By Topic

Circuits and Systems, IEEE Transactions on

Issue 9 • Date September 1983

Filter Results

Displaying Results 1 - 12 of 12
  • Editorial in special issue

    Publication Year: 1983 , Page(s): 617 - 619
    Save to Project icon | Request Permissions | PDF file iconPDF (359 KB)  
    Freely Available from IEEE
  • A criterion of existence and uniqueness of the stable limit cycle in second-order oscillators

    Publication Year: 1983 , Page(s): 680 - 683
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (432 KB)  

    Conditions that ensure the existence of a single stable limit cycle in second-order oscillators are found. These conditions enable to characterize both the required nonlinear element and the range of values of the linear circuit parameters in a simple way. It will be shown how these conditions can be applied to the design of the commonly used oscillators. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Nonelementary catastrophe theory

    Publication Year: 1983 , Page(s): 663 - 670
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1024 KB)  

    This tutorial paper is intended to complement the preceding one on Elementary Catastrophe Theory, and to emphasize that many of the supposed limitations of the elementary catastrophes may be overcome by suitably modifying the mathematical setting. The main generalization discussed here is the Imperfect Bifurcation Theory of Golubitsky and Schaeffer Catastrophe Theory with a distinguished parameter. The effects of symmetry are also discussed, leading to some important results on degenerate Hopf bifurcation. Illustrative examples of applications of these ideas are included, but are kept simple to illuminate the mathematical ideas involved. Surveys of applications in the physical sciences of these and related ideas may be found in Stewart (1981, 1982) and in the forthcoming sequel to this tutorial paper. Applications of Non-elementary Catastrophe Theory, to appear in this journal. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • On the stability of limit cycles in nonlinear feedback systems: Analysis using describing functions

    Publication Year: 1983 , Page(s): 684 - 696
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1320 KB)  

    In this paper we establish computable conditions for the stability and instability of limit cycles in nonlinear feedback systems. In the proof of the present results, we make use of several novel transformations, of averaging, and of a result on integral manifolds and we assume that we can establish the existence of limit cycles by means of the describing function method. Our results, which in part justify the popular quasistatic stability analysis of limit cycles (Loeb's criterion), are significantly different from existing results dealing with the stability analysis of limit cycles. We demonstrate the applicability of our results by means of specific examples. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • On stability preserving mappings

    Publication Year: 1983 , Page(s): 671 - 679
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1080 KB)  

    We view systems as mappings which connect a set of inputs (input functions) with a set of outputs (output functions). Such systems are said to be stability preserving if a stable (asymptotically stable) reference input results in an output with the same stability properties. In the present paper we study the properties of such mappings, we establish a block diagram algebra for such mappings, and we relate the properties of such mappings to BIBO stability and I/O continuity (in the L_{\infty} sense). We show how stability preserving mappings arise in some applications in a natural way. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Uniqueness of a basic nonlinear structure

    Publication Year: 1983 , Page(s): 648 - 651
    Cited by:  Papers (21)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (488 KB)  

    In this paper we show that systems consisting of a memoryless nonlinearity sandwiched between two linear time-invariant (LTI) operators are unique modulo scaling and delays. We mention a few corollaries and applications of general circuit and system theoretic interest. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Synchronization and chaos

    Publication Year: 1983 , Page(s): 620 - 626
    Cited by:  Papers (37)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (832 KB)  

    We believe that synchronization and chaos are closely related. Common intuition suggests that when a circuit is off synchronization the observed output, although not periodic, will be a sum of periodic (intermodulation) components. In fact, at least for a large class of systems we have studied, the output does not have this relatively simple form but is actually chaotic. This paper studies a simple but realistic model for a large class of triggered oscillators. Theory and experiments both confirm that the output shows the properties of sensitivity to initial conditions, nonperiodicity, broad spectrum, and complicated recurrence, that characterize chaotic motion. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • The effects of small noise on implicitly defined nonlinear dynamical systems

    Publication Year: 1983 , Page(s): 651 - 663
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1536 KB)  

    The dynamics of a large class of nonlinear systems are described implicitly, i.e., as a combination of algebraic and differential equations. These dynamics admit of jump behavior. We extend the deterministic theory to a stochastic theory since (i) the deterministic theory is restrictive, (ii) the macroscopic deterministic description of dynamics frequently arises from an aggregation of microscopically fluctuating dynamics, and (iii) to robustify the deterministic theory. We compare the stochastic theory with the deterministic one in the limit that the intensity of the additive white noise tends to zero. We study the modeling issues involved in applying this stochastic theory to the study of the noise behavior of a multivibrator circuit, discuss the limitations of our methodology for certain classes of systems and present a modified approach for the analysis of sample functions of noisy nonlinear circuits. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A generalized Fock space framework for nonlinear system and signal analysis

    Publication Year: 1983 , Page(s): 637 - 647
    Cited by:  Papers (47)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1280 KB)  

    A unified framework is presented for nonlinear (and, in particular, linear) system and signal analysis, whereby a number of problems involving approximation and inversion of nonlinear functions, nonlinear functionals, and nonlinear operators, are cast in a reproducing kernel Hilbert space (RKHS) setting, and solved by orthogonal projection methods. The RKHS's used for the above purpose are the "arbitrarily weighted Fock spaces" introduced by de Figueiredo and Dwyer in II] and called in the present paper "generalized Fock (GF) spaces". These spaces consist of polynomials or power series in one or more scalar variables, or of finite (polynomic case) or infinite Volterra functional series in one or more functions, or of finite or infinite Volterra operator series in one or more functions. In each case, the space is equipped with an appropriate weighted inner product, with the option of making the choice of weights depend on the particular problem under consideration. These developments are illustrated by means of various applications, in particular, the modeling of semiconductor device characteristics, best approximation of nonlinear systems, and cancellation of large nonlinear distortion in signals propagating through electronic equipment. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Chaos and Arnold diffusion in dynamical systems

    Publication Year: 1983 , Page(s): 697 - 708
    Cited by:  Papers (14)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1488 KB)  

    Chaotic motion refers to complicated trajectories in dynamical systems. It occurs even in deterministic systems governed by simple differential equations and its presence has been experimentally verified for many systems in several disciplines. A technique due to Melnikov provides an analytical tool for measuring chaos caused by horseshoes in certain systems. The phenomenon of Arnold diffusion is another type of complicated behavior. Since 1964, it has been playing an important role for Hamiltonian systems in physics. We present a tutorial treatment of this work and its place in dynamical systems theory, with an emphasis on results that can be checked in specific systems. A generalization of the Melnikov technique has been recently developed to treat n -degree of freedom Hamiltonian systems when n > 3 . We extend the Melnikov technique to certain non-Hamiltonian systems of ordinary differential equations. The extension is made with a view to applications in the physical sciences and engineering. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Effect of a periodic perturbation on radio frequency model of Josephson junction

    Publication Year: 1983 , Page(s): 633 - 636
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (472 KB)  

    By using the analytical method of Mel'nikov the qualitative behavior of the single differential equation \ddot{x}+\delta dot{x}- \alpha \sin x = f_{0} + f_{1} \sin(\omega t), dot{x}stackrel{\Delta }{=} frac{dx}{dt} where \delta > 0, \alpha > 0, f_{0} \geq 0, f_{1} > 0, \omega > 0 is studied. The parameter space (\delta , \alpha , f_{0}, f_{1}, \omega ) of the nonlinear oscillator (A) is decomposed by the threshold curve into two regions, where significantly different behavior of oscillations occurs. In the first part of the parameter space the existence of chaotic solutions of (A) is possible, whereas in the second part of the parameter space only regular oscillations are expected. A radio frequency network modeling the very high-frequency (VHF) phenomena in current driven Josephson junction with capacitance but without dc bias current is described. The results of the measurements of the frequency spectrum of voltage oscillations are presented. The theoretical predictions and experimental data are not in disagreement. In order to pinpoint exactly the parameter subspace of the nonlinear oscillator (A) with chaos, a more general and detailed analytical criterium than Mel'nikov method is needed. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Complicated, but rational, phase-locking responses of an ideal time-base oscillator

    Publication Year: 1983 , Page(s): 627 - 632
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (752 KB)  

    A model is advanced to account for the complicated phase-locking responses of a prototypical time-base oscillator driven by a train of excitory pulses. The model predicts that the intervals of stability for different ratios of phase locking should occur in specific sequences as functions of the parameters. With respect to variation of one parameter (a strength of coupling), these sequences comprise the odd convergents and associated semiconvergents of the simple continued fraction for the fixed parameter (a natural frequency ratio). With respect to variation of this second parameter, the sequences comprise a previously undescribed arithmetical series, which is closely related to the Farey series. An experimental test of the model is described. The results are by and large confirmatory. However, there are narrow intervals on the parameter space where pseudo-randomness versus the effects of true noise are an unresolved issue. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.