Nonlinear Circuit Research Articles

INFORM: Inverse Design Methodology for Constrained Multiobjective Optimization

Many system design methods use population-based optimization or a surrogate model for solving constrained multi-objective optimization. When designing a system with multiple objectives and constraints, the designer may first be interested in understanding the trade-offs among different objectives from a small number of simulations. In the next step, the designer may focus on specific regions of interest in the design space near a set of non-dominated solutions to further improve performance on the targeted objectives. This may help make the search process sample-efficient. We propose INFORM: a two-step approach for sample-efficient constrained multi-objective optimization of real-world nonlinear systems. In the first step, we modify a genetic algorithm (GA) to make the design process sample-efficient. We inject candidate solutions into the GA population using inverse design methods instead of determining the candidate solutions for the next generation using only crossover and mutation, as is done in standard GA. We present three types of inverse design techniques based on a (i) neural network verifier, (ii) neural network, and (iii) Gaussian mixture model. The candidate solutions for the next generation are thus a mix of those generated using crossover/mutation and solutions generated using inverse design. At the end of the first step, we obtain a set of non-dominated solutions. In the second step, we choose the regions of interest around the non-dominated solutions to further improve the objective function values using inverse design methods. We demonstrate the efficacy of INFORM through synthesis of nonlinear systems and analog circuits. The experimental results show that INFORM reduces synthesis time by up to 29× and improves the value of the objective function by up to 33% compared to a state-of-the-art baseline design methodology.

Nonlinear Energy-Harvesting for D2D Networks Underlaying UAV With SWIPT Using MADQN

Energy Efficiency (EE) has become an essential metric in Device-to-Device (D2D) communication underlaying Unmanned Aerial Vehicles (UAVs) Among the several technologies that provide significant energy, simultaneous wireless information and power transfer (SWIPT) has been proposed as a promising solution to improve EE. However, it is a challenging task to study the EE under nonlinear energy harvesting (EH) due to the limited sensitivity and the composition of the non-linear circuit. Moreover, when D2D users transmit information using the EH from UAVs, interferences to cellular users occur and deteriorate the throughput. To tackle these problems, we leverage concepts from artificial intelligence (AI) to optimize EE of UAV-assisted D2D communication. Specifically, multi-agent deep reinforcement learning was proposed to jointly maximize throughput and EE, where the reward function is defined in terms of the introduced goal. Simulation results verify the supremacy of proposed approach over traditional algorithms.

Robust stabilization and adaptive H∞ control of nonlinear singular systems via static output feedback

This article studies robust stabilization and adaptive [Formula: see text] control problems for a class of continuous-time nonlinear singular systems by static output feedback. First, under sufficient conditions which the system is impulse controllable, the static output feedback controller is designed, and the stabilization problem of the system is discussed. Second, the [Formula: see text] and adaptive [Formula: see text] controllers are designed for the continuous-time nonlinear singular systems with external disturbances. Compared with the existing conclusions, the controller can be designed for more nonlinear singular systems. Finally, an example of a nonlinear singular circuit is given, and the simulation results verify the validity of the proposed controllers.

Noise–dissipation relation for nonlinear electronic circuits

An extension of fluctuation–dissipation theorem is used to derive a “speed limit” theorem for nonlinear electronic devices. This speed limit provides a lower bound on the dissipation that is incurred when transferring a given amount of electric charge in a certain amount of time with a certain noise level (average variance of the current). This bound, which implies a high energy dissipation for fast, low-noise operations (such as switching a bit in a digital memory), brings together recent results of stochastic thermodynamics into a form that is usable for practical nonlinear electronic circuits, as we illustrate on a switching circuit made of an nMOS pass gate in a state-of-the-art industrial technology.

A bimembrane neuron for computational neuroscience

A biological neuron has endomembrane and extracellular membrane, and its capacitive effect can be described in an equiavlent neural circuit composed of two capacitors. In this paper, a smooth nonlinear resistor with cubic term for the current-voltage (i-v) is introduced into a nonlinear circuit connected with two capacitors and one inductor. The characteristic of field energy is analyzed and unknown parameters are identified with adaptive law. Furthermore, a magnetic flux-controlled memristor (MFCM) is connected to this circuit to estimate its memristive effect on dynamics and energy flow. After scale transformation, the two kinds of nonlinear circuits are replaced by equivalent neuron models, which can present similar spiking, bursting patterns as those presented in biological neurons. Energy function is obtained in theoretical way for discerning the relation between mode selection and energy level. Noisy disturbance is applied to induce coherence resonance, and the involvement of memristive current can induce coherence resonance with lower noise intensity. The results confirmed that energy flow can be controlled to regulate the electric activities in neurons, and higher energy level is obtained in periodic patterns of neuron under coherence resonance. This neural circuit and the memristive model are more suitable for identifying the neural activities in nervous system composed of biological neurons.

Coupled electro-aeroelastic energy harvester model based on piezoelectric transducers, VIV-galloping interaction and nonlinear switching circuits

Miniaturization, multi-functionality, and low power consumption are key features in the development of electronic devices today. These characteristics open up the possibility for the development of small, self-powered systems. Piezoelectric materials have emerged as a promising solution due to their ability to convert mechanical energy into electrical energy from the surrounding environment, such as wind. In this research work, we investigate an aeroelastic piezoelectric energy harvester based on the interaction between vortex-induced vibrations and galloping. The device, a bimorph cantilevered beam with a square-section bluff body attached to its tip, produces mechanical oscillations that are extracted by various electrical circuits, including a nonlinear switching interface. A numerical model, implemented in a Simulink environment, is developed to solve the coupled electro-aeroelastic problem for each electrical interface. The results are compared to experimental data collected from wind tunnel tests conducted at various wind velocities and load resistances, and a satisfactory correlation is observed. The validated model is finally used to carry out a parametric analysis aimed at optimizing the performance of the harvester in a low wind speed range. This investigation could contribute to a better understanding of an aeroelastic harvesting system and potentially assist in the optimization of design parameters and electrical interfaces for specific applications.

Features of the Relaxation Process in an RC Circuit under the Influence of a Sinusoidal Voltage

The article is devoted to the study of the properties of the relaxation process in a nonlinear electrical circuit under the sinusoidal voltage influence. Electronic devices and processes the operation of which is based on relaxation principles are sources of specific series of pulses, the monitoring of which allows one to draw conclusions about the technical parameters of these devices and processes. The occurrence of a series of partial discharges in a high-voltage device can serve as an example. An essential factor of partial discharges is their multiplicity both in time and in space, which are dispersed in an a priori unknown number of defects. The aim is to determine the number of defects and to perform appropriate grouping of the entire set of partial discharges by defects. Internal deterministic correlations derived as a result of solving the problem and presented in terms of the classical theory of electrical circuits should be regarded as a key to solving the problem that was set forth. Analytical correlations for the deterministic component of partial discharges in potential electrical insulation defects are revealed. The obtained correlations characterize the time intervals between individual discharges inside the insulation defect. These time intervals are uniquely related to the defect parameters and can serve as a basis for identifying this defect against the background of other partial discharges. As an example, the result of mathematically modeling a relaxation process with the specified parameters is given.

Optical soliton solutions, bifurcation, and stability analysis of the Chen-Lee-Liu model

The Chen-Lee -Liu model has many applications in assorted fields, particularly in the study of nonlinear dynamics, chaos theory, circuit design, signal processing, secure communications, encryption and decryption of chaotic signals, as well as cryptography. The modified extended auxiliary equation mapping method has been applied to the Chen-Lee-Liu model in this article and explores new wave profiles, such as singular periodic solutions, periodic solutions, and kink-type soliton solutions. The complex wave conversion is considered to make a simple differential equation. Three- and two-dimensional images are plotted using Mathematica and MATLAB, and their dispersion and nonlinearity effects are discussed. We also discuss the bifurcation analysis of the studied model. The stability of the equilibrium points is studied, and the phase portrait of the system is presented graphically. The obtained wave profiles might play an important role in telecommunication systems, fiber optics, and nonlinear optics.

Analysis and Compensation of Hysteresis Effect on Electromagnetic Force in Axial Magnetic Bearings

Magnetic bearings (MBs) enable the rotor to run at high speed without lubrication due to no mechanical contact. However, the inherent hysteresis of ferromagnetic materials affects the support characteristics, reducing the design performance and stability margin of MBs, especially for axial MBs using materials with high coercive force. To analyze and compensate for the hysteresis effect on the electromagnetic force in axial MBs, an efficient method is proposed in this paper. Firstly, the hysteresis properties of the ferromagnetic materials are simulated by the Preisach model, and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> relationships under any external magnetic field can be determined. Taking into account the non-ideal factors such as hysteresis and saturation effects, the nonlinear magnetic circuit model of the axial MBs is established. The magnetic flux density working point under different control currents and eccentric displacements can be determined through iterative calculation, and then the air gap flux density distribution and electromagnetic force of the axial MBs are calculated. On this basis, the adverse effects of hysteresis on the bearing capacity and system stability of axial MBs are analyzed. A compensation algorithm is designed based on the inverse model to reduce the hysteresis effect. The inverse model is approximated modeled by the Lissajous curve. Finally, the proposed analysis and control methods are verified by the finite element method (FEM) or experiments. The results show that the proposed analysis method is capable of accomplishing good accuracy and requires less computation time than FEM, it can be applied to arbitrary current variation processes. In addition, the phase lag of the system is effectively improved with the compensation algorithm.

Signal and Power Integrity IO Buffer Modeling Under Separate Power and Ground Supply Voltage Variation of the Input and Output Stages

This work presents an improved input–output (IO) buffer model for signal and power integrity simulation, including power/ground supply voltage (PGSV) variations for the buffer’s input and output stages. Both stages are mathematically modeled from a formulation that is derived from nonlinear electrical circuit analysis, an important aspect that grants these models a good level of generality and, simultaneously, high accuracy. The proposed IO buffer model is linear in the parameters and, therefore, extractable through the linear least-squares technique from the signals acquired in an IO buffer characterization setup. Several validation scenarios, supported on two CMOS driver’s transistor technologies, are performed to evaluate the accuracy of the proposed model. In addition, a comparative analysis is provided, confronting the proposed model’s performance against that of the input/output buffer information specification (IBIS) model, evidencing an outstanding modeling improvement provided by the proposed model.

Optimal Energy Signal Design for Multiuser MISO WPCNs With Non-Linear Energy Harvesting Circuits

The optimal energy signal design for wireless powered communication networks (WPCNs) enabling energy-sustainable communication for a large number of low-power devices is still an open problem in practical systems. In this work, we study a multi-user WPCN, where a multi-antenna base station (BS) sends an energy signal to multiple single-antenna users, which, in turn, harvest energy from the received signal and utilize it for information transmission in the uplink. In contrast to the existing works on multiple-input single-output (MISO) WPCN design, in this paper, we jointly optimize the energy signal waveform and downlink beamforming at the BS for energy harvesting (EH) devices described by non-linear circuit-based models. To this end, we assume that the BS broadcasts a pulse-modulated signal employing multiple energy signal vectors and we formulate an optimization problem for the joint design of the downlink transmit energy signal vectors, their number, the durations of the transmit pulses, and the time allocation policy for minimization of the average transmit power at the BS. We show that for single-user WPCNs, a single energy signal vector, which is collinear with the maximum ratio transmission (MRT) vector and drives the EH circuit at the user device into saturation, is optimal. Next, for the general multi-user case, we show that the optimal signal design requires a maximum number of energy signal vectors that exceeds the number of users by one and propose an algorithm to obtain the optimal energy signal vectors. Since the complexity of the optimal design is high, we also propose two suboptimal schemes for WPCN design. First, for asymptotic massive WPCNs, where the ratio of the number of users to the number of BS antennas, i.e., the system load, tends to zero, we show that the optimal downlink transmit signal can be obtained in closed-form and comprises a sequence of weighted sums of MRT vectors. Next, based on this result, for general WPCNs with finite system loads, we propose a suboptimal closed-form MRT-based design and a suboptimal semidefinite relaxation (SDR)-based scheme. Our simulation results reveal that the proposed optimal scheme and suboptimal SDR-based design achieve nearly identical performance and outperform two baseline schemes, which are based on linear and sigmoidal EH models. Furthermore, we show that, if the system load of the WPCN is low, the performance gap between the proposed suboptimal solutions is small and becomes negligible as the number of BS antennas tends to infinity.

Asynchronous Control of Fuzzy Singularly Perturbed System With a Dynamic Event-Triggered Strategy

This paper is mainly concerned with the asynchronous control problem of fuzzy singularly perturbed systems (FSPSs) by designing an effective dynamic event-triggered control (ETC) strategy. Different from the existing results, a sample-based dynamic eventtriggering condition related to the singular perturbation parameter (SPP) " is proposed. Particularly, an auxiliary variable is employed in the eventtriggered mechanism (ETM), which changes with the fluctuation of the system state. By constructing a novel parameter-dependent Lyapunov functional, some sufficient conditions are derived to stabilize FSPSs and solve the "-dependent control gain. Furthermore, the upper bound of SPP _" related with the proposed control gain is determined. The Zeno behavior can be naturally avoided by applying the sample-based dynamic ETC. Finally, two examples including a nonlinear circuit are presented to validate the effectiveness of obtained results.

Identification of low-SNR Coulter signals based on strongly coupled Lorenz-like oscillators

A Coulter prototype experiment is established and innovatively combined with coupled Lorenz-like oscillators to identify low-signal-to-noise ratio (SNR) Coulter signals. Coulter signals are collected by a Wheatstone bridge and fitted by Gaussian pulse signals. Using numerical simulation, low-SNR Gaussian pulses are added to the oscillators, and the synchronization mutation phenomena in the chaotic oscillators performed by the time scale transformation are analyzed. The maxima in the phenomena are used to detect the low-SNR pulses and construct an identification formula for different particle sizes. The nonlinear circuit of the oscillators is designed and fabricated. Then, it is applied to process low-SNR Coulter signals in the experiment. By selecting the maxima in the output signals from the circuit, according to the identification formula containing the correction coefficient, the particle size distribution can be obtained. The nonlinear circuit can effectively process low-SNR Coulter signals, which provides a good foundation for reducing the lower limit of detection in Coulter signals.

Long-term potentiation mechanism of biological postsynaptic activity in neuro-inspired halide perovskite memristors

Perovskite memristors have emerged as leading contenders in brain-inspired neuromorphic electronics. Although these devices have been shown to accurately reproduce synaptic dynamics, they pose challenges for in-depth understanding of the underlying nonlinear phenomena. Potentiation effects on the electrical conductance of memristive devices have attracted increasing attention from the emerging neuromorphic community, demanding adequate interpretation. Here, we propose a detailed interpretation of the temporal dynamics of potentiation based on nonlinear electrical circuits that can be validated by impedance spectroscopy. The fundamental observation is that the current in a capacitor decreases with time; conversely, for an inductor, it increases with time. There is no electromagnetic effect in a halide perovskite memristor, but ionic-electronic coupling creates a chemical inductor effect that lies behind the potentiation property. Therefore, we show that beyond negative transients, the accumulation of mobile ions and the eventual penetration into the charge-transport layers constitute a bioelectrical memory feature that is the key to long-term synaptic enhancement. A quantitative dynamical electrical model formed by nonlinear differential equations explains the memory-based ionic effects to inductive phenomena associated with the slow and delayed currents, invisible during the ‘off mode’ of the presynaptic spike-based stimuli. Our work opens a new pathway for the rational development of material mimesis of neural communications across synapses, particularly the learning and memory functions in the human brain, through a Hodgkin–Huxley-style biophysical model.

Saddle-node bifurcation of periodic orbit route to hidden attractors.

Hidden attractors are present in many nonlinear dynamical systems and are not associated with equilibria, making them difficult to locate. Recent studies have demonstrated methods of locating hidden attractors, but the route to these attractors is still not fully understood. In this Research Letter, we present the route to hidden attractors in systems with stable equilibrium points and in systems without any equilibrium points. We show that hidden attractors emerge as a result of the saddle-node bifurcation of stable and unstable periodic orbits. Real-time hardware experiments were performed to demonstrate the existence of hidden attractors in these systems. Despite the difficulties in identifying suitable initial conditions from the appropriate basin of attraction, we performed experiments to detect hidden attractors in nonlinear electronic circuits. Our results provide insights into the generation of hidden attractors in nonlinear dynamical systems.

Resistance Tracking Control of Memristors Based on Iterative Learning.

A memristor is a kind of nonlinear two-port circuit element with memory characteristics, whose resistance value is subject to being controlled by the voltage or current on both its ends, and thus it has broad application prospects. At present, most of the memristor application research is based on the change of resistance and memory characteristics, which involves how to make the memristor change according to the desired trajectory. Aiming at this problem, a resistance tracking control method of memristors is proposed based on iterative learning controls. This method is based on the general mathematical model of the voltage-controlled memristor, and uses the derivative of the error between the actual resistance and the desired resistance to continuously modify the control voltage, making the current control voltage gradually approach the desired control voltage. Furthermore, the convergence of the proposed algorithm is proved theoretically, and the convergence conditions of the algorithm are given. Theoretical analysis and simulation results show that the proposed algorithm can make the resistance of the memristor completely track the desired resistance in a finite time interval with the increase of iterations. This method can realize the design of the controller when the mathematical model of the memristor is unknown, and the structure of the controller is simple. The proposed method can lay a theoretical foundation for the application research on memristors in the future.

Cost effective Tanh activation function circuits based on fast piecewise linear logic

In this paper, an approximate 16-bit non-linear Tanh function circuit design is proposed for activation function in neural networks and digital signal processing, which is based on piecewise linear calculation. By sacrificing acceptable accuracy in computation, the proposed logic circuit structure can furtherly improve the overall performance of the design, with marked reduction in delay, area and power consumption. Linear calculation segments with simple shift-and-add logic architectures are adopted for easy hardware implementation. Additionally, tailored bias tuning and approximate accumulator design make a fine balance between complexity and error distribution. The mean absolute error (MAE) of the entire design is 0.0049. Compared with other state-of-art works in 90 nm CMOS process, the area of the circuit is 582μm2, and the energy is 0.0996 mW/GHz at 0.71 GHz. Moreover, the area-delay product is reduced by over 79.7% and the energy-delay product is reduced by over 42.4%. In the evaluation of its suitability in large applications, the accurate Tanh circuit and the proposed Tanh circuit are adopted in two neural networks to classify the Fashion-MNIST data and emotional EEG data. When the model converges, the accuracies of the test set only differs with a maximum of 0.2% and 0.3%.

Analysis and Control of Chaos in Current Mode Controlled Superbuck Converter for Photovoltaic Systems

Background: Superbuck converter is a strong nonlinear system. However, with the changes in parameters, Superbuck converter performance may be reduced due to nonlinear phenomena, such as bifurcation, chaos, etc. Current mode controlled Superbuck converters have been extensively applied in photovoltaic (PV) systems that require a stable output voltage. Superbuck converters, as nonlinear circuits, exhibit plentiful nonlinear phenomena, such as bifurcation and chaos. In this study, we analyze and control the nonlinear phenomena in the current mode controlled Superbuck converter. The piecewise switching model and discrete iteration mapping model of the Superbuck converter are established. The evolution process of the Superbuck converter from steady state to bifurcation and chaos is revealed when the reference current, input voltage, and load are used as bifurcation parameters, and the bifurcation forms of the converter are all period-doubling bifurcations. The stability criterion of Superbuck converter under current mode has been deduced from reference current by analyzing the stability of the converter. Through the resonant parametric perturbation (RPP) method, the chaos control of the Superbuck converter has been realized for the first time. The converter changes from a chaotic state to a stable single-cycle state about 0.4ms after control and the output voltage ripple is reduced from 3.905V to 0.679V, which effectively improves the output stability of the converter. Objective: This study aimed to analyze and control nonlinear phenomena in current-mode controlled Superbuck converters. Method: Bifurcation diagram, time-domain waveform diagram, phase portrait and Poincare section are used as analytical methods for the nonlinear dynamic characteristics of Superbuck converters. The chaotic control method of the Superbuck converter is Resonant Parameter Perturbation (RPP). Results: After applying RPP control to the Superbuck converter in the chaotic state, it is converted into a single-cycle stable state in about 0.4ms. After the converter is controlled, the output current ripple is reduced from 0.71479A to 0.31A, and the output voltage ripple is reduced from 3.905V to 0.679V. Conclusion: With the increase in the reference current, the decrease in the input voltage, or the increase in the load, the system enters the chaotic state through the period-doubling bifurcation path. In this study, the chaos control of the Superbuck converter is carried out for the first time, and the control method used is the resonant parametric perturbation method. After RPP control, the converter is changed from an unstable, chaotic state to a stable period state in about 0.4ms.

Deep Independent Recurrent Neural Network Technique for Modeling Transient Behavior of Nonlinear Circuits

This paper introduces a novel macromodeling method based on a recurrent neural network called deep independently recurrent neural network (DIRNN). The proposed method applies to time-domain modeling of nonlinear circuits and components, resulting in better training. It overcomes the vanishing and exploding gradient problems encountered with conventional RNNs. In conventional RNNs, all neurons in each layer are involved in recurrent connections that cause unnecessary connections, increasing the model’s complexity over time and making it hard to train for long-time sequences. To solve this problem, the proposed DIRNN’s neurons are independent of each other in recurrent connections, because each neuron only receives connections from its own previous hidden state. The validity of the proposed method is verified by modeling two nonlinear circuit examples, namely, a multi-stage driver terminated by a multi-line interconnect, and an on-chip voltage generator.

A flux-tunable YBa2Cu3O7 quantum interference microwave circuit

Josephson microwave circuits are essential for the currently flourishing research on superconducting technologies, such as quantum computation, quantum sensing, and microwave signal processing. To increase the possible parameter space for device operation with respect to the current standards, many materials for superconducting circuits are under active investigation. Here, we present the realization of a frequency-tunable, weakly nonlinear Josephson microwave circuit made of the high-temperature cuprate superconductor YBa2Cu3O7 (YBCO), a material with a high critical temperature and a very high critical magnetic field. An in situ frequency-tunability of ∼300 MHz is achieved by integrating a superconducting quantum interference device (SQUID) into the circuit based on Josephson junctions directly written with a helium ion microscope (HIM). Our results demonstrate that YBCO-HIM-SQUID microwave resonators are promising candidates for quantum sensing and microwave technology applications.