Nonlinear Inductance Research Articles

Light-Load Efficiency Improvement for Buck Voltage Regulators

Extending battery life is a big challenge for today's laptop, and light-load efficiency is very important for battery life extension. In this paper, adaptive ON-time control is proposed to achieve higher efficiency when the buck converter is running in continuous current mode. A novel nonlinear inductor is then proposed to improve discontinuous-current-mode efficiency. A control method with a thorough analysis is proposed for the nonlinear inductor to achieve high efficiency, the required output voltage ripple, and sufficient transient response. The experimental results demonstrate the benefits of the proposed methods.

Parametrically-induced tunable coupling between flux qubits — dependence on the coupler bias

We have studied a tunable coupling scheme of two superconducting flux qubits biased at the degeneracy point. The qubits are coupled parametrically under microwave driving, via nonlinear inductance of a third qubit biased slightly away from the degeneracy point. The observed on-state coupling as well as the off-state residual coupling depend non-monotonically on the coupler bias point and agree quantitatively with calculations based on a three-qubit Hamiltonian. This simple model is useful to optimize the parameters for a large on/off ratio.

Engineered selection rules for tunable coupling in a superconducting quantum circuit

Engineering selection rules of transitions is a useful strategy for coupling and decoupling qubits in superconducting quantum circuits. Following this approach, we implement a tunable coupling scheme between two flux qubits. The qubits are coupled parametrically under microwave driving via the nonlinear inductance of a third qubit. The measured on-state coupling as well as the off-state residual coupling depends on the coupler bias and agrees quantitatively with a calculation of transition matrix elements of a three-qubit Hamiltonian.

Waves Amplification in Discrete Nonlinear Electrical Lines: Direct Numerical Simulation

We study the amplification of a pulse soliton in a discrete nonlinear electrical transmission line using negative nonlinear resistances and inductances linearly varying in space. The numerical simulation is used to solve the resulting set of discrete nonlinear differential equations in each case. In both cases, the dissipative effects of the medium in which it travels are compensated on a short distance of a doped domain. During the crossing of this doped domain, the wave conserves its pulse form and recovers its amplitude when coming out.

Quantum analysis of a nonlinear microwave cavity-embedded dc SQUID displacement detector

We carry out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector, comprising a SQUID with mechanically compliant loop segment, which is embedded in a microwave transmission line resonator. The SQUID is approximated as a nonlinear current-dependent inductance, inducing an external flux tunable nonlinear Duffing self-interaction term in the microwave resonator mode equation. Motion of the compliant SQUID loop segment is transduced inductively through changes in the external flux threading SQUID loop, giving a ponderomotive radiation pressure-type coupling between the microwave and mechanical resonator modes. Expressions are derived for the detector signal response and noise, and it is found that a soft-spring Duffing self-interaction enables a closer approach to the displacement detection standard quantum limit, as well as cooling closer to the ground state.

Direct torque control of switched reluctance motor for minimizing torque ripple

Large torque ripple of the Switched Reluctance Motor (SRM) is a major problem that is an obstacle to spreading over an industry. Nonlinear inductance profile and pulse magnetizing make the torque ripple unavoidable. In order to reduce the torque ripple, it is necessary to control the to rque directly because the torque of the SRM is not linearly proportional to a current. This paper shows direct torque control scheme that reduces the torque ripple of the SRM dramatically. To verify the feasibility of control scheme, simulation and experiment are carried out.

Chaotic ferroresonance in a non-autonomous circuit

Accurate description of magnetization curve has important effect on ferroresonance. In most of earlier ferroresonance studies the magnetization curve is modelled as a 3rd or 5th order polynomial. However, it is not comprehensive. This paper investigates the chaotic ferroresonance behaviour exhibited by a non-autonomous circuit which contains a nonlinear flux-controlled inductance. The ferromagnetic characteristic of this nonlinear inductance represented by a magnetization curve could be expressed as an n th order two-term polynomial. By varying the value of exponent n, the circuit can assume a diverse range of steady-state regimes including fundamental and subharmonic ferroresonance, quasi-periodic oscillations, and chaos. A detailed analysis of some simulations demonstrates that the probability of chaos increases as the exponent of the magnetization curve rises. The effect of varying the magnitude of the source voltage on the chaotic behaviour of the circuit is also studied.

Parameters Affecting Ferroresonance in $LCR$ Electric Circuits

This paper investigates the influence of supply, circuit and magnetic material parameters on the occurring of fundamental-mode ferroresonance in a series inductance-capacitance-resistance (LCR) circuit with a nonlinear inductor. The analysis is developed using a modeling approach, validated by experiments, which accurately describes the magnetic behavior (dynamic hysteresis and eddy currents) of the saturable inductance. The conditions leading to subharmonic ferroresonance are also investigated.

Superconducting quantum bits

Superconducting circuits are macroscopic in size but have generic quantum properties such as quantized energy levels, superposition of states, and entanglement, all of which are more commonly associated with atoms. Superconducting quantum bits (qubits) form the key component of these circuits. Their quantum state is manipulated by using electromagnetic pulses to control the magnetic flux, the electric charge or the phase difference across a Josephson junction (a device with nonlinear inductance and no energy dissipation). As such, superconducting qubits are not only of considerable fundamental interest but also might ultimately form the primitive building blocks of quantum computers.

Study of the Effects of Inductor Nonlinear Behavior on the Performance of Current Controllers for Single-Phase PV Grid Converters

Resonant and repetitive controllers are well suited for single-phase grid-connected inverters due to their optimum tracking and harmonic rejection capability. In particular, in this paper, their application for single-phase photovoltaic systems is considered. The effects of nonlinear inductance on the performance of current controllers designed to track periodic signals and/or to compensate periodic disturbances are investigated. When the inductance has a nonlinear behavior, a distorted current waveform is produced. Two different nonlinearities have been considered: saturation for high currents and a light nonlinearity, which occurs in the first portion of the magnetization curve, for low currents. A current-dependent model of the nonlinear inductance has been developed. It is mathematically based on the Volterra-series expansion, and it allows us to prove how the harmonic compensation provided by resonant and repetitive controllers can also mitigate the effects of the inductance saturation. This result is the main contribution of this paper, and it is also substantiated with experimental evidence. Moreover, the repetitive controller is able to comply with the harmonic limits reported in IEEE 1547 and IEC 61727, even in very hard saturation conditions.

Analytical Formula to Estimate the Maximum Inrush Current

This letter presents an analytical formula to predict the peak inrush current for a nonlinear inductor in series with a resistor. The formula is developed using nonlinear circuit analysis and its accuracy is verified by comparing the calculated peak inrush current to those obtained through time-domain simulations. The formula is very useful to estimate the impact of damping resistors on the transformer inrush current.

Nonlinear buffer layers relevant for reduced nonlinear effects in HTS microwave devices

Microwave devices made of a High-Temperature Superconductor (HTS) exhibit a nonlinear response as the microwave power increases. The HTS nonlinearities generate a nonlinear inductance Ld(irf) and a nonlinear resistance Rd(irf) in a device. Ld(irf) and Rd(irf) are responsible for an increase of the device loss, a small frequency dispersion as well as the generation of spurious signals like Intermodulation Distortion (IMD). Nevertheless, the HTS nonlinearities in a microwave device can be reduced using a nonlinear dielectric like a ParaElectric Material (PEM). This assumption has recently been demonstrated theoretically. In a microwave device made of a HTS and a PEM, the nonlinear contribution to the capacitance Cd(vrf) from the PEM acts oppositely to the nonlinear contribution to Ld(irf). This may cancel the effect of the HTS inductive nonlinearities. The PEM also produces a nonlinear conductance Gd(vrf) in a device. All these nonlinear terms contribute to the IMD output power and the nonlinear quality factor (Q0) of a resonant passive microwave device. In this paper, the dependence of the different nonlinear contributions on frequency and applied dc bias voltage (Vdc) is investigated. The relevance to employ PEM in order to reduce the nonlinearities in HTS microwave devices is discussed.

A unified discrete model for PWM switching DC to DC converters with current-mode control

This paper presents a unified discrete model for pulse-width modulated (PWM) switching DC to DC converters. The major achievement is that, without any topology modification, the proposed model can be used for performance analysis of the buck, boost and buck-boost converters with any of the two current-mode controls: peak current-mode control and average current-mode control. Three important factors are considered: parasitical effects of circuit elements, non-linear inductance dependent on the current flowing through it, and control time delay, such that the accuracy of performance prediction is greatly improved. Magnetic field finite element analysis (FEA) is conducted to calculate the non-linear differential inductance. By implementing the proposed model into Matlab/Simulink, a simulation model is built. The model has been used for the performance analysis of an existing flyback converter with the peak current-mode control. The simulation results are in good agreement with the actual performance, validating the proposed model.

Using TACS Functions Within EMTP to Set Up Current-Transformer Model Based on the Jiles–Atherton Theory of Ferromagnetic Hysteresis

The subject of this paper is to construct a current- transformer (CT) model based on the Jiles-Atherton (J-A) theory of ferromagnetic hysteresis using transient analysis of control systems (TACS) functions within the electromagnetic transients program (EMTP) in a closed-loop manner. The J-A theory of ferromagnetic hysteresis is presented by the nonlinear first-order ordinary differential equations and inclusive of five parameters that can be found by measurements of hysteresis characteristic. We can use TACS functions within EMTP to describe the J-A theory of ferromagnetic hysteresis. The powerful advantage of this way is the interaction between the electrical network and TACS in EMTP. Compared with the CT model based on the type 96 nonlinear hysteresis inductor, the simulated result of the CT model based on the J-A theory of ferromagnetic hysteresis is almost the same in steady-state situations, but apparently different in a fault transient situation. The analysis and simulation of the actual measured fault profiles in the Taiwan power system is an example of the validation of this proposed model. Therefore, this proposed CT model based on the J-A theory of ferromagnetic hysteresis has the analysis capability of the transient response. The flexibility of TACS makes the simulation of any other situation easier and is another advantage.

Wideband Nonlinear Response of High-Temperature Superconducting Thin Films From Transmission-Line Measurements

We report on a technique for extracting an accurate value of the nonlinear inductance in superconducting transmission lines. This novel technique assesses the frequency dependence of the transmission line's nonlinear response. A wideband nonlinear measurement system was used to simultaneously measure the third-order spurious signals at 2f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> - f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,</sub> 2f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> - f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> + f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , 2f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> + f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , 3f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , and 3f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> frequencies. Measurements for different values of the fundamental frequencies f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> allow us to study the spurious signal generation from 1 to 21 GHz. We demonstrate this technique by measuring several superconducting YBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7-x</sub> coplanar waveguide transmission line geometries patterned in a single chip at 80 K. The results show a linear frequency dependence of the nonlinear response, indicating a dominant contribution of the nonlinear inductance over the nonlinear resistance omegaDeltaL(i) Gt DeltaR(i). The experimentally obtained nonlinear inductances are then used to determine device-independent measures of the linearity of the thin-film material in order to provide the foundation for modeling the nonlinear response of specific devices.

Nonlinear Response of Combined Superconductor/Ferroelectric Devices: First Experimental Step

Superconducting thin films are known to possess a nonlinear response at microwave frequencies. These nonlinear effects can be described quantitatively by a nonlinear inductance, and for high-Tc superconductors, are believed to be an intrinsic consequence of d-wave superconductivity. Similar nonlinear effects can be observed in ferroelectric materials, such as SrTiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> . We experimentally explore the interaction between nonlinear effects of different character arising from these two different origins. We consider a number of different device configurations, and measure the generation of harmonic and intermodulation products as function of temperature, in order to assess how these two different types of nonlinear response would interact in devices fabricated from both types of nonlinear materials. We use these measurements to assess whether nonlinear effects in high-Tc superconductor devices may be mitigated by some form of active cancellation. Effects of the ferroelectric losses are also discussed.

Nonlinear Inductance of Intrinsic Josephson Junction Arrays and Its Application to Tunable Filters

Nonlinear inductance of intrinsic Josephson junction arrays in Tl-2212 thin films has been investigated. Misaligned Tl-2212 thin films were fabricated on 20deg vicinal substrates and then patterned into long bridges by standard photolithography and wet chemical etching. Each bridge forms a large array of intrinsic Josephson junctions. We have measured the Josephson inductance of the bridges in the zero-DC-voltage state at 77 K and show that its dependence on the critical current is in a good agreement with theory. Also, we have numerically studied the nonlinearity of the Josephson inductance and present dependence of the distortion factor on the bias and AC signal currents. Based on the obtained results, we have designed a 10-pole narrow-band lumped-element filter with the tunable center frequency in the range from 1900 MHz to 1960 MHz. Simulations show that the filter has good selectivity.

Quantum Coherent Tunable Coupling of Superconducting Qubits

To do large-scale quantum information processing, it is necessary to control the interactions between individual qubits while retaining quantum coherence. To this end, superconducting circuits allow for a high degree of flexibility. We report on the time-domain tunable coupling of optimally biased superconducting flux qubits. By modulating the nonlinear inductance of an additional coupling element, we parametrically induced a two-qubit transition that was otherwise forbidden. We observed an on/off coupling ratio of 19 and were able to demonstrate a simple quantum protocol.

Experimental and modelling analysis of ferroresonant electric circuits

This paper presents a numerical and an experimental investigation on the ferroresonance in a LCR series electric circuit with the aim of deepening the effects of the magnetization phenomena in the ferromagnetic core. In the experiments an Epstein-like FeSi core, enabling an accurate material characterization under the same test conditions, constitutes the non-linear inductance. The model couples the circuit equations with a finite element solution of the one-dimensional electromagnetic field along the lamination thickness. The analysis of the numerical results, which are confirmed by experiments, shows that the accurate prediction of ferroresonance requires the use of detailed constitutive models, when the role of the magnetic losses is significant.

Frequency dependence of the nonlinear response in YBa2Cu3O7−x transmission lines

The authors evaluate the frequency dependence of the nonlinear response in high-temperature superconductor YBa2Cu3O7−x thin films by simultaneously measuring the nonlinear intermodulation products and harmonic generation in broadband superconducting transmission lines at 76K. The frequencies of the two-tone incident signal are set to produce spurious signals from 1to21GHz. They extract a nonlinear term ∣ΔR2+jωΔL2∣ by applying a model of spurious signal generation in superconducting transmission lines to their measurement results. They found that this nonlinear term follows a linear dependence on frequency, indicating a dominant contribution of the nonlinear inductance ΔL2 over the nonlinear resistance ΔR2, (ωΔL2⪢ΔR2), for the superconducting nonlinear response.