Pair Of Oscillators Research Articles

Capacitance-to-Digital Converter for Harvested Systems Down to 0.3 V With No Trimming, Reference, and Voltage Regulation

In this work, a capacitance-to-digital converter (CDC) suitable for direct energy harvesting is introduced. The nW peak power and the ability to operate at any supply voltage in the 0.3-1.8 V range allow complete suppression of any intermediate DC-DC conversion, and hence direct supply provision from the harvester, as demonstrated with a mm-scale solar cell. The proposed CDC architecture eliminates the need for any additional support circuitry, preserving true nW-power operation, and reducing design and integration effort. In detail, the architecture is based on a pair of double-swappable oscillators, and avoids the need for any voltage/current/frequency reference circuit in the oscillator mismatch compensation. The digital and differential nature of the architecture counteracts the effect of process/voltage/temperature variations. A load-agnostic one-time self-calibration scheme compensates mismatch, and can be run from boot to run stage of the chip lifecycle. The proposed self-calibration scheme suppresses any trimming or testing time for low-cost systems, and avoids any input capacitance disconnection requirement. A 180-nm testchip shows 7-bit ENOB down to 0.3 V and 1.37-nW total power, when powered by a 1-mm2 indoor solar cell down to 10 lux (i.e., late twilight).

A Unified Multibit PUF and TRNG Based on Ring Oscillators for Secure IoT Devices

Physically Unclonable Functions (PUFs) and True Random Number Generators (TRNGs) are cryptographic primitives very well suited for secure IoT devices. This paper proposes a circuit, named multibit-RO-PUF-TRNG, which offers the advantages of unifying PUF and TRNG in the same design. It is based on counting the oscillations of pairs of ring oscillators (ROs), one of them acting as reference. Once the counter of the reference oscillator reaches a fixed value, the count value of the other RO is employed to provide the TRNG and the multibit PUF response. A mathematical model is presented that supports not only the circuit foundations but also a novel and simple calibration procedure that allows optimizing the selection of the design parameters. Experimental results are illustrated with large datasets from two families of FPGAs with different process nodes (90 nm and 28 nm). These results confirm that the proposed calibration provides TRNG and PUF responses with high quality. The raw TRNG bits do not need post-processing and the PUF bits (even 6 bits per RO) show very small aliasing. In the application context of obfuscating and reconstructing secrets generated by the TRNG, the multibit PUF response, together with the proposal of using error-correcting codes and RO selection adapted to each bit, provide savings of at least 79.38% of the ROs compared to using a unibit PUF without RO selection. The proposal has been implemented as an APB peripheral of a VexRiscv RV32I core to illustrate its use in a secure FPGA-based IoT device.

Explosive synchronization in phase oscillator populations with attractive and repulsive adaptive interactions

The attractive and repulsive adaptive coupling schemes among dynamical agents are ubiquitous in systems ranging from physics, biology to neuroscience, which have attracted increasing interest and ample attention during recent years. Here, we extend the classical Kuramoto model to the coupling with mixed signs by considering a particular adaptive scheme in a system of globally coupled phase oscillators. The time-varying coupling weight between each pair of oscillators is correlated with the local coherence that involves according to a nonlinear differential equation. The studied model is capable of capturing the essential properties of the explosive synchronization induced by the adaptive interactions. We carry out extensive simulations to explore the collective dynamics in different perspectives. Remarkably, we reveal that the occurrence of the abrupt transitions of the macroscopic overall weights, as well as the emergence of the correlations between the microscopic structure features (including degrees and frequency dissasortativity) and local dynamics trigger the explosive synchronization, which manifests the suppression rule for the formation of small synchronized clusters. Furthermore, we provide an analytical treatment for the reduced system that allows us to grasp the underlying mechanism of the observed phenomena. Our study can deepen the understanding of the explosive synchronization transitions and other related abrupt dynamic phenomena occurring in networked oscillators with generic adaptive schemes.

Digital quantum simulation of quantum gravitational entanglement with IBM quantum computers

We report the digital quantum simulation of a hamiltonian involved in the generation of quantum entanglement by gravitational means. In particular, we focus on a pair of quantum harmonic oscillators, whose interaction via a quantum gravitational field generates single-mode squeezing in both modes at the same time, a non-standard process in quantum optics. We perform a boson-qubit mapping and a digital gate decomposition specific for IBM quantum devices. We use error mitigation and post-selection to achieve high-fidelity, accessing a parameter regime out of direct experimental reach.

A Tiny Flexible Differential Tension Sensor.

Modern applications of Internet of Things (IoT) devices require cheap and effective methods of measurement of physical quantities. Cheap IoT devices with sensor functionalities can detect a lack or excess of substances in everyday life or industry processes. One possible use of tension sensors in IoT applications is the automated replenishment process of fast moving consumer goods (FMCG) on shop shelves or home retail automation that allows for quick ordering of FMCG, where the IoT system is a part of smart packaging. For those reasons, a growing demand for cheap and tiny tension sensors has arisen. In this article, we propose a solution of a small flexible tension sensor fabricated in an amorphous InGaZnO (a-IGZO) thin-film process that can be integrated with other devices, e.g., near-field communications (NFC) or a barcode radio frequency identification (RFID) tag. The sensor was designed to magnify the slight internal changes in material properties caused by mechanical stress. These changes affect the dynamic electrical properties of specially designed inverters for a pair of ring oscillators, in which the frequencies become stress-dependent. In the article, we discuss and explain the approach to the optimum design of a ring oscillator that manifests the highest sensitivity to mechanical stress.

Amplitude death and growth in a pair of nonidentical thermoacoustic oscillators interacting via time-delay and dissipative coupling

We numerically explore the effect of asymmetric limit-cycle amplitudes on the quenching and growth of self-excited thermoacoustic oscillations in two nonidentical Rijke tubes interacting via time-delay and dissipative coupling. When either type of coupling is applied separately, we find that increasing the asymmetry of the (uncoupled) limit-cycle amplitudes can shrink the regions of amplitude death (AD) in both oscillators, while producing a new region in which one of the oscillators becomes amplified, a state we refer to here as amplitude growth (AG). We find that the AG region resembles a 1:1 Arnold tongue when only dissipative coupling is applied, but that it splits into two discrete branches when only time-delay coupling is applied. When both types of coupling are applied simultaneously, we find that the AD and AG regions change in ways that depend sensitively on the detuning between the two oscillators. The findings of this study could be used to gain a better understanding of the can-to-can acoustic interactions in modern gas turbines, facilitating the development of both passive and active strategies to control thermoacoustic instability.

Dynamical systems model of development of the action differentiation in early infancy: a requisite of physical agency

Young infants are sensitive to whether their body movements cause subsequent events or not during the interaction with the environment. This ability has been revealed by empirical studies on the reinforcement of limb movements when a string is attached between an infant limb and a mobile toy suspended overhead. A previous study reproduced the experimental observation by modeling both the infant’s limb and a mobile toy as a system of coupled oscillators. The authors then argued that emergence of agency could be explained by a phase transition in the dynamical system: from a weakly coupled state to a state where the both movements of the limb and the toy are highly coordinated. However, what remains unexplained is the following experimental observation: When the limb is connected to the mobile toy by a string, the infant increases the average velocity of the arm’s movement. On the other hand, when the toy is controlled externally, the average arm’s velocity is greatly reduced. Since young infants produce exuberant spontaneous movements even with no external stimuli, the inhibition of motor action to suppress the formation of spurious action-perception coupling should be also a crucial sign for the emergence of agency. Thus, we present a dynamical system model for the development of action differentiation, to move or not to move, in the mobile task. In addition to the pair of limb and mobile oscillators for providing positive feedback for reinforcement in the previous model, bifurcation dynamics are incorporated to enhance or inhibit self-movements in response to detecting contingencies between the limb and mobile movements. The results from computer simulations reproduce experimental observations on the developmental emergence of action differentiation between 2 and 3 months of age in the form of a bifurcation diagram. We infer that the emergence of physical agency entails young infants’ ability not only to enhance a specific action-perception coupling, but also to decouple it and create a new mode of action-perception coupling based on the internal state dynamics with contingency detection between self-generated actions and environmental events.

Generation of stochastic mixed-mode oscillations in a pair of VDP oscillators with direct-indirect coupling.

Environmental noise can lead to complex stochastic dynamical behavior in nonlinear systems. In this paper, we studied the phenomenon of a pair of Van der Pol (VDP) oscillators with direct-indirect coupling affected by Gaussian white noise. That is to say, a noise-induced equilibrium transition oscillation was observed in three types of different parameter regions, where the deterministic system had two kinds of stable equilibrium points. Meanwhile, with the noise intensity increasing, we found that the stochastic system will constantly switch between two stable equilibrium points. To analyze the stochastic behavior, we used the stochastic sensitivity equation and confidence ellipse method. When the confidence ellipsoid crossed the boundary of the attraction basin of the equilibrium point, the system entered into the state of stochastic mixed-mode oscillations, which was consistent with the simulation results.

Amplitude death, oscillation death, and stable coexistence in a pair of VDP oscillators with direct–indirect coupling

<abstract><p>In this paper, we investigated the dynamics of a pair of VDP (Van der Pol) oscillators with direct-indirect coupling, which is described by five first-order differential equations. The system presented three types of equilibria including HSS (homogeneous steady state), IHSS (inhomogeneous steady state) and NPSS (no-pattern steady state). Employing the corresponding characteristic equations of the linearized system, we obtained the necessary conditions for the pitchfork and Hopf bifurcations of the equilibria. Further, we illustrated one-dimensional bifurcation and phase diagrams to verify theoretical results. The results show that the system exhibited two types of oscillation quenching, i.e., amplitude death (AD) for HSS equilibria and oscillation death (OD) for IHSS equilibria. In some special regions of the parameters, the system proposed multiple types of stable coexistence including HSS and IHSS equilibria, periodic orbits or quasi-periodic oscillations.</p></abstract>

Synchronization of a pair of nonholonomic oscillators

The paper introduces the novel problem of the synchronization of a pair of identical mobile nonholonomic oscillators, the so-called Chaplygin sleighs, moving on a movable platform with springs. Each Chaplygin sleigh is actuated by a periodic torques of the same amplitude and frequency, resulting in a limit cycle in a reduced velocity space. The frictional constraint forces couple the motion of the two Chaplygin sleighs and the platform. The limit cycles of the coupled oscillators are dependent on the relative phase of actuation on the sleighs. We show that the coupled limit cycles become identical but with anti-phase synchronization, where the amplitude and frequency of oscillations and the average translational speeds of the two sleighs become equal. Moreover, in such anti-phase synchronization, the heading angle of both sleighs converge, producing motion in a formation.

Entanglement Dynamics of Coupled Quantum Oscillators in Independent NonMarkovian Baths.

This work strives to better understand how the entanglement in an open quantum system, here represented by two coupled Brownian oscillators, is affected by a nonMarkovian environment (with memories), here represented by two independent baths each oscillator separately interacts with. We consider two settings, a 'symmetric' configuration wherein the parameters of both oscillators and their baths are identical, and an 'asymmetric' configuration wherein they are different, in particular, a 'hybrid' configuration, where one of the two coupled oscillators interacts with a nonMarkovian bath and the other with a Markovian bath. Upon finding the solutions to the Langevin equations governing the system dynamics and the evolution of the covariance matrix elements entering into its entanglement dynamics, we ask two groups of questions: (Q1) Which time regime does the bath's nonMarkovianity benefit the system's entanglement most? The answers we get from detailed numerical studies suggest that (A1) For an initially entangled pair of oscillators, we see that in the intermediate time range, the duration of entanglement is proportional to the memory time, and it lasts a fraction of the relaxation time, but at late times when the dynamics reaches a steady state, the value of the symplectic eigenvalue of the partially transposed covariance matrix barely benefit from the bath nonMarkovianity. For the second group of questions: (Q2) Can the memory of one nonMarkovian bath be passed on to another Markovian bath? And if so, does this memory transfer help to sustain the system's entanglement dynamics? Our results from numerical studies of the asymmetric hybrid configuration indicate that (A2) A system with a short memory time can acquire improvement when it is coupled to another system with a long memory time, but, at a cost of the latter. The sustainability of the bipartite entanglement is determined by the party which breaks off entanglement most easily.

Incomplete synchronization of chaos under frequency-limited coupling: Observations in single-transistor microwave oscillators

The synchronization of chaotic systems has been extensively studied based on diverse coupling schemes and media which allow almost unaltered energy exchange over the entire spectral range of oscillation. Less is known about the dynamics of systems encompassing couplings that restrict interaction to a narrower frequency interval, such as through band-pass filtering. Here, this situation is systematically investigated in the context of a master–slave pair of single-transistor chaotic oscillators operating in the microwave region. Albeit incomplete, phase synchronization remains detectable down to a fractional bandwidth on the order of 5% when the pass band is centered around the predominant spectral peaks, leading to a well-evident directed causal influence alongside intricate spectral effects. Concordant results are obtained between numerical simulations using an LC network and experimental measurements based on an electrically-tunable filter as a coupling medium. The possibility of maintaining selective locking over a channel shared between two oscillator pairs is shown. It is furthermore demonstrated that, in this circuit, frequency-limited coupling entrains one aspect of the chaotic dynamics, namely damped resonance, without significantly impacting the relaxation process that irregularly excites it. These results demonstrate in a realistic setting that chaos synchronization does not unavoidably require broadband couplings, thus enabling future applications of chaos communication using realistic antennas such as in distributed sensing. Some considerations about the construction of a hypothetical cellular network based on the coupling scheme under consideration are given.

Voltage-Controlled Polarization at 0.1 THz Based on Phase-Tuned Coupled Oscillation via a Magic Tee

We propose a technique to implement voltage-controlled polarization at 0.1 THz using a pair of phase-tuned Gunn diode oscillators coupled through a WR10 magic tee hybrid coupler. By finely tuning the free-running oscillation frequency with bias voltage, we can control the phase difference between the two coupled oscillators. Since the two output ports of the hybrid coupler correspond to the sum and difference of the signals from the two coupled oscillators, the power ratio between the two output ports can be adjusted arbitrarily by tuning their phase difference. Thus, by connecting a pair of orthogonal horn antennas to the output ports, an arbitrary polarization ratio can be obtained. The maximum polarization ratio observed in this study is 31.8 dB. To fully switch the polarization between the vertical and horizontal directions, a frequency shift of 26.6 MHz (0.03%) at around 94.3 GHz is involved when changing the bias voltage of one of the two oscillators. This frequency shift could be compensated by carefully controlling the bias voltages of the two oscillators simultaneously. The proposed approach enables fully electrical control of the polarization of subterahertz waves using a waveguide platform, which will be of importance for a variety of applications in sensing and communication.

Occasional coupling enhances amplitude death in delay-coupled oscillators.

This paper aims to study amplitude death in time delay coupled oscillators using the occasional coupling scheme that implies intermittent interaction among the oscillators. An enhancement of amplitude death regions (i.e., an increment of the width of the amplitude death regions along the control parameter axis) can be possible using the occasional coupling in a pair of delay-coupled oscillators. Our study starts with coupled limit cycle oscillators (Stuart-Landau) and coupled chaotic oscillators (Rössler). We further examine coupled horizontal Rijke tubes, a prototypical model of thermoacoustic systems. Oscillatory states are highly detrimental to thermoacoustic systems such as combustors. Consequently, a state of amplitude death is always preferred. We employ the on-off coupling (i.e., a square wave function), as an occasional coupling scheme, to these coupled oscillators. On monotonically varying the coupling strength (as a control parameter), we observe an enhancement of amplitude death regions using the occasional coupling scheme compared to the continuous coupling scheme. In order to study the contribution of the occasional coupling scheme, we perform a detailed linear stability analysis and analytically explain this enhancement of the amplitude death region for coupled limit cycle oscillators. We also adopt the frequency ratio of the oscillators and the time delay between the oscillators as the control parameters. Intriguingly, we obtain a similar enhancement of the amplitude death regions using the frequency ratio and time delay as the control parameters in the presence of the occasional coupling. Finally, we use a half-wave rectified sinusoidal wave function (motivated by practical reality) to introduce the occasional coupling in time delay coupled oscillators and get similar results.

Modeling the tonotopic map using a two-dimensional array of neural oscillators.

We present a model of a tonotopic map known as the Oscillatory Tonotopic Self-Organizing Map (OTSOM). It is a 2-dimensional, self-organizing array of Hopf oscillators, capable of performing a Fourier-like decomposition of the input signal. While the rows in the map encode the input phase, the columns encode frequency. Although Hopf oscillators exhibit resonance to a sinusoidal signal when there is a frequency match, there is no obvious way to also achieve phase tuning. We propose a simple method by which a pair of Hopf oscillators, unilaterally coupled through a coupling scheme termed as modified power coupling, can exhibit tuning to the phase offset of sinusoidal forcing input. The training of OTSOM is performed in 2 stages: while the frequency tuning is adapted in Stage 1, phase tuning is adapted in Stage 2. Earlier tonotopic map models have modeled frequency as an abstract parameter unconnected to any oscillation. By contrast, in OTSOM, frequency tuning emerges as a natural outcome of an underlying resonant process. The OTSOM model can possibly be regarded as an approximation of the tonotopic map found in the primary auditory cortices of mammals, particularly exemplified in the studies of echolocating bats.

Frequency-amplitude correlation inducing first-order phase transition in coupled oscillators

The first-order phase transitions in coupled oscillators have been widely studied because of their discontinuity and irreversibility. In previous research, the designed coupling mechanisms between each pair of oscillators can cause the first-order phase transitions occur stably. In the present study, we propose a new mechanism which requires the existence of an inversely proportional relationship between the natural frequencies and the intrinsic amplitudes in the homogeneously coupled oscillators. Based on two classical oscillator models, i.e., the Poincaré model and the Stuart–Landau model, the emergence of explosive oscillation death is independent of the frequency distributions. Our findings indicate that the first-order phase transitions can be induced by the frequency-amplitude correlation for the first time. Therefore, it provides a novel perspective to understand explosive phenomena in coupled oscillators.

A low‐power amplitude shift keying modulator based on adaptive body‐biased injection‐locked current‐reuse voltage controlled oscillator for high data rate radio frequency identification applications

AbstractA low‐power consuming amplitude‐shift keying (ASK) modulator designed in 130 nm CMOS technology and operating at 10.5 GHz frequency is presented in this work. The modulator is based on current‐reuse voltage‐controlled oscillator (VCO) which uses the effects of adaptive body‐biasing and injection locking (IL) to achieve low‐phase noise and low‐power operation. The VCO has a phase noise of −106 dBc/Hz at 1 MHz offset. The ASK modulator consumes 790 μW with a 1.1 V voltage supply and draws an average current of 719 μA. For applying the bulk‐biasing signal, a deep n‐well NMOS is used in the PMOS‐NMOS oscillator pair which isolates the substrate and avoids the current path through it. The post‐layout simulation results of the 0.5 × 0.5 mm2 modulator IC verify its low‐power, low‐phase noise operation. It is intended for use in self‐powered active high data rate radio‐frequency identification (RFID) tags.

A classical analog for defects in quantum band formation

When many individual atoms come together to form a solid, their interaction splits their electronic energy levels to form continuous bands separated by forbidden energy ranges known as band gaps. Introducing defects in a solid results in new electron energy levels that may lie inside the bandgaps. The presence of these defect levels is the heart of the semiconductor-based devices that play a significant role in the modern world. Quantum mechanics provides the best description of interacting atoms. However, band formation is not unique to small-scale atomic interactions but rather is a result of the wave-nature of Schrödinger's equation, which governs quantum mechanics. Using oscillations in a mass-spring system, we present a table-top, classical analog to the quantum system illustrating how defects in a one-dimensional lattice produce changes to the band structure. A pair of masses connected by a spring plays the role of a single atom. Interactions between “atoms” are introduced with weak coupling springs producing two distinct frequency bands from the translational and fundamental modes. Defects are introduced by altering an oscillator pair's total mass or internal spring constant. We provide the theoretical groundwork and experimental verification of the model along with a discussion of the value and limitations of the model as a macroscopic tool to visualize the microscopic world.

Synchronization of relaxation oscillators with adaptive thresholds and application to automated guided vehicles.

The present paper proposes an adaptive control law for inducing in-phase and antiphase synchronization in a pair of relaxation oscillators. We analytically show that the phase dynamics of the oscillators coupled by the control law is equivalent to that of Kuramoto phase oscillators and then extend the results for a pair of oscillators to three or more oscillators. We also provide a systematic procedure for designing the controller parameters for oscillator networks with all-to-all and ring topologies. Our numerical simulations demonstrate that these analytical results can be used to solve a dispatching problem encountered by automated guided vehicles (AGVs) in factories. AGV congestion can be avoided and the peak value of the amount of materials or parts in buffers can be suppressed.

Coexisting Oscillations, Heterogeneous Multistability and Multi-Scroll Chaos in a Pair of Coupled Memristor-Based Duffing Oscillators

Coexisting Oscillations, Heterogeneous Multistability and Multi-Scroll Chaos in a Pair of Coupled Memristor-Based Duffing Oscillators