陕西理工学院毕业论文（设计）

致谢

经过18周的毕业设计，我的毕业设计终于完成了，它不光光是我自己的成果，而是给予我帮助的老师、同学共同的成果。

在次我要真诚的感谢帮助过我的老师和同学，尤其是我的指导老师冉起武老师。在毕业设计过程中他不厌其烦的给我指导和帮助，就像是一盏油灯指引着走着夜路的人我，我想没有他的帮助我也不可能完成我的毕业设计。接着我还要感谢我们学校里的王学智老师，他虽说不是我的指导老师，但在我作毕业设计的过程中多次为我排忧解难。最后我还要感谢我的同学们，是他们陪同我走过这18个星期的毕业设计，在其间我们一起相互帮助，相互鼓励。

最后我在这里向那些帮助了我的老师和同学真诚的说一声：“谢谢你们了，没有你们也不会有我今天的成功”！

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陕西理工学院毕业论文（设计）

参考文献

[1]张华，王牛等。蔡氏电路及蔡氏震荡器中非线性电阻的实验研究。西南工学院学报。2000 [2]冯久超，陈宏滨。蔡氏电路的仿真研究。华北航天工业学院学报。2005 [3]常文利，网新新。蔡氏电路的计算机仿真研究。兰州铁路学院学报。2002 [4]卢元元，薛利萍。蔡氏电路实验研究。电气电子教学学报。2003 [5]袁国炜，网力洋。对蔡氏电路的简单研究。邢台学院学报。2005

[6]C. MIGUEL BLAZQUEZ AND EL~AST UMA。Dynamics of the Double Scroll Circuit。IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, VOL. 37, NO. 5, MAY 1990

[7]Marco Gotz, Ute Feldmann, and Wolfgang Schwarz。Synthesis of Higher Dimensional Chua Circuits。IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS-I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 40, NO. 11, NOVEMBER 1993

[8]LEON 0. CHUA, FELLOW, IEEE, MOTOMASA KOMURO, AND TAKASHI MATSUMOTO, FELLOW, IEEE。The Double Scroll Family。IEEE TRANSACTIONSO N CIRCUITSA ND SYSTEMSV,O L. CAS-33, NO. 11, NOVEMBER1 986

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陕西理工学院毕业论文（设计）

附录Ａ 英文资料以及翻译

出处：IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS-I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 40, NO

Synthesis of Higher Dimensional Chua Circuits

Marco Gotz, Ute Feldmann, and Wolfgang Schwarz

[Abstract] In this paper, we present a universal method to design n-dimensional piecewise linear circuits. These circuits are described by a system of differential equation associated with a piecewise linear continuous vector-field in the n-dimensional state-space, which consists of two different linear regions. The circuits contain only two-terminal elements, one piecewise linear resistor and a number of linear resistors capacitors and inductors. The developed method leads to a variety of structures. It is possible to design n-dimensional canonical circuits containing a minimum number of inductors as well as inductor-free circuits. A surprising result is the transformation of the 3-D Chua circuit into an inductor-free circuit that exhibits the double scroll as well. We compare our results with the recently published method of Kocarev . Using our approach, a theorem that specifies the restriction of eigenvalue patterns associated with a piecewise linear vector-field having at least two equilibrium points can be proved.

I. INTRODUCTION

TH E INVESTIGATION of nonlinear autonomous dynamic systems which can exhibit a large variety of behaviour was strongly forced in the past. One direction of efforts is the design of physical systems generating chaotic motion in the state space. For this purpose especially electrical circuits are easy to handle. Under certain conditions we can realize a piecewise linear continuous vector-field with such circuits and study any possible behaviour experimentally. From this point of view one goal is to design a circuit capable of realizing every member of the higher dimensional Chua Circuit family . One 3-D canonical Chua circuit is given in . Furthermore, one extension to higher dimensional canonical circuits is published by Kocarev . Both represent an analysis of a given structure in the time domain and made sure that the structure is canonical. Here we choose a synthesis approach in the frequency domain which is capable of generating a whole class of structures containing both ones mentioned above. With this method, we design as examples a canonical as well as a noncanonical n-dimensional piecewise linear circuit. Canonical in our sense means

1) canonical with respect to the behavior i.e., capable of realizing all possible behaviour of the associated vectorfield. We will call it canonical in behavior

2) canonical with respect to the number of circuit elements i.e., containing the minimum number of elements necessary. We will call it canonical in structure. Manuscript received March 15, 1993; revised May 10, 1993. This paper was recommended by Associate Editor L. 0. Chua. The authors are with the

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陕西理工学院毕业论文（设计）

Technical University of Dresden, Facultat fur Electrotechik, Dresden, Germany.

11. NETWORK-DESIGN-ALGOFUTFHORM T HE DIMENSIONAL PIECEWISE LINEAR CIRCUIT

A. General Approach

We choose an electrical network consisting of a nonlinear static two-terminal element connected to a linear two-terminal dynamic network. Consider the class L(n, 2) of n-dimensional two-region continuous piecewise linear vector-fields and the class C(n, 3) of n-dimensional symmetric with respect to the origin three-region continuous piecewise linear vector-fields defined in . One realization of this class of

vector-fields is shown in principle in Fig. 1. This system consists of either a two-segment static resistor as a member of L(n, 2) or a threesegment symmetric (with respect to the origin) static resistor as a member of C(n, 3) and a n-dimensional two-terminal linear network. The common feature of both classes is the existence of two different linear regions. Now we increase the number of segments to IC retaining the feature of then two different linear regions. Let us call this more common class L(n, IC/m). N represents the dimension, k the region and m the number of the different regions. Consider now a L(n, k / 2 ) and a subset C(n, k / 2 ) that represents a vectorfield symmetric (with respect to the origin). Subsequently the vector-field of L(n, k / 2 ) or C(n, k / 2 ) shall be represented by the eigenvalues of the linear systems of differential equations in the two different regions. Assuming that the eigenvalues in each region are given, a circuit that realizes all possible patterns of 2n eigenvalues has to be designed. This circuit will be canonical in behaviour. First, we have to decide on the minimum number of element parameters needed for a circuit that is canonical in structure. It is pointed out in and that at least 2 . n + 1 parameters are needed to generate any set of 2 . n eigenvalues because of the impedance scaling property of linear systems . This impedance scaling deals with normalized parameters: Zn/a for impedances and Y, . a for admittances with the scaling factor a.

B. Coeficients of the Characteristic Polynomials

The state equations of an autonomous piecewise linear network are given by

where Do an D1 denote the two different regions.

The eigenvalues of these systems of homogeneous differential equations are determined by det (Ai - SI) = 0, i = 0, 1, where I is the unity matrix

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