Small-signal harmonic analysis of non-linear circuits

An approximate harmonic analysis method for non-linear circuits is introduced. the method solves the steady state, time domain representation as well as the frequency response of non-linear circuits. It allows simulation of non-ideal switched capacitor circuits composed of any kinds of linear components and non-linear transistors as switches. All switches must have the same period, but they can be opened and closed at any time. the method proposed may also be applied to mixer analysis for the case of strong LO and weak RF signals. Examples are given to demonstrate that the method is efficient and sufficiently fast to be used in circuit design. the simulation results show good agreement with those obtained by harmonic balance and transient analysis.     

Theory of weakly non-linear noisy systems

This paper gives a treatment of the theory of noise in general non-linear multiport systems by use of the Volterra series representation. Expressions for the response of a non-linear noisy (N + l)-port system with N signal input ports and one output port under excitation of noise and a deterministic signal at each input port are determined. Noise generated in the system itself is accounted for by equivalent random variable noise voltage or current generators. These internal noise generators are extracted from the system and applied at separate external ports. A noise-free equivalent of the noisy system is obtained with N signal input ports and Q – I input ports accounting for the systemgenerated noise. the Volterra series representation is used to describe the input-output response relation of the system. Once the Volterra transfer functions of the system are determined and cross-and autocorrelations of the noise generators are specified, it is possible to determine the noise performance of the system under arbitrary noise and deterministic signal excitation. the investigation leads to the determination of expressions for the equivalent average exchangeable output noise power density and the average output noise power flow from the system. Expressions for the noise power densitypand the noise power flow at the load of the non-linear system are determined. As an example of the theory an expression is derived for the effective input noise temperature of a non-linear system.     

Steady-state response of non-linear circuits: A frequency-domain relaxation method

We propose here an efficient algorithm for finding the steady-state response of stiff non-linear circuits. It is based on a frequency-domain relaxation method and can be applied efficiently to obtain the steady-state waveforms of both periodic systems and multi-frequency-component systems. the solution at each iteration is obtained by solving an associated linear time-invariant circuit at every frequency component via modified nodal analysis. Our algorithm is very simple and can be applied efficiently to solve a large class of practical non-linear communication circuits which are notoriously stiff and hence rather time-consuming to solve with existing methods.     

Non-linear optimization with constraints: A cook-book approach

Based on the stationary co-content theorem in non-linear circuit theory and the penalty function approach in non-linear programming theory, a canonical circuit for simulating general non-linear programming problems with equality and/or inequality constraints has been developed. the task of solving a non-linear optimization problem with constraints reduces to that of finding the solution of the associated canonical circuit using a circuit simulation program, such as SPICE. A catalogue of canonical circuits is given for each class of non-linear programming problem. Using this catalogue, an engineer can solve non-linear optimization problems by a cook-book approach without learning any theory on non-linear programming. Several examples are given which demonstrate how SPICE can be used, without modification, for solving linear programming problems, quadratic programming problems, and polynomial programming problems.     

Spatio-temporal co-operative phenomena in CNN arrays composed of chaotic circuits—simulation experiments

This paper presents results of a simulation study of complex dynamic phenomena in arrays composed of interacting chaotic circuits. Such arrays can be thought of as a new paradigm for modelling non-linear phenomena in spatially extended (high-dimensional or infinite-dimensional) systems and active media with potential applications in signal processing. Depending on the connection structure between the cells, the array can show disorganized hyperchaotic behaviour or spatially ordered chaotic waves. Patterns of behaviour depending on the excitation of the array and the connection structure are studied in this paper. Chua circuits are taken as standard chaotic cells.     

Method of analysis of non-linear systems on the basis of generalization of the volterra functional series relative to complex envelopes

The paper considers the mathematical modelling of weakly non-linear narrow-band circuits and systems on the basis of application of the Volterra functional series. the investigation uses multidimensional pulse and transfer functions as well as the Volterra functional series relative to the narrow-band signal envelopes. Examples are given of the construction of Volterra kernels of narrow-band non-linear circuits and systems.     

Photovoltaic generator modelling to improve numerical robustness of EMT simulation

Numerical simulation is an indispensable tool for studying photovoltaic (PV) systems, to derive component ratings, optimise protections, design controllers as well as to evaluate the impact of embedded generation on distribution system operation. In EMT simulation, the non-linear equations representing the PV generators are separated from the linear equations of the rest of the power system. This technique presents high computational efficiency but introduces a one-step delay, which can cause problems of numerical instability. These problems are particularly evident when the PV generator is represented by multiple single-diode equivalent circuits, such as in the cases of PV generators composed of different types of arrays or subject to partial shading or interfaced by multilevel inverters. To overcome such problems, in this paper a new approach is proposed to include the PV generator model into EMT simulation. A convergence analysis gives proof of the obtained improvements, which are also confirmed by numerical results. The robustness of the proposed technique is tested by simulation of an IEEE benchmark system in the cases of partial shading and of electric faults.     

COMPUTER SIMULATION OF RANDOM SIGNALS AND ROUGH SURFACES WITH GIVEN STATISTICAL CHARACTERISTICS

Recurrence relations are developed to determine the weighting coefficients used in the simulation of random signals and rough surfaces with given statistical characteristics. These results can provide (in real time) straightforward, accurate solutions to the system of non-linear, algebraic equations associated with the method of moving summations. Three possible numerical methods have been reported to obtain approximate solutions to the system of non-linear, algebraic equations. However, none of them is straightforward, and they all require a large amount of computing time. This work can be applied to the numerical solution of the generalized telegraphist's equations used to analyze vertically and horizontally polarized radio wave scattering problems from permeable media with random rough interfaces. © 1997 by John Wiley & Sons, Ltd.     

Development of highly reliable control systems for thegas-insulated switchgear

Microprocessor-based control, protection and monitoring devices, such as digital relays and diagnostic systems, have been applied to electric power fields. The highly reliable control systems (HRCS) based on microprocessor techniques for gas-insulated switchgear (GIS) have been developed. From the results of the CIGRE circuit breaker reliability survey, the need for improving the reliability of switchgear control circuits is presented. The HRCS for the GIS uses the programmable logic controller (PLC), solid-state electronics and optical sensors as a replacement for conventional hard-wired electromechanical control circuits which improves reliability and availability of the GIS control circuits. The HRCS has been verified and applied to the substation. This paper introduces the results of verification tests together with the principle of the HRCS. Also reported is application to the high voltage substation     

Analysis of non-linear transmission lines by frequency domain perturbation method

We discuss a numerical method for solving non-linear transmission lines in the frequency domain. Such transmission lines are widely used for communications such as in GaAs integrated circuits and varactor diode circuits. The circuit equations are described by non-linear partial differential equations, so their analysis is very complicated compared with that of linear transmission lines. In this paper we propose a frequency-domain perturbation method for weakly non-linear transmission lines where the wave-forms are approximated by Fourier expansions and each frequency component is calculated by a modified perturbation method. To improve convergence, we introduce two new techniques, the compensation method and the homotopy method, which help to make the iteration stable and can be applied to a wide class of non-linear transmission lines. We have analysed shock wave phenomena in example. © 1997 by John Wiley & Sons, Ltd.     

基于粒子滤波与EEMD的低频振荡模式识别方法研究

为克服传统方法对非线性非高斯系统信号中噪声处理的缺点,提出一种基于粒子滤波算法与改进的EMD分解—EEMD分解法相结合的新方法。所提方法首先利用粒子滤波将非线性非高斯系统的初始信号的噪声去除,减少了噪声对后续操作的影响,再采用EEMD分解对去噪后的信号进行分解得到此征模态分量IMF,进而对此征模态分量IMF计算出瞬时频率,从而得出低频振荡的模式。通过算例仿真分析表明文中方法的可行性及有效性,并通过与Prony分析算法得到的结果进行了对比,验证了文中方法的正确性。为电力系统低频振荡处理非线性非高斯系统信号提供了一种新的途径和方法。     

CNN-based difference-controlled adaptive non-linear image filters

In this paper, we develop a common cellular neural network framework for various adaptive non-linear filters based on robust statistic and geometry-driven diffusion paradigms. The base models of both approaches are defined as difference-controlled non-linear CNN templates, while the self-adjusting property is ensured by simple analogic (analog and logic) CNN algorithms. Two adaptive strategies are shown for the order statistic class. When applied to the images distorted by impulse noise both give more visually pleasing results with lower-frequency weighted mean square error than the median base model. Generalizing a variational approach we derive the constrained anisotropic diffusion, where the output of the geometry-driven diffusion model is forced to stay close to a pre-defined morphological constraint. We propose a coarse-grid CNN approach that is capable of calculating an acceptable noise-level estimate (proportional to the variance of the Gaussian noise) and controlling the fine-grid anisotropic diffusion models. A combined geometrical–statistical approach has also been developed for filtering both the impulse and additive Gaussian noise while preserving the image structure. We briefly discuss how these methods can be embedded into a more complex algorithm performing edge detection and image segmentation. The design strategies are analysed primarily from VLSI implementation point of view; therefore all non-linear cell interactions of the CNN architecture are reduced to two fundamental non-linearities, to a sigmoid type and a radial basis function. The proposed non-linear characteristics can be approximated with simple piecewise-linear functions of the voltage difference of neighbouring cells. The simplification makes it possible to convert all space-invariant non-linear templates of this study to a standard instruction set of the CNN Universal Machine, where each instruction is coded by at most a dozen analog numbers. Examples and simulation results are given throughout the text using various intensity images. © 1998 John Wiley & Sons, Ltd.     

Swann-a programme for analysis of switched analogue non-linear networks

This paper describes SWANN, a programme for fast simulation of non-linear switched analogue networks. the switches act as open and short circuits and are used to model switching diodes, transistors or thyristors. Non-linearities of other elements such as capacitors, inductors, resistors, conductors and dependent sources, are modelled by polynomials. Possible inconsistent conditions which can appear in networks with ideal switches are correctly handled. At switching instants the values from left and right are obtained and are available for plotting. Examples show applications in communications and power electronics.     

Switched-capacitor neural networks for differential optimization

The primary goal of this paper is to solve some types of optimization problems whose objective functions and constraints are smooth and continuously differentiable and which are not suited for digital signal processing. the optimization problems are mapped into systems of first- and second-order non-linear ordinary differential equations and/or systems of difference equations. These systems of equations are simulated by appropriate switched-capacitor (SC) circuits employing some neural network (neurobiological) principles. New switched-capacitor architectures for on-line solving of non-linear optimization problems are proposed and their properties are investigated. Various circuit structures are investigated to find which are best suited for SC CMOS implementation. the structures developed exhibit a high degree of modularity, and a relatively small number of basic building blocks (computing cells) are required to implement effective and powerful optimization algorithms. Basic mathematical operations, e.g. multiplication, addition and non-linear scaling transformation, are accomplished employing advanced SC techniques. the validity and performance of the circuit structures developed are illustrated by intensive computer simulations employing TUTSIM and NAP programmes.     

Integral manifolds for non-linear circuits

Although the theory of integral manifolds is well known among applied mathematicians as a powerful tool in non-linear oscillations, it is relatively unknown, let alone applied, among circuit engineers. the purpose of this mostly tutorial paper is to illustrate the applications of integral manifolds to explain various non-linear phenomena widely observed in non-linear circuits. Numerous examples and graphical illustrations are included in order to present the theory with a minimum amount of mathematics.     

Blind identifiability of quadratic non-linear systems in higher-order statistics domain

Quadratic non-linear systems are widely used in various engineering fields such as signal processing, system filtering, predicting and identification. Some conditions to blindly estimate kernels of any discrete and finite extent quadratic system in the higher-order cumulants domain are introduced in this paper. The input signal is assumed as an unobservable i.i.d. random sequence which is viable for engineering practice. Due to properties of the output third-order cumulant functions, identifiability of the non-linear system holds even if the system's output measurement is corrupted by a Gaussian random disturbance. It provides a useful starting point for implementating the identification of a truncated Volterra non-linear system using conventional techniques or neural network methodologies. © 1998 John Wiley & Sons, Ltd.     

Envelope simulation by SPICE-compatible models of linear electriccircuits driven by modulated signals

SPICE-compatible equivalent circuits were developed to facilitate the analysis and envelope simulation of electric circuits driven by modulated signals. The circuits are based on a novel complex phasor-domain transformation. The proposed method facilitates simulation of any general linear circuit driven by a modulated signal such as amplitude modulation, frequency modulation, or phase modulation. Simulation time by the proposed envelope simulation is much faster than the full cycle-by-cycle simulation of the original circuit and excitation     

Synthesizing variant impedances in SPICE. A fast solution for powerelectronics and electric power systems simulations

The Simulation Program with Integrated Circuit Emphasis (SPICE) is a program widely used to simulate electric circuits. Characteristics such as versatility, large component libraries, integration of schematic edition, simulation and analyses have made it popular. As many students use this program early on, there is a natural tendency to continue using it in power electronics, electrical drives and electric power system courses. SPICE was initially developed to simulate integrated circuits. Therefore, sometimes the program parameters and components must be adapted to power circuits and systems. For example, the tolerances and component parameters have to be changed. Variant impedances frequently are present in electrical/electronic circuits. For example, an incandescent bulb is a power-variant resistance. A thermistor is a resistance that varies according to the temperature. An ideal thyristor controlled reactor (TCR), used to control voltage in electric power systems, is a variable inductance that changes its value depending on a control signal. A thyristor controlled series capacitor (TCSC) or a static reactive power compensator are ideally modeled as variable capacitances. Simulating such circuits requires defining the sub-circuits that, at their terminals, behave like the desired variant impedance