Showing papers in "IEEE Transactions on Circuit Theory in 1971"
TL;DR: In this article, the memristor is introduced as the fourth basic circuit element and an electromagnetic field interpretation of this relationship in terms of a quasi-static expansion of Maxwell's equations is presented.
Abstract: A new two-terminal circuit element-called the memristorcharacterized by a relationship between the charge q(t)\equiv \int_{-\infty}^{t} i(\tau) d \tau and the flux-linkage \varphi(t)\equiv \int_{- \infty}^{t} v(\tau) d \tau is introduced as the fourth basic circuit element. An electromagnetic field interpretation of this relationship in terms of a quasi-static expansion of Maxwell's equations is presented. Many circuit-theoretic properties of memistors are derived. It is shown that this element exhibits some peculiar behavior different from that exhibited by resistors, inductors, or capacitors. These properties lead to a number of unique applications which cannot be realized with RLC networks alone. Although a physical memristor device without internal power supply has not yet been discovered, operational laboratory models have been built with the help of active circuits. Experimental results are presented to demonstrate the properties and potential applications of memristors.
7,585Â citations
TL;DR: A unified method for handling the mixed differential and algebraic equations of the type that commonly occur in the transient analysis of large networks or in continuous system simulation is discussed.
Abstract: A unified method for handling the mixed differential and algebraic equations of the type that commonly occur in the transient analysis of large networks or in continuous system simulation is discussed. The first part of the paper is a brief review of existing techniques of handling initial value problems for stiff ordinary differential equations written in the standard form y' f(y, t) . In the second part one of these techniques is applied to the problem F(y, y', t)=0 . This may be either a differential or an algebraic equation as \partial F/ \partial y' is nonzero or zero. It will represent a mixed system when vectors F and y represent components of a system. The method lends itself to the use of sparse matrix techniques when the problem is sparse.
636Â citations
IBM1
TL;DR: The tableau approach to automated network design optimization via implicit, variable order, variable time-step integration, and adjoint sensitivity computation is described and the bulk of computation and program complexity is located in the sparse matrix routines.
Abstract: The tableau approach to automated network design optimization via implicit, variable order, variable time-step integration, and adjoint sensitivity computation is described. In this approach, the only matrix operation required is that of repeatedly solving linear algebraic equations of fixed sparsity structure. Required partial derivatives and numerical integration is done at the branch level leading to a simple input language, complete generality and maximum sparsity of the characteristic coefficient matrix. The bulk of computation and program complexity is thus located in the sparse matrix routines; described herein are the routines OPTORD and 1-2-3 GNSO. These routines account for variability type of the matrix elements in producing a machine code for solution of Ax=b in nested iterations for which a weighted sum of total operations count and round-off error incurred in the optimization is minimized.
305Â citations
TL;DR: In this article, a solution obtained by a direct approximation procedure in the z plane is presented, where the denominator of the transfer function turns out to be a Gaussian hypergeometric function, connected with the Legendre functions.
Abstract: A well-known limitation of the recursive digital filter, when compared to the nonrecursive filter, is its incapability of having a strictly linear phase characteristic; thus it may only approximate a constant group delay. For the analog filters the choice of the maximally flat criterion leads to the use of the Bessel polynomials. Yet digital approximations of these continuous filter functions are inadequate to yield the true maximally flat delay approximation of the recursive filters. Our purpose is to provide for the problem at hand a solution obtained by a direct approximation procedure in the z plane. The denominator of the transfer function turns out to be a Gaussian hypergeometric function, more particularly connected with the Legendre functions. The stability of the filters is discussed and some numerical results in regard to the amplitude and phase responses as well as the pole loci are given.
247Â citations
TL;DR: In this paper, a comprehensive report on the Biquad, an active topology based on analog computer concepts, is given, where the authors describe the electrical characteristics of Biquads that make it a manufacturable realization for precision networks.
Abstract: The use of active elements in linear networks offers new degrees of freedom to both network and system designers. A comprehensive report on the Biquad, an active topology based on analog computer concepts, is given. We describe the electrical characteristics of the Biquad that make it a manufacturable realization for precision networks. Analysis and experimental data describe the dependence of Biquad performance on nonideal operational amplifiers. Compensation techniques are derived which allow high- Q operation at several hundred kilohertz with existing devices. The 8-V rms signal capacity and 80-dB dynamic range of the voice-frequency Biquad are illustrated.
237Â citations
TL;DR: The calculation of the statistical mean-squared error at the output of the filter is discussed in detail and some of the approaches used in investigating them are reviewed.
Abstract: The accuracy of a digital filter is limited by the finite word length used in its implementation. Techniques have been developed to analyze this problem. Good agreement between the theoretical and experimental results has been reported. This paper discusses some of these accuracy problems and reviews some of the approaches used in investigating them. The calculation of the statistical mean-squared error at the output of the filter is discussed in detail.
217Â citations
TL;DR: In this paper, a new class of selective non-recursive digital filters with a maximally flat frequency response in the passband and stopband is introduced, based on a special solution of the general Hermite polynomial interpolation and allows computation of the parameters of these filters in closed form.
Abstract: A new class of selective nonrecursive digital filters with a maximally flat frequency response in the passband and stopband is introduced. The proposed design method is based on a special solution of the general Hermite polynomial interpolation and allows computation of the parameters of these filters in closed form. Therefore it yields some advantage over numerical iterative methods. Design examples are given and an extension to the design of unsymmetrical bandpass systems is made.
205Â citations
TL;DR: It is shown that this approach provides a very general family of filters that includes both the conventional scalar implementation and batch processing, and is based on a matrix representation of convolution and results in a state-variable description with block feedback.
Abstract: A theory for implementation of recursive digital filters that process signals by blocks is presented. It is shown that this approach provides a very general family of filters that includes both the conventional scalar implementation and batch processing. The approach is based on a matrix representation of convolution and results in a state-variable description with block feedback. An eigenvalue analysis guarantees stability of the realization and indicates a reduction in sensitivity to roundoff and coefficient accuracy.
171Â citations
TL;DR: An alternate derivation of the dual condition (called the severance-value condition in this article ) to feasibility of the multicommodity flow problem is given by graph theoretical arguments.
Abstract: An alternate derivation of the dual condition (called the severance-value condition in this paper) to feasibility of the multicommodity flow problem is given by graph theoretical arguments That is, a multicommodity flow of given requirements is feasible if and only if the capacity of every severance is no less than its least capacity consumption for the flow A severance is a set of the edges with nonnegative integer coefficients Even when the severance-value condition is satisfied by a certain finite subset of severances, the multicommodity flow is shown to be still feasible if each requirement is allowed to be reduced by an appropriate amount \mu This truncation allowance \mu is estimated in terms of the network topology and the capacity function
138Â citations
TL;DR: A deterministic analysis of limit-cycle oscillations, which occur in fixed-point implementations of recursive digital filters due to roundoff and truncation quantization after multiplication, is performed in this paper.
Abstract: A deterministic analysis of limit-cycle oscillations, which occur in fixed-point implementations of recursive digital filters due to roundoff and truncation quantization after multiplication, is performed. Amplitude bounds, based upon a correlated (nonstochastic) signal approach using Lyapunov's direct method, as well as a general matrix formulation for zero-input limit cycles, are derived and tested for the two-pole filter. The limit cycles are represented on a successive-value phase-plane-type diagram from which certain symmetry properties are derived. The results are extended to include limit cycles under input-signal conditions.
107Â citations
TL;DR: A node renumbering algorithm which is specifically directed at preserving the sparse structure of nodal admittance matrices during the solution by Gaussian elimination is described in detail.
Abstract: Sparse matrix storage and solution techniques are used extensively in solving very large systems of hundreds of linear equations which arise in the analysis of multiply interconnected physical systems These techniques have often been overlooked in the analysis of relatively small electric networks even though their use can result in very significant improvements in computer storage requirements and execution times The time savings is particularly noticeable when many solutions for the same circuit with different parameter values are required particular sparse matrix storage, reordering, and solution technique is described A node renumbering algorithm which is specifically directed at preserving the sparse structure of nodal admittance matrices during the solution by Gaussian elimination is described in detail Computer flow charts for the renumbering are included along with specific circuit examples which compare the relative computational effort required for sparse solution versus full matrix solution
TL;DR: Two efficient computer algorithms are presented for finding the dc solutions of resistive nonlinear networks containing two-terminal linear and nonlinear resistors, independent dc voltage and current sources, and linear controlled sources.
Abstract: Two efficient computer algorithms are presented for finding the dc solutions of resistive nonlinear networks containing two-terminal linear and nonlinear resistors, independent dc voltage and current sources, and linear controlled sources. The first algorithm is designed specifically for networks with multiple solutions, while the second algorithm is designed for networks with a unique solution. The first algorithm is based on the sign of the hybrid parameters associated with the linear n-port portion of the network. The second algorithm is a piecewise-linear version of the Newton-Raphson method, but it differs from the differentiable version in two important aspects. First, rather than diverging to \pm \infty , as in the usual case, the divergence phenomenon of the piecewise-linear algorithm takes the form of a cyclic repetition of two or more segment combinations. Second, the iteration formula depends not directly on the solution at the preceding iteration, but on the updated segment combination. These observations lead to an algorithm which assures that the piecewise-linear version of Newton-Raphson formula will always converge. Moreover, an important connection between the two algorithms is established on the basis that the iteration formula for the second algorithm is identical to the network equations associated with the first algorithm.
TL;DR: In this paper, the concept of the multipurpose active filter was introduced. But the Biquad topology offers unique flexibility compared to other active realizations, for example, switchable and adaptive filters are easily realized and different functions (e.g., bandpass and band-reject) are obtainable simultaneously from the same structure.
Abstract: While the electrical performance of the Biquad insures that active filter designs using this structure will be useful over a wide range of conditions, the Biquad topology offers unique flexibility compared to other active realizations. We now present the concept of the multipurpose active filter. For example, switchable and adaptive filters are easily realized and different functions (e.g., bandpass and band-reject) are obtainable simultaneously from the same structure.
TL;DR: In this paper, it was shown that if a set of cofactors of the Jacobian matrix satisfies a "ratio condition," the network has a unique solution, and the class of matrices under consideration is a generalization of the class P recently introduced by Fiedler and Ptak, and includes the familiar uniformly positive-definite matrix as a special case.
Abstract: This paper deals with nonlinear networks which can be characterized by the equation f(x) = y , where f(\cdot) maps the real Euclidean n -space R^{n} into itself and is assumed to be continuously differentiable x is a point in R^{n} and represents a set of chosen network variables, and y is an arbitrary point in R^{n} and represents the input to the network. The authors derive sufficient conditions for the existence of a unique solution of the equation for all y \in R^{n} in terms of the Jacobian matrix \partial f/ \partial x . It is shown that if a set of cofactors of the Jacobian matrix satisfies a "ratio condition," the network has a unique solution. The class of matrices under consideration is a generalization of the class P recently introduced by Fiedler and Ptak, and it includes the familiar uniformly positive-definite matrix as a special case.
TL;DR: In this article, the differential voltage controlled current source (DVCCS) was shown to yield in a relatively simple manner and in integrated form all components needed for linear circuit construction.
Abstract: In conjunction with the capacitor, the differential voltage controlled current source (DVCCS) is shown to yield in a relatively simple manner and in integrated form all components needed for linear circuit construction. The effects of dissipative losses in the DVCCS are tabulated for several configurations. Finally, a new building block having two outputs is introduced.
TL;DR: A concise relationship is developed between the amount of digital filter hardware required and the sample rate, clock rate, data word length, number of channels being multiplexed, and order of the filter.
Abstract: In keeping with the trend toward greater use of digital circuits for signal processing, a project was undertaken to realize an important telecommunication function using as great a proportion of digital hardware as possible. The function in question concerns the translation between the traditional analog frequency division multiplex (FDM) format and the newer digital time division multiplex (TDM) format. This paper describes the design of the digital filters for such a translating device and discusses some of the problems encountered in the hardware realization of these filters. In particular, a concise relationship is developed between the amount of digital filter hardware required and the sample rate, clock (bit) rate, data word length, number of channels being multiplexed, and order of the filter. This relationship is then used as the basis of comparison between various methods of accomplishing the desired function.
TL;DR: In this paper, a plausible set of network laws are formulated and two main theorems are proved for infinite networks of resistors, namely, in an infinite network consisting of nonnegative resistors (with no short circuits) and a finite number of sources, there exists a unique current flow.
Abstract: There are several examples of infinite networks of resistors; it is always assumed that a unique current exists as a consequence of Kirchhoff's laws. Actually, unlike the situation in finite networks, these laws are insufficient to determine a unique current. A plausible set of network laws are formulated and two main theorems are proved. 1) In an infinite network consisting of nonnegative resistors (with no short circuits) and a finite number of sources, there exists a unique current flow. 2) This current flow is the limit of the unique current flows in finite, subnetworks that approximate the whole network. Methods of algebraic topology and Hilbert space theory are used in the formulations and proofs.
TL;DR: In this article, a new statistical multiparameter measure of sensitivity is presented, which realistically accounts for component tolerances and component tolerance correlations and is shown to be particularly useful in the design of integrated circuits.
Abstract: A new statistical multiparameter measure of sensitivity is presented. The new measure realistically accounts for component tolerances and component tolerance correlations and is shown to be particularly useful in the design of integrated circuits. For illustration the measure is used to analyze several high- Q low-sensitivity networks. It is shown that for high- Q networks the new measure is readily interpreted in terms of the Q and center frequency sensitivities of the circuit elements. The measure is also generalized for high- Q analysis to account for the error in realization due to the ampliler pole as well as the element variations. This enables an evaluation of the circuit response versus center frequency to be performed.
TL;DR: In this article, all-pole recursive digital low-pass filters approximating a constant group delay in an equal-ripple sense are described, where the equalripple conditions are given by a system of nonlinear equations in the poles of the transfer function.
Abstract: All-pole recursive digital low-pass filters approximating a constant group delay in an equal-ripple sense are described. The equalripple conditions are given by a system of nonlinear equations in the poles of the transfer function. The closed-form solution obtained for a particular value of the cutoff frequency yields good first approximations for the iterative procedure required in the general case. The set of approximated delays and ripples leading to realizable filters is discussed. Numerical examples illustrating the procedure are included.
TL;DR: Two design concepts are discussed which have been implemented as new computer-aided design tools of large-change sensitivities which are a significant departure from the classical first-order sensitivities and of a performance contour which is, in effect, a second-order largechange sensitivity.
Abstract: Two design concepts are discussed which have been implemented as new computer-aided design tools. The first concept is that of large-change sensitivities which are a significant departure from the classical first-order sensitivities. The second concept is that of a performance contour which is, in effect, a second-order largechange sensitivity. The information provided by large-change sensitivities and performance contours is applicable in the phase of design after an acceptable nominal design has been found. Applications of this information to desensitize a design, to specify tolerances, and to indicate parameter correlation with respect to the performance criteria are discussed. The correlation information is useful not only in specifying tuning component matching but also in determining whether a design is consistent with expected statistical correlations in manufacture or in the field. Two real-world examples, some useful properties of contours, and a brief description of the program are included.
TL;DR: A survey is made of the principal techniques, procedures, and routines that are used in present programs for computeraided circuit analysis.
Abstract: A survey is made of the principal techniques, procedures, and routines that are used in present programs for computeraided circuit analysis. Programs (simulators) are reviewed and selected features compared for the four major classes of circuit analysis: linear dc and ac, nonlinear dc, nonlinear transient, and linear pole zero.
TL;DR: An automatic design package has been developed, and examples of computer implemented designs are presented, regarding circuit design algorithms made to correspond to unconstrained minimization algorithms.
Abstract: Upon defining a suitable scalar performance index to measure the error between desired and actual bias levels in a given circuit configuration, well-known unconstrained minimization algorithms may be made to correspond to circuit design algorithms. The design parameters for the problem considered are taken here to be a subset of the circuit resistance values. An automatic design package has been developed, and examples of computer implemented designs are presented.
TL;DR: A completely topological algorithm for determining a minimal essential set (minimum feedback vertex set) of a linear oriented graph is presented and is a modified version of the well-known McCluskey method for the prime implicant problem of switching theory.
Abstract: A completely topological algorithm for determining a minimal essential set (minimum feedback vertex set) of a linear oriented graph is presented. From a logical point of view, the algorithm is a modified version of the well-known McCluskey method for the prime implicant problem of switching theory. From a computational point of view, it avoids the need of the covering table, i.e., the need of generating the set of the elementary circuits of the graph.
TL;DR: In this article, a recurrence relation for the number of spanning trees f(n) in the wheel W{k, where n \geq 3, is obtained as f( n+1)-f(n)=L 2 n + 1 + 1, where f(3)=16 and where L is the k th number in the Lucas series.
Abstract: A recurrence relation for the number of spanning trees f(n) in the wheel W_{k}, where n \geq 3 , is obtained as f(n+1)-f(n)=L_{2^{n}+1}, where f(3)=16 and where L_{k} is the k th number in the Lucas series 1, 3, 4, 7, \cdots , L_{k}, \cdots , where L_{k} = L_{k+1} L_{k-1} for k > 1 . Alternately, f(n) =L_{k}^{2} - 4 \delta where \delta = 0 for n odd and 1 for n even, thus confirming f(n) as a square number for n odd and serving to verify a previous finding in 1969 by Sedlacek that f(n)=((3 + \sqrt{5})^{n} + (3 - \sqrt{5})^{n}/2^{n}-2 .
TL;DR: In this article, an RC active-network synthesis method described by Bruton for the realization of low-pass filters is extended to the case of bandpass filters, which use frequency-dependent negative-resistance (conductance) elements as active elements, and these can be realized by using generalized-immittance converters (GICs).
Abstract: An RC -active-network synthesis method described by Bruton for the realization of low-pass filters is extended to the case of bandpass filters. Networks are obtained which use frequency-dependent negative-resistance (conductance) elements as active elements, and these can be realized by using generalized-immittance converters (GICs). In turn, GICs can be implemented by using operational amplifiers. The method is illustrated by designing a sixth-order bandpass elliptic filter; experimental results are also given.
TL;DR: In this paper, the authors extended the mathematical representation of the short-time spectral analysis from the case of uniform bandpass filters (that is, filters having the same complex envelope) to non-uniform filters, where the signal taken up to the observation time appears weighted by a function depending on the frequency of analysis.
Abstract: The mathematical representation of the short-time spectral analysis is extended from the case of uniform bandpass filters (that is, filters having the same complex envelope) to the case of nonuniform filters (that is, filters whose complex envelope depends upon their center frequency). This leads to an integral transform, formally similar to the Fourier transform, where the signal taken up to the observation time appears weighted by a function (namely, the complex envelope) depending on the frequency of analysis. Of course, for every choice of such a complex envelope (or of the equivalent set of filters), one has a corresponding integral transform to deal with. The particular case of complex envelopes as functions of the time-frequency product is studied here because of its great physical interest (it applies, for instance, to many existing "real-time audio analyzers"). The corresponding integral transform is shown to have two remarkable properties: 1) it admits an inverse integral transform; 2) it is "form invariant" under linear time scaling of the signal, and no other integral transform (that is, no other class of complex envelopes, even frequency independent) shares this property. The physical significance of such results is discussed, together with some ideas for applications and further theoretical work.