Formulating hybrid equations and state equations for nonlinear circuits using SPICE

Hybrid equations are often used in the theoretical study of nonlinear resistive circuits because they have an easy‐to‐analyze structure. They are also advantageous in the numerical analysis of nonlinear resistive circuits because they are separable and consist of a relatively small number of variables. However, the hybrid equations are seldom used in practical applications because their formulation is complicated. In this letter, we propose a simple method for formulating the hybrid equations using SPICE. In the proposed method, we only perform the transient analysis of SPICE on a linear circuit that is obtained through a small modification to the original circuit. It is also shown that state equations for nonlinear dynamic circuits can also be formulated by using the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

A unified set‐theoretic approach to the analysis of PWL resistive circuits and composite N‐ports

We consider the search for all DC solutions of resistive piecewise‐linear (PWL) circuits and the analysis of the characteristics of resistive PWL composite N‐ports. These problems are unified from a theoretical and operating point of view by introducing the so‐called N‐augmented circuit, obtained from the N‐port by closing its ports with N norators. Set‐theoretic approach is used to describe the properties of the N‐augmented circuits leading to the formulation of a general DC analysis algorithm, based on linear programming techniques. The examples at the end of the paper show some practical and efficient application of the general DC analysis algorithm. Copyright © 2010 John Wiley & Sons, Ltd.     

Analysis and optimization of a novel biasing for constant‐gain CMOS open‐loop amplifiers

A replica biasing circuit is presented which allows open‐loop gain in CMOS amplifiers to be accurately set. The proposed solution is a new biasing which takes advantage of a triode‐biased transistor instead of the ΔV_GS approach which is the traditional one. The circuit can be applied to both RF and IF amplifiers which are based on resistive loads in order to achieve high‐frequency and/or low‐noise performance. A detailed analysis of second‐order effects is then given which emphasizes the effects due to mobility degradation, channel‐length modulation and threshold voltage mismatches. Simulated results show a good sensitivity to process variations. Copyright © 2001 John Wiley & Sons, Ltd.     

A unified theory of symmetry for nonlinear multiport and multiterminal resistors

Simple group-theoretic concepts are used to develop a rigorous and comprehensive theory of symmetry for nonlinear multiport and multiterminal resistors which do not rely on geometrical arguments or other ad hoc techniques normally invoked in such studies. This theory unifies all forms of symmetry, including rotation, reflection and complementary symmetry, into a single framework. It also includes all known nonlinear symmetry principles as special cases. Moreover, a general method for identifying all symmetry characteristics possessed by a nonlinear multiport and multiterminal element is given. The main results of this paper:

• 1 Several algorithms for synthesizing a nonlinear multiport or multiterminal element having any prescribed form of symmetry are presented. In particular, various examples are given which illustrate how these algorithms can be used to derive well-known symmetrical nonlinear circuit modules such as push-pull amplifiers, complementary-symmetric amplifiers, rectifiers, modulators, etc.;
• 2 A reduction algorithm is presented which allows a complicated symmetric element to be analysed by a much simpler reduced element;
• 3 A general principle is derived for applying symmetry to achieve frequency separation in nonlinear communication circuits where the even harmonic components are separated from the odd harmonic components.

     

MOS‐integrable circuitry for multi‐scroll chaotic grid realization: A SPICE‐assisted proof

A MOS‐integrable circuit realization of the class of Multi‐Scroll Grid attractor using an implementation of nonlinear transconductor is presented. The design can be seen as the MOS‐integrable circuit implementation of modified jerk equations presented in the literature (Int. J. Bifurcat. Chaos 2002; 12 (1):23–41). The proposed design of Multi‐Scroll Grid attractor is adequately supported by SPICE simulation results. Copyright © 2008 John Wiley & Sons, Ltd.     

Envelope analysis of nonlinear electronic circuits based on harmonic balance method

We propose here a Spice‐oriented envelope analysis based on the HB (harmonic balance) method, where Fourier coefficients are assumed to be slowly varying. The Fourier expansions of nonlinear devices are executed by MATLAB in the symbolic forms. In this time, the nonlinearities need to be approximated by the polynomial functions. The determining equation of the HB method is formulated as Sine–Cosine circuit in the form of schematic diagram using ABMs (analog behavior models) of Spice. Each sub‐circuit corresponding to the higher harmonic component is almost the same circuit topology as the original one and has dynamic elements such as capacitors and inductors. The Sine–Cosine circuit can be solved by the transient analysis of Spice. Thus, our method is rather a symbolic approach in the meaning that the HB determining equation is given by the schematic diagram of Spice. Our method can be easily applied to the analysis of middle order of nonlinear communication circuits such as mixers and amplitude modulators and to the analysis of interesting phenomena in the nonlinear oscillations. After many simulation experiments, the results show that our envelope analysis is about 50 times faster than the direct transient analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

A new CMOS astable multivibrator and its nonlinear analysis

We present a nonlinear analysis of a new inductively tuned astable multivibrator obtained by connecting a timing inductor across a composite nonlinear resistor with a characteristic of N‐type, which is made up of the parallel connection of two complementary pairs of cross‐coupled MOS devices. Some possible practical applications of the circuit are also envisaged. Closed‐form expressions for the amplitude and the period of the periodic oscillation are derived in both cases when the circuit exhibits a relaxation oscillation and in the more difficult case when, due to the effect of parasitic capacitances of the devices, the circuit has an almost‐discontinuous relaxation oscillation with a nonzero switching time. The accuracy of the presented formulas, which are useful for both the analysis and design, is validated through circuit simulations and experimental results. Copyright © 2009 John Wiley & Sons, Ltd.     

基于多元线性回归的阻性和容性电流分解

为了研究交流电压作用下非线性半导体器件和非线性绝缘电介质的绝缘状态和介电性能,提出一种阻性和容性电流分解算法。以非线性电阻和非线性电容构成的并联等效电路为研究对象,推导响应电流关于激励电压的非线性方程。通过坐标变换,将其转化成多元线性方程。利用多元线性回归方法,获得等效电路参数且实现了阻性和容性电流的分解。定性分析该算法的抗干扰能力和对非标准正弦波电压的适应能力。仿真结果表明:该算法可以准确地实现阻性和容性电流的分解;当响应电流含有55 d B的噪声时,电路参数的求解误差较小;激励电压谐波分量对电路参数的求解几乎没有影响。实验结果表明:该算法可以实现MOA阀片在交流电压作用下全泄露电流的分解。     

Parameter identification of simplified common‐mode equivalent circuit for inverter‐fed motor drive systems by applying computer‐aided optimization software

This paper deals with common‐mode (CM) electromagnetic interference (EMI) in an inverter‐fed motor drive system. A simplified CM equivalent circuit including π‐type equivalent circuit for the motor winding is proposed by using the waveform of the common‐mode current flowing in the ground conductor. Moreover, a parameter identification method applying the computer‐aided software modeFRONTIER is proposed to decide objectively the circuit parameters of the proposed simplified equivalent circuit. Validity and effectiveness of the proposed equivalent circuit are confirmed by comparing the measured impedance characteristics with the calculated ones. Finally, the possibility of a nonlinear phenomenon is discussed in this system. It is shown that the accuracy of simulation result can be improved by introducing the nonlinear element. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Accurate substrate modelling of RF CMOS

The losses within the substrate of an RF IC can have significant effect on performance in a mixed signal application. In order to model substrate coupling accurately, it is represented by an RC network to account for both resistive and dielectric losses at high frequency (> 1 GHz). A small‐signal equivalent circuit model of an RF IC inclusive of substrate parasitic effect is analysed in terms of its y‐parameters and an extraction procedure for substrate parameters has been developed. By coupling the extracted substrate parameters along with extrinsic resistances associated with gate, source and drain, a standard BSIM3 model has been extended for RF applications. The new model exhibits a significant improvement in prediction of output reflection coefficient S₂₂ in the frequency range from 1 to 10 GHz in device mode of operation and for a low noise amplifier (LNA) at 2.4 GHz. Copyright © 2006 John Wiley & Sons, Ltd.     

An interval algorithm for finding all solutions of non‐linear resistive circuits

In this letter, an efficient algorithm is proposed for finding all solutions of non‐linear (not piecewise‐linear) resistive circuits. This algorithm is based on interval analysis, the dual simplex method, and the contraction methods. By numerical examples, it is shown that the proposed algorithm could find all solutions of systems of 500–700 non‐linear circuit equations in acceptable computation time. Copyright © 2004 John Wiley & Sons, Ltd.     

A theory of nonenergic N-ports

A circuit element is nonenergic if the instantaneous power flow into it is always zero. Well-known examples include the ideal diode, transformer, gyrator and circulator. Most of the interesting nonenergic elements are nonlinear N-ports with N ? 2, and many of their properties are quite counterintuitive. For example, there exists a surprisingly large class of nonenergic multiport capacitors and inductors, all of which, it turns out, are nonlinear and reciprocal. Nonenergic linear N-ports, on the other hand, are necessarily resistive and antireciprocal. In this paper, we present a rigorous fundamental theory of nonenergic N-ports that results in a general canonical representation. Special canonical forms are developed for nonenergic resistors, capacitors and inductors, and numerous examples are given.     

Magnetic instability of ac multifilamentary superconductors in spatially distributed magnetic field

Alternating current (ac) superconducting machines such as superconducting generators, transformers, or resistive current limiters need large‐current‐capacity conductors. These conductors are generally fabricated as multistrand cables stacked with multifilamentary NbTi superconductors whose current capacity is a few tens of amperes. ac quench current degradation has often been observed in ac use of such multistrand cables. Several reasons for this degradation have been pointed out: nonuniformity of each strand current, mechanical disturbances, thermomagnetic instability, and ac losses. However, it has not as yet been overcome. Since the angle between the strand axis and the cable axis changes along the cable axis in multistrand cables, the strands are exposed to a spatially (axially) distributed magnetic field, which has longitudinal and transverse components changing periodically due to multiple cabling. This paper mainly discusses the thermomagnetic instability due to the distributed transverse magnetic field, which was compared with the self‐field instability and the longitudinal field instability experimentally and theoretically. It was confirmed that the ac quench current degradation due to the distributed transverse field could be induced by the following: nonlinear E–j characteristic, strong dependence of E–j characteristic on magnetic field in low field region, uniformity of the axial current profile inside the superconductor with the high resistive matrix, and the poor thermal diffusion of CuNi/NbTi composites. © 2000 Scripta Technica, Electr Eng Jpn, 131(1): 45–55, 2000     

Cellular non‐linear networks for minimization of functionals. Part 1: Theoretical aspects

A method for the definition of cellular non‐linear networks able to find approximate minima of rather a large class of continuous functionals is proposed and discussed from a theoretical point of view. The method is based on the spatial discretization of continuous functionals and on the theory of potential functions for resistive circuits. The discretization of the continuous functionals is obtained by resorting to the finite difference method or to the finite element method. The spatial discretization converts a functional into a function of a finite set of variables. By exploiting the theory of potential functions for resistive circuits, from such a function one can derive a lumped circuit that makes it possible to find an approximate minimum of the given functional. Copyright © 2001 John Wiley & Sons, Ltd.     

Symmetry‐aware placement algorithm using transitive closure graph representation for analog integrated circuits

Recently several topological representations have been explored as alternatives to the conventional absolute‐coordinate representation for integrated circuit layout automation. Those topological representations, however, lack one or more aspects in capturing the solution space subject to symmetry constraints, which are abundant in analog layouts. In this paper, we explore the use of transitive closure graphs (TCGs) to represent analog placements, i.e. placements with symmetry constraints. We define a set of conditions so that a TCG satisfying these conditions, referred to as a symmetric‐feasible TCG, will correspond to a valid symmetric placement and vice versa. We then present an O(n²) algorithm, where n is the number of cells to be placed, to build a symmetric placement from a symmetric‐feasible TCG, a problem known as packing. We further describe a set of random perturbation operations on existing symmetric‐feasible TCGs to generate new symmetric‐feasible TCGs with time complexity of O(n) . This allows our TCG‐based symmetry‐aware analog placer to search only the symmetric‐feasible TCG solution space, leading to a substantial reduction of the search space and solution time. Experimental results on several analog circuits have confirmed the superiority of the TCG representation to the conventional absolute‐coordinate representation as well as several other topological representations in analog layout design. Copyright © 2008 John Wiley & Sons, Ltd.     

磁脉冲压缩系统元件参数及电路仿真

应用Pspice电路分析软件,对单级磁脉冲压缩系统在纯电阻负载(400Ω)情况下的压缩过程进行比较全面、准确的模拟,其中磁开关的模型基于微秒脉冲激励下的磁芯B-H曲线。当负载为400Ω时,Pspice模拟结果揭示了饱和变压器PT和磁开关MS1的磁芯所需的饱和时间分别为4μs和400 ns,输出的负极性脉冲峰值-55 kV,半高宽为100 ns,下降沿为50 ns,实验结果很好地验证了这一结论。     

Stability analysis and adaptive control for nonlinear discrete‐time systems with time delays and dead zone via state‐feedback technique

This research addresses the stability analysis and adaptive state‐feedback control for a class of nonlinear discrete‐time systems with multiple interval time‐varying delays and symmetry dead zone. The multiple interval time‐varying delays and symmetry dead zone are considered in the nonlinear discrete‐time system. The multiple interval time‐varying delays are bounded by the nonlinear function with unknown coefficients, and the symmetry dead zone is considered without the knowledge of the dead zone parameters. The adaptive state‐feedback controller is designed for the nonlinear discrete‐time systems with multiple interval time‐varying delays and dead zone. The discrete Lyapunov‐Krasovskii functional is introduced, such that the solutions of the closed‐loop error system converge to an adjustable bounded region and the state errors can be rendered arbitrarily small by adjusting the adaptive parameters. The designed adaptive state‐feedback controller does not require the knowledge of maximum and minimum values for the characteristic slopes of the dead zone. Finally, three simulation examples are given to show the effectiveness of the proposed methods.     

A CCII‐based wide frequency range square waveform generator

In this paper, we propose a novel current‐mode solution suitable for the square waveform generation. The designed oscillator, which utilizes only two positive second‐generation current conveyors as active blocks, six resistors and a capacitor, is based on a current differentiation, instead of voltage integration, typical of developed solutions both in voltage‐mode and in current‐mode approaches, so avoiding circuit limitations due to the node saturation effects. The proposed circuit has been designed, as an integrated solution at transistor level, in a standard CMOS technology, with low‐voltage (± 1V) and low‐power (430µW) characteristics. Simulation results have confirmed the good circuit behaviour, also for working temperature drifts, showing good linearity in a wide oscillation frequency range, which can be independently adjusted through either capacitive (in the range pF ? µF) or resistive (in the range M Ω–G Ω) external passive components. Waiting for the chip fabrication, preliminary measurements have been performed using a laboratory breadboard employing the CCII with AD844 commercial component and sample capacitors and resistors. The experimental results have shown good agreement with both simulations and theoretical expectations. Copyright © 2011 John Wiley & Sons, Ltd.     

Development of a high‐speed electromagnetic repulsion mechanism for high‐voltage vacuum circuit breakers

This paper presents a design and testing of a new high‐speed electromagnetic driving mechanism for a high‐voltage vacuum circuit breaker (VCB). This mechanism is based on a high‐speed electromagnetic repulsion and a permanent magnet spring (PMS). This PMS is introduced instead of the conventional disk spring due to its low spring energy and more suitable force characteristics for VCB application. The PMS has been optimally designed by the 3D nonlinear finite‐elements magnetic field analysis and investigated its internal friction and eddy‐current effect. Furthermore, we calculated the dynamic of this mechanism coupling with the electromagnetic field and circuit analysis, in order to satisfy the operating characteristics—contact velocity, response time, and so on, required for the high‐speed VCB. A prototype VCB, which was built based on the above analysis, shows sufficient operating performance. Finally, the short circuit interruption tests were carried out with this prototype breaker, and we have been able to verify its satisfying performance. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 163(1): 34–40, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20398