IEEE Transactions on Circuit Theory

Issue 6 • November 1972

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Displaying Results 1 - 23 of 23
  • Editorial [Intro to the Special Issue on Nonlinear Circuits]

    Publication Year: 1972, Page(s): 543
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    Freely Available from IEEE
  • Transient waveform generation with lumped nonlinear dynamic networks

    Publication Year: 1972, Page(s):544 - 554
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1153 KB)

    Simple step-driven nonlinear dynamic networks are examined for their transient waveform generation properties. It is shown that a wide class of waveforms can be produced with networks of standard form involving two nonlinear resistors. This class is primarily characterized by the behavior of its elements att = inftyThese networks exhibit several advantages over other wave generation tec... View full abstract»

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  • Modeling of three terminal devices: A black box approach

    Publication Year: 1972, Page(s):555 - 562
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (963 KB)

    A unified black box approach is presented for synthesizing nonlinear dc circuit models of 3-terminal devices characterized by two families ofupsilon-icurves in piecewise-linear form. In order to model arbitrary curves with nonuniform spacings and slopes, three simple but versatile building blocks-a controlled linear resistance, a controlled concave resistor, and a controlled convex resi... View full abstract»

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  • Trajectories of nonlinear RLC networks: A geometric approach

    Publication Year: 1972, Page(s):562 - 571
    Cited by:  Papers (60)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1158 KB)

    The response of a nonlinear time-varying coupledRLCnetwork starting from a given operating point is considered. We view the response as motion occurring in a differentiable manifoldSigmainR^{2b} times R_{+}, wherebis the number of branches. We impose two basic manifold conditions (MC) on the network. First, the resistor characteristics are required to be... View full abstract»

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  • A sparse matrix method for analysis of piecewise-linear resistive networks

    Publication Year: 1972, Page(s):571 - 584
    Cited by:  Papers (63)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1408 KB)

    Nonlinear resistive networks, which can be characterized by the equationf(x) =y, wheref(cdot)is a continuous piecewise linear mapping ofR^{n}into itself, are discussed.xis a point inR^{n}and represents a set of chosen network variables andyis an arbitrary point inR^{n}and represents the input to the network. New theorems ... View full abstract»

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  • Formulation of normal form equations of nonlinear networks containing memristors and coupled elements

    Publication Year: 1972, Page(s):585 - 594
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (927 KB)

    This paper presents a variety of sufficient conditions for the existence of a set of normal form equations of a connected nonseparableRLCMnetwork, which may contain coupled elements. AnRLCMnetwork is defined as a network containing independent (but not necessarily time-independent) current and voltage sources, nonlinear time-invariant resistors, inductors, capacitors, and mem... View full abstract»

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  • Existence conditions forL_1Lyapunov functions for a class of nonautonomous systems

    Publication Year: 1972, Page(s):594 - 598
    Cited by:  Papers (18)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (486 KB)

    A class of natural Lyapunov functions of the formSigma lambda_{i} |x_{i}|, lambda_{i} > 0, is considered for the stability analysis of a general class of nonautonomous differential equations associated with many physical systems. It is shown that recent results on the existence of solutions to a class of linear inequalities directly yield necessary and sufficient conditions for the e... View full abstract»

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  • Some applications of spectral-radius concept to nonlinear feedback stability

    Publication Year: 1972, Page(s):607 - 615
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (953 KB)

    Several results are derived concerning the input-output stability of nonlinear time-varying feedback systems. These results all share the common feature that they are based on an application of the concept of the spectral radius of a bounded linear operator. Section I contains the preliminary notions, including that of the spectral radius. In Section II, bounds are obtained for the spectral radius... View full abstract»

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  • Stability and instability criteria for nonlinear distributed networks

    Publication Year: 1972, Page(s):615 - 622
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (838 KB)

    Electrical networks consisting of lumped linear and memoryless nonlinear elements and an arbitrary number of lossless transmission lines are considered. It is shown that a large class of such networks can be described by a system of functional-differential equations having the formdot{x}(t) =f(x_{t}), where the state of the system at timet geq 0is represented byx_{t} View full abstract»

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  • Relaxation oscillations, parasitics, and singular perturbations

    Publication Year: 1972, Page(s):623 - 625
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (391 KB)

    The rate at which solutions oflambda dot{x} = F(x, y), dot{y} = G(x, y), 0 leq lambda ll 1, xann-vector,yanm-vector, approach the solutions ofF(x, y) = 0, dot{y} = G(x, y)is obtained. Physically, this is important in the study of parasitics, in relaxation oscillations, and in other applications. The behavior of solutions of the Liénard eq... View full abstract»

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  • Digital filtering and prolate functions

    Publication Year: 1972, Page(s):674 - 681
    Cited by:  Papers (43)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (577 KB)

    A class of trigonometric polynomialsp(x) = sum_{n=-N}^{N} a_{n} e^{j n pi x}of unit energy is introduced such that their energy concentrationalpha = int_{-e}^{e} p^{2}(x) dxin a specified interval(- epsilon, epsilon)is maximum. It is shown that the coefficientsa_{n}must be the eigenvectors of the systemsum_{m=-N}^{N} frac{sin (n - m)pi epsilon}{(n -... View full abstract»

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  • Passive Q-sensitivities of the twin-T selective amplifier

    Publication Year: 1972, Page(s):685 - 686
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (167 KB)

    Passive sensitivities of the twin-Tselective amplifier are derived without assuming pole-zero cancellation. If the twin-Tis unloaded, the sensitivities are a linear function ofQ. They should not differ greatly in the loaded case since the design formulas in the two cases are shown to be closely similar. View full abstract»

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  • Pseudo-passivity, sensitivity, and stability of wave digital filters

    Publication Year: 1972, Page(s):668 - 673
    Cited by:  Papers (118)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (624 KB)

    Two basic properties of wave digital filters, their property of requiring fewer digits for the multiplier coefficients (to which the property of roundoff noise reduction is related) and their stability, had so far only been inferred from certain analogies with unit element filters. These properties are now proved in a direct way by introducing the concepts of pseudopower, pseudopassivity, and pseu... View full abstract»

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  • Fault isolation via components simulation

    Publication Year: 1972, Page(s):634 - 640
    Cited by:  Papers (28)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (704 KB)

    The problem of deducing the internal component parameters from external measurements of a large-scale system is studied in the context of the fault isolation problem. By assuming an appropriate algebraic connection model matrix, algebraic necessary and sufficient conditions for the exact determination of the internal component parameters are obtained for both the single-test frequency and multiple... View full abstract»

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  • A method of limit-cycle synthesis and its applications

    Publication Year: 1972, Page(s):631 - 633
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (360 KB)

    A method to determine a dynamical system, the limit cycle of which is given as a closed curve in state space, is presented. The relationship between the limit cycle and the limit surface for a specific higher order system is discussed, and it is shown that the results obtained can be applied to the synthesis of a finite-time stable system. View full abstract»

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  • Driving-Point Synthesis of Resistor-Terminated Cascades Composed of Lumped Lossless Passive 2-ports and Commensurate TEM Lines

    Publication Year: 1972, Page(s):648 - 664
    Cited by:  Papers (27)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1536 KB)

    It has long been appreciated that microwave filters incorporating cascades of lumped reactive 2-ports and equi-delay ideal TEM lines offer many practical advantages over those designed with lines alone. To develop an insertion-loss design theory for these fiters comparable in precision to the one now available in the lumped case, it is first necessary to solve the intermediate problem of discoveri... View full abstract»

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  • Some observations concerning the boundedness of solutions of coupled Lienard's equations

    Publication Year: 1972, Page(s):625 - 626
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (304 KB)

    First Page of the Article
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  • Basic constraints from graph theory for dc-to-dc conversion networks

    Publication Year: 1972, Page(s):640 - 648
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (936 KB)

    Some theorems in graph theory, which have received little use in circuit theory, are used to derive constraints on the voltage, current, and power associated with the elements in a dc-to-dc conversion network. The result is an insight into the necessary roles of the switches and reactances in the network. The application of the graph theorems to this problem shows their flexibility, and it is expe... View full abstract»

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  • Multiple dc solutions of one-transistor circuits

    Publication Year: 1972, Page(s):626 - 628
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (384 KB)

    The necessary and sufficient conditions are given for the existence of multiple dc solutions of circuits consisting of one ideal Ebers-Moll transistor embedded in an admittance-described circuit consisting of dc sources, linear passive resistors, and ideal transformers. The results rest upon the previous theories of Sandberg and Willson. View full abstract»

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  • Sensitivity invariants for nonlinear networks

    Publication Year: 1972, Page(s):599 - 606
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (736 KB)

    For a general class of nonlinear networks, explicit expressions for sensitivities of a response due to nonlinear elements are derived. These expressions are used to establish invariance relationships for the sums of sensitivities over different sets of parameters of two classes of nonlinear networks. It is indicated how these relationships can be used to establish the invariant nature of the sum o... View full abstract»

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  • On line reduction methods for computer analysis of high-order electrical circuits with widely separated time constants

    Publication Year: 1972, Page(s):664 - 667
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (440 KB)

    A greal deal of effort has recently been spent to develop numerical integration techniques suitable for the solution of stiff state equations. Instead of dealing with the integration method itself, a procedure for gradually removing the stiffness of the state equations during the course of the solution is presented. This is accomplished by gradually discarding the state variables corresponding to ... View full abstract»

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  • Harmonic synchronization of oscillators revisited

    Publication Year: 1972, Page(s):682 - 685
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (368 KB)

    A novel technique of direct synchronization called pseudoindirect synchronization has been proposed. The performance of the system utilizing pseudoindirect synchronization has been studied and compared with that of the directly synchronized oscillator. Experimental results are also presented. View full abstract»

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  • An exponential voltage-controlled oscillator improves the performance of a phase-locked loop

    Publication Year: 1972, Page(s):628 - 631
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (608 KB)

    A design example is worked out to demonstrate how to stabilize a phase-locked loop containing an exponential voltage-controlled oscillator. It is shown that this kind of loop can be designed with an arbitrarily large capture range, a wide lock-in range, and a short transient receovery-time constant. View full abstract»

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