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Circuit Theory, IRE Transactions on

Issue 1 • Date March 1955

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Displaying Results 1 - 23 of 23
  • Editorial

    Page(s): 3
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  • Four methods for the analysis of time-variable circuits

    Page(s): 4 - 12
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    THE GENERAL theory of electric circuits whose component parameters are linear and constant has been extensively developed and is well understood. In recent years, considerable attention and effort has been directed to the analysis and performance of circuits whose parameters vary with the time. Many of the most important and interesting problems of circuit theory involve variable. parameters. For example, the equivalent circuits of the microphone transmitter, the condenser microphone, the induction generator, the superregenerator and of many other practical devices contain parameters that are time-varying. Many systems in mechanical and acoustical engineering in which the compliance or the inertia parameters vary with the time lead to the same mathematical formulation of their behavior as do the time-varying circuit problems. View full abstract»

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  • Analysis of time-dependent linear networks

    Page(s): 12 - 16
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    LET $bar f$ (an overbarred letter) denote the operator of a linear system; x(τ) an input signal, which depends on time τ and y(t) the output response, as recorded at time t. The functional relationship between x(τ) and y(t) will be written $y = {bar f} x. eqno{hbox{(1)}}$. View full abstract»

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  • Steady-state transmission through networks containing periodically operated switches

    Page(s): 17 - 21
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    THE GENERAL problem of transmitting signals through linear systems in which one or more parameters vary periodically with time has an extensive literature. One widely used method is based on Fourier series representation of the varying parameters. This leads to an infinite number of simultaneous linear equations expressing the relations between the coefficients in the corresponding Fourier series representation of the steady-state response. The solution of the equations can be expressed in terms of determinants of infinite order which in turn can be evaluated by various approximation techniques. In practical cases it is often permissible to neglect all but a few dominant components; the number of equations is thereby made finite and reasonably small. View full abstract»

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  • A time-variable transform and its application to spectral analysis

    Page(s): 22 - 25
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    THE USE OF integral transforms to solve dynamical problems in physics and engineering has received considerable prominence in the last half century. Integral transforms have, since their usefulness was discovered by Heaviside in the late nineteenth century, gone through the cycle of: (1) rigorization of technique;1, 2 (2) tabulation of many specific transform pairs;3, 4 and (3) generalization of transform methods.5–8. In the present paper on extension of this generalization will be made which is applicable only to time series and its use precludes the acceptance of the fundamental postulate of cause and effect. That is, the present response anywhere in a physical system can in no way depend on future values of a stimulus elsewhere in the system. View full abstract»

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  • Properties of impulsive responses and Green's functions

    Page(s): 26 - 31
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    THE INVESTIGATION of general communication systems usually starts by considering a black box, N, with an input u and an output v (see Fig. 1). We express the relation between u and v symbolically by the equation $v = N_u. eqno{hbox{(1)}}$ (1) View full abstract»

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  • Application of complex symbolism to linear variable networks

    Page(s): 32 - 35
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    THE APPLICATION of complex symbolism to linear fixed networks (i.e. networks governed by linear differential equations with constant coefficients) is effective by virtue of the fact that the principle of superposition is applicable to such networks. The same principle is applicable also to linear variable networks (i.e. networks governed by linear differential equations with coefficients that are dependent on time, but not on current or voltage). This suggests that it must also be possible to make use of the complex symbolism in the case of linear variable networks. View full abstract»

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  • Resonance phenomena in time-varying circuits

    Page(s): 35 - 41
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    ASA logical continuation of the studies of systems with fixed parameters, there has been increasing interest in systems whose parameters are functions either of the dependent variable (nonlinear systems) or of the independent variable (time-varying systems). A general approach to the analysis of time-varying systems is so difficult, that at the present stage of development in this field one is restricted to the solution of relatively simple problems arising in practical applications. View full abstract»

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  • Effect of rectifier capacitances on the conversion loss of ring modulators

    Page(s): 41 - 44
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    THE SMALL-signal theory of rectifier modulators is normally developed by assuming that rectifiers switch periodically from their forward to their backward resistance, neglecting the capacitive component of the backward impedance. Such a resistive theory has been quite invaluable to compare the performance of various circuits and especially to study the effect of selective terminations.1 It is well established, however, that capacitive effects are not negligible, and become quite important at high frequencies. For small dissipation, the resistive and capacitive losses clearly add up without interaction, so that it will be sufficient for practical purposes to develop the theory for ideal rectifiers (zero forward and infinite backward impedance) shunted by a parasitic capacitance C. The Cowan modulator of Fig. 1 is then equivalent to a periodic switch shunted by C (Fig. 2). Similarly; a well-known equivalence for lattice networks reduces the ring modulator of Fig. 3, next page (with ideal auto transformers) to an ideal commutator enclosed between two capacitances C (Fig. 4, on the following page). The first step is to develop the theory of the linear variable 4-poles of Figs. 2 and 4 working between purely resistive and frequency independent source and load. The next important case of selective terminations has not yet been attacked. View full abstract»

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  • An application of analog computers to the statistical analysis of time-variable networks

    Page(s): 44 - 49
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    IN RECENT years an extensive body of mathematical techniques has been developed for the analysis of the response of linear constant coefficient control systems to stationary random processes as inputs. In many cases it is possible to achieve direct synthesis of the optimum system for an assigned task. For nonstationary inputs or variable coefficient systems, no corresponding theory exists, even though problems of this nature arise quite often in practice. In the present paper an analog method is presented for the rms error analysis of a class of nonstationary problems. However, no attempt is made at the synthesis of an optimum system. Following a brief discussion of analog methods applicable to the general nonstationary case, our attention is concentrated on the special problem of a variable coefficient linear system with a stationary random input. Exploitation of the properties of the adjoint system in this case is shown to reduce considerably the labor in computing rms errors in comparison with the general method for nonstationary inputs. The simulation of the adjoint system is shown to be readily obtainable from the simulation of the original system. View full abstract»

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  • The response of linear networks to suddenly applied stationary random noise

    Page(s): 49 - 57
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    IN RECENT years time-varying circuits have attracted considerable attention in the literature,1 but little seems to have been done2 for those cases in which the input to such circuits is a random one. View full abstract»

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  • Frequency memory in multi-mode oscillators

    Page(s): 58 - 66
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    THE BASIC idea of frequency memory is conveniently illustrated by Fig. 1 in which it is assumed that the antiresonant circuits are of comparable selectivity and impedance and are tuned to frequencies that are unrelated but of the same order of magnitude. Oscillation at either f1 or f2 can be initiated by supplying to the input a signal of suitable magnitude and the desired frequency. An input of short duration suffices, for once started the oscillation persists without change until the other frequency is injected or the power is turned off. That is, the circuit remembers the frequency of the last input. The output may be taken from other points, but the plate node is particularly convenient. View full abstract»

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  • A mathematical analysis of a series circuit containing periodically varying resistance

    Page(s): 67 - 72
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    IN RECENT years a great deal of attention has been given to the general theory and performance of circuits the parameters of which are functions of the time. The mathematical analysis of circuits of this type leads to the solution of linear differential equations with variable coefficients. Examples of linear time-varying circuits of practical importance occur in the theory of electrical communications. Frequency modulation circuits, for example, involve variations of capacitance or, to a lesser extent, inductance. The carbon microphone circuit consists of essentially of a variable resistance the value of which is varied by some source of energy outside the circuit. The condenser microphone circuit contains a variable capacitance. Super-regeneration involves circuits that contain a periodically-varying resistance parameter. View full abstract»

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  • Comment on the paper “A mathematical analysis of a series circuit containing periodically varying resistance” by L. A. Pipes

    Page(s): 72 - 73
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    AT FIRST sight, the application of W.K.B. approximation to a time-dependent circuit seems perfectly straightforward. Unfortunately, there are two different and equally plausible ways to apply it to the circuit treated by Pipes, and the two results will generally not agree. The W.K.B. solution of the homogeneous equation (43) contains two arbitrary constants. These can be chosen so that at some particular time τ, q = 0 and dq/dt = 1. Call this solution q1(t, τ). Alternatively, the constants can be chosen so that q = 1 and dq/dt = 0 at time τ. Call this solution q2(t, τ). The response of the system at time t to a unit voltage impulse applied at some earlier time τ is q1(t, τ)/L, hence, by the superposition principle, we get a general solution of the inhomogeneous equation $q_1 (t) = {1 over L} int_{-infty}^t q_1(t, tau) E(tau) dtau. eqno{hbox{(1)}}$. View full abstract»

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  • A practical method of designing RC active filters

    Page(s): 74 - 85
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    IN THE FREQUENCY range below about 30 cps, the dissipation factors of available inductors are generally too large to permit the practical design of inductance-capacitance (LC) or resistance-inductance-capacitance (RLC) filter networks. The circuits described in the following pages were developed and collected to provide an alternative method of realizing sharp cut-off filters at very low frequencies. In many cases the active elements can be simple cathode-follower circuits that have stable gain, low output impedance and a large dynamic range. View full abstract»

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  • The potential analog applied to the synthesis of stagger-tuned filters

    Page(s): 86 - 96
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    Frequency Selectors THE SCIENCE of communications is built on waves, amplifiers, and frequency selectors, the last of these being the subject of this monograph. Half a century ago, the electrical resonator and the wave filter were in their early stages of evolution. As they became more familiar, they merged into a unified philosophy embracing frequency selectors of all kinds, not merely electrical but also mechanical, acoustical, etc. A family of frequency selectors having certain desirable properties is the immediate topic. View full abstract»

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  • Resistance-capacitance filter networks with single-component frequency-control

    Page(s): 97 - 102
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    IN RECENT years resistance-capacitance filters employing the Wein bridge, the parallel-T and other circuits have come into widespread use for the frequency control of oscillators and tuned amplifiers. Normally two or more ganged components are used for this purpose although a single component control has been used in several variants of an oscillator circuit described by Johnson.1–3 In certain applications, such as low frequency tuned amplifiers, two or more stages of filtering are desirable in order to achieve adequate selectivity together with quick response to changes in amplitude. The problem of ganging the many variable components then becomes formidable. For example, in an actual case which led to this investigation, a tuned amplifier was required to cover the range from 20 to 60 cps with two stages of filtering. A resistance-capacitance filter was sought for this purpose in which frequency could be controlled over a continuous range of 3 to 1 using a minimum number of variable components. The results of this investigation are reported in the present paper where several new bridge and ladder networks are described in which the balance frequency is controlled by means of a single variable component. View full abstract»

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  • Improved matrix and determinant methods for solving networks

    Page(s): 102 - 103
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  • The application of statistical methods to servomechanisms

    Page(s): 103
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  • Rational feedback and equalizer circuits or regulators with prescribed properties

    Page(s): 104
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  • Some passive networks under transient conditions

    Page(s): 104
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  • On the expansion of a network response into a series of orthogonal functions

    Page(s): 104 - 105
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  • Tchebycheff or Chebyshev?

    Page(s): 105
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