Systematic realization of a class of hysteresis chaotic oscillators

A systematic method for realizing a class of hysteresis RC chaotic oscillators is described. The method is based on direct coupling of a general second‐order sinusoidal oscillator structure to a passive non‐monotone current‐controlled non‐linear resistor. Owing to this passive non‐linearity, the power consumption, supply voltage and bandwidth limitations imposed upon the chaotic oscillator are mainly those due to the active sinusoidal oscillator alone. Tunability of the chaotic oscillator can be achieved via a single control parameter and the evolution of the two‐dimensional sinusoidal oscillator dynamics into a three‐dimensional state‐space is clearly recognized. The flexibility of this method is demonstrated by two examples using PSpice simulations and experimental results. Numerical simulations of derived mathematical models are also shown. Copyright © 2000 John Wiley & Sons, Ltd.     

Optimum design of high power and high efficiency mm‐wave fundamental oscillators

A systematic method to design high power and high efficiency mm‐wave fundamental oscillators is presented. By using a linear time variant method, we first obtain the optimum conditions and show that these conditions can be significantly different for high power and high efficiency fundamental oscillation. Next, we propose a modified multistage ring oscillator with interstage passive networks to exploit the full capacity of the transistors in terms of output power or efficiency. Analytical expressions are also derived to determine the value of passive elements used in the oscillator. To verify the validity of the method, a 77‐GHz two‐stage (differential) VCO is designed in a 65‐nm CMOS process. Careful electromagnetic and circuit simulations demonstrate that the designed VCO has 2‐GHz tuning range, maximum output power of 10.5 dBm and maximum DC to RF efficiency of 24.1%. The designed VCO shows 54.8% and 108.7% improvement in terms of maximum output power and efficiency compared with a conventional cross‐coupled VCO with the same tuning range.     

Nonlinear behavioural model of charge pump PLLs

Despite the nonlinear nature of even the simplest versions of phase locked loops (PLLs), linear models are still used during the first phases of the design of modern PLLs. Even though the linear model may represent a crude approach, its use is justified by the fact that accurate numerical simulations often require a too large amount of CPU time, being PLLs by construction stiff circuits, characterised by very different time scales. This aspect has triggered the need for compact models that allow fast and accurate numerical simulations. The scientific literature numbers several models that have been developed with different approaches and tailored to different simulation environments. In this context, we propose a nonlinear model of a type‐II PLL, which (1) considers both the switching behaviour of the phase/frequency detector and charge pump and the complex dynamics (including the presence of amplitude and phase noise) of the voltage controlled oscillator, (2) is compact and can be easily implemented in modern mixed analog/digital simulators as a behavioural block, and (3) allows the simulation of spurs owing to the nonlinearities of both the charge pump and the fractional frequency divider. Copyright © 2012 John Wiley & Sons, Ltd.     

Discontinuity correction in piecewise‐linear models of oscillators for phase noise characterization

Decomposition of noise perturbation along Floquet eigenvectors has been extensively used in order to achieve a complete analysis of phase noise in oscillator. Piecewise‐linear approximation of nonlinear devices is usually adopted in numerical calculation based on multi‐step integration method for the determination of unperturbed oscillator solution. In this case, exact determination of the monodromy matrix can be hampered by the presence of discontinuities between models introduced by the approximation. In this paper we demonstrate that, without the proper corrections, relevant errors occur in the determination of eigenvalues and eigenvectors, if adjacent linear models presents discontinuities. We obtain this result by the analysis of a simple 2‐D oscillator with piecewise‐linear parameter. We also demonstrate that a correct calculation can be achieved introducing properly calculated state vector boundary conditions by the use of interface matrices. This correction takes into account the effects of discontinuities between the linear models, leading to exact calculation of eigenvalues and eigenvectors, and, consequently, of the phase noise spectrum. Copyright © 2006 John Wiley & Sons, Ltd.     

Kalmen estimator as a robust solution for output power maximization of wave energy converter

In this paper, the application of linear quadratic Gaussian (LQG) control for a buoy‐type point absorber of a wave energy converter (PA‐WEC) system is investigated. The proposed wave energy conversion is considered as a two‐body system, which is taut‐anchored to the sea floor using three cables. The main goal of this study is to extract the maximum available power from the ocean wave. This is accomplished via determining the optimal value of the force exerted on the power take‐off (PTO) system taking in account the physical constraints on the position and velocity. First, the reduced nonlinear dynamical model of the WEC system is obtained. The nonlinearity in the mooring force is replaced by a linear law to yield the state space linear model of the system. Then, the standard Kalman filter technique is employed to estimate the full states of the system. Based on the LQG control approach, the optimal PTO force is computed at which the maximum output power can be easily harvested. The computational burden is minimized to a great extent by computing the optimal state feedback gains and the Kalman state space model offline. The feasibility of the proposed control approach in extracting the optimal power of the ocean wave is validated via the simulation example even under different values of the mooring constant and without violating the system limitation. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Analysis of power-frequency trade-offs in millimeter-wave CMOS oscillators

In this paper, considering the nonlinear effects in two ports consisting of transistor, a general method is proposed for estimating the amplitude of high-frequency ring oscillators. The proposed method can be generalized to various structures that can be disassembled into similar two ports. Moreover, in each CMOS process, a design procedure can be followed to obtain the desired output power and frequency. This is the first time that the frequency and amplitude of oscillator are related to each other in a system of nonlinear equations. First, considering the maximum achievable oscillation frequency, the analysis of ring oscillator structure is performed for the given output power. The results show that the proposed structure operates at 7 to 18% higher oscillation frequency compared with conventional structures. In the next step, assuming that the oscillator structure and passive network topology are known, another system of nonlinear equations is defined for designing the oscillator for the given frequency and amplitude of oscillation. Finally, the implicit solution, which includes the passive network elements connecting to the transistor, is obtained. The results of equations follow the simulation results with an acceptable error (1% frequency error and about 5% amplitude error).     

A practical guide to multidimensional wave digital algorithms using an example of fluid dynamics

The wave digital concept for numerical integration of partial differential equations leads to algorithms with highly advantageous features as robustness, full localness and massive parallelism. However, the required synthesis of an internally multidimensionally passive reference circuit, from which the algorithm is derived, usually demands an in‐depth knowledge of circuit theory and a high level of intuition. In this practical guide, a step‐by‐step approach for the synthesis of such reference circuits is introduced to relax these requirements, using the nonlinear fluid dynamic equations as a nontrivial example. General implementation issues for the wave digital algorithm are discussed as well as applying arbitrary passive linear multistep methods in place of the commonly used trapezoidal rule. As an example, we take the well‐known numerically critical shock tube problem, the solution of which is problematic when the trapezoidal rule is used as unwanted oscillations occur. These oscillations are suppressed when using the second‐order accurate Gear method instead. Copyright © 2010 John Wiley & Sons, Ltd.     

A kernel approach to implementation of local linear discriminant analysis for face recognition

The multiple linear model is used successfully to extend the linear model to nonlinear problems. However, the conventional multilinear models fail to learn the global structure of a training data set because the local linear models are independent of each other. Furthermore, the local linear transformations are learned in the original space. Therefore, the performance of multilinear methods is strongly dependent on the results of partition. This paper presents a kernel approach for the implementation of the local linear discriminant analysis for face recognition problems. In the original space, we utilize a set of local linear transformations with interpolation to approximate an optimal global nonlinear transformation. Based on the local linear models in the original space, we derive an explicit kernel mapping to map the training data into a high‐dimensional transformed space. The optimal transformation is learned globally in the transformed space. Experimental results show that the proposed method is more robust to the partition results than the conventional multilinear methods. Compared with the general nonlinear kernels that utilize a black‐box mapping, our proposed method can reduce the negative effects caused by the potential overfitting problem. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Real-time digital simulation of power electronics systems with Neutral Point Piloted multilevel inverter using FPGA

Most of actual real time simulation platforms have practically about ten microseconds as minimum calculation time step, mainly due to computation limits such as processing speed, architecture adequacy and modeling complexities. Therefore, simulation of fast switching converters’ instantaneous models requires smaller computing time step. The approach presented in this paper proposes an answer to such limited modeling accuracies and computational bandwidth of the currently available digital simulators.As an example, the authors present a low cost, flexible and high performance FPGA-based real-time digital simulator for a complete complex power system with Neutral Point Piloted (NPP) three-level inverter. The proposed real-time simulator can model accurately and efficiently the complete power system, reducing costs, physical space and avoiding any damage to the actual equipment in the case of any dysfunction of the digital controller prototype. The converter model is computed at a small fixed time step as low as 100 ns. Such a computation time step allows high precision account of the gating signals and thus avoids averaging methods and event compensations. Moreover, a novel high performance model of the NPP three-level inverter has also been proposed for FPGA implementation. The proposed FPGA-based simulator models the environment of the NPP converter: the dc link, the RLE load and the digital controller and gating signals. FPGA-based real time simulation results are presented and compared with offline results obtained using PLECS software. They validate the efficiency and accuracy of the modeling for the proposed high performance FPGA-based real-time simulation approach. This paper also introduces new potential FPGA-based applications such as low cost real time simulator for power systems by developing a library of flexible and portable models for power converters, electrical machines and drives.     

A matrix pencil approach to the local stability analysis of non‐linear circuits

This paper addresses local stability issues in non‐linear circuits via matrix pencil theory. The limitations of the state–space approach in circuit modelling have led to semistate formulations, currently framed within the context of differential‐algebraic equations (DAEs). Stability results for these DAE models can be stated in terms of matrix pencils, avoiding the need for state–space reductions which are not advisable in actual circuit simulation problems. The stability results here presented are applied to electrical circuits containing non‐linear devices such as Josephson junctions or MOS transistors. Copyright © 2004 John Wiley & Sons, Ltd.     

Estimation algorithm for system with non‐Gaussian multiplicative/additive noises based on variational Bayesian inference

This paper considers estimation algorithms for linear and nonlinear systems contaminated by non‐Gaussian multiplicative and additive noises. Based on the variational idea, in order to derive optimal estimation algorithms, we combine the multiplicative noise with states as the joint parameters to estimate. The application of variational Bayesian inference to joint estimation of the state and the multiplicative noise is established. By treating the states as unknown quantities as well as the multiplicative noise, there are now correlations between the states and multiplicative noise in the posterior distribution. There are two main goals in Bayesian learning. The first is approximating the marginal likelihood (PDF of multiplicative noise) to perform model comparison. The second is approximating the posterior distribution over the states (also called a system model), which can then be used for prediction. The two goals constitute the iterative algorithm. The rules for determining the loop is the Kullback‐Leibler divergence between the true distribution of state and a chosen fixed tractable distribution, which is used to approximate the true one. The iterative algorithm is deduced, which is initialized based on the idea of sampling. Meanwhile, the convergence analysis of the proposed iterative algorithm is presented. The numerical simulation results in a comparison between the proposed method and these existing classic algorithms in the context of nonlinear hidden Markov models, state‐space models, and target‐tracking models with non‐Gaussian multiplicative noise demonstrate the superiorities, not only in speed, precision, and computation load but also in the ability to process non‐Gaussian complex noise.     

Fully nonlinear oscillator noise analysis: an oscillator with no asymptotic phase

Oscillators exist in many systems. Detailed and correct characterization and comprehension of noise in autonomous systems such as oscillators is of utmost importance. Previous approaches to oscillator noise analysis are based on some kind of perturbation analysis, some linear and some nonlinear. However, the derivations of the equations for perturbation analysis are all based on information that is produced by a linearization of the oscillator equations around the periodic steady‐state solution, where it is assumed that the oscillator is orbitally stable and it has the so‐called asymptotic phase property. In this paper, we first discuss these notions from a qualitative perspective, and demonstrate that the asymptotic phase property is crucial in validating all of the previous approaches. We then present the case of a simple oscillator that is orbitally stable but without asymptotic phase, for which previous approaches fail. We then present a fully nonlinear noise analysis of this oscillator. We derive and compute nonlinear, non‐stationary and non‐Gaussian stochastic characterizations for both amplitude and phase noise. We arrive at results that are distinctly different when compared with the ones obtained previously for oscillators with asymptotic phase. We compare and verify our analytical results against extensive Monte Carlo simulations. Copyright © 2006 John Wiley & Sons, Ltd.     

Analysis and design of an isolated single-phase power factor corrector with a fast regulation

This paper presents an analysis and a modeling approach to obtain a small-signal model design and the digital implementation of a linear control technique for single-phase boost power factor correctors (PFC). Such converters present nonlinear characteristics and approximations of them are used to drive the models. The proposed circuit significantly improves the dynamic response of the converter to load steps without the need of a high crossover frequency of the voltage loop by adding low-pass filter. So, a low distortion of the input current is easily achieved. This controller has been verified via simulation in Simulink using a continuous time plant model and a discrete time controller. Real-time implementation is performed on an experimental test bench utilizing a rapid prototyping tool. The controller is experimentally confirmed for steady-state performance and transient response.     

电流互感器的数字实时仿真

电流互感器电磁暂态过程仿真,在电力系统动态仿真系统中是必不可少的,为此提出了一个电流互感器的非线性实时仿真模型。模型中考虑了磁饱和和磁滞的影响,同时给出了相应的数字积分方法。对该电流互感器正常工作电流状态、一次侧大电流故障状态及一次侧开路故障状态的电磁暂态过程进行了仿真。仿真结果表明,提出的实时仿真模型和选用的数字积分方法是正确、有效的。     

Teaching nonlinear modeling, simulation, and control of electronic power converters using MATLAB/SIMULINK

This paper describes an efficient method to teach analysis and simulation of power electronic converters to undergraduate students, using system level nonlinear state-space models. System-level modeling of power electronic converters reproduces only the ideal switching behavior of the semiconductors and is a useful concept for the numerical simulation of power converters, since simulations present no convergence problems and require little computational time. Switched state-space models, programmed in the MATLAB/SIMULINK software package, can be advantageously used to simulate power converters at the system level and also to design and study their controllers. Switched state-space nonlinear models should be obtained using a theoretical framework suitable for the enhanced control of variable structure power systems. Since the method is inherently nonlinear, no approximated linear models are needed; and since state-space models are used, modern control techniques (sliding mode, neural networks, fuzzy logic) for power converters can easily be used. This paper summarizes the proposed methodology and gives some examples.     

Piecewise linear second moment statistical simulation of ICs affected by non‐linear statistical effects

This paper presents a methodology for statistical simulation of non‐linear integrated circuits affected by device mismatch. This simulation technique is aimed at helping designers maximize yield, since it can be orders of magnitude faster than other readily available methods, e.g. Monte Carlo. Statistical analysis is performed by modeling the electrical effects of tolerances by means of stochastic current or voltage sources, which depend on both device geometry and position across the die. They alter the behavior of both linear and non‐linear components according to stochastic device models, which reflect the statistical properties of circuit devices up to the second order (i.e. covariance functions). DC, AC, and transient analyses are performed by means of the stochastic modified nodal analysis, using a piecewise linear stochastic technique with respect to the stochastic sources, around a few automatically selected points. Several experimental results on significant circuits, encompassing both the analog and the digital domains, prove the effectiveness of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

Novel chaotic behavior in the Muthuswamy–Chua system using Chebyshev Polynomials

In this paper, three kinds of memristors with memristance functions obtained from the Chebyshev polynomials are used in the Muthuswamy–Chua system, which has only three circuit elements: a linear passive inductor, a linear passive capacitor and a nonlinear active memristor. We use multivariable second‐order polynomial functions of current and memristor state for the internal state function of the memristor. This enables our system to generate not only double‐scroll but also four‐scroll attractors. Systematic studies of chaotic behavior in these systems are performed using phase portraits, bifurcation diagrams and Lyapunov exponents. Simulation results show that all these systems exhibit chaotic behavior over a range of control parameters. Copyright © 2014 John Wiley & Sons, Ltd.     

Immitance data modelling via linear interpolation techniques: A classical circuit theory approach

With the advancement of the manufacturing technologies to produce new generation analog/digital communication systems, immitance data modelling has gained renewed importance in the literature. Specifically, models are utilized for behaviour characterization, simulation of physical devices or to design sub‐systems with active and passive solid‐state devices. Therefore, in this paper, new computer aided tools are presented to model one port immitance data by means of linear interpolation techniques. The basic philosophy of the new modelling tools is based on the numerical decomposition of the immitance data into its minimum and Foster parts. Computer algorithms are presented to model the minimum and the Foster parts of the given immitance data. Implementations of these algorithms are exhibited by means of examples. Depending on the application, modelling tools based on linear interpolation techniques may present ‘computational and practical’ advantages over the existing interpolation techniques, non‐linear curve fittings or regression methods. It is expected that the new modelling tools will be utilized to provide initial circuit topologies to the commercially available analysis/simulation and design packages. Copyright © 2004 John Wiley & Sons, Ltd.