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IRE Transactions on Circuit Theory

Issue 4 • December 1960

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Displaying Results 1 - 25 of 26
  • Prof. Dr. Balthasar Van der Pol - In Memoriam

    Publication Year: 1960, Page(s):360 - 361
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    Freely Available from IEEE
  • A tribute [Into. to special issue deicated to Balthasar van der Pol]

    Publication Year: 1960, Page(s): 362
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  • Periodic Solutions of van der Pol's Equations with Large Damping Coefficientlambda = 0 sim 10

    Publication Year: 1960, Page(s):382 - 386
    Cited by:  Papers (15)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (475 KB)

    A method of computing a periodic solution of van der Pol's equation is devised reducing the problem to the solution of a certain equation by means of Newton's method. For computing the value of the derivative necessary to apply Newton's method, the properties of variation of the orbit in the phase plane are used and, for step-by-step numerical integration of differential equations, a somewhat new ... View full abstract»

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  • A Method of Analysis in the Theory of Sinusoidal Self-Oscillations

    Publication Year: 1960, Page(s):398 - 413
    Cited by:  Papers (22)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1909 KB)

    The article is devoted to the theory of weak resonance action on self-oscillating systems. The theory is based on the method of secondary-simplification of "shortened" equations for amplitudes and phases of the self-oscillating process. A series of new results is obtained. These results are taken as a basis for the creation of new radiotechnical devices. View full abstract»

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  • Periodic Solutions of Forced Systems Having Hysteresis

    Publication Year: 1960, Page(s):423 - 431
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (897 KB)

    In Section I, the motion of a mass on a material rod is discussed. The stress-strain law exhibits a hysteresis effect, so that the stress at any time is a function of the whole strain history. A "rupture restriction" which limits the magnitudes of the admissable displacements, velocities, and accelerations is also discussed. It is shown that the appropriate formulation of the phenomenon is in term... View full abstract»

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  • Multistable Circuits Using Nonlinear Reactances

    Publication Year: 1960, Page(s):432 - 440
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (830 KB)

    This paper presents some results in the asymmetric resonant circuit, which is constructed by applying a dc voltageE_0and a sinusoidal voltageE_1 sin {omega}tto a series resonant circuit containing a nonlinear capacitance. The circuit is analyzed using the Ritz-Galerkin method. Assuming that the first approximation for the chargeqtakes on the form... View full abstract»

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  • The Problem of Quality for Nonlinear Self-Regulating Systems with Quadratic Metric

    Publication Year: 1960, Page(s):469 - 473
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    The systems considered in this paper are characterized by differential equations of the formdot{x}_{k} = sum_{alpha} b_{kalpha} x_{alpha} + f_{k}(alpha_1,cdots,x_n, t) (k= 1, cdots, n)which are defined over a region N of Euclidean spaceE_nwith metricR^2 = sum_{i=1} x_i^2, and withtranging over some intervalT. Thef_k (k+1,cdots, n)ar... View full abstract»

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  • On Nonlinear Networks with Random Inputs

    Publication Year: 1960, Page(s):479 - 490
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1467 KB)

    The paper attempts to combine the Wiener-Bose method for characterizing and synthesizing nonlinear systems with the Ku-Wolf method for analyzing nonlinear systems with random inputs. A simple partition theory is first presented. It is shown that a general nonlinear system can be partitioned into two portions: one linear portion with memory or storage, and one nonlinear portion which may also inclu... View full abstract»

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  • A Method for Determining Optimum Systems Using General Bayes Criterion

    Publication Year: 1960, Page(s):491 - 505
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1642 KB)

    A method for obtaining an optimum system using general Bayes criterion is developed. This method is applicable to the cases in which a signal to be estimated depends on certain finite-dimensional vectorU, and where the input is the sum of a function depending on the vectorUand a normally distributed noise which is independent of the vector, or may be reduced to this form by s... View full abstract»

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  • Differential Equations with a Small Parameter Attached to the Highest Derivatives and Some Problems in the Theory of Oscillations

    Publication Year: 1960, Page(s):527 - 535
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (936 KB)

    This paper presents a brief review, for the most part, of the authors' results concerning systems of differential equations of the formepsilon dot{x}^1 = f^i(x^1,cdots,x^k,y^1,cdots,y^l) i =1, 2,cdots,kdot{y}^i = g^i(x^1,cdots,x^k,y^1,cdots,y^l) j =1,2,cdots,whereepsilonis a small positive parameter. The emphasis is on periodic solutions of such systems which are c... View full abstract»

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  • On the Number of Stable Periods of a Differential Equation of the van der Pol Type

    Publication Year: 1960, Page(s):535 - 542
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (929 KB)

    Van der Pol's differential equation with forcing term can, for some values of the parameterb, have stable periodic solutions of two distinct periods. The paper examines whether, with a generalization of the equation not too unlike the original, there can be more than two distinct periods. The answer is affirmative. The example (with three periods-in principle, there can be many), while ... View full abstract»

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  • Reviews of Current Literature

    Publication Year: 1960, Page(s):554 - 555
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    Freely Available from IEEE
  • Statistical Theory of Systems Reducible to Linear

    Publication Year: 1960, Page(s):506 - 513
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (840 KB)

    A statistical theory for nonlinear systems, whose operators are reducible to linear, is given. The analysis as well as the synthesis problems of such systems are considered. View full abstract»

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  • On the Method of Averaging

    Publication Year: 1960, Page(s):517 - 519
    Cited by:  Papers (1)
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    The method of averaging of van der Pol was devised to obtain periodic and almost periodic solutions of quasi-linear systems of differential equations. A theorem is stated for a particular case where this method has been justified mathematically and an example is given to illustrate the results. View full abstract»

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  • On Coding Theorems for General Simultaneous Channels

    Publication Year: 1960, Page(s):513 - 516
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (448 KB)

    This paper deals with the lengths of codes for several simultaneous channels in a general formulation. The paper is almost self-contained, and requires for its reading no prior knowledge of information theory. View full abstract»

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  • Frequency Entrainment in a Self-Oscillatory System with Ex-ternal Force

    Publication Year: 1960, Page(s):413 - 422
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (864 KB)

    This paper deals with forced oscillations in a self-oscillatory system of the negative-resistance type. When no external force is applied, the system produces a self-excited oscillation. Under the impression of a periodic force, the frequency of the self-excited oscillation falls in synchronism with the driving frequency within a certain band of frequencies. This phenomenon of frequency entrainmen... View full abstract»

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  • Theoretical Aspects of Nonlinear Oscillations

    Publication Year: 1960, Page(s):368 - 381
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1800 KB)

    This review gives an outline of the modern theory of nonlinear oscillations. This field, originated about four decades ago by the late Prof. B. van der Pol, acquired a considerable momentum in recent years with a gradually increasing number of ramifications, some of which are still in a state of development. For this reason the selection of topics for this review is narrowed down to matters which ... View full abstract»

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  • Directions of Mathematical Research in Nonlinear Circuit Theory

    Publication Year: 1960, Page(s):542 - 553
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1488 KB)

    In this paper we wish to present a potpourri of problems of some interest and difficulty arising in the field of nonlinear circuit theory. Perhaps the only sensible way to catalogue scientific problems is in terms of "solved or unsolved." Yet this classification is itself a very subjective one, dependent upon the times and the fashions. Recall the dictum of Poincaré that the solutions of one ... View full abstract»

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  • Amplification in Nonlinear Reactive Networks

    Publication Year: 1960, Page(s):440 - 446
    Cited by:  Papers (2)  |  Patents (5)
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    Sufficient conditions for validity of the Manley-Rowe equations in a classical nonlinear reactive network are shown to be conservation of energy and proportionality of average power with frequency. It is shown by counter example that conservation of energy alone is insufficient. A sufficient condition for a quantum mechanical maser model is found to be equilibrium of state populations. In this cas... View full abstract»

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  • The Transient Behavior of Nonlinear Systems

    Publication Year: 1960, Page(s):446 - 458
    Cited by:  Papers (2)
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    It is shown that the classical perturbation procedure for treating nonlinear systems leads to solutions expressed as Fourier-like series with slowly varying coefficients. These slowly varying coefficients contain the information about the long term behavior of the system. Inconsistently, the classical perturbation procedure expresses these coefficients as power series, a mode of expression which h... View full abstract»

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  • Two-Stroke Oscillators

    Publication Year: 1960, Page(s):387 - 398
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1408 KB)

    A four-stroke oscillator, whether symmetrical or moderately dissymmetrical, is one in which the linear, conservative elements receive energy from the source two times per period; such are typically a Class A vacuum tube oscillator, a Class C push-pull oscillator, or a clock with anchor escapement. This paper presents a number of nonlinear, second-order differential equations which correspond to tw... View full abstract»

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  • Analysis and Synthesis of Nonlinear Systems

    Publication Year: 1960, Page(s):459 - 469
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1192 KB)

    The input-output relation of linear systems (convolution integral) is generalized to a class of nonlinear systems. This class is represented by analytic functionals as studied by Volterra and Fréchet. The analysis can be performed by measuring the response of nonlinear systems to series of impulse functions. The synthesis involves linear systems, zero-memory nonlinear systems and multiple mul... View full abstract»

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  • Some Extensions of Liapunov's Second Method

    Publication Year: 1960, Page(s):520 - 527
    Cited by:  Papers (339)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1064 KB)

    >In the study of the stability of a system, it is never completely satisfactory to know only that an equilibrium state is asymptotically stable. As a practical matter, it is necessary to have some idea of the size of the perturbations the system can undergo and still return to the equilibrium state. It is never possible to do this by examining only the linear approximation. The effect of the no... View full abstract»

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  • Balth. van der Pol's Work on Nonlinear Circuits

    Publication Year: 1960, Page(s):366 - 367
    Cited by:  Papers (8)
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    First Page of the Article
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  • On Automatic Controls

    Publication Year: 1960, Page(s):474 - 475
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    The problem of automatic controls has been treated more or less linearly by a number of Soviet authors (Lurye, Letov, Yacubovich). Here a treatment is presented taking into account the nonlinearity of the regulated system. Certain consequences of this nonlinearity are also made clear. View full abstract»

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