# Showing papers in "International Journal of Circuit Theory and Applications in 1977"

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TL;DR: In this article, the theory and a time domain synthesis procedure for a class of orthogonal digital filters derived from discrete Laguerre polynomials are presented. But the authors do not consider the problem of time domain optimization.

Abstract: This paper presents the theory and a time domain synthesis procedure for a class of orthogonal digital filters. These filters are derived from discrete Laguerre polynomials and in the case of exact representation possess an infinitely long structure whilst exhibiting an infinite impulse response.
In practice the desired impulse response of a filter to be synthesized is truncated in time whilst speed and economic considerations impose a constraint on its length. By the nature of these filters, very few stages usually suffice to yield excellent fidelity in most practical cases. The filters, whose cascaded stages are eminently suited to multiplexing, are inherently stable.
A computer-aided design algorithm using a Fibonacci search algorithm is presented for optimizing the practical case having finite length and span. Two examples illustrate the procedure.

84 citations

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TL;DR: In this article, the authors apply the theory of the degree of a map to the study of the existence of solutions and some related problems for resistive nonlinear networks, which leads to a better understanding of the geometric structure of the vector fields associated with the network equations.

Abstract: This paper presents an application of the theory of the degree of a map to the study of the existence of solutions and some related problems for resistive nonlinear networks. Many well-known results in this area have been generalized to allow coupling among the nonlinear resistors. The usual hypothesis requiring the nonlinear resistors to be eventually increasing has been weakened considerably by only requiring the resistors to be eventually passive. Instead of investigating special cases by special techniques, we study the network equations from a geometrical point of view. The concept of homotopy of odd fields provides a unified yet simple approach for analyzing a large class of practical nonlinear networks. Many known results belong to this category and are derived as special cases of our generalized theorems. This approach leads to a much better understanding of the geometric structure of the vector fields associated with the network equations. As a result, in so far as the existence of solutions is concerned, the concept of eventual passivity is shown to be far more basic than that of eventual increasingness. The emphasis of the concept of eventual passivity also leads naturally to the inclusion of coupling among the nonlinear resistors.
The homotopy of odd fields also provides some useful techniques for locating the solutions. Along this line, we also study the bounding region of solutions and discuss the operating range of nonlinear resistors.

69 citations

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TL;DR: In this article, a gradient method was proposed to find a periodic response by minimizing the square magnitude of the discrepancy vector, i.e., the variance of the variance vector with respect to the initial condition vector.

Abstract: For systems of differential equations of the form ẋ = f(x) or x = f(x, t), a periodic response may be identified by the requirement that x(kT) = x(0), where k = 1, 2, … and T is the period, x(0) = x0 being the initial-condition vector. We describe a gradient method for finding this x0 vector by minimizing the square magnitude of the ‘discrepancy vector’ δ(x0) = x(T)–x0. The gradient of the scalar function P(x0) = δt(x0)δ(x0) with respect to x0 is calculated by one full-period forward integration of the original differential equation to obtain δ(x0), and then one full-period backward integration of the adjoint variational equations, using δ(x0) as the initial-condition vector. The gradient of P(x0) is then twice the adjoint discrepancy vector. We use Fletcher's method of optimization to minimize P(x0).

50 citations

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TL;DR: A new algorithm is proposed to realize a digital transfer function in the form of cascaded lattice two-pairs with the right-most two-pair being constrained such that one of its output terminals is connected directly to an input terminal.

Abstract: A new algorithm is proposed to realize a digital transfer function. The final realization is in the form of cascaded lattice two-pairs with the right-most two-pair being constrained such that one of its output terminals is connected directly to an input terminal. The complete realization uses m delays, 2m + 1 multipliers and 2m two-input adders where m is the order of the transfer function. Several special cases are included, along with an example illustrating the general algorithm.

43 citations

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TL;DR: In this paper, various methods for designing multidimensional digital filters exhibiting approximately circular, spherical or hyperspherical attenuation symmetry are discussed and simple means for ensuring excellent symmetry at frequencies remote from the origin are presented.

Abstract: Various methods for designing multidimensional digital filters exhibiting approximately circular, spherical or hyperspherical attenuation symmetry are discussed. It is shown how, by means of appropriate series expansions, symmetry requirements for filters with any number of dimensions can be fulfilled with arbitrary precision by adopting transformations of correspondingly increased degree. Some of these transformations are generalizations of the known McClellan transformation. Simple means for ensuring excellent symmetry at frequencies remote from the origin are presented.

25 citations

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TL;DR: In this paper, a rigorous fundamental theory of non-energic N-port capacitors, capacitors and inductors is presented, which results in a general canonical representation.

Abstract: A circuit element is nonenergic if the instantaneous power flow into it is always zero. Well-known examples include the ideal diode, transformer, gyrator and circulator. Most of the interesting nonenergic elements are nonlinear N-ports with N ⩾ 2, and many of their properties are quite counterintuitive. For example, there exists a surprisingly large class of nonenergic multiport capacitors and inductors, all of which, it turns out, are nonlinear and reciprocal. Nonenergic linear N-ports, on the other hand, are necessarily resistive and antireciprocal.
In this paper, we present a rigorous fundamental theory of nonenergic N-ports that results in a general canonical representation. Special canonical forms are developed for nonenergic resistors, capacitors and inductors, and numerous examples are given.

23 citations

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TL;DR: In this paper, the integrand of these sensitivities are furthermore equivalent to the variance of magnitude and phase variations and general formulas are derived which would simplify calculations for gain, phase as well as the transfer function.

Abstract: Statistical multiparameter sensitivity proposed by Rosenblum and Ghausi, for transfer function of a linear system, has been studied with regard to gain and phase sensitivities. It is shown that for small element changes a very simple relationship exists between these quantities. The integrand of these sensitivities are furthermore equivalent to the variance of magnitude and phase variations. Finally general formulas are derived which would simplify calculations for gain, phase as well as the transfer function. These formulas are helpful in optimization and comparison of various low sensitivity networks.

14 citations

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TL;DR: In this paper, a new method for the computation of the state and output equations is given, and a procedure is described to obtain the switching equations, in the most general form, at a switching instant.

Abstract: The state–space formulation of linear circuits containing periodically operated switches requires one to obtain the state and output equations. Further, it requires one to obtain the switching equations where discontinuities in the state variables occur at a switching instant. A new method for the computation of the state and output equations is given. Further, a procedure is described to obtain the switching equations, in the most general form, at a switching instant. Examples are given to illustrate these methods in finding the state, the output and the switching equations.

12 citations

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TL;DR: The applications of the least-mean-square-approximation technique to filter synthesis are discussed, and explicit expressions for the characteristic function of all-pole lowpass filters are derived using a weighted least mean-square error norm as discussed by the authors.

Abstract: The applications of the least-mean-square-approximation technique to filter synthesis are discussed, and explicit expressions for the characteristic function of all-pole lowpass filters are derived using a weighted least mean-square error norm. The weight function depends on one variable parameter which controls the shape of the magnitude response both in the passband and in the stopband. It is shown that most of the filter functions in common use are special cases of this approximation procedure, including Legendre monotonic passband filters as a limiting, degenerate case. Also, a useful generalization of Legendre filter functions is proposed.

11 citations

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TL;DR: State models based on graph-theoretical concepts are presented for the computer-aided analysis of large-scale linear networks by decomposition in time as well as frequency domains to exploit the sparsity and the repetitive structure present in most large- scale networks.

Abstract: State models based on graph-theoretical concepts are presented for the computer-aided analysis of large-scale linear networks by decomposition in time as well as frequency domains. Several examples are analysed which illustrate the validity and efficiency of these models. These models exploit the sparsity and the repetitive structure present in most large-scale networks.

11 citations

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TL;DR: In this article, a method is introduced for designing recursive digital filters with very low roundoff noise, which is based on reducing the magnitudes of the noise transfer functions on the unit circle by ensuring the presence of zeros.

Abstract: A novel method is introduced for designing recursive digital filters with very low roundoff noise. The proposed method is based on reducing the magnitudes of the noise transfer functions on the unit circle by ensuring the presence of zeros, while simultaneously synthetizing the prescribed transfer function. The final structure, which exhibits steady-state roundoff noise with low variance, is simple and economical, and canonic with respect to delay elements, although not always canonical with respect to multipliers. An illustrative example is included. The realization method is also shown to reduce the multiplier coefficient sensitivities.

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TL;DR: In this article, the slope compensation in microwave amplifiers with stubs and cascaded lines 1/8 wavelength long has been studied and shown to be realizable with 1 μm gate f.t.

Abstract: Sloped commensurate transmission-line functions realizable with stubs and cascaded lines 1/8 wavelength long are presented. These functions may be applied to synthetizing matching networks required for slope compensation in microwave amplifiers. Examples for the broadband design of 7–14 GHz chip 1 μm gate f.e.t. and 4–8 GHz packaged f.e.t. amplifiers are given.

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TL;DR: A graph theoretical interpretation has been given to nonsymmetric permutations on A, which can be considered a fundamental step towards the solution of the above-mentioned optimization problems.

Abstract: In the tableau approach to large-electrical-network analysis, as well as in structure analysis, the finite-element method, linear programming etc., a very sparse linear algebraic set of equations Ax = b has to be solved repeatedly. To efficiently solve the system via Gaussian elimination, an optimization problem has to be faced: the selection of a pivot strategy to maintain the sparsity of the matrix A. It is possible also to follow a different strategy to fully exploit the sparsity of A, i.e. to transform A into an equivalent but more convenient form. Both of these problems have been studied and partially solved by means of directed graphs associated with A when symmetric permutations on A are allowed.
In this paper, a graph theoretical interpretation has been given to nonsymmetric permutations on A, which can be considered a fundamental step towards the solution of the above-mentioned optimization problems. This interpretation is obtained through decomposition theorems on nonsymmetric permutations, correspondence theorems between column (row) permutations and topological operations on a directed graph representing A.

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TL;DR: In this article, root-locus concepts are expanded to treat characteristic expressions of systems and circuits with two parameters which vary along straight lines through the origin of the complex plane, and a new absolute stability criterion is proved which does not necessitate checking a polynomial for nonnegativeness along the imaginary axis.

Abstract: Root-locus concepts are expanded to treat characteristic expressions of systems and circuits with two parameters which vary along straight lines through the origin of the complex plane. Theorems are stated and proved by which the problem of finding the boundary of root regions of such expressions is reduced to the problem of plotting 1-parameter root loci.
The concepts of 2-parameter root loci are then used to investigate the absolute stability of arbitrarily passively terminated 2-ports.
The following results are obtained by this method:
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The complete root regions of the characteristic equation are found, rendering more information about the dynamic behaviour of the 2-ports than just determining absolute stability.
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A new absolute stability criterion is proved which does not necessitate checking a polynomial for nonnegativeness along the imaginary axis.
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A new proof of the Llewellyn criterion is arrived at.
A numerical example is also provided for further clarification.

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TL;DR: In this paper, a simplified method based on the concept of reflection filters is presented for designing linear phase filters with arbitrary amplitude to phase constraints, which can be used to design more selective phase filters.

Abstract: A simplified method—based on the concept of reflection filters—is presented for designing linear phase filters with arbitrary amplitude to phase constraints This method starts with transfer functions with 2: 1 amplitude to phase constraints, and through varying the recurrence relation of the polynomials involved, transfer functions with more selective amplitude are obtained

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TL;DR: In this paper, an analytical procedure for the sensitivity analysis of digital filters is presented, which applies to the sensitivity investigation of digital-filter poles and zeros due to parameter quantization.

Abstract: An analytical procedure for the sensitivity analysis of digital filters is presented. The procedure applies to the sensitivity investigation of digital-filter poles and zeros due to parameter quantization. Suitably defined sensitivities and a computer-aided technique, presented in the paper, allow a rapid evaluation of displacements of digital-filter poles and zeros due to parameter quantization in different realizations of a given digital filter.

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TL;DR: In this article, it is shown how noncanonic wave digital filters corresponding to reference filters containing unit elements can be transformed such that a canonic realization of these filters can be obtained as well.

Abstract: Recently, a method has been developed by means of which canonic wave digital filters can be derived from originally noncanonic ladder wave digital filters. This method applies only to wave digital filters which are derived from pure LC-ladder reference filters. In the paper, it is shown how noncanonic wave digital filters corresponding to reference filters containing unit elements can be transformed such that a canonic realization of these filters can be obtained as well.

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TL;DR: In this article, a synthesis procedure for RC-active filters of the "follow-the-leader" feedback type is presented, suitable for application also to the general case in which differently tuned biquadratic functional blocks are used Their losses can either be concentrated in one of the blocks, or given by a prescribed distribution.

Abstract: For RC-active filters of the ‘follow-the-leader’ feedback type, a synthesis procedure is presented that is suitable for application also to the general case in which differently tuned biquadratic functional blocks are used Their losses can either be concentrated in one of the blocks, or given by a prescribed distribution

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TL;DR: In this paper, bounds for the amplitude of the error at the output of fixed-point 1st-order 2-dimensional filters due to roundoff after multiplications are obtained are obtained.

Abstract: Bounds for the amplitude of the error at the output of fixed-point 1st-order 2-dimensional filters due to roundoff after multiplications are obtained. These bounds apply to the transient as well as the steady-state response when the signal is present.

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TL;DR: In this article, the complete solvability and the order of complexity of passive RLCT networks were investigated and necessary and sufficient conditions for complete solvable networks were derived, and two algorithms were given to determine the complexity topologically without having explicit state-space representation.

Abstract: The paper considers the complete solvability and the order of complexity of passive RLCT (T = multiwinding ideal transformer) networks. A topological approach based on the determinant polynomial of the matrix of hybrid equations, formed as a set of 1st-order differential and algebraic equations, reveals the structure of the formulation tree and the subnetworks accountable for degeneracies. Topological and algebraic degeneracies are defined. Necessary and sufficient conditions for complete solvability are derived, and two algorithms are given to determine the order of complexity topologically, i.e. without having an explicit state-space representation.

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TL;DR: In this paper, a new property of impedance transformation is presented that can be applied to semiconductor switching-diode Q factor measurements, where the only parameter that must be known for the diode holder and diode package is the efficiency of the energy transmission from the source of the signal to the semiconductor junction.

Abstract: A new property of impedance transformation is presented that can be applied to semiconductor switching-diode Q factor measurements The only parameter that must be known for the diode holder and the diode package is the efficiency of the energy transmission from the source of the signal to the semiconductor junction

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TL;DR: A method is indicated by which wave digital filters of the true ladder structure can be realized efficiently using programmable hardware consisting of the following parts: arithmetic memory, program memory, coefficient memory and arithmetic unit.

Abstract: A method is indicated by which wave digital filters of the true ladder structure can be realized efficiently using programmable hardware consisting of the following parts: arithmetic memory, program memory, coefficient memory and arithmetic unit.
It is shown how to minimize the complexity of the first two mentioned memories.

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TL;DR: In this paper, an iterative method of solution of negative-resistance oscillators with piecewise-analytical characteristics is presented, which allows the determination of the frequency and the harmonic content of the waveform as a function of the circuit parameters and bias of the nonlinear device.

Abstract: An iterative method of solution of negative-resistance oscillators with piecewise-analytical characteristics is presented. The method allows the determination of the frequency and the harmonic content of the waveform as a function of the circuit parameters and bias of the nonlinear device.
An application of the method, extended to the second order, for a polynomial characteristic limited by two straight lines is also reported. The results are compared with those obtained by numerical integration.

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TL;DR: In this article, a general procedure is outlined to realize an arbitrary stable 2-variable transfer function using only resistors, capacitive elements and operational amplifiers; moreover, it is characterized by low active and passive sensitivities.

Abstract: A general procedure is outlined to realize an arbitrary stable 2-variable transfer function. The complete realization utilizes only resistors, capacitive elements and operational amplifiers; moreover, it is characterized by low active and passive sensitivities. The method may easily be extended to the realization of multivariable transfer functions.

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TL;DR: In this article, the authors established invariant lower bounds on the sensitivity of the input-output transfer function to perturbations of the gains and delays of the analogue delay lines.

Abstract: Analogue delay lines, in the form of charge-coupled or bucket-brigade devices, are important network elements that may be used in connection with gain elements and summer–subtractor elements to realize microelectronic filters. This paper establishes invariant lower bounds on the sensitivity of the input–output transfer function to perturbations of the gains and delays of the analogue delay lines. Conventional sensitivity criteria, known as the Worst-case and Schoeffler criteria, are used to represent the nonideal deviation of the transfer function.
It is demonstrated that, insofar as tolerance limitations are concerned, the conventional direct-form structure (which is extensively employed to realize charge-coupled-device filters), is far inferior to the ladder structure.

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TL;DR: In this article, a 3-port active hybrid network is constructed from an op-amp and a 5-port network composed of a few resistors and the design admittance y0.

Abstract: The building block for the new generalized immittance inverter is a 3-port known as the active hybrid network. One of its ports is bidirectional, and matches a design admittance y0. The second port operates in the send, while the third port operates in the receive direction. The hybrid is constructed from an op-amp and a 5-port network composed of a few resistors and the design admittance y0. There are two versions of the hybrid: the voltage-inverting (i.h.) and the noninverting hybrid (n.i.h.).
The inverter consists of an i.h. and an n.i.h. connected at their unidirectional ports in a loop. The gyration admittances are actual driving-point admittances in the circuit, namely the design admittances y0, y'0 of the two hybrids. Such an inverter, when terminated at its output port by a load admittance y, will give at its input port an input admittance yin = y0y'0/y.
Expressions are derived for the y parameters of the inverter at higher frequencies, thus accounting for the finite bandwidth of the op-amp.
Two special cases are particularly treated, and experimental results are obtained for them. The first is the case of the resistive gyrator, for which y0 and y'0 are pure conductances. The second is the case of the capacitive gyrator, for which y0 and y'0 are pure capacitive susceptances. The capacitive gyrator is used to produce the supercapacitor, or f.d.n.r., and the results of measurements on a number of f.d.n.r. networks are given.

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TL;DR: In this paper, a simple relationship is derived that enables one to calculate the root (pole and zero) sensitivities of F(s) in terms of the coefficient sensitivities.

Abstract: For any realization of a network function F(s) = N(s)/D(s), the sensitivities that can be most readily calculated are those of the coefficients in N(s) and D(s). A simple relationship is derived that enables one to calculate the root (pole and zero) sensitivities of F(s) in terms of the coefficient sensitivities. The root sensitivities, in turn, enable one to calculate the root pair Q and root frequency sensitivities, which can be used to characterize and compare different realizations of F(s). Application to 3rd- and 4th-order filters reveals formulations that are more elegant than those already known in the literature.

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TL;DR: In this paper, the continuously equivalent realizability of 3rd-order real symmetric paramount matrices is discussed and the existence of a 3rd order real-symmetric paramount matrix is investigated.

Abstract: The continuously equivalent realizability of 3rd-order real symmetric paramount matrices is discussed.

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Philips

^{1}TL;DR: In this paper, the perturbations from the periodic steady state are dealt with by a sensitivity matrix H. In order to illustrate the applicability of this theory, the performance of the dynamic limiter of Zaalberg van Zelst will be treated.

Abstract: The systems to be considered consist of linear and nonlinear elements and are driven by a priori known periodic signals (carriers). The present theory deals with small perturbations from the periodic steady state. Use has been made of the ‘amplitude-phase’ representation of the perturbations. The operator (jω0 + λ) is used, in which jω0 indicates the time differentiation of the carrier components and the operator λ ( = d/dt) affects the perturbation only. The perturbations will be related by a ‘sensitivity’ matrix H. In order to illustrate the applicability of this theory, the performance of the dynamic limiter of Zaalberg van Zelst will be treated.