Square-wave Oscillations Research Articles

Square-wave optoelectronic oscillators: Effects of noise in bit generators

Optoelectronic oscillators delivering optical square waves may potentially serve as sources of optical or microwave bits. Noise analysis and prediction of eye diagrams and various figures of merit can involve intensive numerical simulation specific to a given problem at hand. Here we present an analytically tractable model of the effects of amplitude noise and timing jitter on the use of such a square-wave generator as an optical binary bit train. The approach depends on a small number of empirical parameters characterizing the temporal correlations of noise in the system. We compute in closed form the time-averaged signal, autocorrelation function, power spectral density, eye diagram, quality factor, bit-error rate, and Allan variance. While the model exploits simplification as the cost of tractability, the availability of such a model is expected to be of interest more broadly in digital communications to provide a simple tool for analysis and characterization.

Unstable oscillatory flow of non-Brownian suspensions in Hele-Shaw cells

The behavior of neutrally buoyant, non-Brownian suspensions subject to square-wave flow oscillations in Hele-Shaw cells is investigated experimentally. The velocity field across the cell gap is determined by tracking particles in a plane parallel to the main flow. The suspension develops an instability characterized by the growth of a transverse velocity component that is periodic along the main flow direction and in time. No influence of inertia on the development of the instability was observed. The characteristic onset time varies as the inverse of the oscillation amplitude with particle volume fraction dependence similar to that of the shear-induced diffusivity across the cell aperture.

Neuromorphic model of hippocampus place cells using an oscillatory interference technique for hardware implementation

In this paper, we propose a simplified and robust model for place cell generation based on the oscillatory interference (OI) model concept. Aiming toward hardware implementation in bio-inspired simultaneous localization and mapping (SLAM) systems for mobile robotics, we base our model on logic operations that reduce its computational complexity. The model compensates for parameter variations in the behaviors of the population of constituent theta cells, and allows the theta cells to have square-wave oscillation profiles. The robustness of the model, with respect to mismatch in the theta cell’s base oscillation frequency and gain—as a function of modulatory inputs—is demonstrated. Place cell composed of 48 theta cells with base frequency variations with a 25% standard deviation from the mean and a gain error with 20% standard deviation from the mean only result in a 20% deformations within the place field and 0.24% outer side lobes, and an overall pattern with 0.0015 mean squared error on average. We also present how the model can be used to achieve the localization and path-tracking functionalities of SLAM. Hence, we propose a model for spatial cell formation using theta cells with behaviors that are biologically plausible and hardware implementable for real world application in neurally-inspired SLAM.

Intermittent dynamical state switching in discrete-mode semiconductor lasers subject to optical feedback

Intermittent dynamics switching on the route to chaos in a discrete-mode laser with long time-delayed feedback is experimentally and numerically studied by analyzing the time series, power spectra, and phase portraits. The results show two types of dynamics switching: one or multiple times regular intermittent dynamics switching between stable state and square-wave envelope period-one oscillation within one feedback round time, and the irregular intermittent dynamics switching between stable state and quasi-periodic or multi-states or chaos with higher feedback ratio and bias currents. The relationship between the duty cycle of period-one oscillation and the feedback ratio has been analyzed. The map of the dynamics distribution in the parameter space of feedback ratio and bias current is plotted for a better understanding of dynamics evolution in long external cavity discrete-mode lasers.

Simplified Harmonic Rejection Mixer Analysis and Design Based on a Filtered Periodic Impulse Model

Hard-switched mixers have attractive linearity and noise properties, but are plagued by spurious responses due to the harmonic content of square-wave local oscillator (LO) signals. Harmonic rejection mixers (HRMs) reject (some of) these responses and can be constructed combining polyphase mixing and amplitude weighting. This brief presents a generalized model for the analysis of the harmonic rejection (HR) of such HRMs, based on circular convolution. We show that the effective LO signal can be modeled as a periodic Dirac impulse filtered by a time-discrete filter. For a multi-stage HR system, this filter consists of multiple stages as well, and the coefficients of each stage can be found simply by inspection. The total HR is shown to be the sum (in dB) of the rejection of the individual filtering stages, highly simplifying analysis and design of HRMs.

Design And Construction Of Alternating And Direct Current Operated Electroejaculator For Animal Breeders

The supply of voltage is obtained by using a transistorised converter. It is designed to give a square wave output of 200v at up to 80mA from an input of 12 volt d.c car battery. The output of the 12v push-pull square-wave oscillator is transformer-coupled to step up 30 volts square wave by a specially wound transformer. The transformed voltage is then used as output to energize the probe that will go into the rectum of an animal in order to stimulate it for the ejaculation of the semen. The semen collected is analysed and used to inseminate female animals.

Ocular Motor System Control Models and the Cerebellum: Hypothetical Mechanisms.

To review our studies and "top-down" models of saccadic intrusions and infantile nystagmus syndrome with the aim of hypothesizing areas of cerebellar connections controlling parts of the ocular motor subsystems involved in both types of function and dysfunction. The methods of eye-movement recording and modeling are described in detail in the cited references. Saccadic intrusions, such as square-wave jerks and square-wave oscillations, can be simulated by a single malfunction, whereas staircase saccadic intrusions required two independent malfunctions. The major infantile nystagmus syndrome waveforms are traceable to a failure to calibrate the damping ratio of the smooth pursuit system. The use of a behavioral ocular motor system model demonstrated how putative cerebellar dysfunctions could accurately simulate both the oscillations and the ocular motor responses seen in patients with both saccadic and pursuit disorders.

Novel Schmitt Trigger and Square-Wave Generator Using Single Current Amplifier

This paper presents an important missing building block for mixed-mode signal processing: a Schmitt trigger circuit based on the current amplifier. Schmitt trigger is used extensively in both the analogue and digital areas. The transfer characteristics of the proposed design are independent on the supply voltage. Unlike Schmitt triggers incorporating other types of amplifiers, the proposed design is totally active. It does not require passive resistors and hence it shall be more attractive for VLSI implementation. The proposed circuit is utilized to implement a novel current mode square-wave oscillator using a single current amplifier that provides differential current signals. The output amplitude can be controlled without additional circuitry. Current generators are particularly essential for bio-impedance measurement. Comparison with their counterparts using the operational amplifier, transconductance operational amplifier, transresistance operational amplifier, and current conveyor demonstrates several advantageous features of the proposed circuits. The experimental results obtained from primary prototypes fabricated using standard 150 nm CMOS process are provided. It is shown that the proposed Schmitt trigger and the square wave generator nominally consume $8~\mu \text{W}$ and $11~\mu \text{W}$ while working in the MHz range.

Numerical Verification of an Analytical Model for Phase Noise in MEMS Oscillators

A new analytical formulation for phase noise in MEMS oscillators was recently presented encompassing the role of essential nonlinearities in the electrical and mechanical domains. In this paper, we validate the effectiveness of the proposed analytical formulation with respect to the unified theory developed by Demir et al. describing phase noise in oscillators. In particular, it is shown that, over a range of the second-order mechanical nonlinear stiffness of the MEMS resonator, both models exhibit an excellent match in the phase diffusion coefficient calculation for a square-wave MEMS oscillator.

Square-wave oscillations in a semiconductor ring laser subject to counter-directional delayed mutual feedback.

Square-wave (SW) switching of the lasing direction in a semiconductor ring laser (SRL) is investigated using counter-directional mutual feedback. The SRL is electrically biased to a regime that supports lasing in either counter-clockwise (CCW) or clockwise (CW) direction. The CCW and CW modes are then counter-directionally coupled by optical feedback, where the CCW-to-CW and CW-to-CCW feedback are delayed by τ1 and τ2, respectively. The mutual feedback invokes SW oscillations of the CCW and CW emission intensities with a period of T≈τ1+τ2. When τ1=τ2, symmetric SWs with a duty cycle of 50% are obtained, where the switching time and electrical linewidth of the SWs can be reduced to, respectively, 1.4 ns and 1.1 kHz by strengthening the feedback. When τ1≠τ2, asymmetric SWs are obtained with a tunable duty cycle of τ1/(τ1+τ2). High-order symmetric SWs with a period of T=(τ1+τ2)/n can also be observed for some integer n. Symmetric SWs of order n=13 with a period of T=10.3 ns are observed experimentally.

Effects of an in-plane magnetic field on the energy dispersion, spin texturing and conductance of double quantum wires

We investigate the electronic structure, spin and transport properties of double quantum wires formed by a symmetric, double quartic-well potential subjected to an in-plane magnetic field by taking into account Rashba and Dresselhaus spin-orbit couplings. The energy dispersion relation of the system is analyzed for different strengths of spin-orbit interactions, magnitude and direction of magnetic field. Our numerical results reveal that the existence of aforementioned parameters modifies strongly the energy band structure, introduces a wave vector dependence to energies and also leads to crossings and anticrossings between subbands. This complex structure of energy dispersion gives rise to the appearance of square-wave like oscillations in the conductance. The spin-orbit couplings, magnetic field, potential profile and Fermi energy of an electron significantly affect the depth and width of conductance steps. Moreover, we found that the competing effect between spin-orbit couplings and magnetic field leaves its marks on the spin texturing.

Uncalibrated operational amplifier‐based sensor interface for capacitive/resistive sensor applications

In this paper, a new configuration of operational amplifier -based square-wave oscillator is proposed. The circuit performs an impedance-to-period (Z–T) conversion that, instead of a voltage integration typically performed by other solutions presented in the literature, is based on a voltage differentiation. This solution is suitable as first analogue uncalibrated front-end for capacitive and resistive (e.g. relative humidity and gas) sensors, working also, in the case of capacitive devices, for wide variation ranges (up to six capacitive variation decades). Moreover, through the setting of passive components, its sensitivity can be easily regulated. Experimental measurements, conducted on a prototype printed circuit board, with sample passive components and using the commercial capacitive humidity sensor Honeywell HCH-1000, have shown good linearity and accuracy in the estimation of capacitances, having a baseline or reaching a value ranging in a wide interval [picofarads–microfarads], as well as, with a lower accuracy, in the evaluation of more reduced variations of resistances, ranging from kiloohms to megaohms, also when compared with other solutions presented in the literature.

The Impact of Damping on the Frequency Stability of Nonlinear MEMS Oscillators

Linear models for oscillator noise predict an improvement in frequency stability with increasing quality factor. Although it is well known that this result does not apply to oscillators embedding nonlinear resonators, systematic experimental investigations of the impact of damping on frequency stability of nonlinear microelectromechanical system (MEMS) oscillators has not been previously reported. This paper studies the frequency stability of a nonlinear MEMS oscillator under variable damping conditions. Analytical and experimental investigation of a MEMS square-wave oscillator embedding a double-ended tuning fork resonator driven into the nonlinear regime is introduced. The experimental results indicate that for a preset drive level, the variation of air damping changes the onset of nonlinear behavior in the resonator, which not only impacts the output frequency, but also the phase/frequency noise of a nonlinear MEMS square wave oscillator. The random walk frequency noise and flicker frequency noise levels are strongly correlated with the nonlinear operating point of the resonator, whereas the white phase and white frequency noise levels are impacted both by the output power and by operative nonlinearities.

Synchronization of tunable asymmetric square-wave pulses in delay-coupled optoelectronic oscillators.

We consider a model for two delay-coupled optoelectronic oscillators under positive delayed feedback as prototypical to study the conditions for synchronization of asymmetric square-wave oscillations, for which the duty cycle is not half of the period. We show that the scenario arising for positive feedback is much richer than with negative feedback. First, it allows for the coexistence of multiple in- and out-of-phase asymmetric periodic square waves for the same parameter values. Second, it is tunable: The period of all the square-wave periodic pulses can be tuned with the ratio of the delays, and the duty cycle of the asymmetric square waves can be changed with the offset phase while the total period remains constant. Finally, in addition to the multiple in- and out-of-phase periodic square waves, low-frequency periodic asymmetric solutions oscillating in phase may coexist for the same values of the parameters. Our analytical results are in agreement with numerical simulations and bifurcation diagrams obtained by using continuation techniques.

Multirhythmicity in an optoelectronic oscillator with large delay.

An optoelectronic oscillator exhibiting a large delay in its feedback loop is studied both experimentally and theoretically. We show that multiple square-wave oscillations may coexist for the same values of the parameters (multirhythmicity). Depending on the sign of the phase shift, these regimes admit either periods close to an integer fraction of the delay or periods close to an odd integer fraction of twice the delay. These periodic solutions emerge from successive Hopf bifurcation points and stabilize at a finite amplitude following a scenario similar to Eckhaus instability in spatially extended systems. We find quantitative agreements between experiments and numerical simulations. The linear stability of the square waves is substantiated analytically by determining the stable fixed points of a map.

An analytical formulation for phase noise in MEMS oscillators.

In recent years, there has been much interest in the design of low-noise MEMS oscillators. This paper presents a new analytical formulation for noise in a MEMS oscillator encompassing essential resonator and amplifier nonlinearities. The analytical expression for oscillator noise is derived by solving a second-order nonlinear stochastic differential equation. This approach is applied to noise modeling of an electrostatically addressed MEMS resonator-based square-wave oscillator in which the resonator and oscillator circuit nonlinearities are integrated into a single modeling framework. By considering the resulting amplitude and phase relations, we derive additional noise terms resulting from resonator nonlinearities. The phase diffusion of an oscillator is studied and the phase diffusion coefficient is proposed as a metric for noise optimization. The proposed nonlinear phase noise model provides analytical insight into the underlying physics and a pathway toward the design optimization for low-noise MEMS oscillators.

All-optical controlled switching between time-periodic square waves in diode lasers with delayed feedback.

We investigate the square-wave (SW) self-modulation output of an edge-emitting diode laser subject to polarization rotated optical feedback in detail, both experimentally and theoretically. Our experimental results show that the 2τ-periodic SW, where τ is the delay of the feedback, coexists with other SW oscillations of shorter periods. We have found that these new SWs are specific harmonics of the fundamental one and their periods are P(n)≃2τ/(1+2n), where n is an integer. Numerical simulations and analytical studies of laser rate equations confirm the multistability of SW solutions. By adding a weak conventional optical feedback, we show that the switching between the different periodic SWs can be easily controlled. The delay of this feedback control is the key parameter determining the harmonic that is stabilized. Numerical simulations corroborate the effectiveness of our experimental control scheme.

Synchronization in a coupled architecture of microelectromechanical oscillators

There has been much recent interest in engineering the phenomenon of synchronization in coupled micro-/nano-scale oscillators for applications ranging from precision time and frequency references to new approaches to information processing. This paper presents descriptive modelling detail and further experimental validation of the phenomenon of mutual synchronization in coupled MEMS oscillators building upon recent experimental validation of this concept by the present authors. In particular, the underlying dependence of the observation of synchronization on system parameters is studied through numerical and analytical modelling while considering essential nonlinearities in both the resonator and circuit domain. Experimental results demonstrating synchronized response are elaborated based on the realization of electrically coupled MEMS resonator based square-wave oscillators. The experimental results on frequency entrainment are found to be in general agreement with results obtained through analytical modeling and numerical simulation. The concept presented here is scalable and could be used to investigate the dynamics of large-arrays of coupled MEMS oscillators.

Tuning the period of square-wave oscillations for delay-coupled optoelectronic systems.

We analyze the response of two delay-coupled optoelectronic oscillators. Each oscillator operates under its own delayed feedback. We show that the system can display square-wave periodic solutions that can be synchronized in phase or out of phase depending on the ratio between self- and cross-delay times. Furthermore, we show that multiple periodic synchronized solutions can coexist for the same values of the fixed parameters. As a consequence, it is possible to generate square-wave oscillations with different periods by just changing the initial conditions.

Relaxation and square-wave oscillations in a semiconductor laser with polarization rotated optical feedback

The rate equations for a laser with a polarization rotated optical feedback are investigated both numerically and analytically. The frequency detuning between the polarization modes is now taken into account and we review all earlier studies in order to motivate the range of values of the fixed parameters. We find that two basic Hopf bifurcations leading to either stable sustained relaxation or square-wave oscillations appear in the detuning versus feedback rate diagram. We also identify two key parameters describing the differences between the total gains of the two polarization modes and discuss their effects on the periodic square-waves.