# Showing papers in "IEEE Transactions on Circuit Theory in 1973"

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IBM

^{1}TL;DR: This paper describes how variable-order implicit integration, tableau formulation, and sparse-matrix solution methods have been implemented in the ASTAP program.

Abstract: The advanced statistical analysis program (ASTAP) is a general-purpose network-analysis program which performs nonlinear transient, dc, and ac analyses and provides statistical simulation to determine the distribution of circuit outputs due to parameter variations. The program combines a user-oriented input language capable of describing completely general nonlinear devices with the latest advances in numerical and programming techniques: variable-order implicit integration, tableau formulation, and sparse-matrix solution methods. This paper describes how these techniques have been implemented in the ASTAP program. Attention is focused on the computational algorithms.

288 citations

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Rice University

^{1}TL;DR: In this paper, a method for designing finite-duration impulse-response (FIR) linear-phase digital filters is presented in which the four possible cases for such filters are treated in a unified approach.

Abstract: A method for designing finite-duration impulse-response (FIR) linear-phase digital filters is presented in which the four possible cases for such filters are treated in a unified approach. It is shown how to reduce each case to the proper form so that the Remez exchange algorithm can be used to compute the best approximation to the desired frequency response. The result is that a very flexible and fast technique is available for FIR linear-phase filter design.

277 citations

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TL;DR: This work has proposed a new approach to the computation of the terminal reliability of a network by transforming a Boolean sum of products into an equivalent form in which all terms are disjoint.

Abstract: Given the set of all simple paths between two nodes in a network, the terminal reliability can be symbolically computed by transforming a Boolean sum of products into an equivalent form in which all terms are disjoint. This new approach seems to be promising in respect to existing 4[ 6 methods both for the exact and for the approximate computation of the terminal reliability.

211 citations

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Bell Labs

^{1}TL;DR: The effect of digital implementation on the gradient (steepest descent) algorithm commonly used in the mean-square adaptive equalization of pulse-amplitude modulated data signals is considered and the optimum step-size sequence reflects a compromise between these competing goals.

Abstract: The effect of digital implementation on the gradient (steepest descent) algorithm commonly used in the mean-square adaptive equalization of pulse-amplitude modulated data signals is considered. It is shown that digitally implemented adaptive gradient algorithms can exhibit effects which are significantly different from those encountered in analog (infinite precision) algorithms. This is illustrated by considering the often quoted result of stochastic approximation that to achieve the optimum rate of convergence in an adaptive algorithm the step size should be proportional to 1/n , where n is the number of iterations. On closer examination one finds that this result applies only when n is large and is relevant only for analog algorithms. It is shown that as the number of iterations becomes large one should not continually decrease the step size in a digital gradient algorithm. This result is a manifestation of the quantization inherent in any digitally implemented system. A surprising result is that these effects produce a digital residual mean-square error that is minimized by making the step size as large as possible. Since the analog residual error is minimized by taking small step sizes, the optimum step-size sequence reflects a compromise between these competing goals. The performance of a time-varying gain sequence suggested by stochastic approximation is contrasted with the performance of a constant step-size sequence. It is shown that in a digital environment the latter sequence is capable of attaining a smaller residual error.

145 citations

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TL;DR: In this paper, a Walsh series is expressed as a series of Walsh functions, and the coefficients of the input series will change, but there will be no new terms not in the original groups.

Abstract: Any well-behaved periodic waveform can be expressed as a series of Walsh functions. If the series is truncated at the end of any group of terms of a given order, the partial sum will be a stairstep approximation to the waveform. The height of each step will be the average value of the waveform over the same interval. If a zero-memory nonlinear transformation is applied to a Walsh series, the output series can be derived by simple algebraic processes. The coefficients of the input series will change, but there will be no new terms not in the original groups. Nonlinear differential and integral equations can be solved as a Walsh series, since the series for the derivatives can always be integrated by simple table lookup. The differential equation is solved for the highest derivative first and the result is then integrated the required number of times to give the solution.

135 citations

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IBM

^{1}TL;DR: The adjoint network approach, though still valid, proves to be unnecessary for solving two problems, since equivalent (and slightly simpler) formulas can be derived using well-known matrix manipulations alone.

Abstract: Formulas are easily derived for computing the sensitivity of all the response variables of a network with respect to variation of a single parameter, and the computations can be carried out very efficiently. The converse problem of computing the sensitivity of a single response variable with respect to variations of several parameters, though apparently more difficult, has recently been solved with equal efficiency by appealing to the concept of an "adjoint network." This concept, however, is shown here to be superfluous, since equivalent (and slightly simpler) formulas can be derived using well-known matrix manipulations alone. The problem of computing the signal/noise ratio of a single network response variable has also been solved by using the adjoint network, concept. But, here again, standard matrix manipulations suffice to yield the same results with less conceptual encumbrance. Thus the adjoint network approach, though still valid, proves to be unnecessary for solving these two problems.

89 citations

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TL;DR: A computer program [Network Analysis Program Using Parameter Extractions (NAPPE)] that incorporates all of the concepts discussed in this paper has been written and several examples illustrating the usefulness and efficiency of NAPPE are included.

Abstract: A new method is presented for obtaining network functions in which some, none, or all of the network elements are represented by symbolic parameters (i.e., symbolic network functions). Unlike the topological tree enumeration or signal flow graph methods generally used to derive symbolic network functions, this new process uses fast, efficient, numerical-type algorithms to determine the contribution of those network branches not represented by symbolic parameters. A computer program [Network Analysis Program Using Parameter Extractions (NAPPE)] that incorporates all of the concepts discussed in this paper has been written. Several examples illustrating the usefulness and efficiency of NAPPE are included.

79 citations

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TL;DR: In this article, the use of the second-generation current conveyor as the active element in realizing all-pass transfer functions is illustrated by two circuits, where the second generation is used to realize all pass transfer functions.

Abstract: The use of the second-generation current conveyor as the active element in realizing all-pass transfer functions is illustrated by two circuits.

74 citations

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TL;DR: A survey of applications of symbolic network functions is presented in which some network elements, in addition to the complex frequency s , are represented by variables, and a fundamental theorem on the form of symbolicnetwork functions is proved.

Abstract: A survey of applications of symbolic network functions is presented in which some network elements, in addition to the complex frequency s , are represented by variables. The concept of "closed systems" is generalized. A fundamental theorem on the form of symbolic network functions is proved.

72 citations

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TL;DR: In this paper, a simple analytical model is developed for the subthreshold region of insulated-gate field-effect transistors (IGFETs) for short channels, it is necessary to extend the model to include two-dimensional band-bending effects at the source in order to describe correctly the reduction in threshold caused by high drain and substrate voltages.

Abstract: A simple analytical model is developed for the subthreshold region of insulated-gate field-effect transistors (IGFET). For short channels, it is necessary to extend the model to include two-dimensional band-bending effects at the source in order to describe correctly the reduction in threshold caused by high drain and substrate voltages. The model is experimentally verified over a wide range of bias conditions and channel lengths and is compared with one- and two-dimensional numerical models.

67 citations

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TL;DR: In this article, a component-connection model for large-scale dynamical systems (LSDSs) is proposed and conditions under which an LSDS has a state equation representation are determined.

Abstract: Linear time-invariant large-scale dynamical systems (LSDS's) are considered. A component-connection model is first proposed. Conditions under which an LSDS has a state equation representation are determined. A characterization of a class of dynamical systems, called unimodules, is established. A unimodule has the property that any given dynamical system can be realized by an interconnection of such unimodules.

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TL;DR: A general method based on the Laplace expansion for determining the transfer function of a wide variety of linear electronic circuits is discussed, and Dominant-pole techniques are used and extended, making the procedure useful in both analysis and design.

Abstract: A general method based on the Laplace expansion for determining the transfer function of a wide variety of linear electronic circuits is discussed. The technique developed requires only the calculation of a number of driving-point resistances to specify the coefficients of the transfer function. Dominant-pole techniques are used and extended, making the procedure useful in both analysis and design. As computation only involves resistance networks, complex arithmetic is not required in determination of the response.

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TL;DR: In this article, the class of all impedance matrices which achieve maximum power transfer is described and the maximum power-transfer theorem is proved by an elementary and simple method, where the class is described in terms of the maximum-power transfer theorem.

Abstract: The maximum power transfer theorem is proved by an elementary and simple method. The class of all impedance matrices which achieve maximum power transfer is completely described. Cases where Z_{0}+Z_{0^\ast} is not positive definite are completely discussed.

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TL;DR: In this article, the sensitivity of a doubly terminated reactance two-port circuit is derived from a single circuit analysis and the worst case error of the loss response is predicted.

Abstract: Equations are derived which enable the designer to predict, from a single circuit analysis, all sensitivities and the worst case error of the loss response for a doubly terminated reactance two-port. The method is extended to the important practical class of resonanceadjusted circuits. The results confirm the experimentally observed dependence of the sensitivities on the reflection factor and on the tuning process used in the construction of the circuit. Interestingly, the sensitivities depend only on the properties of the reflection coefficients and on the complex power in the individual reactive elements.

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TL;DR: In this article, the foundational aspects of an important subclass of time invariant nonlinear n-ports are dealt with; namely, the class of algebraic n -ports that includes resistors, inductors, capacitors, and memristors as special cases.

Abstract: The foundational aspects of an important subclass of timeinvariant nonlinear n -ports are dealt with; namely, the class of algebraic n -ports that includes, among other things, resistors, inductors, capacitors, and memristors as special cases. Sufficient conditions that guarantee an algebraic n -port to admit all 2^n hybrid representations are given. Both global and local characterizations are considered in detail. In particular, certain global properties are shown to be invariants relative to the various modes of hybrid representation. The concept of reciprocity is explored in depth and shown to play an important role in determining such global properties as losslessness and passivity. Several generalized potential functions are defined for reciprocal algebraic n -ports. These functions are then used to derive a number of interesting circuit theoretic properties for nonlinear n -ports.

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TL;DR: Computer results for several transistor circuits using Western Electric highfrequency transistors are all in excellent agreement with the measured data over a wide range of bias conditions and frequencies, demonstrating the validity of the approach treated in the paper.

Abstract: In the design of long-haul analog communication systems, it is essential to understand the nonlinear distortion behavior of the electronic circuit realization. Distortion analysis of weakly nonlinear circuits has been developed based on the well-known perturbation method. In the frequency domain, the nonlinearities of a transistor are shown to be equivalently represented by intermodulation distortion sources whose amplitudes and phases are iteratively determined by the linear circuit characteristics and the Taylor-series coefficients associated with the nonlinearities. For all practical purposes, only two iterations are sufficient to yield accurate results. An algorithm for computing the second- and third-order intermodulation distortions is described. This algorithm has been implemented in a program called NODAP (nonlinear distortion analysis program). NODAP computes the smallsignal nonlinear transistor model from the recently developed integral change-control model (ICM). It then passes this information through a linear circuit analysis program for distortion computations. Computer results for several transistor circuits using Western Electric highfrequency transistors are all in excellent agreement with the measured data over a wide range of bias conditions and frequencies. This demonstrates the validity of the approach treated in the paper.

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TL;DR: A new analysis approach to understand and minimize nonlinear distortion in bipolar transistors is presented, employing a recently developed nonlinear device model, known as the integral charge control model, and a powerful analysis tool: the Volterra series representation.

Abstract: A new analysis approach to understand and minimize nonlinear distortion in bipolar transistors is presented. It employs a recently developed nonlinear device model, known as the integral charge control model, and a powerful analysis tool: the Volterra series representation. The salient analytical features of this paper are: a simple representation of the Volterra transfer functions of the transistor, compact expressions for frequency-dependent distortion coefficients, and physically meaningful asymptotic low- and high-frequency distortion coefficients. The analytical results have been experimentally verified. Finally, specific design examples are furnished to illustrate the powerful nature of the above analytical expressions.

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TL;DR: In this article, a general procedure for determining bounds on the difference between the states and outputs of a finite precision fixed-point digital filter and its infinite precision ideal counterpart is presented.

Abstract: Spectral theory of operators is used to determine a general procedure for determining bounds on the difference between the states and outputs of a finite precision fixed-point digital filter and its infinite precision ideal counterpart. The results bound quantization errors for transients as well as limit cycles and apply when input signals are present. The procedure is extended to digital filters associated with difference equations, including the important special case of the basic second-order section.

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TL;DR: A graph-theoretic study of the computational efficiency of the generalized loop analysis and the generalized cutset analysis is presented and it is shown that the choice of an optimum mode of analysis will give rise to the sparsest loop impedance matrix and thesparsest cutset admittance matrix.

Abstract: A graph-theoretic study of the computational efficiency of the generalized loop analysis and the generalized cutset analysis is presented. It is shown that the choice of an optimum mode of analysis will give rise to the sparsest loop impedance matrix and the sparsest cutset admittance matrix, respectively. The problem of formulating efficient algorithms for determining the optimum choice is shown to be strictly a problem in nonoriented linear graph. Two algorithms based on the concept of basis graph are presented and illustrated in detail with examples. A nonplanar version of the mesh analysis which generally yields a rather sparse loop impedance matrix is also included.

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TL;DR: In this article, the MOST model of Pao and Sah is extended to take into account the two-dimensional nature of the electrostatic potential, and the basic equations can be cast into a form suitable for Gummel's iterative scheme.

Abstract: The MOST model of Pao and Sah is extended to take into account the two-dimensional nature of the electrostatic potential. By keepig the current one dimensional, the basic equations can be cast into a form suitable for Gummel's iterative scheme. The numerical model is based on a finite-difference approximation to Poisson's equation and a closed-form expression for the current flow. The model is verified by comparing its results with experimental data. Good agreement is obtained. Deviations of the threshold voltage from the conventional expression for short-channel structures outside the range of the gradual channel approximation are investigated. In particular, the dependence of threshold voltage on channel length, drain-source, and substrate-source bias are illustrated with numerical and experimental results. Practical results from these investigations are summarized in graphical form.

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TL;DR: In particular, the entries of the Q -matrix of the matrix transformation b] = Qa] are generated in easily obtained combinatorial rules as mentioned in this paper, and various applications of the transformations in the stability study of discrete systems in aperiodicity conditions in evaluation of total square integrals and in digital-filter design are enumerated.

Abstract: The various transformations involved in transforming the polynomial F(z) = \Sigma_{k=0}^{n}a_{k}z^{k} into the polynomial G(s) = \Sigma_{k=0}^{n} b_{k}s^{k} are discussed. In particular, the entries of the Q -matrix of the matrix transformation b] = Qa] are generated in easily obtained combinatorial rules. The various applications of the transformations in the stability study of discrete systems in aperiodicity conditions in evaluation of total square integrals and in digital-filter design are enumerated.

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TL;DR: In this paper, a general expression was established which relates the output roundoff noise generated by a fixed-point multiplier in a digital filter to the sensitivity of the filter attenuation with respect to the corresponding multiplier coefficient.

Abstract: A general expression is established which relates the output roundoff noise generated by a fixed-point multiplier in a digital filter to the sensitivity of the filter attenuation with respect to the corresponding multiplier coefficient. It confirms that filters with low sensitivity of the attenuation also produce less roundoff noise.

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TL;DR: The exact nature of the relationship between the wave-digital-filter structure and the MAP networks and how the sensitivity property arises is examined, which permits implementation of the digital structure with a lower coefficient word length than that possible with the conventional structures.

Abstract: The wave digital filter patterned after doubly terminated maximum available power (MAP) networks by means of the Richard's transformation has been shown to have low-coefficient-sensitivity properties. This paper examines the exact nature of the relationship between the wave-digital-filter structure and the MAP networks and how the sensitivity property arises, which permits implementation of the digital structure with a lower coefficient word length than that possible with the conventional structures. The proper design procedure is specified and the nature of the unique complementary outputs is discussed. Finally, an example is considered which illustrates the wave filter design, the conversion techniques, and the low sensitivity properties.

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TL;DR: It will be shown that one can create the complementary transfer function t' = 1 - t by first synthesizing t with a threeterminal network and then interchanging the network's input and ground leads, i.e., the former network ground is the new input and the former input is grounded.

Abstract: Active filters are frequently realized as grounded threeterminal networks. It will be shown that one can create the complementary transfer function t' = 1 - t by first synthesizing t with a threeterminal network and then interchanging the network's input and ground leads, i.e., the former network ground is the new input and the former input is grounded. The output voltage continues to be taken with respect to common ground. If the active element in the network is a differential-input op amp, then this maneuver can be carried out without changing the dc power-supply common-ground connection. It is shown that this is not true in general of finite-gain amplifier networks or of single-input op amp networks. Several uses are suggested and the example of a 360° all-pass section is examined in detail. It is shown that in the particular case of a multiinput biquad all-pass section there is a small increase in the variability of the delay due to resistor changes, and experimental results are given which confirm this. Both the all-pass and band-reject realizations are attractive because the zero frequency is guaranteed to track the pole frequency. A proof of the results for an N -terminal network is outlined.

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TL;DR: In this paper, a method for calculating the noise voltage at the output of quadratic filter sections is developed, where the amplifiers are assumed to have infinite input impedance, infinite gain, and zero output impedance.

Abstract: A method for calculating the noise voltage at the output of quadratic filter sections is developed. Multiple-feedback low-pass, bandpass, and high-pass quadratic filter sections realized using differential-input single-ended output operational amplifiers are analyzed. The amplifiers are assumed to have infinite input impedance, infinite gain, and zero output impedance. The noise sources associated with the amplifiers are assumed to be statistically independent, but can have both white and l/f noise components. A noise analysis of a fourthorder maximally flat low-pass filter realized by cascading two quadratic filter sections is included.

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TL;DR: In this paper, it was shown that sensitivity can be expressed as a sum of terms, where each term is the product of two sensitivity functions, the gain-to-coefficient sensitivity and the well-known coefficient-tocomponent sensitivity.

Abstract: In attempting to predict the behavior of a filter during and at the end of its life, one is led to the study of sensitivity and then one must compare worst-case and expected results. This paper shows that sensitivity can be expressed as a sum of terms, where each term is the product of two sensitivity functions. One is the frequency-dependent sensitivity of the gain to the transfer function coefficients (the gain-to-coefficient sensitivity) and the other is the well-known coefficient-to-component sensitivity. The gain-to-coefficient sensitivity clearly shows that the gain of a biquadratic function is far more sensitive to changes in the resonant frequency f_0 than to changes in Q only near the 3-dB frequencies. The gain is actually less sensitive to changes in f_0 near f_0 . It is also shown that coefficient-to-component sensitivities for resistors and capacitors have no effect on the mean value of the change in the gain, but have marked effects on the standard deviation.

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TL;DR: In this paper, an explicit solution for the synthesis of resistively terminated one- or two-variable cascaded transmission-line networks is derived using the properties of polynomials orthogonal on the unit circle.

Abstract: Using the properties of polynomials orthogonal on the unit circle, an explicit solution is derived for the synthesis of resistively terminated one- or two-variable cascaded transmission-line networks. In the two-variable case, in addition to the cascade of ideal commensurate transmission lines, passive lossless lumped two-ports are allowed to exist between the junctions of adjacent lines. For this case, the explicit solution form enables the test for two-variable positive reality to be discarded in favor of a matrix factorization condition. In the onevariable case, due to the intimate relationship between the synthesis of a cascade of transmission lines and the generation of a sequence of polynomials orthogonal on the unit circle, Richards' theorem is not required for the explicit-form solution. Initially, the main theorem describing the explicit solution for the one- and two-variable cases is presented. After the formulation of the proofs, two nontrivial examples are cited to illustrate the use of the explicit-form solution in the two-variable case.

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TL;DR: By assuming a typical range of amplifier specifications, a model is derived for a capacitively terminated operational-amplifier Rgyrator circuit that clearly shows the influence of each amplifier imperfection on the performance of the gyrator circuit.

Abstract: By assuming a typical range of amplifier specifications, a model is derived for a capacitively terminated operational-amplifier Rgyrator circuit. Amplifier imperfections such as finite input and output resistances and also finite frequency-dependent amplifications are taken into account. The validity of the model is confirmed by using an exact computer-aided analysis and also by experiment. The model clearly shows the influence of each amplifier imperfection on the performance of the gyrator circuit, and it should prove useful to the network designer.

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TL;DR: A general-purpose electronic-circuit simulation program is employed to efficiently compute second- and third-order distortion due to weak nonlinearities in bipolar junction transistor (BJT) circuits of arbitrary complexity.

Abstract: A general-purpose electronic-circuit simulation program is employed to efficiently compute second- and third-order distortion due to weak nonlinearities in bipolar junction transistor (BJT) circuits of arbitrary complexity. The method is based on the Volterra-series representation of the electronic circuit and is valid at all frequencies. The transistors are represented by a simple modified Ebers-Moll model, and the adjoint-network concept is employed to efficiently compute the contribution of each nonlinearity in the circuit to the distortion at the output. The method is illustrated with a practical electronic-circuit example.

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TL;DR: In this article, a closed-form solution for the scattering transfer function of a resistively terminated lossless reciprocal two-port prototype network of degree 2n was derived for arbitrary phase polynomials of the first and second kinds.

Abstract: The closed-form solution is derived for the scattering transfer function S_{12}(p) of a resistively terminated lossless reciprocal two-port prototype network of degree 2n which satisfies the following constraints: |S_{12}(j\omega) | \leq 1 |S_{12}({\pm}j{\omega}_i) | = 1 , i = 1 \rightarrow n \arg S_{12}({\pm}j{\omega}_i) = \pm \psi({\omega}_i), i = 1 \rightarrow n where the \omega_i are arbitrary and \psi(\omega) is any odd function. The solution is obtained in terms of the arbitrary phase polynomials of the first and second kinds, which are capable of being generated through simple recurrence formulas.