference with the parameters of coupling and latency.

Analysis of phase-locked oscillations in multi-channel single-unit spike activity with wavelet cross-spectrum

Electrophysiological measures of neural activity frequently display oscillatory patterns at various frequencies. Furthermore, these oscillatory patterns can become dynamically synchronized across a wide region of the brain in a task-dependent manner. In this study, phase-locked oscillations in simultaneously recorded spike trains were analyzed using the wavelet cross-spectrum. Adaptation of the existent methods of calculating wavelet cross-spectrum to spike train data was straightforward. In contrast, new methods were needed for evaluating the statistical significance of the cross-spectrum. Although a permutation test based on a large number of re-sampled cross-spectra can provide a reliable estimate of statistical significance, this was quite time-consuming. As an alternative, statistical significance was determined with a normal probability density function estimated from a small number of re-sampled cross-spectra. When applied to neuron pairs recorded in the primate supplementary motor area, the re-sampling procedure produced a reliable outcome even when it was based on as few as ten re-sampled cross-spectra. These results suggest that the wavelet analysis in combination with a re-sampling procedure provides a useful tool to examine the dynamic patterns of temporal correlation in cortical spike trains.

Determination of the viscoelastic properties of polymer films using a compensated phase-locked oscillator circuit.

Using a combination of the quartz crystal microbalance and a corresponding physical model for the compound resonator, the viscoelastic properties of polymer films have been studied. By using a compensated phase-locked oscillator system, both resonant frequency and resistance (motional resistance of the Butterworth-Van Dyke equivalent circuit) can be measured simultaneously. The behavior of resistance as a function of film thickness or corresponding frequency shift provides a means not only for quantitatively determining the shear viscosity and elastic modulus of films but also for qualitatively comparing various systems. The physical model is extended to include four layers for describing dissolving/swelling films that form an energy-dissipative, interfacial layer. If the underlying film is rigid and acoustically thin, then the four-layer case can be reduced to a simplified three-layer description.

Phase modulation of a loop phase-locked grid oscillator array

In this letter, we describe a method for phase modulation of a loop phase-locked grid oscillator array and report results obtained in a test bed implementation of the method. The key to the scheme lies in introducing the phase-locked loop (PLL) in such a way that the modulating data stream is introduced in parallel with the loop rather than through it, thereby circumventing the bandwidth limitation of the PLL. The experiment was performed at 4.7 GHz with a phase-locked grid oscillator array. The grid oscillator was successfully modulated by a 1 MHz signal, which is ten times higher than the bandwidth of the phase-locked loop.

Structured population on two patches: modeling dispersal and delay.

We derive from the age-structured model a system of delay differential equations to describe the interaction of spatial dispersal (over two patches) and time delay (arising from the maturation period). Our model analysis shows that varying the immature death rate can alter the behavior of the homogeneous equilibria, leading to transient oscillations around an intermediate equilibrium and complicated dynamics (in the form of the coexistence of possibly stable synchronized periodic oscillations and unstable phase-locked oscillations) near the largest equilibrium.

Effects of stimulus synchrony on mechanisms of perceptual organization

When neurons adopt a synchronized, oscillatory response to stimulus Gestalten, the phase of those oscillations almost always varies relative to stimulus activity. This has been taken to indicate that form-coding mechanisms are synchronized by internal timing mechanisms, and/or may be sensitive to stimulus activity only via motion detectors. This proposal is problematic for interpreting recent demonstrations of the effects of stimulus synchrony particularly when stimuli are stationary. Here we offer an account of stimulus-driven synchronization supported by evidence that segmentation by stimulus synchrony can be relatively insensitive to explicit motion signals. The argument is made that qualitative similarities between the effects of phase-independent and phase-locked oscillations in the EEG, the effects of phase synchronization at the cellular level and evidence for phase-enhanced stimulus grouping should be considered as functionally equivalent. This argument emphasizes the flexibility of temporal synchrony as a code for perceptual organization.

Abnormal early stages of task stimulus processing in children with attention-deficit hyperactivity disorder – evidence from event-related gamma oscillations

Objectives: Attention-related differences in early stages of stimulus processing were assessed in healthy controls and children with attention-deficit hyperactivity disorder (ADHD) by analyzing phase-locked gamma band (31–63 Hz) responses to auditory stimuli in a selective-attention task. Methods: A total of 28 children aged 9–12 years (ADHD and matched healthy controls) pressed a button in response to each target stimulus presented at the attended side (right or left). Auditory gamma band responses (GBRs) within 0–120 ms were analyzed at 8 electrodes with wavelet transform. Effects of attended channel, stimulus type, and group were evaluated for GBR power and phase-locking. Results: For both groups, GBRs had a frontal-central distribution, were significantly larger and more strongly phase-locked to target than to non-target stimuli, and did not differentiate the attended from the unattended channel. ADHD children produced larger and more strongly phase-locked GBRs than controls only to right-side stimuli, irrespective of whether these were the attended or the ignored stimuli. Conclusions: The association between auditory GBR and motor task stimulus in children suggests that phase-locked gamma oscillations may reflect processes of sensory-motor integration. ADHD-related deviations of GBRs indicate that early mechanisms of auditory stimulus processing are altered in ADHD, presumably as a result of impaired motor inhibition.

Quasilinear theory of mode interaction in gyrotrons with azimuthally inhomogeneous electron emission

A theory is developed which describes the effect of the azimuthal inhomogeneity of the electron current on the gyrotron operation. The theory is simplified by using a quasilinear approach, which allows one to study analytically the stability of oscillations in free-running and phase-locked gyrotron oscillators with inhomogeneous current emission. Also the numerical analysis of nonstationary processes in a three-mode gyrotron oscillator is carried out. The results show that, at low currents, the inhomogeneity may cause excitation of additional modes at the frequency of the operating one. At higher currents, one can observe the onset of phase-locked triplets with equidistant frequency spectrum. As the inhomogeneity increases, this enhances the beating effects in such triplets, e.g., the mode amplitudes exhibit some oscillations whose period is inversely proportional to their frequency separation and whose modulation increases with the inhomogeneity in the beam current.

Multi-stage onset of the summer monsoon over the western North Pacific

The climatological summer monsoon onset displays a distinct step wise northeastward movement over the South China Sea and the western North Pacific (WNP) (110°–160°E, 10°–20°N). Monsoon rain commences over the South China Sea-Philippines region in mid-May, extends abruptly to the southwestern Philippine Sea in early to mid-June, and finally penetrates to the northeastern part of the domain around mid-July. In association, three abrupt changes are identified in the atmospheric circulation. Specifically, the WNP subtropical high displays a sudden eastward retreat or quick northward displacement and the monsoon trough pushes abruptly eastward or northeastward at the onset of the three stages. The step wise movement of the onset results from the slow northeastward seasonal evolution of large-scale circulation and the phase-locked intraseasonal oscillation (ISO). The seasonal evolution establishes a large-scale background for the development of convection and the ISO triggers deep convection. The ISO over the WNP has a dominant period of about 20–30 days. This determines up the time interval between the consecutive stages of the monsoon onset. From the atmospheric perspective, the seasonal sea surface temperature (SST) change in the WNP plays a critical role in the northeastward advance of the onset. The seasonal northeastward march of the warmest SST tongue (SST exceeding 29.5 °C) favors the northeastward movement of the monsoon trough and the high convective instability region. The seasonal SST change, in turn, is affected by the monsoon through cloud-radiation and wind-evaporation feedbacks.

A W-Band Frequency Tracing Transceiver System

In millimeter-wave, phase-locked oscillators are often used because the frequency drift of oscillators is very large. However, they are very complex. In this paper, a W-band frequency tracing transceiver system is presented and tested, which is used for digital communication. Although the communication distance is less than that of phase-locked systems, the scheme is simple and the cost is low.

Cold test measurements on components of the 1 MW, 140 GHz, CW gyrotron for the stellarator Wendelstein 7-X

For the development of a 1 MW, 140 GHz gyrotron for CW operation which will be installed at the stellarator facility Wendelstein 7-X at IPP Greifswald, a collaboration between different European research institutes and an industrial company has been established. In order to prove the proper functioning of the millimeter wave components installed in the gyrotron — such as the cavity, the waveguide taper and the quasioptical mode converter — these components should be cold tested, preferably before installation. However, due to lack of time as well as long delivery times, this was not possible. Therefore, two units of the quasioptical mode converter and the cavity were fabricated with identical geometry, one of those being used for measurements on the low power test device. To perform these cold tests for tapers and mode converters, the gyrotron cavity output mode has to be simulated. This means that a high order rotating mode (TE 28,8 mode) must be generated at low power. This can be achieved by means of a mode generator consisting of two mirrors and a coaxial cavity with a perforated outer wall. Before applying the mode generator to the components, its proper behavior and the accurate alignment of the system must be verified either by radiation pattern measurements or k-spectrometer measurements. As the coupling through the holes of the k-spectrometer is extremely low, a special vector network analyzer with a dynamic range of at least 100 dB had to be developed. This has been achieved by integration of a phase locked backward-wave oscillator with a line width of 100 Hz and an output power of 10 mW. A non-destructive measurement of the resonance frequency and the quality factor of the cavity does not seem possible. The second cavity will be prepared for the cold measurement by drilling a small radial hole into its wall in the plane of the field maximum. This hole is then used for the input coupling. The accuracy required for this hole is rather critical. The coupling coefficient must be high for sufficient excitation of the rf field, but on the other hand it must neither change the frequency nor the quality factor strongly. The transmission is measured by a probe at the output of the uptaper.