Nonlinear Circuit Elements Research Articles

On-demand transposition across light-matter interaction regimes in bosonic cQED

The diverse applications of light-matter interactions in science and technology stem from the qualitatively distinct ways these interactions manifest, prompting the development of physical platforms that can interchange between regimes on demand. Bosonic cQED employs the light field of high-Q superconducting cavities coupled to nonlinear circuit elements, harnessing the rich dynamics of their interaction for quantum information processing. However, implementing fast switching of the interaction regime without deteriorating the cavity coherence is a significant challenge. We present an experiment that achieves this feat, combining nanosecond-scale frequency tunability of a transmon coupled to a cavity with lifetime of hundreds of microseconds. Our implementation affords a range of useful capabilities for quantum information processing; from fast creation of cavity Fock states using resonant interaction and interchanging tomography techniques at qualitatively distinct interaction regimes on the fly, to the suppression of unwanted cavity-transmon dynamics during idle evolution. By bringing flux tunability into the bosonic cQED toolkit, our work opens up the possibility to probe the full range of light-matter interaction dynamics within a single platform and provides valuable pathways towards robust and versatile quantum information processing.

Symplectic Geometry and Circuit Quantization

Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose degrees of freedom are either magnetic fluxes or electric charges in the circuit. By combining nonlinear circuit elements (such as Josephson junctions or quantum phase slips), it is possible to build circuits where a standard Lagrangian description (and thus the standard quantization method) does not exist. Inspired by the mathematics of symplectic geometry and graph theory, we address this challenge, and present a Hamiltonian formulation of nondissipative electrodynamic circuits. The resulting procedure for circuit quantization is independent of whether circuit elements are linear or nonlinear, or if the circuit is driven by external biases. We explain how to rederive known results from our formalism, and provide an efficient algorithm for quantizing circuits, including those that cannot be quantized using existing methods. Published by the American Physical Society 2024

Bir Direnç ve İki Kapasitörlü Lineer Bir RC Devresi için Cauchy Probleminin Fourier Serisi Cinsinden Çözümü

As it is known, solutions obtained in terms of Fourier series are widely used for more detailed analysis of mathematical models defined for different engineering problems. In this study, for the mathematical analysis of transient events in active RC based linear electronic circuits, the Cauchy problem is defined and solved in terms of Fourier series. For this reason, first of all, the mathematical model needed for the mathematical definition of the investigated problem was created. Based on the defined mathematical model, a quadratic differential equation for the linear RC electric circuit is obtained and the voltage and current changes are analysed for simple special cases using the Fourier series. As a result, mathematical modelling of transient processes occurring in linear RC circuits and mathematical problems defined as the Cauchy problem for such circuits have been solved analytically. It is thought that the results of the research will contribute theoretically and practically to the solution of the problems that arise in the study and design automation of different electronic circuits containing nonlinear circuit elements.

Dynamic Analysis of A Three Dimension Chaotic System

Memristor is a newly realized physical element, and it is a non-linear circuit element with memory function. We constructed a new three-dimensional chaotic system is constructed which contains four parameters and five non-linear terms. The system is analyzed by nonlinear dynamic analysis methods such as theoretical deduction analysis, numerical simulation, lyapunov exponent spectrum, and bifurcation diagram. The dynamic behavior of the system. This paper proposes a new three-dimensional chaotic system. The system contains four parameters, and each equation contains a non-linear product term. Based on theoretical derivation, numerical simulation, Lyapunov exponential spectrum, bifurcation diagram, the basic dynamic characteristics of the chaotic system are analyzed.

Investigation of memristive memory in the framework of low power consumption and improved Read/Write time

Memristor is a non-linear passive circuit element. It was visualized by Leon Chua in 1971. Memristor can form a non-linear relationship with electric charge and magnetic flux. Memristor has the capability to hold data even if it is not connected to any power source. This property makes it non-volatile in nature. Memristor is a non-volatile memory which can be used for data storage. International Technology Roadmap for Semiconductors acknowledges that it is difficult to scale the transistor beyond its current size and to overcome the existing memory issues, emerging memristor technology is being developed. The objective of this research is to realize the memristor based non-volatile memory which can consume less power with better Read/Write time. In this research, properties and construction of memristor is analyzed. In order to construct a memristor, various softwares like LTspice and MATLAB are used.

A memristor-based circuit approximation of the Hindmarsh–Rose model

Neuron models exist in different levels of complexity and biological modeling depth. The Hindmarsh–Rose model offers a rich repertoire of neuronal dynamics while being moderately mathematically complex. Existing circuit realizations of this neuron model, however, require a large amount of operational amplifiers due to the model’s quadratic and cubic nonlinearity. In contrast to hardware realizations of simpler neuron models, this leads to a higher power consumption. In this work, the Hindmarsh–Rose model is approximated by an ideal electrical circuit that relies mostly on passive circuit elements and thus reduces the power consumption. For this purpose, we analyze the power flows of an equivalent electrical circuit of the Hindmarsh–Rose model and replace several nonlinear circuit elements by constant ones. Moreover, we approximate the cubic nonlinearity by three memristors in combination with a negative impedance converter. This negative impedance converter represents the only active circuit element required for the complete circuit, leading to an increased energy efficiency compared to the existing circuit realizations. Simulations verify the circuit’s ability to generate spiking and bursting dynamics comparable to the original Hindmarsh–Rose model.Graphic abstract

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.

Investigations on enhanced plasma expansion in pseudospark discharge assisted by a magnetic switch

Electrode erosion caused by dense plasma in constrictive discharge channel is one of the fundamentally detrimental effects existing in pulsed discharge switches. An enhanced plasma expansion in pseudospark discharge assisted by a magnetic switch (MS) is observed from ICCD images in this paper, accompanied by reduced commutation loss, and the mechanisms are revealed by experiments and simulations. The characteristics of the discharge waveforms and channel images of the pseudospark discharge with and without a series-connected MS are compared, and the influence of the number of magnetic cores is studied. As the loop current increases, the discharge channel expands radically and reaches the maximum as the current rising rate reaches the maximum. As the number of magnetic cores increases from 0 to 8, the maximum diameter of the discharge channel increases from 16 mm to about 38 mm, and the commutation loss is reduced from 30 mJ to 11 mJ. The electrode erosion rate of the case with a MS is lower than that without a MS. A particle in cell/Monte Carlo collision model coupling to nonlinear external circuit elements is established. The simulation results fit well with the experiment phenomena, including the discharge waveforms and the profiles of the discharge channel. The distribution of ions shows more diffused features than that of electrons, while the distribution of electrons is more similar to the discharge channel observed in experiments. The enhanced plasma expansion is mainly caused by the higher radial acceleration component of the charged particles during the magnetically delayed time.

Effects of Electric Vehicles and Charging Stations on Microgrid Power Quality

In this study, integration of renewable energy sources and Electric Vehicles (EVs) into a micro-grid was modeled and analyzed. The microgrid is divided into four important parts; a diesel generator, acting as the base power generator; a photovoltaic (PV) farm combined with a wind farm, to produce electrical energy; a vehicle to grid (V2G) system installed next to the last part of the microgrid which is the load of the microgrid. The size of the microgrid represents approximately a community of a thousand households during a low consumption day in spring or fall. There are 100 electric vehicles in the base model which means that there is a 1:10 ratio between the cars and the households. This is a possible scenario in a foreseeable future. The continuous increase in their rate in energy production makes micro-grids important. Microgrids can be designed to meet the energy needs of hospitals, universities or charging stations of electric cars, as well as to meet the energy needs of a district, village or industrial site. Charging stations are needed to charge the electric vehicle battery. In this study, the effects of electric vehicles on the microgrid network are analyzed. Electric vehicles have non-linear circuit elements in their structures. Therefore, they are a source of harmonic current in the microgrid. They negatively affect the power quality of the microgrid. The battery in electric vehicles is charged with direct current. The alternating current from the microgrid needs to be converted to direct current.

Physics-based compact modeling of electro-thermal memristors: Negative differential resistance, local activity, and non-local dynamical bifurcations

Leon Chua's Local Activity theory quantitatively relates the compact model of an isolated nonlinear circuit element, such as a memristor, to its potential for desired dynamical behaviors when externally coupled to passive elements in a circuit. However, the theory's use has often been limited to potentially unphysical toy models and analyses of small-signal linear circuits containing pseudo-elements (resistors, capacitors, and inductors), which provide little insight into required physical, material, and device properties. Furthermore, the Local Activity concept relies on a local analysis and must be complemented by examining dynamical behavior far away from the steady-states of a circuit. In this work, we review and study a class of generic and extended one-dimensional electro-thermal memristors (i.e., temperature is the sole state variable), re-framing the analysis in terms of physically motivated definitions and visualizations to derive intuitive compact models and simulate their dynamical behavior in terms of experimentally measurable properties, such as electrical and thermal conductance and capacitance and their derivatives with respect to voltage and temperature. Within this unified framework, we connect steady-state phenomena, such as negative differential resistance, and dynamical behaviors, such as instability, oscillations, and bifurcations, through a set of dimensionless nonlinearity parameters. In particular, we reveal that the reactance associated with electro-thermal memristors is the result of a phase shift between oscillating current and voltage induced by the dynamical delay and coupling between the electrical and thermal variables. We thus, demonstrate both the utility and limitations of local analyses to understand non-local dynamical behavior. Critically for future experimentation, the analyses show that external coupling of a memristor to impedances within modern sourcing and measurement instruments can dominate the response of the total circuit, making it impossible to characterize the response of an uncoupled circuit element for which a compact model is desired. However, these effects can be minimized by proper understanding of the Local Activity theory to design and utilize purpose-built instruments.

Bir İletim Hattından Beslenen Bir Memristörün Zamanda Sonlu Farklar Yöntemi İle Çözümü

Memristor is a new nonlinear circuit element. Examination of its use with other circuit elements is important from Circuit analysis point of view. A memristor connected at the end of a transmission line will exhibit a different behavior than a resistor does. It is difficult or impossible to solve such a problem since the memristor is a nonlinear circuit element. In this study, the equation of the electromagnetic wave propagating over the transmission line with a memristor load is solved using the finite-difference time-domain (FDTM) method. Memristor current and voltage are calculated depending on time. The simulations are made with the MATLAB program.

The Equivalent Circuits Thévenin and Norton

Abstract The main objectives of this paper are to correctly define the equivalent Thévenin and Norton circuits and to presents the complete and exact proof of Thévenin and Norton theorems. These circuits allow the separation of the linear portions of the electronic circuits from the nonlinear ones and in this way the polarization process of the electronic devices becomes much more efficient. When linear and/or nonlinear analyzed circuits have a small number of nonlinear circuit elements, their analysis, synthesis, and simulation are performed much more efficiently if the nonlinear part of the circuit is separated from the linear one. By determining the equivalent Thévenin or Norton circuits in relation to the load to connected terminals of a system with two or more magnetic coupled coils, that are part of the wireless power transfer systems, optimal load parameters are determined so that the maximum active power is transmitted to the load.

Method for the Analysis of Three-Phase Networks Containing Nonlinear Circuit Elements in View of an Efficient Power Flow Computation

The present paper is devoted to applying the Hănțilă method for solving nonlinear three-phase circuits characterized by different reactance values on the three sequences (positive, negative and zero). Nonlinear elements, which are components of the circuit, are substituted by real voltage or current sources, whose values are an iteratively corrected function of the voltage across or the current through them, respectively. The analysis is carried out in the frequency domain and facilitates an easy evaluation of the power transfer on each harmonic. The paper presents numerical implementations of the method for two case studies. For validation, the results are compared against those obtained using the software LTspice in the time domain. Finally, the power flow on the harmonics and the overall power balance are analyzed.

Identification of Multiple Noise Sources Improves Estimation of Neural Responses across Stimulus Conditions.

Most models of neural responses are constructed to reproduce the average response to inputs but lack the flexibility to capture observed variability in responses. The origins and structure of this variability have significant implications for how information is encoded and processed in the nervous system, both by limiting information that can be conveyed and by determining processing strategies that are favorable for minimizing its negative effects. Here, we present a new modeling framework that incorporates multiple sources of noise to better capture observed features of neural response variability across stimulus conditions. We apply this model to retinal ganglion cells at two different ambient light levels and demonstrate that it captures the full distribution of responses. Further, the model reveals light level-dependent changes that could not be seen with previous models, showing both large changes in rectification of nonlinear circuit elements and systematic differences in the contributions of different noise sources under different conditions.

Overlap junctions for superconducting quantum electronics and amplifiers

Due to their unique properties as lossless, nonlinear circuit elements, Josephson junctions lie at the heart of superconducting quantum information processing. Previously, we demonstrated a two-layer, submicrometer-scale overlap junction fabrication process suitable for qubits with long coherence times. Here, we extend the overlap junction fabrication process to micrometer-scale junctions. This allows us to fabricate other superconducting quantum devices. For example, we demonstrate an overlap junction-based Josephson parametric amplifier that uses only two layers. This efficient fabrication process yields frequency-tunable devices with negligible insertion loss, a gain of ∼30 dB, and quantum limited noise performance. Compared to other processes, the overlap junction allows for fabrication with minimal infrastructure, high yield, and state-of-the-art device performance.

Nonlinear Analog Spintronics with van der Waals Heterostructures

The current generation of spintronic devices, which use electron-spin relies on linear operations for spin-injection, transport and detection processes. The existence of nonlinearity in a spintronic device is indispensable for spin-based complex signal processing operations. Here we for the first time demonstrate the presence of electron-spin dependent nonlinearity in a spintronic device, and measure up to 4th harmonic spin-signals via nonlocal spin-valve and Hanle spin-precession measurements. We demonstrate its application for analog signal processing over pure spin-signals such as amplitude modulation and heterodyne detection operations which require nonlinearity as an essential element. Furthermore, we show that the presence of nonlinearity in the spin-signal has an amplifying effect on the energy-dependent conductivity induced nonlinear spin-to-charge conversion effect. The interaction of the two spin-dependent nonlinear effects in the spin transport channel leads to a highly efficient detection of the spin-signal without using ferromagnets. These effects are measured both at 4K and room temperature, and are suitable for their applications as nonlinear circuit elements in the fields of advanced-spintronics and spin-based neuromorphic computing.

Experimental Investigation of a Nonlinear Energy Storage Effect due to High Power Electromagnetic Excitation

Abstract. The susceptibility of interference victims can significantly be influenced by the presence of nonlinear circuit elements. In addition to the well known occurrence of intermodulation-frequencies, other effects can be observed as well. Recently, a nonlinear energy storage effect has been discovered which is due to the presence of nonlinearly loaded loop antennas if excited by an HPEM-excitation. In this contribution, this effect is further studied by experiment. It is seen that the nonlinear energy storage effect can be reproduced by means of a rather simple experimental setup. This allows to straighforwardly study parameter variations in order to attain an improved understanding of the considered effect.

A Dream that has Come True: Chaos from a Nonlinear Circuit with a Real Memristor

In the last decade, researchers, who work in the field of nonlinear circuits, have the “dream” to use a real memristor, which is the only nonlinear fundamental circuit element, in a new or other reported nonlinear circuit in literature, in order to experimentally investigate chaos. With this intention, for the first time, a well-known nonlinear circuit, in which its nonlinear element has been replaced with a commercially available memristor (KNOWM memristor), is presented in this work. Interesting phenomena concerning chaos theory, such as period-doubling route to chaos, coexisting attractors, one-scroll and double-scroll chaotic attractors are experimentally observed.

Fracmemristor chaotic oscillator with multistable and antimonotonicity properties

Memristor is a non-linear circuit element in which voltage-current relationship is determined by the previous values of the voltage and current, generally the history of the circuit. The nonlinearity in this component can be considered as a fractional-order form, which yields a fractional memristor (fracmemristor). In this paper, a fractional-order memristor in a chaotic oscillator is applied, while the other electronic elements are of integer order. The fractional-order range is determined in a way that the circuit has chaotic solutions. Also, the statistical and dynamical features of this circuit are analyzed. Tools like Lyapunov exponents and bifurcation diagram show the existence of multistability and antimonotonicity, two less common properties in chaotic circuits.

Optimizing Josephson-ring-modulator-based Josephson parametric amplifiers via full Hamiltonian control

Josephson Parametric Amplifiers (JPA) are nonlinear devices that are used for quantum sensing and qubit readout in the microwave regime. While JPAs regularly operate in the quantum limit, their gain saturates for very small (few photons) input power. In a previous work, we showed that the saturation power of JPAs is not limited by pump depletion, but instead by the high-order nonlinearity of Josephson junctions, the nonlinear circuit elements that enable amplification in JPAs. Here, we present a systematic study of the nonlinearities in JPAs, we show which nonlinearities limit the saturation power, and present a strategy for optimizing the circuit parameters for achieving the best possible JPA. For concreteness, we focus on JPAs that are constructed around a Josephson Ring Modulator (JRM). We show that by tuning the external and shunt inductors, we should be able to take the best experimentally available JPAs and improve their saturation power by $\sim 15$ dB. Finally, we argue that our methods and qualitative results are applicable to a broad range of cavity based JPAs.