bluuebunny/crossref_metadata_2025 huggingface dataset:
On the solvability and computation of D.C. transistor networks
Authors: Tadeusiewicz Michal
Published: July 2007

A study of non‐linear d.c. networks containing transistors, diodes, linear resistors, independent voltage and current sources and linear controlled voltage and current sources, described by Tf(x) + Gx = b is presented. A few theorems concerning both the solvability and numerical computation of d.c. transistor networks are proved. The conditions sufficient for the existence of at least one solution and of a unique solution are defined. A method for numerical computation of the networks without the need to determine inverse matrices is presented and the convergence of the iterative technique is analysed. Suggestions are formulated regarding applicability of the method for computation of an approximate solution (close to the exact solution) which may subsequently be quickly corrected using the Newton‐Raphson method.
Filter realization using a generalized lagrange polynomial representation
Authors: Liu Frank C. , Marshall Thomas G.
Published: July 2007

A polynomial representation using a set of generalized Lagrange polynomials for a basis is considered as an alternative to the natural representation. This new representation, which is employed in a previously described APL filter design package,8 is considered in detail, here, with regard to its algebraic and numerical properties for solving the realization problem of electrical filter synthesis. The necessary polynomial operations for filter realization are described in this representation. Then vector space algorithms are presented for these operations. The accuracy obtained from this representation is discussed. Advantages in both accuracy and simplicity of the new algorithms are noted.
A routing system based on a single‐row router and its wirability
Authors: Asahara Shigeo , Odani Maysayasu , Ogura Yasunori , Shirakawa Isao , Ozaki Hiroshi
Published: July 2007

A new routing system is described, which can be applied to printed wiring boards of different wiring densities such that the number of wiring tracks permitted between two consecutive pins of an ordinary dual in line package ranges from one to four. This system is distinctive in that a single‐row router is combined with a line‐search router in such a way that the search for possible wire segments at the stage of the line search router is implemented channel by channel, with all interconnections within each channel completed later by the single‐row router.

The program operates on an ACOS 77/900 computer, and has been applied to numbers of boards. Some of the implementation results are also shown to reveal how much the described system may attain its potentialities in the practice of layout of high density printed wiring boards.
A new approach to routing of two‐layer printed circuit board
Authors: Marek‐Sadowska M. , Kuh E. S.
Published: July 2007

This paper presents a new method for routing two‐layer printed circuit boards with fixed geometry, i.e. alternate columns of pins and vias. Circuit components are mounted on top of the board, and conductor wires are to be laid on the board such that circuit connections can be properly made. The proposed approach gives 100 per cent routability. The method consists of three steps, namely: partitioning of multi‐pin nets into 2‐pin subnets, via assignment, and routing on the two layers. In comparison with the traditional unidirectional routing, the method offers more flexibility and it requires usually about half as many vias. A computer program based on the presented algorithms was written. Its implementation is presented along with testing examples.
Optimum lowpass and bandpass filter approximation
Authors: Beccari Claudio , Molinaro Maurizio
Published: July 2007

The attenuation characteristics of lowpass and bandpass rational filters are approximated by optimizing a weighted error criterion. The analytical approach yields the solution in terms of kernel polynomials, and if the weight function has a particular form, the solution may be given explicitly in terms of the Szegö–Bernstein polynomials; with other weight functions it is necessary to resort to numerical procedures. The solution exhibits a passband behaviour that depends on the chosen weight function; when the Szegö–Bernstein polynomials are used both lowpass and bandpass filters may exhibit equiripple passband attenuation.
Energy‐related concepts for non‐linear time‐varying n‐ports: Passivity and losslessness
Authors: Gannett J. W. , Chua L. O.
Published: July 2007

Definitions of passivity and losslessness are presented that apply to n‐port networks which are not necessarily linear, time‐invariant, or lumped; in fact, these definitions apply to any n‐port that has an abstract dynamical system representation. For lumped, non‐linear n‐port networks that can be mathematically represented by a finite‐order dynamical system, conditions for passivity and losslessness are formulated in terms of properties of the state equation function, the output function, etc. These conditions can be verified without solving the state equation, and can be viewed as non‐linear generalizations of the well‐known time‐domain and frequency‐domain passivity and losslessness conditions for linear time‐invariant lumped n‐port networks.
Computer‐Aided partial synthesis of lossless non‐uniform lines of finite length
Authors: Chen Y. M. , Weng X. T.
Published: July 2007

A computer‐aided method for solving the problem of partial or one‐parameter synthesis of a lossless non‐uniform transmission line of finite length is presented. This method is essentially the same as the pulse‐spectrum technique for solving the inverse problems of determining the velocity coefficients of the wave equation from known information of the solution on the boundary. The basic idea of this method is that the original synthesis problem in the time‐domain is first reduced to a CW synthesis problem in the frequency‐domain, by either Fourier transform or Laplace transform, and then the synthesis is carried out in the frequency‐domain by using an iterative numerical algorithm. Numerical simulations are carried out to test the feasibility and to study the general performance of this computer‐aided synthesis procedure without the real design data. It is found that this computer‐aided method does give excellent results.
Finding all solutions of piecewise‐linear circuits
Authors: Chua Leon O. , Ying Robin L. P.
Published: July 2007

A new algorithm is given for solving the d.c. piecewise‐linear equations of non‐linear electronic circuits. The device models are assumed, with little loss of generality, to be made of 2‐terminal piecewise‐linear resistors and linear controlled sources. Unlike other methods, this algorithm guarantees that all solutions will be found in a finite number of steps. The method depends crucially on a recent development which allows a multi‐dimensional piecewise‐linear function to be represented in a closed canonical form. This highly compact representation requires only a minimum amount of computer storage and is responsible for the efficiency of the algorithm.
Non‐Recursive adaptive impulse noise canceller
Authors: Kazovsky Leonid G. , Turgeman Eli
Published: July 2007

A non‐recursive adaptive impulse noise canceller (AINC) is investigated. The AINC is designed to suppress long impulsive interferences which are a primary source of errors in many communication systems. Performance of the AINC depends upon the input filter of the receiver. It is shown that the optimum input filter is LPF; the optimum LPF bandwidth exists which provides the minimum error rate of the receiver. The system error rate is studied by means of a computer simulation. Simulation results indicate that the AINC provides a very effective suppression of impulse noise. However, conditions in a real communication channel may be quite different from those chosen for simulation. Therefore, further research remains to be done before the AINC can be recommended for practical applications.
Fault diagnosis in non‐reciprocal networks
Authors: Plotkin E. , Roytman L. M. , Swamy M. N. S.
Published: July 2007

Based on the theorem concerning the maximum number of independent simulations in an m‐port together with Tellegen's theorem, some methods are proposed for the determination of the values of the faulty elements. These methods require a minimum number of measurements at the external nodes of the circuit. A numerical example of the application of such a method is given.
Generalized second‐order active R filters
Authors: Nedungadi A. , Venkateswaran S.
Published: July 2007

A generalized treatment of second‐order active R filters is presented. A general circuit configuration is derived whose transfer functions are expressed in terms of defined resistive transfer functions and the gains of two operational amplifiers. The general network uses fewer resistances than reported configurations and can be used to realize all second order functions including oscillators. This approach facilitates simple and systematic analysis of second‐order active R networks and leads to configurations having minimum component count.
On the passivity criterion for lti N‐ports
Authors: Boyd S. , Chua L. O.
Published: July 2007

Existing proofs of the passivity criterion for linear, time‐invariant, distributed N‐ports are either incorrect or too involved, requiring the use of advanced mathematics such as distribution theory. This paper presents a simple but completely rigorous proof using only basic real and complex analysis. For the sake of completeness we have included simple proofs of the Paley‐Wiener theorem and the Poisson formula for the half plane. We show that solvability, a non‐intuitive technical assumption made in rigorous theories of LTI passive networks, is virtually always satisfied. Finally, we give a passivity criterion applicable to N‐ports described by general co‐ordinates, from which passivity criteria for any specific representation (e.g. impedance, admittance, hybrid, transmission, scattering, etc.) can be trivially derived.
Optimum flat delay filter characteristics
Authors: Pang Khee K. , Kirton Paul A.
Published: July 2007

The problem of finding optimum filter characteristics that produce flat delay in the passband is formulated as a convex programming problem for minimum‐phase lowpass filters. The flatness of the group delay is indicated by an error norm, which is a measure of the deviation of delay characteristic from a constant reference level. When the attenuation specifications are relaxed, it is possible to achieve a constant delay characteristic and the problem is solved analytically. When the attenuation constraints are too tight to achieve the constant delay characteristic, the problem is solved numerically. If the least squares error criterion is used, the problem is a quadratic programming problem. It reduces to a linear programming problem for the minimax criterion. Some resulting optimum attenuation characteristics and their associated error norms are given. The tabulated error norms represent the lowest theoretical limits that lowpass, minimum‐phase filters can ever attain. This is confirmed by comparing the limits against the performance of some well‐known filters.
High frequency active‐R filters
Authors: Bermudez José Carlos M. , Calôba Luiz P.
Published: July 2007

Limitations on active‐R filter pole displacements are studied. the maximum magnitude of the natural frequencies is presented as a function of the op. amp. GB. Structures to realized biqads with two op. amps. and a predistortion technique, to take into account the amplifier's high frequency pole, are proposed. Experimental results are presented which confirm the theory.
Simple solution curves of non‐linear resistive networks
Authors: Yun C. W. , Chao K. S.
Published: July 2007

A generalized sufficient condition for the existence of a (unique) simple solution curve defined by fi(x1, x2,…, xn) = 0 for i = 1, 2. … n − 1 is developed. the condition is deduced based on a parametric representation of a solution curve. Modified networks having identical (n − 1) network equations are generated and topological criteria associated with the sufficient condition are obtained from the examination of modified networks.
On the dynamics of non‐linear RLC networks from a geometric point of view
Authors: Szatkowski Andrzej
Published: July 2007

The dynamics of non‐linear RLC networks is considered from a geometric point of view. the concept of the Kirchhoff‐Maxwell space is presented and next it is explored in the formulation of the equations of motion for a broad class of dynamic non‐linear networks. Linearized networks and eventually strictly passive networks are examined. Several new structural stability results are given.
Negative resistance devices
Authors: Chua Leon O. , Yu Juebang , Yu Youying
Published: July 2007

Two‐terminal devices which exhibit a type‐S (current‐controlled) or type‐N (voltage‐controlled) negative differential resistance can be built using only two bipolar transistors and linear positive resistors without any internal biasing power supply. Two general algorithms are presented in this paper for systematically generating all such devices. Hundreds of negative resistance devices have been derived to date using these algorithms and a selection of these circuits is presented in this paper along with their computer‐simulated v‐i curves. Laboratory measurements of a few sample circuits agree remarkably well with the computer‐simulated results.
High‐order non‐linear circuit elements: Circuit‐theoretic properties
Authors: Chua Leon O. , Szeto Ellen W.
Published: July 2007

Highei‐ and mixed‐order non‐linear circuit elements have been introduced to provide a logically complete formulation for non‐linear circuit theory. In this paper, we analyse the circuit‐theoretic properties of these elements, including reciprocity, passivity and losslessness. We have derived necessary and sufficient conditions for a higher‐ or mixed‐order n‐port element to be reciprocal or antireciprocal. We have shown that under very mild assumptions, most non‐linear higher‐order 2‐terminal elements are active and not lossless. Finally, we show that the number of lossless linear higher‐order 2‐terminal elements far exceeds that of the passive linear elements.
An efficient numerical derivation of group delay characteristic from prescribed characteristic function
Authors: Kida Takuro , Kurogochi Katsumi
Published: July 2007

This paper proposes an efficient method of deriving the group delay characteristic only from the prescribed characteristic function of a resistively terminated LC 2‐port network with the aid of a special numerical integration technique. As a by‐product of the method, the transfer function of the network can also be derived. the idea of the method is based on the Hilbert transform relation between the attenuation and phase of the minimum‐phase polynomial. A simplified Hilbert transform relation is presented which avoids the improper integral of its original form. the analysis of the error due to the numerical integration applied in the method and the comparison with a conventional method concerning execution time and accuracy are included.
New sensitivity measures for resistively terminated LC filters
Authors: Kida Takuro , Kurogochi Katsumi
Published: July 2007

Two new sensitivity measures for resistively terminated LC filters with arbitrary network structures are proposed. One gives an upper bound of the absolute sum of the second‐order sensitivities of the operating propagation attentuation function with respect to the reactive elements. This measure, however, is based on the supposition of the invariance of the attenuation poles. the other gives an upper bound of the absolute sum of the first‐order sensitivities of the group delay characteristic with respect to the reactive elements. Both the measures can be evaluated only from the prescribed characteristic function of the network. Some examples are included which show the utility of these measures for designing filters with favourable statistical tolerance in the passband.
Efficient computer analysis of ideal switched‐capacitor circuits using matrix compaction techniques
Authors: Claesen Luc , Vandewalle Joos , de Man Hugo
Published: July 2007

In this paper we describe how three simple observations can be used in order to obtain an efficient algorithm for the computer analysis of ideal switched‐capacitor circuits. the resulting algorithm is linear in the number of phases. the first observation uses the structure of the r‐domain MNA‐matrix to come up with a new LU‐decomposition scheme which is gradual per timeslot. the second observation allows a great reduction in size of the z‐domain MNA‐matrix by a matrix compaction algorithm which also operates gradually per timeslot and which can be interleaved with the first gradual LU‐decomposition process. This leads to a small matrix which can then be used for a time‐ and direct frequency‐domain analysis. Third, the computations of transfer functions, aliasing functions and sensitivities can be optimized by applying appropriate excitations and making appropriate combinations of the terms in the expressions. These algorithms have been implemented in the SC‐analysis program DIANA.SC. the usefulness and efficiency of the program is then illustrated with some examples.
A solution for an infinite electrical network arising from various physical phenomena
Authors: Zemanian A. H. , Subramaniam Prasad
Published: July 2007

A procedure for determining the currents and voltages in a square or cubic grounded grid, wherein the grounding conductances can differ in quite arbitrary ways, is presented. Such a semi‐infinite electrical network is of practical importance, for it arises naturally from the discretization of a number of physical phenomena. There are very few classes of infinite electrical networks for which computational methods of solution exist; the present work adds one more class to that brief list.
A classification of multiple‐source feedback filters
Authors: Bowron P. , Stephenson F. W.
Published: July 2007

A family of two‐amplifier active‐RC filters having a single positive and/or negative‐feedback path is identified and evaluated. Four distinct categories emerge with respect to the input summing‐amplifier arrangement. These are embedded in buffered, differential and allpass‐pair networks to reveal many familiar and new configurations. the selectivity and sensitivity to gain‐bandwidth product are then presented in general expressions capable of describing the performance of all such circuits. Conditions for zero first‐order sensitivities and tuning flexibility are then developed.
A predistortion technique for RC‐active biquadratic filters
Authors: Goodman Ken , Zurada Jacek
Published: July 2007

A general method of forcing the transfer function of a biquadratic active filter to have poles/zeros in the desired locations is presented. Examples of the required calculations are shown. an example predistortion of a Thomas‐Tow section has been performed, and the resulting predistorted natural frequency and selectivity are presented graphically for a wide range of q‐factors and amplifier gain‐bandwidth products. the technique has also been applied to the point‐by‐point predistortion of a digitally tuneable filter. the general predistortion method has been used to obtain estimates of frequency and selectivity errors in non‐predistorted filters. the expression for relative q errors agrees with previous high‐q approximations of this error.
On street congestion in single‐row routing
Authors: Andersen Lars
Published: July 2007

A necessary and sufficient condition for realization with a given street congestion is presented. Based on this, an improved lower limit for the necessary street capacity is derived.
A generator of a poisson stream and its engineering applications
Authors: Wulich D.
Published: July 2007

A simple method of generating a Poisson stream is proposed. the method is based on the theorem which states that if a normal (Gaussian) and stationary process ‘upcrosses’ a ‘high’ threshold level, then the stream ‘upcrossings’ behave as a Poisson process. It is shown that it is sufficient to take a level equal to 3 xstandard deviation of the normal process (3σ) as the high level. the Poisson stream generator may be built from three blocks: a Gaussian noise generator, a lowpass filter and an ‘upcrossing’ detector. the intensity of the generated Poisson stream depends on the cutoff frequency of the lowpass filter and is proportional to it. Variation of intensity affects the variance of the normal process and, therefore, in a practical realization of the proposed generator, a circuit which automatically keeps the threshold level at 3σ must be added. Some engineering applications of the Poisson stream generator are given.
Local and global inconsistencies in the n‐port interconnection problem
Authors: Recski András
Published: July 2007

Conditions are given such that multiports, each possessing at least one hybrid immittance description possess no hybrid immittance description when interconnected.
Analysis of wave switched‐capacitor filters
Authors: Pandel Jürgen , Dawei Huang
Published: July 2007

For a special class of switched‐capacitor filters, the wave SC filters, a very efficient analysis method will be given. It is based on a block partitioning technique, i.e. the whole wave SC network is divided into small subnetworks. Only small matrices have to be processed which saves computation time, so that even large wave SC filters can be analysed very fast and with high accuracy. It will also be shown that the methods can be extended for the analysis of other SC networks. Some numerical examples of different wave SC structures will be given.
A method of design for a class of 2‐D filters
Authors: Prasad K. P. , Unbehauen R.
Published: July 2007

This paper discusses a method of designing quadrantally symmetric cascaded two‐dimensional (2‐D) digital recursive filters by subjecting a one variable approximating function to successive transformations. the needed approximation is done in the one variable domain rather than in the 2‐D domain, hence leading to a large reduction of computational labour. Using cepstral techniques each denominator polynomial is spectrally factorized into recursible non‐symmetric half plane components. A significant feature of the method is in decoupling the problems of approximation and stability. Consequently spectral factorization needs to be performed only once for each denominator polynomial. Effects of truncation on filter stability are minimized by ensuring rapid convergence of cepstra. the choice of an adequate DFT size in cepstral computations is shown to be an important consideration for many problems associated with spectral decomposition. Attempts are also made to stabilize the unstable transfer function using an existing 2‐D discrete Hilbert transform method. Considerable distortion in magnitude characteristics is shown to result on stabilization. Finally the method is illustrated by two examples.
Multifrequency approach to fault diagnosis
Authors: Swamy M. N. S. , Roytman L. M. , Plotkin E.
Published: July 2007

This paper deals with multiple‐fault diagnosis for linear analogue circuits. the proposed approach is based on multifrequency measurements of some voltage (transfer function) at the accessible output port and can be used for multiple‐fault location. It uses certain algebraic invariant properties of the transfer function with respect to the set of faulty elements. Computationally this approach reduces checking the problem of multiple‐fault diagnosis to one of the existence or non‐existence of a common solution of two systems of linear equations; this amounts to the finding of the rank of a matrix. These linear equations are derived via symbolic representation of the measured voltage (transfer function) accessible for measurements. A numerical example of the application of such an approach is given.
Interpolation with positive real functions of several variables
Authors: Gregor J.
Published: July 2007

The interpolation problem for n‐dimensional positive real functions is formulated in two different settings: with interpolation knots either contained on the distinguished boundary of the Cartesian product of open right half planes or in this n‐dimensional ‘open right half plane’. A complete solution of the first problem is given. Necessary conditions of existence of a solution of the second problem are proved and the well known Nevanlinna‐Pick algorithm is generalized so that construction of interpolating n‐dimensional positive real functions becomes possible at least in case when the interpolation knots are real vectors. Examples illustrate the suggested methods, show the complexity and significance of the problem and methods under discussion.

Interpolation in special classes of functions has for some time been an important problem in mathematics. General schemes of solution in linear functional spaces with orthogonality are well known. For classes of functions which do not satisfy the axioms of a linear space special methods have been studied in detail, because they are closely connected to other important parts of mathematics such as approximation theory, numerical analysis and the theory of moments. Considerable efforts have been put into interpolation in the complex domain with functions analytic in the unit disc and with positive real functions. the significance of interpolation procedures in the class of one‐variable positive real functions in network theory, e.g. in broadband matching and approximation problems has been recognized in References 1‐3. an excellent survey paper has recently been devoted to these problems;4 in this paper some new ideas for the use of interpolation in system theory were outlined. the growing interest in multivariable network theory calls for generalizations of interpolation procedures to multivariable cases. Many of the one‐variable applications can easily be extended to the multivariable case and it is hoped that in passive network theory and in problems of n‐dimensional digital systems the solution of the interpolation problem will contribute to the difficult synthesis problems in the multivariable theory.

In this paper conditions for the existence of multivariable positive real interpolating functions will be investigated and some procedures for the construction of such functions will be described.
A simplified design‐oriented analysis of switched‐capacitor active filters
Authors: Zhou Zhong‐Xuan
Published: July 2007

The method presented in this paper provides a simplified approach to obtain the z‐domain equivalent circuit of an SC active filter by one‐for‐one substitution of each basic SC element with its z‐domain equivalent admittance, if a specific terminal condition is met. Then, traditional circuit analysis techniques can be used to derive the z‐domain transfer function of the filter. This method makes the analysis and the design of the SC active filter simple and similar to the S‐domain method. Two application examples are given.
A generalized, complex adjoint approach to power network sensitivities
Authors: Bandler J. W. , El‐Kady M. A.
Published: July 2007

A unified study of the class of adjoint network approaches to power system sensitivity analysis which exploits the Jacobian matrix of the load flow solution is presented. Generalized sensitivity expressions which are easily derived, compactly described and effectively used for calculating first‐order changes and gradients of functions of interest are obtained. These generalized sensitivity expressions are common to all modes of formulating the power flow equations, e.g. polar and Cartesian. the approach exploits a special complex notation and complex matrix manipulations to define the adjoint system and to derive the sensitivity formulae. the approach is applicable to both real and complex function sensitivities.
All‐pole biquadratic filter realization with the minimum ripple due to parameter variations
Authors: Tan M. Ali , Acar Cevdet
Published: July 2007

In this work, the minimization of the ripple in the relative change of the transfer function amplitude due to parameter variations is studied for the signal‐flow graph of the state equations realizing all‐pole second‐order transfer function. First the measure for the ripple is defined and then branch transmittances minimizing the measure are found. the results obtained in this study can be used in all‐pole active filter realizations with the minimum ripple measure.
Synthesis of passive networks containing periodically operated thyristors
Authors: Kropacz Witold S. , Mikolajuk Kazimierz , Tobola Andrzej
Published: July 2007

This paper gives a new approach to the designing of power electronic networks. A method for the determination of passive time‐varying networks is given when time functions of the excitation and response are given. These time functions are periodic. the period is divided into intervals. the network is linear and time‐invariant in each interval. A sequence of the linear time‐invariant networks is realized using switches. Switched windings of a multiport transformer are defined. Such elements enable one to realize the sequence of the linear time‐invariant networks. Conditions for the substitution switches for thyristors are formulated. A structure of a thyristor converter is presented as an example.
Design of switched‐capacitor elements with voltage inverter switches for the simulation of FDNR Reference Structures
Authors: Brückmann Diter
Published: July 2007

A number of new elements for switched‐capacitor filters based on voltage inverter switches will be described. the new circuits simulate elements which are obtained from the normally used ones by FDNR transformation. They are insensitive to bottom plate parasitics and the influence of the to plate parasitics can be reduced. No matching is required between any capacitors in the SC circuit, so that the same low sensitivity to element variation holds as for the reference structure. These new elements allow realization of some further filter structures.
A generalized Chebyshev channelizing filter
Authors: Zabalwai Isam H.
Published: July 2007

In this paper some issues concerning the design and implementation of a satellite transponder's channelizing filter of degree 6 are discussed. In particular, the construction of the transmission coefficient, the synthesis procedure and the realization are discussed. the amplitude and the group delay responses of the filter are optimized simultaneously to meet prescribed requirements. the prototype filter has been synthesized as a cross‐coupled array. Explicit formulae for the element values in terms of the real and the imaginary parts of the poles of the transmission coefficient are derived. Single mode direct coupled cavity realization with positive and negative couplings has been developed. an experimental filter has been constructed, the measured responses are very close to the computed ones.
On discrete scattering Hurwitz polynomials
Authors: Fettweis Alfred , Basu Sankar
Published: July 2007

Discrete scattering Hurwitz polynomials play for discrete systems a similar role as scattering Hurwitz polynomials do for classical systems. A number of properties of discrete scattering Hurwitz polynomials are presented. These properties are obtained by deriving them from the corresponding properties of scattering Hurwitz polynomials. This is achieved by considering polynomials associated in a proper way to given polynomials and by examining the nature of the corresponding transformations.
Canonic forms of Brune and Darlington 2n‐ports
Authors: Belevitch V.
Published: July 2007

The Brune and Darlington syntheses for one‐ports have been extended to n‐ports by several authors. the synthesis algorithms are well established and are not discussed in this paper, which is essentially concerned with the minimal realizations (in the total number of elements, including ideal transformers) of the 2n‐ports occurring as building‐blocks in the synthesis. A unified view of that subject is presented, including many new results and a critical survey of the literature. an appendix dealing with the contragradient reduction of a pair of rectangular matrices is of independent algebraic interest.
On solving broadband matching design equations
Authors: Landau P. , Zeheb E.
Published: July 2007

Algorithms are presented which may be applied to:

Determining the real solution set in one variable plane, of a polynomial equation in many variables, where each variable other than the chosen one is confined to given intervals.

Determining the real solution set in one variable plane, of a system of polynomial equations and inequalities, where the number of variables is greater than the number of equations, and each variable other than the chosen one is confined to given intervals.

These algorithms are applied in certain cases of broadband matching design, which presented in the past some numerical difficulties. Illustrative examples are provided.
A very‐low‐frequency block‐digital oscillator
Authors: Acha José I. , Ayerbe Aranzau
Published: July 2007

The development of a block‐digital oscillator when the oscillating frequency fo is very low with respect to the sampling frequency fs is outlined. Explicit relations for the sensitivity to coefficient quantization, for scaling and for mean‐squared round‐off error analysis are derived. the principal conclusion is that both the sensitivity and the mean‐squared round‐off error remain constant and do not depend on the ration fs/fo. Finally, the block oscillator is compared with the scalar oscillator proposed in Reference 7; some numerical results are also included.
Designing non‐linear single OP‐AMP circuits: A cook‐book approach
Authors: Chua L. O. , Ayrom F.
Published: July 2007

The inherent saturation non‐linearity of the op amp is used to design circuits having a wide variety of useful non‐linear v‐i characteristics. These circuits are made of one op amp and 3 or 4 linear resistors which are passive under a rather mild assumption derived from the 3‐port paramountcy condition. Explicit design formulae are given for each prototype circuit and numerous examples are given and validated by actual measurements.
Design of digital filters with maximally flat passband and equiripple stopband magnitude
Authors: Saramäki Tapio
Published: July 2007

This paper introduces a general class of digital filters with maximally flat passband magnitude, equiripple stopband magnitude, and different order numerator and denominator. the classical Chebyschev type II (inverse Chebyschev) filters having equal numerator and denominator orders are considered as special members of this filter class. the filter types to be considered are lowpass, highpass and bandpass. the proposed filter class consists both of filters having all the zeros on the unit circle and of filters having some zeros off the unit circle to contribute to the passband shaping.

An efficient iterative algorithm for the design of filters of the given type is presented. It is based on shaping the passband and stopband responses alternately until the difference between successive solutions is within given tolerance limits.

Several comparisons show that in wideband applications filters with numerator order higher than denominator order present considerable advantages over equivalent Chebyschev type II designs, in terms of multiplication rate and/or frequency selectivity. In narrowband applications, in turn, filters with higher denominator order are shown to be the most effective.
On a class of SC resistors and its application to the synthesis of non‐linear driving‐point and transfer‐characteristic plots
Authors: Rodriguez‐Vazquez A. , Huertas J. L. , Chua L. O.
Published: July 2007

The use of switched‐capacitor components for designing non‐linear networks is discussed in this paper. We first introduce a new type of network component, the BESC resistor, and consider its application to the design of non‐linear transfer characteristic and driving point plots. Systematic methods for designing piecewise‐linear BESC resistors using switched capacitors are then given. Finally, experimental results showing the performance of the proposed circuits are included.
On the existence and uniqueness of stable quasi‐sinusoidal oscillations
Authors: Buonomo A. , di Bello C. , Greco O.
Published: July 2007

Conditions are established which ensure the existence and uniqueness of a stable oscillation in quasi‐sinusoidal electronic oscillators of any order. A method is presented whereby both the amplitude and frequency of the oscillation are computed and its stability verified.

Examples are given which illustrate how this method can be employed in synthesizing oscillators.
Canonical structures of DC‐AC thyristor converters
Authors: Mikolajuk Kazimierz , Kropacz Witold S.
Published: July 2007

Realizability conditions of periodic waveforms in passive switched circuits are presented. Formulae for an identification of state matrices in switched circuits are derived. As input data, time functions of excitation and response are chosen. Six general transformer structures of 1‐port thyristor converters have been obtained as a result of the synthesis method. The synthesis methods presented can be applied to create new thyristor and transistor arrangements, particularly thyristor compensators.
Canonic coupling of oscillators in a ring
Authors: Radparvar K. , Kaplan B. Z.
Published: July 2007

The paper deals with the phenomenon of coupling of several sinusoidal oscillators. The oscillators are arranged in a ring, and each oscillator affects its next neighbour in the ring. The coupling is unilateral and its main effect is due to variations in phase differences between neighbouring oscillators. The simple approach to the treatment of the behaviour of the coupling and the relative simplicity of the models of oscillators participating in the system enable an analytical solution of the problem to be found without a need to resort to complicated approximate methods. The results are supported by computer simulations. Several modes of dynamic behaviour of the system are identified. The number of possible modes increases with the number of oscillators in the ring. The paper concludes by demonstrating that the present results possess a potential of being useful in analysing some technological and natural systems.
Large change sensitivity analysis in linear systems using generalized householder formulae
Authors: Bandler J. W. , Zhang Q. J.
Published: July 2007

This paper investigates multiparameter large change sensitivity problems in linear systems by a set of generalized Householder formulae. The newly developed rectangular formulae can accommodate large, small and zero parameter changes directly by avoiding a critical matrix inversion as compared to the traditional square formulae. Possible determination of a minimum order reduced system, whose solution procedure constitutes the major work in large change evaluation is discussed. Applications to linear systems are considered for the original and adjoint systems w.r.t. single as well as multiple input‐output cases. This approach makes it possible to use large change analysis algorithms even if many parameters are changed.
Synthesis of recursive digital filters by state feedback of non‐recursive cascaded lattice filters
Authors: Feng Z. , Unbehauen R.
Published: July 2007

A general method to realize any digital transfer function is presented. The method is understood as a two‐stage process. First, a non‐recursive system having the same transfer zeros as the given transfer function is synthesized in the form of a special cascaded lattice structure. Then the poles of the non‐recursive system, which occur exclusively at the origin, are shifted by extending this system through state feedback so that the shifted poles coincide with the poles of the specified transfer function while the transfer zeros remain unchanged.1 Compared with the well‐known cascaded lattice structures proposed by Mitra et al.2 the resulting filters exhibit advantages in the realization of the adders. Furthermore, it is pointed out how the cascaded lattice structure2 can be derived from the structure introduced here by applying a state transformation.
Using nullors to analyse linear networks
Authors: Svoboda J. A.
Published: July 2007

Analysis of linear networks using nullors is considered. A simplified procedure is presented for doing nodal analysis of RLC nullor networks by computer. It is shown that using nullors to analyse linear networks is equivalent to doing modified nodal analysis.
One‐dimensional orthogonal search—a method for a segment approximation to acceptability regions
Authors: Ogrodzki Jan
Published: July 2007

As is well known, computer‐aided design methods that make use of specific properties of the networks being solved are much more efficient than general approaches suitable for very large classes of problems. In this paper an approach to acceptability regions, grounded on the bilinear theorem convenient for linear networks, is studied. Thanks to the bilinearity, exact analytical solutions on first‐order linear manifolds in the parameter space, i.e. when only one parameter is being changed at time, are available. This so‐called one‐dimensional orthogonal search (ODOS) has been applied to a segment approximation of acceptability regions. This approach lead; to spectacular results concerning shapes of acceptability regions, applicable in fundamental design problems.
Fault diagnosis of non‐linear systems: Graphical approach to detectability, distinguishability and diagnosis algorithm
Authors: Maeda Hajime , Ohta Yoshito , Kodama Shinzo , Takeda Shoichi
Published: July 2007

This paper discusses the problem of fault diagnosis for non‐linear systems described by a set of non‐linear algebraic equations. Necessary and sufficient conditions for fault detectability and fault distinguishability are given as analytic conditions, as well as graphical conditions. These conditions are then used to derive an algorithm for fault diagnosis. The technique is illustrated by an example.
An index of phase distortion
Authors: Clarke B. R.
Published: July 2007

Measures exclusively reflecting phase distortion are examined and a new phase distortion ‘index’ is proposed. This index, based on the mean‐squared degradation in the impulse response of a filter, is shown to be equivalent to a phase distortion ‘spot‐measure’ using the variation in the peak value of the impulse response, due to phase distortion, of the cascade combination of two identical filters. This equivalence allows the spot‐measure to be employed for rapid phase distortion evaluation without loss of accuracy in reflecting phase distortion.
Non‐linear non‐reciprocal resistive circuits with a structurally unique solution
Authors: Hasler Martin
Published: July 2007

A purely topological criterion is given, which allows one to determine when a non‐linear non‐reciprocal resistive circuit has exactly one solution, irrespective of its element characteristics. If the criterion is satisfied then it is shown that the solution has the same regularity as the element characteristics.
A unified construction of adjoint systems and networks
Authors: Narayanan H.
Published: July 2007

In this paper we introduce a technique for dealing with implicitly defined complementary orthogonal spaces. Using this technique we give a unified construction of various types of adjoint systems for dynamical systems defined through flow diagrams or graphs and also obtain the state and output equations of the adjoint systems in terms of the corresponding equations for the original system. Among other things we show how to construct the Kalman dual of a linear electrical network.
Switched capacitor filters with a row dominant nodal admittance matrix
Authors: Hasler Martin , Saghafi Morad
Published: July 2007

Stray capacitance insensitive switched capacitor filters are studied, whose nodal admittance matrix is row‐dominant for arbitrary capacitor values. Such filters have low passband sensitivities, because their transfer function is intrinsically bounded by 1, as is the case for LC‐filters. Furthermore, row‐dominant filters have the additional advantage that internal voltages are bounded by one, and reach this bound at each attenuation zero, which ensures optimal dynamic range. However, we show that the attenuation zeros of row‐dominant filters are located at the frequencies z2 with (z2)m = 1, where m is smaller than or equal to the number of operational amplifiers. Therefore, such filters are not suitable for conventional filter applications. Two examples of such filters are given.
Efficient solution of the variational equation for piecewise‐linear differential equations
Authors: Parker Thomas S. , Chua Leon O.
Published: July 2007

A closed‐form solution of the variational equation associated with a piecewise‐linear differential equation is derived. This closed‐form solution is used to develop an efficient method for calculating the solution of the variational equation. The method relies on the matrix exponential and requires no integration beyond the calculation of the trajectory along which the variational equation is being solved. Numerical results for the three‐dimensional case show an increase in efficiency of one to two orders of magnitude over the traditional method.
Devil's staircase route to chaos in a non‐linear circuit
Authors: Chua L. O. , Yao Y. , Yang Q.
Published: July 2007

A driven second‐order negative‐resistance oscillator circuit has been observed experimentally to exhibit infinitely many distinct chaotic states in addition to infinitely many subharmonic responses of all orders. Each chaotic state is found to be born out of a devil's staircase whose steps are spaced in accordance with a definite period‐adding law.

Each devil's staircase emerges at some level of frequency‐tuning resolution, where each level is embedded within an outer level, ad infinitum. The global bifurcation structure is self‐similar in the sense that upon rescaling, the devil's staircases appear to be clones of each other.
On the optimum design of symmetric two‐dimensional IIR digital filters with coefficients of finite word length
Authors: Papamarkos N. , Mertzios B. , Vachtsevanos G.
Published: July 2007

A method is described for the design of octagonally symmetric, non‐symmetric half plane, two‐dimensional IIR digital filters with integer coefficients. The design problem is formulated as an integer non‐linear problem and the solution is achieved via an integer non‐linear optimization algorithm. An example illustrates the features of the proposed approach.
A method of analogue‐digital multiple fault diagnosis
Authors: Reisig David , Decarlo Raymond
Published: July 2007

This paper develops an algorithm for multiple fault diagnosis of analogue‐digital circuits. By sequentially partitioning the devices into those ‘assumed good’ and those ‘under test’, it is possible to develop a set of fault diagnosis equations which account for the special nature of digital components. A modified Newton‐Raphson solution is then described which incorporates a digital state hypothesis testing scheme in the solution of the fault diagnosis equations for each partition. After solving for the input‐output characteristics of the devices under test, a Boolean decision algorithm is used to analyse the test results of each partition and thus sequentially arrive at the set of faulty elements. A generic condition for diagnosability in terms of the circuit topology is given. Two examples are included to illustrate the technique.
Transfer maps and return maps for piecewise‐linear three‐region dynamical systems
Authors: Kahlert Claus , Chua Leon O.
Published: July 2007

Techniques formerly developed in the theory of Poincaré half‐maps are modified and applied to the three‐region piecewise‐linear continuous dynamical system associated with Chua's circuit. Both transfer and return maps, induced by the trajectories inside the intermediate region in state space, are formulated as implicit equations. the boundaries of the domains of these maps are determined explicitly, using the method for calculating the initial points of touching trajectories subject to appropriate switching dynamics. A charting of the canonical parameter space of the dynamics that acts on the intermediate region is indicated. Among other things, this chart reveals the existence of new types of chaotic attractors different from the double scroll and Rössler attractors previously discovered from Chua's circuit.