Free-running Oscillator Research Articles

Delay model of circadian gene expression with two negative feedback loops

In this theoretical paper we propose a quantitative minimal model for circadian gene expression based on two negative feedback loops. We perform numerical simulations to analyse its dynamics and parameter sensitivities in free-running conditions, and verify the entrainability by a single periodic driver. We furthermore apply two simultaneously acting external drivers, leading to aperiodic oscillations in the case of a single-loop system. These can be turned into regular periodic oscillations by introduction of a second loop. Our studies confirm the increasing evidence that multiple feedback loops increase the robustness of regulatory systems, and stress the particular situation of systems that are close to transition from free-running oscillation to steady-state behaviour. We discuss possible molecular realisations of the featured feedback loops and suggest the application of complex patterns of external stimulation as a generally useful approach to assess the functionality of models of circadian systems.

Computing Timing Jitter From Phase Noise Spectra for Oscillators and Phase-Locked Loops With White and<tex>$1/f$</tex>Noise

Phase noise and timing jitter in oscillators and phase-locked loops (PLLs) are of major concern in wireless and optical communications. In this paper, a unified analysis of the relationships between time-domain jitter and various spectral characterizations of phase noise is first presented. Several notions of phase noise spectra are considered, in particular, the power-spectral density (PSD) of the excess phase noise, the PSD of the signal generated by a noisy oscillator/PLL, and the so-called single-sideband (SSB) phase noise spectrum. We investigate the origins of these phase noise spectra and discuss their mathematical soundness. A simple equation relating the variance of timing jitter to the phase noise spectrum is derived and its mathematical validity is analyzed. Then, practical results on computing jitter from spectral phase noise characteristics for oscillators and PLLs with both white (thermal, shot) and 1/f noise are presented. We are able to obtain analytical timing jitter results for free-running oscillators and first-order PLLs. A numerical procedure is used for higher order PLLs. The phase noise spectrum needed for computing jitter may be obtained from analytical phase noise models, oscillator or PLL noise analysis in a circuit simulator, or from actual measurements

V-Band GaAs pHEMT Cross-Coupled Sub-Harmonic Oscillator

A V-band cross-coupled sub-harmonic injection-locked oscillator has been designed and fabricated using 0.15-mum GaAs pHMET technology. Based on the known harmonic injecting circuit topology, this oscillator was designed by a differential output approach, a low-Q microstrip-line resonator, and a current mirror, which has a free-running oscillation frequency around 60GHz with a tuning range of 2.5GHz (from 57.8GHz to 60.3GHz). The maximum single-end output power is 3.8dBm with a dc dissipation of 225mW under a -3V supply voltage. Within the input matching network for second (30GHz) and fourth (15GHz) sub-harmonic signals injection, it demonstrates the maximum locking ranges close to 120MHz and 30MHz, respectively

Considering noise orbital deviations on the evaluation of power density spectrum of oscillators

This brief presents a new application of the theory of noise in free running oscillators based on the Floquet eigenvector decomposition. In oscillators, all orbital deviations contribute to the power density spectrum (PDS) as much as the "phase" term, usually considered. Each orbital deviation component shows a time evolution depending on the related Floquet eigenvalue, which thus characterizes statistical properties related to that component. Orbital deviations are partially correlated, due to their common origin from noise sources, thus also correlation terms are considered in the evaluation of the PDS. In this brief, we introduce a simplified method of calculation of PDS and apply it to an example of RLC negative resistance oscillator. Results show the relevance of orbital deviations in PDS in presence of stationary noise, these contributions becomes particularly relevant when noise is cyclostationary

Dimensional extension of Kurokawa's stability criterion for general multi-port device oscillators

This paper presents a theoretical formulation on the stability criteria for non-linear oscillator circuits. We extend Kurokawa's discriminant to a general free-running oscillator employing an n-port active device. It is shown that the product of device admittance and passive circuit impedance matrices dominates the oscillation behavior. The frequency- and amplitude-partial derivatives of the matrix determinant play a key role in the stability analysis. The obtained results are especially effective for designing broadband micro- and millimeter-wave signal generators and frequency synthesizers.

Circannual excystment of resting cysts of Alexandrium spp. from eastern Gulf of Maine populations

Abstract Species of the marine dinoflagellate Alexandrium, present in most of the Gulf of Maine (GOM), Bay of Fundy and Gulf of St. Lawrence as well as in many other areas of the world, are known to cause toxicity to marine organisms and humans alike. Excystment of Alexandrium fundyense from the eastern region of the GOM (Penobscot Bay to Bay of Fundy) was followed through four germination cycles (4 years). An annual, free-running oscillation in germination was observed under constant environmental conditions, indicating control by an endogenous clock for these eastern cysts, as shown earlier for cysts from the western region of the GOM. This circannual endogenous clock had an average period of 11 months. The phase of germination remained constant for cysts from all three stations sampled. Cysts did not germinate, despite favorable growth conditions, in summer-to-fall and this timing was consistent among cysts from all stations. The timing of cyst germination is highly relevant to modeling of Alexandrium sp. bloom initiation and depletion, as there are cyst “seed beds” near shore and offshore in the eastern and western regions of the GOM.

Study of cylindrical multilayered ceramic resonators with rectangular air cavity for low-phase noise K/Ka-band oscillators

This paper first presents cylindrical low-temperature co-fired ceramic (LTCC) resonator configurations as a means of achieving high-Q values at millimetric frequencies in a reduced-size structure. The resonator contains a rectangular air cavity that only partially fills its volume. Simple analytical expressions are derived, which relate the via waveguide (VWG) heterogeneous structures to their conventional cylindrical resonator counterparts through the use of effective radius and dielectric constant (a/sub eff/ and /spl epsiv//sub eff/). A parametric analysis is then carried out showing the effects of the available design parameters on resonant frequency and Q. Excellent agreement between measured and analytical results is obtained. Finally, a low-cost miniaturized low phase-noise free-running oscillator is proposed by employing the novel high-Q VWG resonator in the same LTCC package that houses the monolithic oscillator active circuit. A 24-GHz low phase-noise oscillator is then carried out with an output power of 13.3 dBm and a phase noise of -106 dBc/Hz at 100-kHz offset, which is among the best results ever published for a free-running K/Ka-band oscillator.

Quasi-optical 150-GHz power combining oscillator

A quasi-optical power combiner for a five-element in-line oscillator array is experimentally investigated at 150 GHz. The combiner consists of a periodic dielectric phase grating (hologram) which transforms the near-field of a rectangular horn antenna array into a pseudo-plane wave. The horn array is excited by IMPATT oscillators operating uniformly in both amplitude and phase. A dual offset reflector set-up transforms the pseudo-plane wave to a Gaussian beam which matches the field pattern of a dual mode receiving antenna. Even though an inter-element spacing of 9.5 /spl lambda/ has been chosen, the passive structure gives a power combining efficiency of 74.1%. The power combining oscillator has been operated in both free-running and injection-locked mode. A CW output power of 78.0 mW and 83.5 mW was measured for the free-running and injection-locked oscillator, respectively, which is corresponding to a power combining efficiency of 66.5% and 71.2%, respectively.

Phase noise: whether identical at all nodes in free-running oscillator circuit

Many years ago it was analytically demonstrated that phase noise in free-running oscillators might be different on the different circuit nodes. Recently this result was questioned. It was claimed that phase noise is identical at all nodes, and characterised by a single scalar constant for white noise sources. Using the time domain Monte Carlo method, which is the only method which does not treat the large signal and the noise signals separately, it is demonstrated that in free-running oscillator circuits the phase noise could be different on the nodes of the circuit and cannot be represented by a single scalar constant. This result is confirmed by simulations performed in the frequency domain using the conversion matrices method.

Phase noise measurement of free-running microwave oscillators at 5.8 GHz using 1/3-subharmonic injection locking

An innovative method using subharmonic injection locking technique for the phase noise measurement of free-running microwave oscillators is presented. To reduce the system cost, a two-tier injection locking approach is used and an effective 1/3-subharmonic injection is established. Measurement on a 1.8-V 5.85-GHz voltage controlled oscillator demonstrates that the measurement system is promising.

Rapid damping of food-entrained circadian rhythm of clock gene expression in clock-defective peripheral tissues under fasting conditions

Restricted feeding-induced free-running oscillation of clock genes in the liver was studied in homozygous Clock-mutant ( Clock/ Clock) mice. Similar to wild-type mice, Clock/ Clock mice showed robust food-anticipatory behavioral activity in accordance with a restricted feeding schedule. Also, the peak of all clock gene mRNAs tested was phase-advanced in the liver of Clock/ Clock mice as well as wild-type mice, although the amplitude of clock gene expression was low in Clock/ Clock mice. The food-anticipatory behavioral rhythm in Clock/ Clock mice maintained a period similar to wild-type mice during 2-day fasting after the cessation of restricted feeding. However, during the fasting days after temporal feeding cues were removed, the oscillation of clock genes in the liver and heart, excluding the suprachiasmatic nuclei, appeared to result in arrhythmicity in Clock/ Clock mice. Thus, although the CLOCK-based molecular mechanism is not required for the expression of food-anticipatory activity, intact CLOCK protein might be involved in sustaining several cycles of peripheral circadian oscillations after restricted feeding-induced resetting.

High-<tex>$Q$</tex>Active Resonators Using Amplifiers and Their Applications to Low Phase-Noise Free-Running and Voltage-Controlled Oscillators

This paper presents a new technique to design high-Q active resonators. The active resonators are then used in the design of low phase-noise oscillators. The proposed new technique uses an amplifier to generate a negative resistance, which compensates for the resonator losses and increases the Q factor. The active resonator using this technique shows a high loaded Q factor of 548.62 from measurement at the fixed 10-GHz resonant frequency. Considerations to design a voltage tunable active resonator is given and measurements show that the loaded Q factors exceed 500 with a 120-MHz tuning range. A low phase-noise free-running and voltage-controlled oscillator (VCO) were designed as an application of the proposed active resonators. The phase noise of the free-running oscillator using the active resonator is -114.36 dBc/Hz at 100-kHz offset, which is 14 dB lower than the phase noise of the passive resonator oscillator. In the case of a VCO using the active resonator, the phase-noise performance is below -110 dBc/Hz over the whole tuning range, which is lower 13 dB compared to the passive resonator VCO. The total dc power consumptions are approximately 500 mW.

V-band harmonic injection-locked frequency divider using cross-coupled FETs

A V-band 1/2 frequency divider is developed using harmonic injection-locked oscillator. The cross-coupled field effect transistors (FETs) and low quality-factor microstrip resonator are employed as a wide-band oscillator to extend the locking bandwidth. The second harmonic of free-running oscillation signal is injected to the gates of cross-coupled FETs for high-sensitivity superharmonic injection locking. The fabricated microwave monolithic integrated circuit frequency divider using 0.15-μm GaAs pHEMT process showed a maximum locking range of 7.4 GHz (from 65.1 to 72.5 GHz) under a low power dissipation of 100 mW. The maximum single-ended output power was as high as -3 dBm.

Membrane electrical excitability is necessary for the free-running larval Drosophila circadian clock.

Drosophila larvae and adult pacemaker neurons both express free-running oscillations of period (PER) and timeless (TIM) proteins that constitute the core of the cell-autonomous circadian molecular clock. Despite similarities between the adult and larval molecular oscillators, adults and larvae differ substantially in the complexity and organization of their pacemaker neural circuits, as well as in behavioral manifestations of circadian rhythmicity. We have shown previously that electrical silencing of adult Drosophila circadian pacemaker neurons through targeted expression of either an open rectifier or inward rectifier K(+) channel stops the free-running oscillations of the circadian molecular clock. This indicates that neuronal electrical activity in the pacemaker neurons is essential to the normal function of the adult intracellular clock. In the current study, we show that in constant darkness the free-running larval pacemaker clock-like that of the adult pacemaker neurons they give rise to-requires membrane electrical activity to oscillate. In contrast to the free-running clock, the molecular clock of electrically silenced larval pacemaker neurons continues to oscillate in diurnal (light-dark) conditions. This specific disruption of the free-running clock caused by targeted K(+) channel expression likely reflects a specific cell-autonomous clock-membrane feedback loop that is common to both larval and adult neurons, and is not due to blocking pacemaker synaptic outputs or disruption of pacemaker neuronal morphology.

The wild-type circadian period of Neurospora is encoded in the residual network of the null frq mutants

We model theoretically the response of the widely studied circadian oscillator of Neurospora crassa to inactivation of the frq gene. The resulting organism has been termed “arrhythmic” under constant conditions. Under entrainment to periodic temperature cycles Roenneberg, Merrow and coworkers have shown that the phase angle at which spore formation occurs depends on the entrainment period, curiously even in the null frq mutants ( frq 9 and frq 10). We show that such a response does not imply the presence of a self-sustained free-running oscillator. We derive a simple candidate model (a damped harmonic oscillator) for the null frq mutants that successfully reproduces the observed phase angle response. An endogenous period of 21 h for the damped harmonic oscillator coincides with the endogenous period of wild-type Neurospora. This suggests that the (noise driven) “residual system” present in the mutants may have a significant timekeeping role in the wild-type organism. Our model (with no change of parameters) was then used to investigate spore formation patterns under constant conditions and reproduces the corresponding experimental data of Aronson et al. (Proc. Natl. Acad. Sci. USA 91 (1994) 7683.)

Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection

We theoretically investigated the physical mechanism of significant bandwidth enhancement in injection-locked semiconductor lasers with strong light injection. Strong light injection can increase the semiconductor laser bandwidth to several times the free-running relaxation oscillation bandwidth. We focused on the fact that an injection-locked semiconductor laser can operate at an optical frequency different from its cavity resonance condition. Resonance is shifted from solitary resonance through the carrier-induced refractive-index change due to strong optical injection. We then framed a theory in which the enhanced resonance can be generated by transient interference between the injection-locked field and the field corresponding to the shifted cavity resonance. To examine the theory, we numerically investigated the rate equations and found that the numerical and theoretical results agree well over a wide range for strong injection. A stability analysis for the rate equations revealed that there is a mode transition from relaxation oscillation to interference-induced oscillation with increased injection, and the relaxation oscillation can become suppressed for higher injection levels. We believed that negligibly small fluctuations of the carrier suppressed the relaxation oscillation and examined it numerically. We also predict that, at strong injection levels, semiconductor lasers can be lower-dimensional systems because of the possibility of adiabatic elimination of the carrier. We further conclude that such low-dimensional systems can generate a high-frequency interference beat in the laser cavity and the resultant enhanced resonance.

Portable digital clock generator for digital signal processing applications

A fully integrated clock generator with behaviour similar to a PLL is proposed. A free-running ring oscillator is used as internal clock and the output clock is generated using two counters. The clock generator is described in synthesisable VHDL-code and can therefore easily be made from standard cells found in any commercial standard CMOS cell library.

Phase noise in self-injection-locked oscillators - Theory and experiment

Phase-noise analysis of the self-injection-locked oscillator is presented in this paper. The analysis is developed for different oscillator models and arbitrary self-injection feedback loops. The results are illustrated with specific cases of simple time-delay cable and a high-Q factor resonator. It is shown that the behavior of the phase noise is similar to an oscillator locked to an external low phase-noise source. The output phase noise can be reduced at the noise offset frequency near the carrier frequency, and returning to the free-running oscillator noise far from the carrier frequency for certain stable feedback delay ranges. The phase-noise reduction is affected by the self-injection signal strength and feedback transfer function for different oscillator equivalent-circuit models. The theory is verified by using a self-injection-locked GaAs MESFET oscillator operating at the X-band with delay cable loops. The self-injection-locked technique may be used to improve the phase noise of the existing oscillators.

Response of the Peroxidase-Oxidase Oscillator to Light Is Controlled by MB+−NADH Photochemistry

Although the peroxidase-oxidase (PO) oscillator has been widely studied [Scheeline et al. Chem. Rev. 1997, 97, 739], 1 the continued lack of quantitative agreement between experiment and theory suggests that the molecularcomponents and reactions essential for oscillation dynamics are not fully understood. Particularly, the role of photochemical reactions has been largely overlooked even though the photosensitizer methylene blue (MB + ) has been routinely added to PO reaction mixes by investigators since the first demonstration of sustained oscillations [Nakamura et al. Nature 1969, 222, 794]. 2 We reasoned that the presence of MB + in the PO reaction should make oscillations sensitive to visible light exposure. We tested this possibility and observed that both the frequency and the amplitude of O 2 oscillations obtained with a free-running periodic PO oscillator were suppressed in a rapid and reversible manner when exposed to visible light. The effect occurred at illumination wavelengths between 600 and 700 nm, was greatest at 670 nm, and was consistent with the absorbance spectrum of MB + . Measurements of the rate of NADH oxidation by MB + during illumination with red light showed a dose dependence consistent with the response curve observed for periodic PO oscillations. We concluded that PO oscillations were influenced by light through a photochemical effect on MB + , with the photosensitive reaction being the oxidation of NADH by MB + . Given these results, photoinduced suppression effects may be a common experimental bias in PO experiments where broadband spectroscopic illumination has been used. Future laboratory work involving the PO oscillator will need to control for MB + -dependent photochemical effects and theoretical modeling efforts should account for photochemistry involving MB + and NADH.

Contribution of C3 carboxylation to the circadian rhythm of carbon dioxide uptake in a Crassulacean acid metabolism plant Kalanchoë daigremontiana.

During the endogenous circadian rhythm of carbon dioxide uptake in continuous light by a Crassula cean acid metabolism plant, Kalanchoë daigremontiana, the two carboxylating enzymes, phosphoenolpyruvate carboxylase (PEPC) and ribulose 1,5 bisphosphate carboxylase/oxygenase (Rubisco), are active simultaneously, although, until now, only the role of PEPC in generating the rhythm has been acknowledged. According to the established model, the rhythm is primarily regulated at the PEPC activity level, modulated by periodic compartmentation of its inhibitor, malate, in the vacuole and controlled by tension/relaxation of the tonoplast. However, the circadian accumulation of malic acid (the main indicator of PEPC activity) dampened significantly within the first few periods without affecting the rhythm's amplitude. Moreover, the amount of malate accumulated during a free-running oscillation was several-fold lower than the amount expected if PEPC were the key carboxylating enzyme, based on a 1:1 stoichiometry of CO(2) and malate. Together with the observation that rates of CO(2) uptake under continuous light were higher than in darkness, the evidence shows that C(3) carboxylation greatly contributes to the generation of rhythmic CO(2) uptake in continuous light in this 'obligate' CAM plant. Because the shift from predominantly CAM to predominantly C(3) carboxylation is smooth and does not distort the trajectory of the rhythm, its control probably arises from a robust network of oscillators, perhaps also involving stomata.