Showing papers in "IEEE Transactions on Circuit Theory in 1972"
TL;DR: An efficient procedure for the design of finite-length impulse response filters with linear phase is presented, which obtains the optimum Chebyshev approximation on separate intervals corresponding to passbands and/or stopbands.
Abstract: An efficient procedure for the design of finite-length impulse response filters with linear phase is presented. The algorithm obtains the optimum Chebyshev approximation on separate intervals corresponding to passbands and/or stopbands, and is capable of designing very long filters. This approach allows the exact specification of arbitrary band-edge frequencies as opposed to previous algorithms which could not directly control pass- and stopband locations and could only obtain (N - 1)/2 different band-edge locations for a length N low-pass filter, for fixed \delta_{1} and \delta_{2} . As an aid in practical application of the algorithm, several graphs are included to show relations among the parameters of filter length, transition width, band-edge frequencies, passband ripple, and stopband attenuation.
806 citations
TL;DR: A Newton algorithm is defined which in the neighborhood of an orbit converges to it rapidly and gives a precise value for the period T of this oscillation.
Abstract: In the computer-aided analysis of nonlinear autonomous oscillators, the steady-state periodic response is usually found by integrating the system equations from some initial state until the transient response appears to be negligible. In lightly damped systems, convergence to the steady-state response is very slow, and this integration could extend over many periods making the computation costly. Also, one is never sure if a stable orbit exists or if the response might eventually decay to a singular point. If a stable orbit does exist, sometimes it is difficult to determine the period T of the orbit. In this paper, a Newton algorithm is defined which in the neighborhood of an orbit converges to it rapidly and gives a precise value for the period T of this oscillation. This algorithm represents a substantial step forward in the analysis of nonlinear systems. In addition, the algorithm meshes easily with most computer-aided circuit-analysis programs, and the initial iterates give information on the transient behavior of the circuit.
202 citations
TL;DR: In this paper, the measure of a matrix is used to bound solutions of ordinary differential equations, bound the computer solution by the backward Euler method, and bound the accumulated truncation error.
Abstract: The measure of a matrix is used to, first, bound solutions of ordinary differential equations, bound the computer solution by the backward Euler method, and bound the accumulated truncation error; second, to give conditions for the existence and uniqueness of a dc operating point; third, to determine a convergence region for the Newton-Raphson technique and establish its convergence properties. The unifying idea of the paper is the use of the measure of a matrix.
167 citations
TL;DR: In this paper, the pseudopower, pseudopassivity and pseudolosslessness properties of wave digital filters have been proved in a direct way by introducing the concepts of pseudo power, pseudo passivity, and pseudo possivity.
Abstract: 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 pseudolosslessness, corresponding to the familiar concepts of power, passivity, and losslessness in classical circuits.
161 citations
TL;DR: In this paper, the authors demonstrate the utility of the function A +B \sqrt{s} for approximating the coaxial line series impedance (skin effect) in applications to transient analysis, and demonstrate that the parameters A and B can be adjusted to provide functions of time which closely approximate the actual time domain response over different intervals.
Abstract: The purpose of this paper is to demonstrate the utility of the function A +B \sqrt{s} for approximating the coaxial line series impedance (skin effect) in applications to transient analysis. The time domain response expansions of Holt are modified in terms of two adjustable parameters which replace the physical parameters R and K . The modified expansions are truncated to yield condensed expressions useful for analysis and design. Two types of terminations are considered: 1) nonreflective, terminated in the characteristic impedance Z_{0}(s) , and 2) doubly reflective, sending and receiving ends each terminated in the nominal characteristic impedance R_{0} = \lim_{s \rightarrow \infty} Z_{0}(s) = \sqrt{L/C} . Experimental data are presented on the frequency and time domain insertion responses of three commercial cables: RG 5B/U-68.6 m (225 ft), RG 21/U-96.8 m (317 ft), and RG 58A/U-137 m (450 ft). Theoretical and experimental time domain responses for the sending- and receiving-end voltages are compared over the time interval from the order of 10 ns to that of 10 \mu s. It is demonstrated that the parameters A and B can be adjusted to provide functions of time which closely approximate the actual time domain response over different intervals.
127 citations
TL;DR: In this paper, a new mathematical model of hysteresis, based upon the previous work of Chun and Stromsmoe, is introduced, which not only provides for hystresis loops at frequencies down to dc but allows for extensive control over higher frequency behavior.
Abstract: A new mathematical model of hysteresis, based upon the previous work of Chun and Stromsmoe, is introduced. The model not only provides for hysteresis loops at frequencies down to dc but allows for extensive control over higher frequency behavior. Loop widening with increased frequency can be included, as well as loop narrowing (a phenomenon present in the i-v curves of fluorescent lamps). Loop widening can be reduced to insignificant amounts beyond an upper threshold or can be eliminated all together. Other behavior with frequency variation can be provided once the model is understood. Applications of the model include the simulation of ferrite "memory" cells and the analysis of hysteretic systems capable of operating at arbitrarily low frequencies.
124 citations
TL;DR: This paper characterizes the amplifier by a one-pole rolloff model and discusses the ensuing limitations on four widely used low-pass realizations.
Abstract: There are many active RC networks that implement the low-pass filter characteristic. It has been the common practice to compare these networks with regard to passive element sensitivities while assuming the amplifier to be ideal. Such an assumption gives results that disagree with experimental observations, particularly when the pole magnitudes are large. This paper characterizes the amplifier by a one-pole rolloff model and discusses the ensuing limitations on four widely used low-pass realizations. The amplifier's open-loop gain-bandwidth product is used as a parameter to generate complex-pole loci that graphically display the effect of the nonideal amplifier. The expression of the slope of these curves at the nominal pole positions is derived and first-order estimates for the resulting changes in the \omega_{0} and Q of the poles are given. These expressions can be used to determine the upper bound on the frequency \omega_{0} that these networks can effectively realize. Experimental results agree with the predicted changes. The methods have also been applied to high-pass, bandpass, band-reject, and other realizations.
123 citations
TL;DR: An exact analysis of linear circuits containing periodically operated switches with exponentially modulated cisoidal inputs using the state-space approach is presented and explicit closed form solutions for both the time and frequency domain suitable for digital computation are obtained.
Abstract: An exact analysis of linear circuits containing periodically operated switches with exponentially modulated cisoidal inputs using the state-space approach is presented. Explicit closed form solutions for both the time and frequency domain suitable for digital computation are obtained. The analysis is applicable to any circuit configuration and can handle cases in which discontinuities in state variables occur at the switching instants. Applications of this analysis to the design of switched filters and modulators are discussed.
121 citations
TL;DR: An efficient computational algorithm which is especially suited for analysis of large piecewise-linear networks is demonstrated and new theorems on the existence of solutions together with a convergent method for obtaining at least one of the solutions are given.
Abstract: Nonlinear resistive networks, which can be characterized by the equation f(x) =y , where f(\cdot) is a continuous piecewise linear mapping of R^{n} into itself, are discussed. 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. New theorems on the existence of solutions together with a convergent method for obtaining at least one of the solutions are given. Also dealt with is an efficient computational algorithm which is especially suited for analysis of large piecewise-linear networks. The effectiveness of the method in terms of the amount of computation and data handling and storage is demonstrated.
81 citations
TL;DR: A simple proof of global inverse function theorem in R n is given in this article, where a global homeomorphic version of the theorem is proved first and then a global diffeomorphic version is presented.
Abstract: A simple proof of global inverse function theorem in R^{n} is given. A global homeomorphic version of the theorem is proved first. A global diffeomorphic version follows by an application of the classical local inverse function theorem.
80 citations
TL;DR: In this article, the trajectory bounds of discontinuous systems are treated within a stability framework, where stability is defined in terms of prespecified subsets of the state space over an infinite time interval (practical stability) and over a finite time interval(finite-time stability).
Abstract: The trajectory bounds of discontinuous systems are treated within a stability framework. In doing so, stability is defined in terms of prespecified subsets of the state space over an infinite time interval (practical stability) and over a finite time interval (finite-time stability). The discontinuous systems considered are those which are described by ordinary discontinuous differential equations which may be autonomous or nonautonomous, linear or nonlinear. In all cases it is assumed that the differential equation possesses solutions in the sense of Filippov. The results obtained yield sufficient conditions for practical stability and finite-time stability. In order to demonstrate application of the methods advanced, specific examples are considered.
TL;DR: Tolerance assignment in linear networks on a worstcase basis is treated as a nonlinear programming problem with the sequential unconstrained minimization technique of Fiacco and McCormick employed as a solution mechanism with network behavior being evaluated by means of a large-change sensitivity model.
Abstract: Tolerance assignment in linear networks on a worstcase basis is treated as a nonlinear programming problem. The sequential unconstrained minimization technique of Fiacco and McCormick is employed as a solution mechanism with network behavior being evaluated by means of a large-change sensitivity model. The solution mechanism also yields worst-case responses at the constraint frequencies. Examples are presented and a comparison is made with the method proposed by Karafin.
TL;DR: A class of trigonometric polynomials p(x) = \sum_{n=-N}^{N} a_{n} e^{j n \pi x} of unit energy is introduced such that their energy concentration \alpha = \int_{-e}^{e} p^{2} (x) dx in a specified interval (- \epsilon, \ep silon) is maximum.
Abstract: A class of trigonometric polynomials p(x) = \sum_{n=-N}^{N} a_{n} e^{j n \pi x} of unit energy is introduced such that their energy concentration \alpha = \int_{-e}^{e} p^{2}(x) dx in a specified interval (- \epsilon, \epsilon) is maximum. It is shown that the coefficients a_{n} must be the eigenvectors of the system \sum_{m=-N}^{N} \frac{\sin (n - m)\pi \epsilon}{(n - m)\epsilon} a_{m} = \lambda a_{n} . corresponding to the maximum eigenvalue X. These polynomials are determined for N = 1, \cdots , 10 and \epsilon = 0.025, \cdots , 0.5 . The resulting family of periodic functions forms the discrete version of the familiar prolate spheroidal wave functions.
TL;DR: In this article, it was shown that roundoff noise can be interpreted as coefficient fluctuation, and any design method requiring fewer digits for the multipliers makes it possible to increase the signal word lengths without an increase in overall complexity.
Abstract: It is shown that for digital filters there exists a direct and an indirect connection between the generation of roundoff noise by a multiplier and the effect that the coefficient word length limitation of this multiplier has upon the response characteristic: rounding can be interpreted as coefficient fluctuation, and any design method requiring fewer digits for the multipliers makes it possible to increase the signal word lengths without an increase in overall complexity. A mathematical formula expressing the noise-to-signal ratio due to roundoff noise generated by a sinusoidal signal, in terms of the attenuation sensitivity, is obtained. It confirms why digital filters with reduced attenuation sensitivity, such as wave digital filters, also produce less roundoff noise.
TL;DR: In this paper, the response of a nonlinear time-varying coupled RLC network starting from a given operating point is considered, and the response is modeled as motion occurring in a differentiable manifold π in R 2b ∆ + ∆ times R +, where b is the number of branches.
Abstract: The response of a nonlinear time-varying coupled RLC network starting from a given operating point is considered. We view the response as motion occurring in a differentiable manifold \Sigma in R^{2b} \times R_{+} , where b is the number of branches. We impose two basic manifold conditions (MC) on the network. First, the resistor characteristics are required to be a manifold \Lambda . Second, the resistor characteristics and their connections are such that the set of branch voltages and branch currents satisfying both the Kirchhoff laws and the resistor characteristics is a manifold \Sigma . We then show that under the conditions imposed on the RLC elements and the topology of the network, the network has a unique response specified by a flow on \Sigma if and only if the capacitor voltages, inductor currents, and time constitute a parametrization for \Sigma . Finally, we show that our conditions include as special cases the determinateness conditions previously obtained by several authors.
TL;DR: This work considers a digital filter model in which the effects of quantization (i.e., roundoff, truncation, etc.) are included, and is sufficiently general in character that consideration is given to a wide variety of types of arithmetic.
Abstract: In this paper we study the control of the amplitude of () EA limit cycles due to adder overflow which occur in the zero-input response of second-order digital filters. We consider a digital filter model in which the effects of quantization (i.e., roundoff, truncation, etc.) are included. Our analysis is sufficiently general in character that consideration is given to a wide variety of types of arithmetic. In addition to our new results, virtually all of the previously known results concerning such limit cycles also follow from our analysis. Since our results are all obtained by a single technique, the work thus tends to unify the body of knowledge in this area. Furthermore, our technique is easily generalized, and there is reason to believe that such generalizations could also be profitably applied to the analysis of higher order systems.
TL;DR: In this paper, 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.
Abstract: 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-test frequency cases. In both cases the linear independence of the rows or columns of certain matrices may be used to determine appropriate test points and test frequencies.
TL;DR: In this article, the authors present necessary and sufficient conditions for a driving-point function to represent the input impedance of a resistor-terminated cascade of generic types of microwave filters.
Abstract: 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 discovering necessary and sufficient conditions for a driving-point function to represent the input impedance of a resistor-terminated cascade of generic type. A simple decisive solution with the aid of the 2-variable positive-real concept is offered by 1) introducing the 1-variable real polynomial "resistivity matrix" associated with the driving-point function and 2) demonstrating that it must satisfy a fundamental structure constraint. Lastly, in addition to elucidating several important corollaries, the class of characteristic polynomials of all such microwave filters is given a description which reveals the difficulties to be overcome before an exact filter design procedure can be achieved. We wish to emphasize that the necessary and sufficient conditions for realizability presented in this paper are not algorithmic in character but explicit. To make the results accessible to as wide an audience as possible we have adopted a leisurely tutorial style with considerable attention paid to some of the more relevant background material.
TL;DR: In this article, two floating negative-impedance converters (FNICs) using operational amplifers are proposed, each circuit uses a common grounded power supply and can simulate floating negative elements.
Abstract: Two floating negative-impedance converters (FNICs) using operational amplifers are proposed. Each circuit uses a common-grounded power supply and can simulate floating negative elements. The stability properties of the two circuits are examined. In line with other published grounded NICs, one of the ports is found to be short-circuit stable and the other open-circuit stable. The application of the FNICs for the design of two-directional constant-resistance amplifiers is considered.
TL;DR: A unified discussion of least p th approximation as it relates to optimal computer-aided design of networks and systems is presented, finding a wider variety of design problems and a wider range of specifications should now be tractable.
Abstract: A unified discussion of least p th approximation as it relates to optimal computer-aided design of networks and systems is presented. General objective functions are proposed and their properties discussed. The main result is that a wider variety of design problems and a wider range of specifications than appear to have been considered previously from the least pth point of view should now be tractable.
TL;DR: In this paper, it was shown that there is no square integrable impulse response that is optimum in Chebyshev's sense since the van der Maas function can be regarded as the limit of a sequence of square integral functions.
Abstract: The optimum impulse response of a band-limited system, viz., the van der Maas function, is derived from considerations based on the theory of entire functions. The ^{2} version of the optimization problem is also discussed. In particular, it is shown that there is no square integrable impulse response that is optimum in Chebyshev's sense since the van der Maas function, which is not square integrable, can be regarded as the limit of a sequence of square integrable functions. Some modified L^{2} versions of the optimization problem, in which weighted square integral measures of the sidelobes are prescribed, are also described.
TL;DR: The wire routing problem in the layout of integrated circuits is formulated as Steiner's problem in graphs and a suboptimal algorithm is described for the problem based on the branch-and-bound method.
Abstract: The wire routing problem in the layout of integrated circuits is formulated as Steiner's problem in graphs. A suboptimal algorithm is described for the problem. The algorithm is based on the branch-and-bound method. The result of the algorithm applied to several examples is also described.
TL;DR: In this article, an optimum topological method for matrix signal flow graphs is presented, in which the gain expression has the minimum number of distinct inverses, and is obtained from the structure of the graph without graph reductions.
Abstract: Some properties of matrix signal flow graphs are investigated and an optimum topological method for evaluating the graph gains is presented. The method is optimum in the sense that the gain expression has the minimum number of distinct inverses. It is topological in the sense that the gain expression is obtained from the structure of the graph without graph reductions.
TL;DR: In this paper, a method of generating sinusoidal voltage-controlled oscillators (VCO) and/or current controlled oscillators suitable for integrated circuits is presented, where each oscillator circuit contains two fixed resistances, two fixed capacitances, and amplifiers.
Abstract: Sinusoidal oscillators with large tuning range and small harmonic distortion offer various applications in integrated electronics. In this paper a method of generating sinusoidal voltage-controlled oscillators (VCO) and/or current-controlled oscillators suitable for integrated circuits is presented. Each oscillator circuit contains two fixed resistances, two fixed capacitances, and amplifiers. It is shown that one amplifier can be used to confine the natural frequencies of the circuit on the j axis of the complex frequency plane, and the other amplifier (or amplifiers) can be used to effectively increase or decrease the RC time constant and hence change the oscillation frequencies.
TL;DR: In this article, the voltage, current, and power constraints on the elements in a dc-to-dc conversion network were derived using graph theorems in graph theory, which have received little use in circuit theory.
Abstract: 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 expected that they will prove useful in other areas of circuit theory.
TL;DR: In this article, the problem of finding minimal or quasi-minimal essential sets in directed graphs is dealt with, and a modified algorithm for minimal essential sets is pointed out and a new algorithm is proposed.
Abstract: This work deals with the problem of finding minimal or quasi-minimal essential sets in directed graphs. Mainly based on a topological approach recently suggested, a modified algorithm for minimal essential sets is pointed out, and a new algorithm is proposed for quasi-minimal essential sets.
TL;DR: In this article, the pole zero cancellation (PZC) based active filter configurations based on the pole-zero cancellation technique are introduced, and the sensitivity problem is discussed in detail.
Abstract: Some new active-filter configurations based on the pole-zero cancellation technique are introduced. First, for the range Q \leq 50 a singleamplifier circuit is suggested. For higher selectivity (50 a twoamplifier circuit is proposed. Another easily cascadable two-amplifier circuit with a reduced number of capacitors is discussed. In the latter case the filter function is determined by certain resistive ratios. All the configurations proposed-employ integrated circuit operational amplifiers (OAs). The sensitivity problem is discussed in detail. Effects of the finite OA frequency response are also investigated.
TL;DR: Bounds on the truncation error as a function of the number of terms used in a Fourier series are obtained using two different error criteria, based on the Hilbert norm and the Chebyshev norm.
Abstract: Bounds on the truncation error as a function of the number of terms used in a Fourier series are obtained. Two different error criteria, based on the Hilbert norm and the Chebyshev norm, are used.
TL;DR: In this article, a state variable approach to inductorless filters that utilize resistors, capacitors, gyrators, controlled sources or negative-impedance converters (NIC), and switches suitable for integration is described.
Abstract: The state-variable approach to inductorless filters that utilize resistors, capacitors, gyrators, controlled sources or negativeimpedance converters (NIC), and switches suitable for integration is described. By using the state equations of active RC networks in the standard form, it is shown that multiplications of resistances, gyration conductances, transfer coefficients of controlled sources, and NIC in active RC network can be achieved by means of the switching technique. From these results, the relations between the input and the output at signal frequency of active RC filters containing periodically operated switches are derived at the steady state for the case where the switching frequency is much higher than the signal frequency. The results show that the cutoff and the center frequencies of active RC filters are adjustable by changing the ratio of the on duration in a period to the period of switching. The experimental results of low-pass, bandpass, and high-pass filters are shown along with the theoretical curves.
TL;DR: In this article, the stability analysis of a general class of nonautonomous differential equations associated with many physical systems has been studied, and it is shown that the existence of solutions to a class of linear inequalities directly yields necessary and sufficient conditions for the existence a Lyapunov function of the form described.
Abstract: A class of natural Lyapunov functions of the form \Sigma \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 existence of a Lyapunov function of the form described.