Showing papers in "IEEE Transactions on Circuit Theory in 1968"
TL;DR: Experience with such programs, using the algorithms described in the paper, indicates that filters up to about degree 30 may be designed using only single precision in the calculations.
Abstract: A concise description is given of some recently developed filter design techniques. The discussion includes equal-ripple and maximally flat passband filters with general stopbands, as well as equal-ripple stopband filters with general passbands. To solve the approximation problem and to improve numerical conditioning, the design is carried out exclusively in terms of one or two transformed frequency variables. A step-by-step description is given for the design of each filter type; the steps are so formulated that the erosion of significant digits is minimized. The design processes given are unique and are directly suitable for automatic computer programs. Experience with such programs, using the algorithms described in the paper, indicates that filters up to about degree 30 may be designed using only single precision in the calculations. A discussion of some practical predistortion techniques, as well as a listing of available tabulated filter design information, is also included.
118 citations
TL;DR: In this article, it was shown that quantization of a digital filter's coefficients in an actual realization can be represented by a "stray" transfer function in parallel with the corresponding ideal filter.
Abstract: The frequency response of a digital filter realized by a finite word-length machine deviates from that which would have been obtained with an infinite word-length machine. An "ideal" or "errorless" filter is defined as a realization of the required pulse transfer function by an infinite word-length machine. This paper shows that quantization of a digital filter's coefficients in an actual realization can be represented by a "stray" transfer function in parallel with the corresponding ideal filter. Also, by making certain statistical assumptions, the statistically expected mean-square difference between the real frequency responses of the actual and ideal filters can be readily evaluated by one short computer program for all widths of quantization. Furthermore, the same computations may be used to evaluate the rms value of output noise due to data quantization and multiplicative rounding errors. Experimental measurements verify the analysis in a practical case. The application of the results to the design of the digital filters is also considered.
114 citations
TL;DR: In this paper, a general solution to the problem of synthesizing positive real functions and matrices of several variables has been presented, except for the two-variable lossless case and the case where a twovariable positive real function is prescribed as a bilinear function with respect to one of the two variables.
Abstract: Positive real functionsandmatrices of several variables arose in the problem of synthesizing a passive network composed of lumped elements with variable parameters. The importance of these functions and matrices has recently been emphasized by the considerable attention concerning their application to the problem of synthesizing passive networks composed of noncommensurable transmission lines and lumped elements. The problem of synthesizing positive real functions and matrices of several variables has been discussed by several authors. However, the problem has not been solved generally, except for the two-variable lossless case and the case where a two-variable positive real function is prescribed as a bilinear function with respect to one of the two variables. In this paper, a general solution to the above synthesis problem is presented. It is shown that an arbitrarily prescribed n \times n positive real matrix, symmetric or nonsymmetric, of several variables is realizable as the impedance or admittance matrix of a finite passive multivariable n -port. It is further shown that, if the matrix is symmetric, then it is realizable as a bilateral passive n -port. Related problems and discussions are also given.
85 citations
59 citations
TL;DR: In this article, a class of realizations (termed uniform realizations) for time-variable impulse response matrices is defined, which plays a role similar to that of minimal (completely controllable and observable) realizations for time invariant systems; members of the class have bounded coefficients and are uniformly asymptotically stable if the impulse response matrix represents a bounded-input boundedoutput (BIBO) stable system.
Abstract: A class of realizations (termed uniform realizations) for time-variable impulse response matrices is defined which plays a role similar to that of minimal (completely controllable and observable) realizations for time-invariant systems; members of the class have bounded coefficients and are uniformly asymptotically stable if the impulse response matrix represents a bounded-input boundedoutput (BIBO) stable system. The necessary and sufficient conditions for an impulse response matrix to be uniformly realizable are derived together with an explicit realization procedure. Sufficient conditions for a system to be realizable as a passive network are also obtained, and it is shown that any BIBO-stable uniformly realizable impulse response matrix may be synthesized as the transfer response of a passive network composed of constant positive inductors and resistors and bounded time-variable gyrators.
45 citations
TL;DR: In this paper, a method of oscillator design that maximizes the output power is presented, which is applicable to the class of nonlinear elements whose single frequency largesignal parameters depend on a single port voltage.
Abstract: A method of oscillator design that maximizes the output power is presented. The embedding network is derived from a set of four linear algebraic equations. The method is applicable to the class of nonlinear elements whose single frequency largesignal parameters depend on a single port voltage.
44 citations
TL;DR: In this article, a detailed analysis of some RC-amplifier resonators whose characteristics are well suited for practical active filters is provided, facilitated by a set of sensitivity identities.
Abstract: Active filters may consist of a cascade of isolated resonators, with each resonator supplying a single pair of complexconjugate poles. This paper supplies a detailed analysis of some RC -amplifier resonators whose characteristics are well suited for practical filters. The calculations are facilitated by a set of sensitivity identities. One resonator, taken from the Sallen and Key catalog, is shown to have extremely low passive sensitivities: S_{Z}^{Q} = \pm \frac{1}{6} for all passive elements. Active Q multiplication is used to extend the usefulness of the circuit. Analysis of the dualintegrator feedback resonator shows that it is notably insensitive to amplifier parasitics. Finally, the dual-integrator concept is realized in a resonator that uses only two amplifiers. The several resonators supply a range of useful pole- Q 's from low values to several hundred.
44 citations
TL;DR: While an edge-numbering convention and a criterion for a tree play the key roles in systematic generation of trees, the storage technique makes it possible to obtain all the co-factors and determinants of a node-admittance matrix of any network by merely operating on one single master forest matrix.
Abstract: A new method of listing all possible trees of any given graph without duplication or redundancy, using simple geometrical properties of the graph, is proposed. The procedure given is suitable for both manual and automatic computation, and any modifications to the given graph can be catered to by suitable interpolation and extrapolation. An alternate method for complete graphs, derived from it, gives the trees arranged in an order most suitable for their storage as master forest matrices and for directly obtaining trees and 2-trees of any given graph through simple modifications to them instead of starting from scratch every time. Some properties of master forest matrices are discussed, which., inter alia, lead to a formula for the number of trees in a sub-graph of a complete graph. While an edge-numbering convention and a criterion for a tree play the key roles in systematic generation of trees, the storage technique makes it possible to obtain all the co-factors and determinants of a node-admittance matrix of any network (within the range of storage) by merely operating on one single master forest matrix.
42 citations
TL;DR: The problem of realizing a network whose transmission characteristics approximate a given function in Chebyshev sense is treated as a nonlinear programming problem, and a method of solving this problem by successively solving linear programming problems, which are derived by locally linearizing the original non linear programming problem.
Abstract: One of the most important problems of computeraided network design is the optimization of network characteristics by iterative calculation. In this paper, the problem of realizing a network whose transmission characteristics approximate a given function in Chebyshev sense is treated as a nonlinear programming problem, and a method of solving this problem by successively solving linear programming problems, which are derived by locally linearizing the original nonlinear programming problem, is proposed. An improvement of the method for reducing the computation time is also considered and is proved to be practical and very effective by many design examples.
38 citations
TL;DR: In this paper, a method of reducing the sensitivity of all-pass frequency-sensitive phase shift networks was proposed to achieve bandpass filters without inductors, which can be realized by using allpass frequencysensitive phase-shift networks.
Abstract: Bandpass filters without inductors can be realized by using all-pass frequency-sensitive phase-shift networks. Filters with Q values approaching 1000 have been constructed. A method of reducing the Q sensitivity is reported.
36 citations
TL;DR: In this paper, a state-space analysis is given for RC networks containing an arbitrary number of periodically operated switches, and the results are then applied to the design of RC integrated circuits in which large values of resistance are achieved by placing a switch in series with each resistor of small resistance.
Abstract: A state-space analysis is given for RC networks containing an arbitrary number of periodically operated switches. The results are then applied to the design of RC integrated circuits in which large values of resistance are achieved by placing a switch in series with each resistor of small resistance. It is shown that the technique provides excellent desensitivity to environmental change. Finally an experiment verifying the usefulness of the method is described.
TL;DR: In this article, it was shown that the problem of finding minimum feedback arc and vertex sets in directed graphs is partly equivalent to the prime implicant problem of switching theory, and the problem was shown to be NP-hard.
Abstract: A method presented by Lempel and Cederbaum to find minimum feedback arc and vertex sets in directed graphs is shown to be partly equivalent to the well-known prime implicant problem of switching theory.
TL;DR: A new method for synthesizing all-pass networks is described, which is suitable for a broad class of practical applications and which was solved by use of a computer program based on the new method.
Abstract: All-pass networks are often used to compensate for phase or delay distortion. A new method for synthesizing such networks is described here. The algorithm that results is suitable for a broad class of practical applications. Results for several problems, which were solved by use of a computer program based on the new method, are included.
TL;DR: In this paper, the sum of sensitivities with respect to all elements in a network is invariant under continuously equivalent transformation, and the individual sensitivity for capacitances and inductances is not invariant if there are no capacitance loops and inductance cut-sets in the network.
Abstract: Two simple sensitivity invariants are derived for continously equivalent networks. The first one states that the sum of sensitivities with respect to all elements in a network is invariant under continuously equivalent transformation. The second one states that the individual sensitivity for capacitances and inductances is invariant if there are no capacitance loops and inductance cut-sets in a network.
TL;DR: A method of generating all complete trees of a pair of linear graphs representing an active network is given because complete trees are generated by sets of complete trees classified by edges in initial complete tree to.
Abstract: A method of generating all complete trees of a pair of linear graphs representing an active network is given. This method is a repetition of two processes, one of which is to obtain a complete tree and the other is to generate all possible complete trees of distance one from the complete tree that is obtained by the first process. These two processes are easily carried out by the use of computers, and there will be no duplications in the generated complete trees. Furthermore, complete trees are generated by sets of complete trees classified by edges in initial complete tree to. Thus, it will be easy to factorize the result according to the weights of these edges.
TL;DR: In this paper, the classical time-energy definition of passivity is employed to generate workable passivity criteria for lumped networks which are characterizable by standard form state equations.
Abstract: The classical time-energy definition of passivity is employed to generate workable passivity criteria for lumped networks which are characterizable by standard form state equations. In general, the demonstration of passivity entails the construction of a Liapunov-type function of the phase. Moreover, in the case of linear (time-variable) networks explicit stability conditions emerge.
TL;DR: In this article, a method for designing Chebyshev filters having flat group-delay characteristics in the main part of the passband is presented from the general approximation theory, which is so determined that the group delay characteristics may be flat in the whole passband.
Abstract: In this paper, a method for designing Chebyshev filters having flat group-delay characteristics in the main part of the passband is presented From the general approximation theory, a method for obtaining the transfer function of Chebyshev filters with complex transmission zeros is derived, which are so determined that the group-delay characteristics may be flat in the main part of the passband A new theory of cascade synthesis, which is an extension of Belevitch's cycle, and an extended bisection theorem are introduced By the applications of these results, Chebyshev filters with flat group delay can be realized A practical design example is also included
TL;DR: In this article, the authors show that by eliminating the ground constraint on the amplifiers, one can realize any rational transfer or admittance matrix with a common-ground RC : VUGA network.
Abstract: Necessary and sufficient conditions exist, which show that only a subset of all rational matrices can be realized as the transfer or admittance matrix of a common-ground network of resistors, inductors, capacitors, and grounded unity-gain voltage amplifiers (VGUGAs). This paper shows that by eliminating the ground constraint on the amplifiers (VUGAs) one can realize any rational transfer or admittance matrix with a common-ground RC :VUGA network. The synthesis is based upon a simple circuit whose transfer function is the ratio of two independent admittances. This is used with one capacitor and one resistor to form a differentiator. The differentiators are cascaded to form an admittance polynomial whose coefficients are determined by RC products. Transfer functions are realized by forming ratios of these polynomial admittances. The synthesis procedure results in selecting component values by inspection and permits tuning the circuits with the resistors.
TL;DR: In this article, the van der Pol oscillator with delayed amplitude limiting was analyzed using the derivative-expansion method and explicit first-order expressions were obtained for the output in the nonresonant case.
Abstract: Forced oscillations of the van der Pol oscillator with delayed amplitude limiting are analyzed using the derivative-expansion method. The forcing function is taken to be either sinusoidal or white noise. The oscillator's output depends on whether the excitation is "hard" [i.e., excitation amplitude is O(1) ] or "soft" [i.e., excitation amplitude is O(\mu) , \mu is a small parameter], and whether the excitation is resonant (i.e., excitation frequency is near natural frequency) or not. Explicit first-order expressions are obtained for the output in the nonresonant case. If the excitation is soft, the steady-state output is a combination of terms having frequencies equal to those of the natural and excitation frequencies, with the forced response being dominated by the natural response. On the other hand, if the excitation is hard, the natural response fades away as time increases over a wide range of frequencies and excitation amplitudes. Consequently, the output is harmonic, having a frequency equal to the excitation frequency. In the resonant case, the steady-state output is synchronized at the excitation frequency, irrespective of whether the excitation is soft or hard. The frequency response equation is a family of curves that depends on the excitation amplitude and the delay time as parameters. The stability of these harmonic oscillations is determined. For the noise perturbed oscillator, the conditional probability distribution for the deviations from the stationary stable state is presented.
TL;DR: In this article, a nonlinear theory of a class of transistor oscillators linear differential equation of the form is developed, using the Ebers-Moll large-signal model for the transistors.
Abstract: The nonlinear theory of a class of transistor oscillators linear differential equation of the form is developed, using the Ebers-Moll large-signal model for the transistors. Simplified versions of tuned-collector, tuned-base, and Hart ley transistor oscillators are shown to be characterized by a nonlinear differential equation of the form \ddot{x} - \mu[e^{a \dot{x}} - \kappa e^{(a+b)\dot{x}}] + \gamma \dot{x} + x = 0 where \mu, \kappa, \gamma, a , and b are positive constants and \kappa\ll 1 . Approximate solutions of the above equation, which are derived in a very simple manner using the phase plane approach, are compared favorably with experimental results. A push-pull version of the tunedcollector oscillator characterized by the above equation with the exponential terms replaced by hyperbolic sines is discussed.
TL;DR: The results provide the decomposition of a tree graphs into complete subgraphs and two procedures for generating a Hamilton circuit in a tree graph are presented.
Abstract: Some topological features of a tree graph are investigated. The results provide the decomposition of a tree graph into complete subgraphs. As an immediate consequence of the decomposition, two procedures for generating a Hamilton circuit in a tree graph are presented.
TL;DR: A strictly energy-absorbing real linear time-invariant one-port network characterized by an impedance function Z(p) is optimally matched by a real linearTimeInvariantOne-Port network characterizedby an impedancefunction Z(-p) .
Abstract: A strictly energy-absorbing real linear time-invariant one-port network characterized by an impedance function Z(p) is optimally matched by a real linear time-invariant one-port network characterized by an impedance function Z(-p) . Z(-p) is not realizable in general, but it is the key to the entire study of matching since it dictates fundamental limitations on matching network behavior and a sequence of approximating matching network structures. The problem is formulated in the time domain, but practical realizations are obtained at the final step by means of passive approximation in the frequency domain. Most of the steps to solution of a specific problem may be carried out virtually by inspection.
TL;DR: In this article, a method is presented which uses topological formulas to find network functions for general linear networks which may contain any type of dependent sources, gyrators, coupled coils, and ideal transformers.
Abstract: A method is presented which uses topological formulas to find network functions for general linear networks which may contain any type of dependent sources, gyrators, coupled coils, and ideal transformers. The general linear network is divided into a passive reciprocal subnetwork and a subnetwork consisting of the active and/or nonreciprocal elements. The topological formulas express the network functions in terms of the tree-admittance products of the passive reciprocal subnetwork, and/or the products' of the active and/or nonreciprocal elements and the (k + 1) -tree products of the passive reciprocal subnetwork.
TL;DR: In this paper, an approximation for current and voltage produced on a skin-effect lossy line by a step-function voltage source with a series lumped resistance was derived for a single wavefront.
Abstract: Approximations are derived for current and voltage produced on a skin-effect lossy line by a step-function voltage source with a series lumped resistance. Differences among computed normalized voltages corresponding to different values of source resistance increase with distance from the source and with time after wavefront arrival.
TL;DR: This paper considers the synthesis of cascaded transmission-line networks of noncommensurate unit elements with the following structures: a transmission line composed of commensurate units with open-ended stubs, partitioned from a multivariable network.
Abstract: Since the concept of multivariable positive real functions was introduced, the synthesis of these functions and matrices, concerning passive networks composed of lumped elements and of lumped and transmission-line elements, has been one of the most interesting problems in the field of circuit theory. This paper considers the synthesis of cascaded transmission-line networks of noncommensurate unit elements with the following structures: 1) a cascade connection of m transmission lines N_{i} (i= 1, 2, \cdots ,m) in a prescribed order, each N_{i} being a transmission line with open-ended stubs, composed of unit elements of a single variable p_{i} ; 2) a transmission line with open-ended stubs composed of unit elements of P_{2} , connected in cascade between two transmission lines composed of unit elements of p_{1} ; 3) a cascade connection of m transmission lines N_{i} (i = 1, 2, \cdots ,m) in an arbitrary order, each N_{i} being a transmission line composed of unit elements of p_{i} ; and 4) a transmission line composed of commensurate unit elements with open-ended stubs, partitioned from a multivariable network.
TL;DR: A method is presented for determining the transfer function of low-pass filters whose attenuation shows a Chebyshev characteristic in the stopband and whole phase or delay time can even be specified independently of the aforementioned attenuation properties.
Abstract: A method is presented for determining the transfer function of low-pass filters whose attenuation shows a Chebyshev characteristic in the stopband and whole phase or delay time can __-_2 for n even be specified independently of the aforementioned attenuation properties The transfer functions may be realized by simple ladder networks In order to obtain, as far as possible, transformerless circuits, the transfer function to be determined has a pole at infinity