Nonlinear Equivalent Circuit Research Articles

Carbon Nanotube Detectors and Spectrometers for the Terahertz Range

We present the compact unified charge control model (UCCM) for carbon nanotube field-effect transistors (CNTFETs) to enable the accurate simulation of the DC characteristics and plasmonic terahertz (THz) response in the CNTFETs. Accounting for the ambipolar nature of the carrier transport (n-type and p-type conductivity at positive and negative gate biases, respectively), we use n-type and p-type CNTFET non-linear equivalent circuits connected in parallel, representing the ambipolar conduction in the CNTFETs. This allows us to present a realistic non-linear model that is valid across the entire voltage range and is therefore suitable for the CNTFET design. The important feature of the model is that explicit equations for gate bias, current, mobility, and capacitance with smoothing parameters accurately describe the device operation near the transition from above- to below-threshold regimes, with scalability in device geometry. The DC performance in the proposed compact CNTFET model is validated by the comparison between the SPICE simulation and the experimental DC characteristics. The simulated THz response resulted from the validated CNTFET model is found to be in good agreement with the analytically calculated response and also reveals the bias and power dependent sub-THz response and relatively wide dynamic range for detection that could be suitable for THz detectors. The operation of CNTFET spectrometers in the THz frequency range is further demonstrated using the present model. The simulation exhibits that the CNT-based spectrometers can cover a broad THz frequency band from 0.1 to 3.08 THz. The model that has been incorporated into the circuit simulators enables the accurate assessment of DC performance and THz operation. Therefore, it can be used for the design and performance estimation of the CNTFETs and their integrated circuits operating in the THz regime.

Lagrangian Model of an Isolated DC-DC Converter With a 3-Phase Medium Frequency Transformer Accounting Magnetic Cross Saturation

This article presents a nonlinear equivalent circuit model of an isolated dc-dc converter with a 3-phase medium frequency transformer. The model takes into account the magnetic cross saturation of the 3-phase core-type magnetic circuit. The model is suitable in detailed electromagnetic transient simulations of power systems involving isolated dc-dc converters. The model is developed using the Lagrange energy method. It involves a matrix of dynamic inductances containing a nonlinear term resulting from core magnetization and a linear term resulting from leakage flux. The model parameters are determined based on a series of magnetostatic finite element method simulations. This approach is convenient when applied to high power transformers offering a limited characterization effort, or if the transformer prototype does not exist. The experimental validation performed on a novel 3-phase MFT prototype in a 100 kW 1.2 kV 20 kHz dual active bridge converter has proved the validity of the model and model parameters. The no-load steady-state and inrush tests and the full-load test show a very good fit between the simulated and experimentally measured waveforms. The comparison with a classical simplified model neglecting magnetic cross saturation shows a significant difference in the no-load inrush test.

Component-Level Optimization of Hybrid Excitation Synchronous Machines for a Specified Hybridization Ratio Using NSGA-II

In this article, a Hybrid Excitation Synchronous Machine (HESM) is optimally designed for a specified Hybridization Ratio (HR). A new formulation of the design problem is proposed to be tackled by the Non-dominated Sorting Genetic Algorithm II (NSGA-II), while minimizing the material cost. This formulation includes a more comprehensive explanation of the key concept, HR, which considers the soft and hard saturation effects in the HESM design. The HESM model is based on a 3D nonlinear Magnetic Equivalent Circuit (MEC). For faster convergence, the number of design variables is reduced using two statistical analyses, namely Analysis of Level and Analysis of Variance (ANOVA). A HESM is optimally designed for HR = 0.5 and validated by a commercial Finite Element Analysis (FEA) software.

Real-Time Optimal Lithium-Ion Battery Charging Based on Explicit Model Predictive Control

The rapidly growing use of lithium-ion batteries across various industries highlights the pressing issue of optimal charging control, as charging plays a crucial role in the health, safety and life of batteries. The literature increasingly adopts model predictive control (MPC) to address this issue, taking advantage of its capability of performing optimization under constraints. However, the computationally complex online constrained optimization intrinsic to MPC often hinders real-time implementation. This paper is thus proposed to develop a framework for real-time charging control based on explicit MPC (eMPC), exploiting its advantage in characterizing an explicit solution to an MPC problem, to enable real-time charging control. The study begins with the formulation of MPC charging based on a nonlinear equivalent circuit model. Then, multi-segment linearization is conducted to the original model, and applying the eMPC design to the obtained linear models leads to a charging control algorithm. The proposed algorithm shifts the constrained optimization to offline by precomputing explicit solutions to the charging problem and expressing the charging law as piecewise affine functions. This drastically reduces not only the online computational costs in the control run but also the difficulty of coding. Extensive numerical simulation and experimental results verify the effectiveness of the proposed eMPC charging control framework and algorithm. The research results can potentially meet the needs for real-time battery management running on embedded hardware.

Modeling, analysis and suppression of current harmonics of Langevin-type ultrasonic motors under high voltage

For achieving high speed and large thrust, Langevin-type ultrasonic motors (LTUM) are generally operated under high voltage. However, high voltage causes the current harmonics of piezoelectric material nonlinear phenomena, which will decrease the efficiency, the output force, and the accuracy of LTUMs. In this study, the nonlinearity of current harmonics of LTUM are described and analyzed by a novel nonlinear equivalent circuit model using Lagrange equations. Thereafter, based on a nonlinear tuning method, a specific driver circuit is suggested to suppress the current harmonics. Experimental results validate that the time response of the current is consistent with that of the model and furtherly demonstrate that the total harmonic current distortion decreases by 68% utilizing the proposed nonlinear tuning method under 500 Vpp.

Design, modelling and optimisation of a slot‐less axial flux permanent magnet generator for direct‐drive wind turbine application

Axial flux permanent magnet machines (AFPMs) are potential candidates for direct-drive wind turbines (DDWTs) due to offering high value of torque density. In slotless AFPM topologies, the cogging torque is absent which makes them more suitable for DDWTs, which provides an easier turbine start-up. In this research, a robust design and optimisation procedure of a slotless double-sided AFPM is discussed. The non-linear magnetic equivalent circuit is established and the optimisation is performed by the response surface methodology to achieve a cost-effective generator with high power density value. The generator is prototyped and the test results are presented comparing them with the numerical study and non-optimised design results. To minimise the AFPM torque ripple which is necessary for DDWT application, a cost-effective solution is proposed leading to a dramatic improvement in the AFPM torque ripple without reducing the average torque.

Emphasis mechanism of nonlinear responses caused by transverse modes in RF BAW devices

It is known that nonlinear responses by transverse resonances are more emphasized than those by the main resonance in radio frequency bulk acoustic wave devices. This paper investigates this mechanism using the LCR-based nonlinear equivalent circuit proposed by the authors. Here a number of acoustic branches are newly added to take multiple transverse resonances into account, and amplitudes of nonlinear voltage sources in the model are determined by summation of currents flowing to acoustic branches. Parameters necessary for the analysis are determined experimentally. It is shown that simulated second and third harmonic responses agree well with the measurement. Next, the magnification mechanism is discussed. It is shown that mth harmonics generated by transverse modes are magnified by m-times approximately, and the factor of m is originated to that at the production between field components of transverse and main modes.

An Enhanced Dynamic Simulation Model of a Hybrid Magnetic Bearing Taking Account of the Sensor Noise.

The paper presents simulation and experimental verification of the hybrid magnetic bearing (HMB) performance characteristics. It has been demonstrated that the additional errors from the eddy current sensors have a significant impact on the control signals. An improved mathematical model combines a nonlinear magnetic equivalent circuit of the HMB with the ordinary differential equations of its transients. These equations describe the rotor motion and the electric circuit of the system, as well as the control system required for stable levitation of the rotor. Certain harmonics have been observed in the displacement signals of frequencies equal to the multiples of the cylinder rotations. The calculation model has, therefore, been improved, taking into account the interference of the harmonics. Simulation results were validated by comparing the time responses of the transients obtained from the numerical calculations with those measured on a real object; a satisfactory agreement between the results has been achieved.

Analysis of Nonlinear Dynamics of Permanent Magnet Magnetic Contactor via Novel Computationally Efficient Analytical Method Considering Stray and Leakage Fluxes

Improving the efficiency and end-use of energy distribution can significantly reduce global energy consumption. As the magnetic contactor (MC) is the most common switchgear used for control in most grids, minimizing its energy consumption has motivated the development of a permanent magnet (PM) MC that exhibits several advantages over conventional solenoid MCs. However, analyzing the transient magnetic behavior of a PM MC requires computationally expensive 3D finite element analysis (FEA). Herein, a modified version of a recently proposed nonlinear transient path energy method (NT-PEM) is proposed as an analytical alternative to FEA. Within the modification to NT-PEM, a new topology for nonlinear dynamic magnetic equivalent circuit (ND-MEC) is proposed with a methodology for accurate evaluation of stray and leakage flux path parameters. For coil leakage reluctances, a novel path function based on a conchoid’s arc is proposed. For stray reluctances, a path function based on the average length of an elliptical arc is proposed. This path function, along with the proposed permeability correction for nonlinear core reluctance calculation routines, led to a four-fold reduction in NT-PEM analysis time from the original version of the proposed method. The feasibility of the proposed NT-PEM is verified via comparison with commercial 3D FEA and experimental data obtained from a PM MC with a single coil and single PM. NT-PEM and FEA equally displayed accurate results, indicating that NT-PEM is a promising computationally efficient alternative to FEA owing to significantly reduced analysis time, which is essential when considering numerous designs and design parameters.

Modeling and Control of Double-Sided LCC Compensation Topology with Semi-Bridgeless Active Rectifier for Inductive Power Transfer System

This paper proposes the modeling and design of a controller for an inductive power transfer (IPT) system with a semi-bridgeless active rectifier (S-BAR). This system consists of a double-sided Inductor-Capacitor-Capacitor (LCC) compensation network and an S-BAR, and maintains a constant output voltage under load variation through the operation of the rectifier switches. Accurate modeling is essential to design a controller with good performance. However, most of the researches on S-BAR have focused on the control scheme for the rectifier switches and steady-state analysis. Therefore, modeling based on the extended describing function is proposed for an accurate dynamic analysis of an IPT system with an S-BAR. Detailed mathematical analyses of the large-signal model, steady-state operating solution, and small-signal model are provided. Nonlinear large-signal equivalent circuit and linearized small-signal equivalent circuit are presented for intuitive understanding. In addition, worst case condition is selected under various load conditions and a controller design process is provided. To demonstrate the effectiveness of the proposed modeling, experimental results using a 100 W prototype are presented.

Comprehensive Modeling of Grounding Electrodes Buried in Ionized Soil Based on MoM-HBM Approach

This paper presents a new approach for modelling grounding electrodes buried in two layers soils considering frequency-dependent modeling of soil parameters together with the time-dependent nonlinear behavior arising from soil ionization caused by a lightning current discharge through the grounding system. To this aim, in the absence of soil ionization, a Norton's equivalent circuit is extracted in the frequency domain by means of the method of moment. Then, by adding the nonlinear load representing soil ionization to the Norton's equivalent circuit, the grounding system is changed into a nonlinear Norton's equivalent circuit and treated by using the harmonic balance method. The proposed model is validated by comparing the associated results with published measurement and the numerical data obtained with low- and high-magnitude impulse currents. The results prove that the proposed method is reliable and effective. Finally, an application of the proposed method in predicting the lightning overvoltages across the insulator string is presented and the performance of grounding system for different parameters is discussed.

Modeling and Characterization of a Kinetic Energy Harvesting Device Based on Galfenol.

The proposal of Energy Harvesting (EH) techniques and devices has experienced a significant growth over the last years, because of the spread of low power electronic devices. Small ambient energy quantities can be recovered through EH and exploited to power Wireless Sensor Networks (WSN) used, for example, for the Structural Health Monitoring (SHM) of bridges or viaducts. For this purpose, research on EH devices based on magnetostrictive materials has significantly grown in the last years. However, these devices comprise different parts, such as a mechanical system, magnetic circuit and electrical connections, which are coupled together. Then, a method able to reproduce the performance may be a handy tool. This paper presents a nonlinear equivalent circuit of a harvester, based on multiple rods of Galfenol, which can be solved with standard circuit simulator. The circuital parameters are identified with measurements both on one rod and on the whole device. The validation of the circuit and the analysis of the power conversion performance of the device have been conducted with different working conditions (force profile, typology of permanent magnets, resistive electrical load).

Performance analysis of stand-alone six-phase induction generator using heuristic algorithms

The paper exhibits the performance analysis of six-phase self-excited induction generator for stand-alone wind energy generation system. The analysis is based essentially on solving the nonlinear equivalent circuit of the SP-SEIG, which is to find the per-unit frequency F and the magnetizing reactance Xm minimizing the determinant of the nodal admittance matrix Y instead of solving two non-linear equations with two unknowns. Hence, the equation-solving problem is converted to an optimization problem. The obtained minimum yields the adequate magnetizing reactance and frequency which will be used subsequently to compute the self-excitation process requirements in terms of the prime mover speed, the excitation capacitance and the load impedance on the one hand and to predict the generator steady state performance parameters on the other. In this work, the analysis is performed using three different global search algorithms, the genetic algorithm (GA), the particle swarm optimization (PSO) technique and the Taguchi optimization method (TM). A study of some simulation results is carried out using MatLab to compare between these three algorithms in terms of accuracy and guaranteed convergence in finding the minimum of the admittance.

Study of the surface effect in steel at the industrial frequency by means of magnetoelectric equivalent circuits

Purpose. To work out the methodology and computer program for calculation of processes of the commercial frequency electromagnetic field penetration into steel body taking into account non-linearity of magnetizing steel characteristics.Research methods. The method of magnetoelectric equivalent circuits is used to calculate electromagnetic fields in a ferromagnetic medium. A feature of the method is the use of so-called "magnetic current" - the derivative of the magnetic flux. This made it possible to introduce “magnetic capacitors” into the circuit, which significantly simplified the equations of state, which are compiled on the basis of Kirchhoff's laws for electric and magnetic circuits, the law of electromagnetic induction, and the law of total current. Methods of numerical integration of differential equations are taken in the form of additional equations, which are attached to the state equations. The result is a system of linear algebraic equations, which at each step of integration has a unique solution. The magnetization curve of steel is approximated by splines, which allows to refine variable coefficients of the system of equations at each integration step..The results. The developed methodology and algorithm allowed developing the computer program for calculating the dynamics of penetration of an electromagnetic field into a steel body. Calculations for this program allowed us to calculate the depth of penetration of the electromagnetic field into the steel body. The proposed method allows a coil with a ferromagnetic core to be considered as a linear element in the intervals of the applied voltage determined in this method, to calculate the equivalent magnetic permeability of the core, as well as the inductance of the coil.Originality. For the first time, the method of using nonlinear magnetoelectric equivalent circuits was used to analyze the transient processes of penetration of an electromagnetic field into a steel body, which made it possible to reduce the calculation time by more than two.Practical value. Based on the research, the limits of magnetic field strength values are determined, in which linear methods of analysis can be applied. This allows the use of linear analysis methods for modeling electromagnetic fields in the structural elements of transformers using the finite element.

Improved Characterization and Accurate Modelling of Drain Current Derivatives of InP Based High Electron Mobility Transistors Devices.

InP based HEMTs are of great importance, due to their enormous potential in a high-speed modern microwave circuit, power amplifier, and low noise amplifier applications. Therefore, an accurate non-linear equivalent circuit model of HEMTs is very important for an accurate circuit design. This paper presents improved characterization and accurate modelling of drain current derivatives of InP based HEMTs devices. The proposed model is simple, easy to extract, and suitable for implementation in simulation tools. The Ψ function is extended to increase the flexibility of the proposed model. A gate-drain dependent current source is added to increase the S-parameter fitting. A one-dimensional intrinsic multi-bias capacitances model is introduced to avoid convergence failure. The fitting results of the I-V characteristics and its high order derivatives show high accuracy. In addition, S-parameters and Pout for the proposed model are compared with the original Angelov model. The proposed model shows better accuracy.

Nonlinear magnetic equivalent circuit of the hybrid magnetic bearing

PurposeThe purpose of this paper is to create a reliable nonlinear magnetic equivalent circuit (NMEC) of the hybrid magnetic bearing (HMB). Commonly used magnetic equivalent circuits of HMB omit a saturation effect of the magnetic material as well as the leakage and fringing flux. It results in imprecise modelling of the magnetic field distribution. On the other hand, only 3D finite element analysis (FEA) can be used to precisely simulate the magnetic field in this type of the magnetic bearing. The proposed NMEC incorporates the saturation effect of the magnetic material, as well as the leakage and fringing flux.Design/methodology/approachThe magnetic equivalent circuit of presented HMB is proposed to obtain a reliable model that ensures short calculation time. Developed NMEC incorporates the phenomena as the saturation effect, as well as the leakage and fringing flux. The reluctance of the air gap that includes the fringing flux was calculated using 3D FEA. Kirchhoffs’ laws were used to create a set of nonlinear equations that were iteratively solved by Broyden’s method.FindingsIncorporating into NMEC of the HMB a saturation effect of the magnetic material, as well as the leakage and fringing flux, resulted in the accurate model that was in good agreement with 3 D finite element model and the real object. The developed NMEC offers the calculation time in the range of miliseconds, therefore can be successfully used in the engineering design instead of the FEM.Originality/valuePresented NMEC can be considered as a fundamental model that can be successfully used for accurate and fast simulation of the HMB. Proposed NMEC includes considerable factors that decide about the model accuracy such as the saturation effect of the ferromagnetic material and the leakage and fringing flux. The developed NMEC can be used in the optimization procedures and for simulations of dynamic responses.

Phase-to-phase fault detection method for synchronous reluctance machine using MEC method

This paper presents a novel technique for synchronous reluctance machines model (SynRMs). The model can be used in both healthy and faulty situations with phase-to-phase fault. The machine properties such as the number of poles and slots, as well as rotor and stator dimension, can be selected arbitrarily in the proposed model. Therefore, various SynRMs with selective properties can be modeled by the proposed method. Considering the nonlinear magnetic equivalent circuit, the healthy and faulty saturable machine with phase-to-phase fault between various windings is also studied. Validation is performed by finite-element method (FEM). Regarding the performed validation, very shorter processing time is obtained compared to FEM.

A Nonlinear Lumped Equivalent Circuit Model for a Single Uncollapsed Square CMUT Cell.

An accurate nonlinear lumped equivalent circuit model is used for modeling of capacitive micromachined ultrasonic transducers (CMUTs). Finite-element analysis (FEA) is a powerful tool for the analysis of CMUT arrays with a small number of cells while with the harmonic balance (HB) analysis of the lumped equivalent circuit model, the entire behavior of a large-scale arbitrary CMUT array can be modeled in a very short time. Recently, an accurate nonlinear equivalent circuit model for uncollapsed single circular CMUT cells has been developed. However, the need for an accurate large-signal circuit model for CMUT cells with square membranes motivated us to produce a new nonlinear large-signal equivalent circuit model for uncollapsed CMUT cells. In this paper, using analytical calculations and FEA as the tuning tool, a precise large signal equivalent circuit model of square CMUT dynamics was developed and showed excellent agreement with finite-element modeling (FEM) results. Then, different CMUT single cells with square and circular membranes were fabricated using a standard sacrificial release process. Model predictions of resonance frequencies and displacements closely matched experimental vibrometer measurements. The framework presented here may prove valuable for future design and modeling of CMUT arrays with square membranes for ultrasound imaging and therapy applications.

Nonlinearity in superconducting metamaterial structures, including spirally coupled lines

Superconducting devices can indicate nonlinear behaviors such as harmonic generation and intermodulation distortion (IMD) with regard to nonlinear Meissner effect even at low input powers. Firstly in this paper, a new method for nonlinear modelling of Superconducting Transmission Lines (SMTLs) with complex coupling is proposed. Then, based on the proposed new method, nonlinear equivalent circuit model for Superconducting Spirally Coupled Lines (SSCLs) is suggested. A numerical approach based on three-dimensional finite element method (3D-FEM) is used to compute the current distribution in SSCLs. Closed-form expressions for quadratic and modulus geometrical nonlinear factors (GNFs) of SSCLs are proposed. The proposed model can be analyzed nonlinearly by using of Harmonic Balance (HB) method to predict nonlinear behaviors. To validate the accuracy of the proposed nonlinear model, we modeled a superconducting metamaterial filter consisting of two SSCLs in this paper. Good agreement between calculated results and measured ones was found. Thereafter, based on the proposed model, effects of nonlinearity on main parameters of the superconducting metamaterial structure such as phase constant (β) and attenuation factor (α) are analyzed.

Design, Modeling and Prototyping a Flat Switched Reluctance Machine for Direct-Drive Systems

In this paper, a flat-type 24 by 16 SRM, is considered for the application of direct-drive washing machine. Firstly, the structure is introduced and using the nonlinear equivalent circuit, the researchers present a design for the SRM. Then, using the three-dimensional finite element method, the electromagnetic characteristics of the proposed configuration are analyzed to evaluate the motor’s performance. The motor prototype is fabricated and tested experimentally to authenticate the theoretical and simulation analysis, and subsequently to prove the applicability. Finally, the performance of this proposed motor is compared with an SRM that has the same condition. Since a direct drive motor does not require a reduction gear, the drive system can be made simple without harmonic gears, and therefore it can be used in high-precision, more reliable, and low cost appliances.