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Circuit Theory, IEEE Transactions on

Issue 1 • Date March 1965

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Displaying Results 1 - 25 of 40
  • Circuit Duality and the General Network Inverse

    Publication Year: 1965 , Page(s): 22 - 27
    Cited by:  Papers (7)
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    An n-terminal electrical network is specified by a double-centered equicofactor admittance matrix, which represents the current vector as a rank n - 1 linear transformation of the voltage vector. Several dual impedance descriptions are given in terms of baseset matrices and generalized inverses. The main result is the introduction of a unique general network inverse. View full abstract»

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  • A comment on 'An Active Network Equivalent to the Constant-Resistance Lattice'

    Publication Year: 1965 , Page(s): 131
    Cited by:  Papers (2)
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  • Distributional Stability Criteria

    Publication Year: 1965 , Page(s): 118 - 119
    Cited by:  Papers (3)
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  • Numerical Calculation of the Elliptic-Function Modular Constant

    Publication Year: 1965 , Page(s): 140 - 141
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  • A New Method of Solving the Accuracy Problem in Filter Design

    Publication Year: 1965 , Page(s): 144 - 145
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  • A Simple Algorithm for Listing All the Trees of a Graph

    Publication Year: 1965 , Page(s): 120
    Cited by:  Papers (10)  |  Patents (2)
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  • Note on Completely Partitionable Terminal Capacity Matrices

    Publication Year: 1965 , Page(s): 122 - 124
    Cited by:  Papers (1)
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  • An Iterative Approximation Procedure for Automatic Filter Synthesis

    Publication Year: 1965 , Page(s): 107 - 112
    Cited by:  Papers (19)
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    The design of m -derived image parameter filters, as well as the synthesis of Butterworth or Chebyshev pass band insertion-loss parameter filters with prescribed frequency-dependent minimum stop band attenuation, normally involves the use of graphical methods to find the necessary number and location of the attenuation poles. These methods are tedious and inaccurate. This paper describes an iterative approximation process, somewhat similar to Remez's second method [3], for the synthesis of low-pass and band-pass filters. The process is very fast and its programmed version (containing numerous options) fits into a 40,000-position computer memory. A brief analysis of the optimality and convergence of the procedure is included. Finally, the actual computer programs are described and some examples given. View full abstract»

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  • Stochastic Sampling of a Binary Random Process--II

    Publication Year: 1965 , Page(s): 39 - 43
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    A sampling scheme is considered in which a binary process with statistically independent axis-crossing intervals is sampled according to a given logic by a Poisson pulse process, thereby producing a new binary process. The results derived supplement the results of a previous paper on the sampling of a binary process by a random pulse process. The probability density of the time interval between successive zeros of the resulting binary process is derived, and it is shown how higher-order time interval statistics may be obtained. As an example, a periodic binary process is sampled by a Poisson pulse process, and it is shown that the first-order time interval density function of the resultant process is multimodal, which under certain limiting conditions becomes a symmetric density function. View full abstract»

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  • Some Remarks on Circuits Having the Same Transfer Function as the Constant-Resistance Lattice and the Derivation of All-Pass Networks

    Publication Year: 1965 , Page(s): 132 - 133
    Cited by:  Papers (2)
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  • The Measurement of Transistor Unilateral Gain

    Publication Year: 1965 , Page(s): 91 - 97
    Cited by:  Papers (3)
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    The unilateral gain defined by S. J. Mason, is a basic measure of the transfer activity of a two-port. It can be measured in a circuit made unilateral with lossless reciprocal elements. A general method of measurement is described, which in principle uses two reactances only; no transformers are required. The method has been realized in a coaxial-line circuit, and measurements have been made on a few transistors in the frequency range 100 to 900 Mc . The results confirm that the unilateral gain is indeed measured in this circuit. It is suggested that unilateral gain measurements are useful both for research into basic device performance and for the specification of power-amplifying ability. View full abstract»

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  • Every Passive Time-Invariant Linear n-Port has at least One 'H Matrix'

    Publication Year: 1965 , Page(s): 131 - 132
    Cited by:  Papers (7)
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  • A Stability Criterion for Linear Networks Containing Time-Varying Capacitors

    Publication Year: 1965 , Page(s): 2 - 11
    Cited by:  Papers (8)
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    A frequency-domain stability criterion is presented for networks containing linear, but not necessarily lumped, timeinvariant elements and an arbitrary finite number of linear timevarying capacitors. The criterion is applicable whether or not the capacitors vary periodically. In order to indicate the character of the result, consider the special but important case in which a passive lumped constant RLC network is terminated with a single time-varying capacitor with capacitance c(t) . We say that the overall network is stable if (and only if) for an arbitrary set of initial conditions at t = 0 , the voltage across the time-varying element both approaches zero as t\rightarrow \infty and is square-integrable on (0,\infty ) . Let Z(s) denote the driving-point impedance faced by the time-varying capacitor, and let m and M denote positive constants such that m < M and m \leq [c(t)]^{-1}\leq M for t \geq 0 . Then, assuming that Z(0) is finite and that Z(s) is not a reactance function, it is proved that the overall network is stable if for all real \omega , j\omega Z(j\omega ) takes on values outside the circle of radius (M - m) centered in the complexplane at [-(m + M), 0] . View full abstract»

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  • Dynamically Independent Equilibrium Equations for RLC Networks

    Publication Year: 1965 , Page(s): 82 - 85
    Cited by:  Papers (2)
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    This paper presents a systematic derivation of a system of first-order dynamically independent equilibrium equations for an RLC network. The dynamically independent equations are obtained from a set of topologically independent equilibrium equations which are written in terms of a judiciously chosen set of independent, current and voltage, network variables. It is thus shown that superfluous variables, which are the result of dynamic constraints on the network, can be eliminated by inspection. Finally a method for writing the dynamically independent equilibrium equations by inspection of the network is presented. Thus we show that by the above techniques the set of dynamically independent equations can be obtained with little more labor than the more conventional equilibrium equations whose variables are only topologically independent. View full abstract»

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  • On the Characterization and Measurement of Randomly Varying Filters

    Publication Year: 1965 , Page(s): 44 - 51
    Cited by:  Papers (3)
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    It is well known that time-invariant linear filters can be characterized by their impulse responses. In this paper, a method is presented for characterizing and measuring a class of randomly varying linear filters. The class of filters considered is constrained to have finite memory and bandwidth and is represented by a tapped delay fine with random tap multipliers having a stationary Gaussian multivariate distribution. The filter characterization allows the complete determination of the filter output statistics for any given deterministic input signal which is approximately time- and band-limited. These inputoutput relations are embodied in the filter mean and covariance transfer matrices. It is shown that these transfer matrices are observable in the sense that all of their coefficients are measurable, whereas the covariance matrix of the tap multipliers is not, in general, an observable. A measurement technique is described by which the transfer matrix coefficients can be determined. View full abstract»

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  • An Optimization Problem in Circuits

    Publication Year: 1965 , Page(s): 28 - 31
    Cited by:  Papers (2)
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    Let \eta be a linear, time-invariant, lumped two-port driven at its port 1 by a voltage source e. and loaded at its port 2 by a variable capacitor C . The values of C are restricted by C_{m}\leq \leq C_{m} , where C_{M} and C_{m} , are given positive constants. Given this inequality constraint on C , any initial state of \eta , a time interval [0, T] , and a performance criterion \phi it is shown that the law of variation of C as a function of time which maximizes the value taken by \phi at the state at time T is bang-bang, i.e., C(\cdot) is piecewise constant and takes only the values C_{m} and C_{M} . A subsidiary result as well as some interpretations are also given. View full abstract»

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  • Forced Oscillations in Nonlinear Systems with Hysteresis

    Publication Year: 1965 , Page(s): 52 - 58
    Cited by:  Papers (2)
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    The question of the existence of oscillations in nonlinear systems driven by periodic forces and their calculation, has been receiving considerable attention in circuit and system theory in connection with the problem of frequency conversion. The present paper deals with this question, with particular emphasis on subharmonic response, for systems possessing a general type of hysteresis property. View full abstract»

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  • A Note on Equiripple Functions Used in Filter Design

    Publication Year: 1965 , Page(s): 112 - 116
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    Equiripple rational functions used in filter design are discussed in the light of the algebraic theory of transformation of elliptic functions. Their solutions for order 5 and a number of their properties that seem to be new are given. View full abstract»

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  • Topological Analysis for Active Networks

    Publication Year: 1965 , Page(s): 85 - 91
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    It is shown that a general network determinant and its cofactors can be evaluated by means of "directed trees" and "directed two-trees". There is no sign problem. The products of such directed trees and directed two-trees will automatically give the correct signs. Furthermore, this new method can be applied to either the node-admittance matrix or the loop-impedance matrix. In case the given network is passive and contains no magnetic coupling, the digraph associated with the node-admittance matrix reduces to the original network; the directed trees and directed two-trees reduce to ordinary trees and two-trees, respectively View full abstract»

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  • Some Exactly Solvable Nonuniform RC Lines

    Publication Year: 1965 , Page(s): 141 - 142
    Cited by:  Papers (9)
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  • On the Periodic Solution of the van der Pol Equation

    Publication Year: 1965 , Page(s): 135 - 136
    Cited by:  Papers (1)
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  • A Simplified Cascade Synthesis of RC Transfer Functions

    Publication Year: 1965 , Page(s): 98 - 106
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    This paper presents a new cascade synthesis of RC transfer functions with an unspecified multiplying constant. The method is based on a topological identity for cascaded RLC twoports and a theorem on the realization of RC voltage transfer functions with a prescribed termination. Proofs of the topological identity and the realizability theorem are given. The minimal realization of a class of biquadratic transfer functions is investigated, and some sufficient conditions for a fiveelement realization are found. The use of these results in the present synthesis procedure yields a relatively simple realization of RC transfer functions having one pair of complex zeros and any number of real zeros in the left half-plane. Several numerical examples are given, and comparisons are made with the results obtained by other well-known methods. View full abstract»

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  • Properties of Microwave C-Sections

    Publication Year: 1965 , Page(s): 74 - 82
    Cited by:  Papers (14)
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    In this paper, it is shown that a lossless, three-wire system can act as a C-section in the Richards transformed complex frequency plane lamda[2] . Theoretical limitations on the realization of transmission zeros of such sections are derived. The cascade properties of these networks are also investigated. Specifically, a formulation of an insertion-loss function peculiar to the C -section is made. Finally, integral restrictions on the optimum broadbanding of C -sections, coaxial lines, and frequency sensitive loads are derived. It is hoped that the above treatment will enable the designer to treat the microwave C -section as an additional building block in filter synthesis. View full abstract»

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  • Some Tools for the Analysis and Representation of Linear Two-Port Networks

    Publication Year: 1965 , Page(s): 18 - 21
    Cited by:  Papers (3)
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    The so-called image quantities of a two-port network are often found useful when treating power flow and input impedance under different load conditions. The formal analogy between a symmetric reciprocal two-port network and a uniform transmission line is here extended to unsymmetric networks by means of a wave-symmetric transmission line model. If the network is nonreciprocal it can be decomposed into a reciprocal part cascaded with an antireciprocal transition having simple impedance and power transfer properties. It is further shown that by adding reactances in series with a two-port network its image impedances can be made either real or imaginary. The so reactively modified network has an image attentuation that directly determines the maximum power efficiency of the original network. View full abstract»

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  • Methods for Recovering a Random Waveform from a Finite Number of Samples

    Publication Year: 1965 , Page(s): 32 - 39
    Cited by:  Papers (6)
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    The reconstruction of a random waveform from finite data presents an interesting statistical problem, especially if practical constraints are imposed on the method of reconstruction. Consideration is given to the merits of Lagrange polynomial interpolation; RC filtering; linear, least-squares time-varying interpolation; and linear, least-squares, time-invariant interpolation. Numerical results for random waveforms having various correlation functions are presented. From these results a quantitative comparison of the merits of each of the interpolation procedures can be made. From a theoretical point of view one set of mathematical results is new, namely, those results associated with the optimum, linear, time-invariant interpolation of a finite number of samples. The analysis of this problem is complicated by the combination of the constraints of time invariance (i.e., the same interpolatory function is used for each sample) and a finite number of samples. Removal of either constraint makes the problem simpler and leads one to known results. View full abstract»

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