bluuebunny/crossref_metadata_2025 huggingface dataset:
On filter pairs with butterworth characteristics
Authors: Belevitch Vitold
Published: July 2007

The paper deals with the design of 3‐ports consisting of the parallel connection, at port 1, of a lowpass ladder of degree n having all its attenuation poles at infinity, with a highpass ladder of degree m having all its attenuation poles at DC, the purpose of the design being to achieve a Butterworth (maximally flat) behaviour, simultaneously in the lowpass direction (1‐2) at DC and in the highpass direction (1‐3) at infinity. Norton1 has solved the case m = n for constant impedance filter pairs. the much more difficult case where one of the above restrictions is not met is discussed in general terms and some new results are obtained. Although the problem is far from being completely solved, useful explicit design relations are established for a few filter pairs of low degrees.
Ideal rectifier n‐ports are solvable
Authors: Belevitch Vitold
Published: July 2007

It is proved that an n‐port composed of ideal transformers, gyrators and ideal rectifiers has a unique solution for the port variables when it is excited by generators in series with strictly positive resistances. the multiplicity of solutions for the internal variables is discussed. Connections are established with the theory of linear inequalities and with the coloured branch theorem of graph theory.
Topological transformations of electrical networks
Authors: Narayanan H.
Published: July 2007

This paper deals with effects of modifications of network structure that may be studied without reference to the type of devices present in the network. We introduce and make systematic use of the notion of a generalized minor of a vector space. This operation generalizes the usual short and open circuit operations for a graph. Using the generalized minor operation we show how to make the equations of a given network appear to be the ‘bordered version’ of the equations of some other specified network. We also consider the decomposition of a network into several ‘multiports’ and a ‘port connection diagram’, and study the properties of a minimal decomposition (with port connection diagram having a minimum number of edges). In each case we present efficient algorithms wherever appropriate. Although the paper makes use of ideas from elementary matroid theory it is entirely self‐contained and requires no more than the knowledge of elementary linear algebra from the reader.
Elements of four‐port matrix theory as required for sc network analysis
Authors: Moschytz G. S.
Published: July 2007

Four‐port matrix theory is the foundation for various useful methods of analysing switched‐capacitor networks. Thus, for example, signal‐flow graph techniques, the link‐two‐port concept, and nodal computer analysis methods are based on either the four‐port transmission or admittance matrix. In the derivation of these analysis techniques transmission, reverse‐transmission, and transfer matrices are often used, but the relationship between them has not yet been clearly formulated for four‐port networks. In this paper an attempt at formulation and clarification is made. Furthermore, it is shown that, once the considerable simplifications due to the presence of opamps are taken into account, a simple and elegant method of hand analysis for basic SC circuits using a combination of transmission and transfer matrix parameters results.
Weakly non‐linear oscillator circuits and averaging: A general approach
Authors: Bernstein G. M. , Chua L. O.
Published: July 2007

The method of averaging has been used for years to prove the existence of oscillations in non‐linear circuits. In the past the application of averaging has tended to be ad hoc rather than systematic. In addition the validity of the method was not well established. the purpose of this paper is to rigorize and systematize the analysis of weakly non‐linear oscillator circuits via the method of averaging. In particular this paper will put on a rigorous foundation the work of Kuramitsu et al.1‐3 on the ‘averaged potential’ and the work of T. Endo and others on the oscillatory modes of coupled oscillator circuits. Furthermore we give a novel way of simplifying the calculation of averages when we have a potential function representation.
The topological foundations of electrical networks — complete models
Authors: Acciani G. , Cafaro G. , Dichirico C. , Vacca F.
Published: July 2007

The aim of this paper is to identify the topological entities underlying the construction of a complete (not reduced) network model. Consider an active network as a pair of physically different structures, i.e. a ‘dead network’ and an ‘excitation’. First, we define the general structure of the excitation which can be applied to a dead network; then the graphs Ga and G of the active and dead networks, respectively, are introduced. It is shown that, if a complete network model is to be constructed, the topological relations among the voltages and those among the currents of the network elements must be written choosing maximal independent sets of loops and cut‐sets of Ga. It is successively pointed out that the graph G can be obtained from Ga by means of a reduction operation, and the topological entities of G corresponding to the loops and to the cut‐sets of Ga are singled out. It has been found that a complete model of an electric network implies the use of four topological entities defined on the set of G‐edges, i.e. the closed path, the open path, the cut‐set and the pseudo‐cut, together with two topological entities defined on a maximal set of independent vertex couples of G, i.e. the ‘junction pair’ extreme of an open path and the ‘family of independent node couples’ split by a cut‐set.

Furthermore the different reference frames and the relative topological matrix transformations which allow a complete model of the network to be built up are singled out and discussed.
Bit‐serial vlsi implementation for an optimized transmultiplexer design
Authors: Catthoor Francky , de Man Hugo , Vandewalle Joos
Published: July 2007

The silicon implementation of a transmultiplexer system, from the high level description up to the floor‐plan, is presented. the described realization allows to integrate an entire 12‐channel TDM‐FDM transmultiplexer system on a silicon area of less than 80 mm2in a 5 μm single‐metal race‐free dynamic CMOS technology, making use of an available bit‐serial standard‐cell library. At the architectural level, a hardware‐sharing transformation combined with a number of optimizations for the coefficient quantization and the choice of the data word‐length, have allowed for a global area‐reduction of almost 50 per cent.

First a mainly manual approach has been investigated, where the hierarchical decomposition has been exploited to perform global and local optimizations in terms of the hardware. Later on, based on this experience, it has been employed as a major test vehicle for the CAD tool‐box of the bit‐serial silicon compiler1,2which has been developed during the pilot phase of an ESPRIT research project at our laboratory. Extensive use has been made of programs for filter synthesis, optimization, bit‐serial mapping, delay management and standard‐cell placement and routing. the results obtained with both design strategies are compared.

This research has given a concrete example of how systems, filter, network, circuit and CAD experience can be effectively combined into a VLSI design.
Topological conditions for the unique solvability of linear time‐invariant and time‐varying networks
Authors: Poletti Mario , Terreni Pierangelo
Published: July 2007

The problem of knowing whether the non‐unique solvability depends on the particular values of the components or on their topological interconnections is studied for linear networks with arbitrary, time‐invariant as well as time‐varying n‐ports.

Within every network, the topological notions of its sockets and of their independence are introduced. Networks with independent sockets are shown‐at least when there are no relations among the non‐zero coefficients, nor repetitions of the same coefficient are allowed, i.e. under suitable generality assumptions‐to be uniquely solvable. Networks with dependent sockets are shown to be never uniquely solvable.

Polynomially bounded algorithms, requiring only integer arithmetic, to test independence are available. When independence fails, a topological configuration of components which shows fewer topologically independent variables than equations, is proved to exist.
A substitution algorithm for solving nonlinear circuits with multi‐frequency components
Authors: Ushida A. , Chua L. O. , Sugawara T.
Published: July 2007

In this paper, we present an efficient algorithm for calculating the steady‐state response of nonlinear circuits such as forced circuits driven by multi‐frequency‐component signals, forced oscillators, and coupled oscillators. We call the technique a substitution method because the variation at each step is calculated by solving an associated time‐invariant sensitivity circuit at each frequency component of the residual error, whose circuit is derived from a relaxation method. the algorithm is very simple and efficient, and it can be applied to a wide variety of nonlinear circuits.
A systematic approach to the design of stray‐insensitive sc circuits from active‐RL or RLC prototypes
Authors: Rathore T. S. , Bhattacharyya B. B.
Published: July 2007

A systematic approach to the design of stray‐insensitive switched‐capacitor (SC) circuits from active‐RC or RLC prototypes employing a parasitic insensitive SC differential voltage‐controlled current‐source as a basic building block is attempted. Procedures for transforming active‐RC and RLC circuits into stray‐insensitive SC circuits are formulated and illustrated with typical examples. Restrictions on the pole‐frequency and pole‐Q of the SC biquad are derived so that it closely emulates the frequency response of the original active‐RC biquad. the SC biquad and the ladder filter derived by the proposed procedures were simulated with discrete components and tested in the laboratory. Test results agree closely with the theoretical predictions.
The ranges of transfer and return maps in three‐region piecewise‐linear dynamical systems
Authors: Kahlert Claus
Published: July 2007

The ranges of the transfer and the return maps that are induced by the flow of a piecewise‐linear continuous dynamical system describing Chua's circuit are investigated analytically. the two sets turn out to be intertwined for all values of the parameters. For high enough frequencies of the saddle‐focus, located at the origin of state space, the first set forms ‘inclusions’ inside the second one. A charting of parameter space describing the creation and annihilation of the above inclusions quantitatively is indicated.
Multimode oscillator analysis via integral manifolds part I: Non‐resonant case
Authors: Chua Leon O. , Endo Tetsuro
Published: July 2007

This article represents Part I of a two‐part paper which provides a rigorous mathematical foundation of the modeanalysis method for analysing the periodic and quasi‐periodic oscillations observed in various types of coupled oscillators. Although the results predicted by this method had been confirmed by experiments to some extent, the crucial assumptions used to derive the averaged equations are based on engineering intuition. Moreover, while it is intuitively reasonable to associate an equilibrium solution of the averaged equations whose eigenvalues have negative real parts with that of a stable periodic or quasi‐periodic solution of the original equation, the relationship between the solution of the averaged equations and that of the original equations as t tends to infinity, is not clear in a mathematical sense.

This paper resolves the theoretical ambiguities of the mode analysis method by using the theory of integral manifolds. In particular, we recalculate the averaged equations in a rigorous way, and show that they coincide with those obtained before. Therefore, the theory of integral manifolds guarantees the existence of an integral manifold in the original system which corresponds to a steady‐state periodic or quasi‐periodic solution, provided the equilibrium point of the averaged equation has no eigenvalues with a zero real part (i.e. hyberbolic). This rigorous analysis proved that all our previous results obtained from the mode analysis method, i.e. averaged equations and stability analysis were correct.
Multimode oscillator analysis via integral manifolds part II: Resonant case
Authors: Chua Leon O. , Endo Tetsuro
Published: July 2007

This article represents Part II of a two‐part paper which provides a rigorous mathematical foundation of the modeanalysis method for analysing the periodic and quasi‐periodic oscillation observed in various types of coupled oscillators. Although the results predicted by this method had been confirmed by experiments to some extent, the crucial assumptions used to derive the averaged equations are based on engineering intuition. Moreover, while it is intuitively reasonable to associate an equilibrium solution of the averaged equations whose eigenvalues have negative real parts with that of a stable periodic or quasi‐periodic solution of the original equation, the relationship between the solution of the averaged equations and that of the original equations as t tends to infinity, is not clear in a mathematical sense.

This paper resolves the theoretical ambiguities of the mode analysis method by using the theory of integral manifolds. In particular, we recalculate the averaged equations in a rigorous way, and show that they coincide with those obtained before. Thereore, the theory of integral manifolds guarantees the existence of an integral manifold in the original system which corresponds to a steady‐state periodic or quasi‐periodic solution, provided the equilibrium point of the averaged equation has no eigenvalues with a zero real part (i.e. hyperbolic. This rigorous analysis proved that all our previous results obtained from the mode analysis method, i.e. averaged equations and the analysis were correct.
Layout including parasitics for printed circuit boards
Authors: Wawryn Krzysztof
Published: July 2007

An automatic layout system is developed for optimal simultaneous placement of elements and equipotential nodes and routing interconnection paths that can be applied to multilayer analogue printed circuit boards (PCBs) including parasitic couplings. the objective is to minimize the influence of parasitic capacitance and inductance couplings of printed paths on performance of analogue circuits as an electrical criterion. A force model has been used to determine optimal placement where the sensitivities of network function on parasitic capacitances and inductances are the sets of weighted coefficients between forces of attractions and repulsions. the routing algorithm is a combination of topographic simulation method with minimum length connection path. the topography of predicted parasitic couplings is formed before each connection path is routed where the sensitivities of the network function on parasitic capacitances and inductances create the heights of tops. Placement and routing algorithms have been developed, programmed and compared with conventional force algorithm and the Lee algorithm. Practical results of frequency characteristics of printed circuit boards of a wide‐band HF amplifier have been obtained and presented.
High‐speed non‐linear circuit models for p‐n junction diodes
Authors: Chua Leon O. , Chang Chwen‐Cher
Published: July 2007

Circuit models for both long‐base and short‐base p‐n junction diodes which are valid for non‐linear high‐speed and high‐frequency operations are presented. the diode model consists of a parallel connection of higher‐order dynamic elements and includes the conventional diffusion model as a special case. the new dynamic model can be used for simulating arbitrary p‐n junction diode circuits under all operating conditions. In particular, it is capable of simulating realistically the diode's reverse transient behaviour and providing an increasingly accurate approximation to the diffusion equation as the order of the model gets higher. the model is also shown to be capable of reproducing the frequency‐dependent small‐signal characteristics of p‐n junction diodes.

The model is based mainly upon the device's physical operating principles. Perhaps the most significant implication of the model is the fact that it illustrates the important roles played by higher‐order and dynamic elements in highspeed and high‐frequency non‐linear device modelling.
The overdamped double‐scroll family. Part I: Piecewise‐linear geometry and normal form
Authors: Silva Christopher P. , Chua Leon O.
Published: July 2007

This paper is the first part of a two part work that aims to introduce a new family of piecewise‐linear differential equations that exhibit chaotic behaviour in numerical simulations and to provide a rigorous mathematical proof of its chaotic nature.

The new family presented here has the same eigenvalue distribution as the well‐known Lorenz equations in its chaotic regime but has a different symmetry. It is a derivative of the recently investigated double‐scroll family of piecewise‐linear differential equations.1 It differs, however, from the double‐scroll family in that its members have all real eigenvalues at the origin. In particular, since the associated eigenspace Es(0) is similar to that of an overdamped linear circuit, we will henceforth refer to this family as the overdamped double‐scroll family.

We establish Chua's circuit2 as a member of this family under appropriate conditions. Preliminary numerical simulations exhibit some interesting phenomena such as period‐doubling, periodic windows between chaotic behaviour, and strange attractors of differing geometric structure.

Our approach in the rigorous analysis will be that employed for the double‐scroll family in Reference 1. We derive a linearly equivalent class of piecewise‐linear differential equations which includes the family simulated numerically as a special case. the necessary and sufficient condition for two piecewise‐linear vector fields belonging to this new overdamped double‐scroll family to be linearly equivalent is that their respective eigenvalues at respective equilibrium points be scalar multiples of each other. If the scalars are all identity, then we have linear conjugacy of the vector fields. an explicit normal form equation, in the sense of global bifurcation, is presented that is parametrized by its own eigenvalues.

We find that linearly equivalent vector fields associated with the overdamped double‐scroll family exhibit the same global behaviour even though their equivalence is based on the local concept of normalized eigenvalues. In addition, the piecewise‐linear differential equations associated with these equivalent vector fields can be quite different from each other.
Parallel processing for analogue fault diagnosis
Authors: Wey Chin‐Long
Published: July 2007

The computer‐aided testing (CAT) problem is inherently a large scale systems problem, it is essential to exploit whatever computational power is available to reduce the computational requirements for both on‐line and off‐line test processes. In particular, digital CAT algorithms often use some degree of parallel processing in their implementation. Therefore, the degree to which an analogue CAT algorithm can be implemented in parallel becomes a significant factor in determining its viability.

In this paper, a parallel test algorithm and the associated architecture for the test system for analogue circuits and systems are proposed. the proposed test algorithm is applicable to testing multiple faults. Based on a combinatorial covering set approach, the conditions for the non‐sequential execution of the test algorithm is analysed and the parallel processing to generate the test results is also addressed.

Although this paper is motivated on the discussions of analogue fault diagnosis, the proposed parallel algorithm and the combinatorial covering approach can also be applied to digital testing.
A neural network approach to transform image coding
Authors: Chua L. O. , Lin T.
Published: July 2007

A neural network approach is presented for transform image coding. It is shown that the three steps in the conventional transform image coding, i.e. the unitary transform of spatial domain image data, the quantization of the transform domain data and the binary coding of the quantized data, can be unified into a one‐step optimization problem. Then, the optimization problem is solved by an appropriately constructed Hopfield neural network whose input is the spatial domain image data and whose output is binary codes. A practical circuit implementation is given to perform the transform image coding. the circuit has rM2 neurons, where r is the bit‐rate, in bit/pixel, of the coding and M2 is the size of the images. Each neuron consists of only a non‐linear voltage amplifier, a linear voltage‐controlled current source, a d.c. current source, a linear passive resistor, a linear passive capacitor, and a weighted voltage summer which can be made of a single op amp with some linear passive resistors. Moreover, each neuron is locally connected with no more than b ‐ 1 other neurons by wires, where b is the maximum bit allocated to a transform domain coefficient. Therefore, our proposed approach is particularly suitable for low‐bit‐rate image coding and VLSI implementation. Furthermore, the analogue and parallel nature of our approach matches perfectly the high‐speed requirement of real‐time image coding.
Simulated‐annealing‐based optimization of coefficient and data word‐lengths in digital filters
Authors: Catthoor Francky , de Man Hugo , Vandewalle Joos
Published: July 2007

The accurate characterization of worst‐case limit‐cycle behaviour and other finite word‐length effects in digital filters constitutes a challenging and important optimization application. Indeed, for a chip implementation this can lead to a significant reduction in the signal word‐length and hence to considerable savings in terms of the final chip area. This paper describes a new and accurate method for this investigation which is based on a simulated annealing procedure with a general scope. Novel methods for dynamically and efficiently updating the essential parameters of the annealing schedule keep the required CPU times reasonable.

The quality of the results obtained with our optimization routine and the general applicability of our approach are further substantiated with some promising results for the quantization of coefficients in arbitrary digital filters.
Graphs in floor‐plan design
Authors: Otten Ralph H. J. M.
Published: July 2007

Graph models play an important role in floor‐plan design. In this paper the relations between the various models are investigated. Useful graph‐theoretical facts are presented in this context, and their application is discussed. Special attention is given to the implications of structural restraints, for the models as well as for the applications, geometrical optimization and global routing in particular.
Module placement for large chips based on sparse linear equations
Authors: Tsay Ren‐Song , Kuh Ernest S. , Hsu Chi‐Ping
Published: July 2007

There are many algorithms for automatic placement in IC layout design. However, as chips become increasingly larger and more complex, existing algorithms are no longer suitable. One major drawback in existing algorithms is that the sparsity inherent in the placement specification has not been taken into consideration properly.

In this paper, we propose an efficient method of module placement for large and highly complex chips by repeatedly solving sparse linear equations. the resistive network analogy of the placement problem and the convexity of the objective function play a major role in our approach. Our method employs the SOR (successive over‐relaxation) method to solve the linear equations and uses a top‐down hierarchy in partitioning the chip. We have also devised an effective BGS (block Gauss‐Seidel) iteration scheme to achieve global optimum results.

The method has been implemented and tried with a number of real chips. For a triple‐metal‐layer, 100K sea‐of‐gates with 26,000 instances, it takes 50 min on a VAX 8650 and yields excellent results in terms of total wire length.
An efficient algorithm for two‐ and three‐dimensional IC floor planning
Authors: Kyung C. M. , Lee P. H. , Yang Y. Y. , Park I. C.
Published: July 2007

This paper proposes a new procedure for floor planning of VLSI chips in two‐ and three‐dimensional space using the so‐called ‘scatter‐and‐gather’ approach. In the ‘scattering’ phase of this approach, dots denoting the mass centre of each functional block are ‘scattered’ in 2‐D space using FDR (force‐directed relaxation), UCG (unconstrained cluster growth) or CCG (constrained cluster growth) techniques.

The ‘gathering’ phase is modelled as a computational geometrical problem called MBE (minimal box embedding), for which two practical solution techniques, GBS (growing box scheme) and RBS (reducing box scheme) are described. the 2‐D MBE problem is to find the orientation, shape and size of a rectangle which has the smallest area among those rectangles which stay within the specified aspect ratio range and include (gather), at least, the specified fraction of dots scattered in 2‐D space. Several speed‐up techniques such as incremental transform/sorting and quadrant folding are also explained. It is shown through experiment that the UCG has advantages over FDR in terms of CPU time and the degree of correlation between the area of the minimum embedding box and the routing length.

The proposed MBE algorithm has been extended to the layer assignment of circuit modules in truly three‐dimensional package planning where the circuit modules are placed on multiple layers and inter‐layer connections are allowed in the interior of each layer plane. Experimental results on 2‐D and 3‐D examples have shown that the MBE algorithm is at least 20 times faster than simulated annealing (SA) in the 2‐D case, and min‐cut‐based layering plus force‐cut placement in the 3‐D case. On the other hand, the routeing length overhead of the MBE algorithm was about 30‐40 per cent in the 2‐D case compared to SA, and only 10 per cent in the 3‐D case compared to min‐cut layering followed by the force‐cut placement technique.
Maximally linear FIR digital differentiators for midband frequencies
Authors: Kumar B. , Dutta Roy S. C.
Published: July 2007

Among the known FIR digital differentiators, the minimax relative error (MRE) approximations are the most efficient ones, where the weighting coefficients are derived by using an optimization algorithm. This approximation fails at the frequency ω = π if the order N of the differentiator is odd. A half sample advance (i.e. a delay τ = −1/2) and an even N become necessary to extend the MRE approximation up to ω = χ; these are, however, undesirable features, particularly in large signal processing systems. This paper proposes digital differentiators, which are characterized by maximal linearity of the frequency response at the midband frequency ω = π/2, and gives a mathematical relation for the weighting coefficients. the order N of the differentiator has been ensured to be odd, and no half sample advance has been used. It has been shown that for relative error (RE) ⩽ 1 per cent, the proposed differentiators are more efficient as compared to those based on the MRE approximation, in terms of multiplications required per sample of the input signal for all N (N odd). the proposed approximations are also capable of giving extremely low RE (10−3 to 10−6 per cent), for narrow midband frequencies, with attractively low order N.
Cascade decomposition of a passive 2n‐port network
Authors: Uruski M.
Published: July 2007

This paper deals with a cascade decomposition of a passive 2n‐port network. after a basic discussion relative to complex‐ and unit‐normalized scattering matrices, necessary and sufficient conditions are presented under which given lossless 2n‐ports D1 and D2 are simultaneously extractable from the front‐ and back‐ends of the passive 2n‐port N, respectively, to leave a passive 2n‐port remainder Ne. Based on these conditions, some relations between the individual and simultaneous extractability of D1 and D2 from N for both degenerate and non‐degenerate remainders Ne are discussed. the results are presented in terms of scattering as well as impedance matrices and can be considered as an extension of those given in Reference 1.
‘Lorenz attractor’ from an electrical circuit with uncoupled continuous piecewise‐linear resistor
Authors: Tokunaga R. , Komuro M. , Matsumoto T. , Chua L. O.
Published: July 2007

We present a simple piecewise‐linear circuit which exhibits a chaotic attractor similar to that observed from the well‐known Lorenz equation. Whereas the non‐linearities in the Lorenz equation consists of two product terms between two state variables, the non‐linearities in our circuit consists of two ‘uncoupled’ 2‐terminal continuous non‐linear resistors, each characterized by a 2‐segment v‐i characteristic.

Both experiments and computer simulations of this circuit confirm a Lorenz‐like strange attractor. the nature of the trajectories associated with this attractor is analysed and explained with the help of the circuit's piecewise‐linear‐geometry.
Design of odd‐degree linear‐phase sampled‐data bandpass filters with equiripple amplitude response
Authors: Fahmy M. F. , Abo‐Zahhad M. , Sobhy M. I.
Published: July 2007

This paper presents a novel approach for the design and synthesis of odd‐degree sampled‐data filters. Initially, an efficient iterative scheme is described for the construction of a class of selective linear‐phase distributed bandpass filters with equiripple passband loss response. Then, the filter's transfer function is synthesized using classical distributed circuit networks. Finally, the equivalent switched‐capacitor filter could be constructed. the resulting switched‐capacitor networks are completely insensitive w.r.t. parasitic capacitances, as well as having low Cmax/Cmin Design tables and an illustrative example are also given.
Pseudopassive two‐dimensional recursive digital filters for image processing
Authors: Domanski Marek , Fettweis Alfred
Published: July 2007

This paper describes the theory of two‐dimensional digital filters that are pseudopassive with respect to the lp‐norm of the state vector. As the classical pseudopassive digital filters are a subclass of these filters, the respective theorems referred to stability are also generalized. It is shown that this theory is useful for the two‐dimensional filters that answer with non‐negative‐valued responses to non‐negative‐valued excitations. Such systems are especially suitable for image processing. the synthesis of the l1‐pseudolossless systems is proposed as a tool to guarantee stability of such filters. A technique to obtain local state‐space models for such two‐dimensional l1‐pseudolossless recursive filters with prescribed spatial responses is given. A ‘Gaussian filter’ design illustrates the technique and shows that the proposed two‐dimensional l1‐pseudolossless filters are able to match useful spatial responses.
Fault prediction process for large analogue circuit networks
Authors: Jiang Ben‐Lu , Wey Chin‐Long
Published: July 2007

To make the existing fault diagnosis algorithms suitable and feasible for practical large analogue networks, a large network must be decomposed into small uncoupled subnetworks. Recently, an efficient decomposition approach fault diagnosis process has been proposed by Bandler et al. This approach keeps both the computations and measurements to acceptable bounds. However, the error effect due to component tolerance in practical circuits may drastically affect the identification of the faulty components. In this paper, a fault prediction approach fault diagnosis process is presented to diagnose precisely the faulty components. the result of this study shows that error effect can be alleviated significantly if the network can be continuously monitored. the proposed fault prediction approach results a significant improvement in both computation and error effect over the original decomposition approach.
Design of two‐dimensional pseudolossless digital filters with prescribed spatial responses
Authors: Domanski Marek
Published: July 2007

The paper presents a technique to compute the parameters of the state‐space model of the two‐dimensional pseudolossless (e.g. wave or orthogonal) digital filter that best approximates a given spatial response. the search for the optimal solution is performed using an unconstrained optimization algorithm with reduced number of parameters. the optimization variables are the elements of the upper triangle of a skew‐symmetric matrix which is related to the orthogonal system matrix by the Cayley formula. Thus the resulting system is always stable.
On the development of symmetrically stabilized five‐phase oscillators and some implications
Authors: Kaplan B. Z. , Yardeni D.
Published: July 2007

The paper deals with the development of a symmetrically stabilized five‐phase oscillator. the development results from two origins. It employs on one hand a five‐phase conservative oscillator. On the other hand the stabilization process of the oscillator is due to similar non‐linear damping terms in earlier developments of stabilized three‐phase oscillators. A new feature of the present system is that it possesses an interesting steady state limit‐cycle behaviour. the two possible steady state oscillations are similar, since both of them consist of a five‐phase balanced set of phasors which are arranged symmetrically. However, each mode of possible steady state oscillation possesses its own unique frequency, although the amplitudes are equal. Another interesting feature of the oscillator is related to the way in which the various possible solutions (oscillatory, steady state, stable and unstable dynamic behaviours) evolve from initial conditions. There seem to exist regions where the system solutions appear sensitive to minute changes in initial conditions. It appears that completely different types of dynamic behaviours can develop from initial conditions in close proximity, which may lead eventually to the development of slightly modified systems with chaotic dynamics. the paper concludes by suggesting an application of multiphase oscillators for feeding phased array antennas.
Steady‐state response of non‐linear circuits: A frequency‐domain relaxation method
Authors: Ushida A. , Chua L. O.
Published: July 2007

We propose here an efficient algorithm for finding the steady‐state response of stiff non‐linear circuits. It is based on a frequency‐domain relaxation method and can be applied efficiently to obtain the steady‐state waveforms of both periodic systems and multi‐frequency‐component systems. the solution at each iteration is obtained by solving an associated linear time‐invariant circuit at every frequency component via modified nodal analysis. Our algorithm is very simple and can be applied efficiently to solve a large class of practical non‐linear communication circuits which are notoriously stiff and hence rather time‐consuming to solve with existing methods.
Bifurcation analysis of a cusp‐constrained piecewise‐linear circuit
Authors: Tokunaga Ryuji , Chua Leon O. , Matsumot Takashi
Published: July 2007

This paper gives a detailed bifurcation analysis of a cusp‐constrained circuit in terms of the quantity ‘rotation‐jump ratio’. This turns out to be a very natural quantity to analyse various interesting bifurcation phenomena observed in the circuit.
Simultaneous amplitude and phase approximation for fir filters
Authors: Leeb F. , Henk T.
Published: July 2007

An FIR filter design method with simultaneous amplitude and phase approximation is presented. Two components are proposed in the design method: simultaneous amplitude and phase interpolation in the passband and amplitude interpolation in the stopband. These interpolations are implemented by the Remez exchange algorithm.

The polynomials for the interpolations are generated by recurrence formulae and the recurrence coefficients are calculated by a recursive method. the properties of the filters designed with the simultaneous approximation are investigated and compared with those of exact linear and minimum phase filters.
Cmos latchup theory
Authors: Deng A. C. , Chua L. O.
Published: July 2007

The purpose of this paper is to study the CMOS latchup phenomenon from a non‐linear circuit theoretic standpoint by using some recently developed results on negative‐resistance devices. We introduce a simple mechanism to describe the latchup phenomenon based on a special circuit topology called feedback structure, which is shown to be responsible for the occurrence of latchup. Several guidelines are proposed to prevent latchup by destroying the feedback structure. In addition to the characterization of the steady‐state behaviour, we use a first‐order circuit model to analyze the latchup dynamics during the turn‐on process and give a stability analysis of the circuit dynamics. All existing techniques to prevent latchup are shown to follow naturally from our guidelines, which are derived using nonlinear circuit theory.
Prototype filters with a maximally flat impulse response
Authors: Rhodes J. D.
Published: July 2007

The theory and synthesis of a class of filters designed to give a maximally flat impulse response is presented. A number of different sets of element values can be obtained for each degree of filter, each having the same transmission loss characteristics, but different return loss characteristics when dissipation loss is included in the analysis.
Darlington's theorem and complex normalization
Authors: Pauli Rainer
Published: July 2007

Two novel proofs are presented to establish the equivalence between complex normalization and Darlington representation of the loads. Schwarz reflection of analytic functions and Hermitian metrics serve in these proofs as natural concepts for the analysis of lossless multiports. By use of these tools, the algebraic structure that underlies the physical notion of losslessness is analysed, and a class of matrix representations of lossless 2n‐ports is derived. the fundamental transformations between these matrices are established to facilitate easy conversion of results related to different choices of co‐ordinates (voltages/currents, waves, impedances, reflectances). By virtue of this theory, complex normalization is tacitly extended to include not only impedances but also reflectances as references. Explicit expressions for a 2n‐port normalized to complex loads are derived. Invariance of the complex normalized scattering matrix in a lossless cascade circuit is shown to be the most comprehensive generalization of the well known invariance of scalar reflection magnitudes. the relation between this viewpoint and the general theory of invariants of linear fractional maps in terms of cross‐ratios is pointed out explicitly. the factorization problem, common to complex normalization as well as Darlington representations, is also reviewed, and it is shown that the concept of minimal factorization (well known in linear prediction theory) leads to more satisfactory results than those of established factorization recipes in complex normalization.
The large‐change sensitivity network
Authors: Aeyels Dirk , Wlllems Jacques L.
Published: July 2007

In this paper the large‐change sensitivity network is introduced as a notion which is helpful in the investigation of sensitivity problems. the relation with the small‐change sensitivity network is discussed. Three problems are considered, chosen mainly to illustrate the power of this new concept: for example, we show how the classical Thévenin and Norton theorems follow directly from the large‐change sensitivity network and its properties.
The dynamics of a non‐linear discrete oscillator
Authors: Wu Jingtang , Yang Yongyi
Published: July 2007

The dynamic behaviour of a simple second‐order discrete system with a single non‐linear factor, specified by (x, y)‐ (Ax + B(y + sin(2π(x +y))), x), (A, B) ϵ D = {(A, B): A, B ≥ 0, A + B < 1} ‐ is studied. the parameter subspace of D is analysed in detail. the bifurcation sets of the system are found. the existence of chaos in the system is proved by applying Marotto's theorem. the result of computer simulation agrees well with its analytical counterpart, and confirms that the single non‐linear factor ϕ = sin(2π(x + y)) is indeed the crucial point of a very complicated dynamic behaviour, including the alternative emergence of periodic, quasi‐periodic and chaotic phenomena, of this simple second‐order oscillator.
Analysis and design of self‐limiting single‐OP‐AMPRC oscillators
Authors: Huertas José L. , Pérez‐Verdú Belén , Rodríguez‐Vázquez Angel
Published: July 2007

This paper considers the design of self‐limiting single‐op‐amp RC oscillators inside the frequency range where the slew rate is the dominant non‐linearity. It is first demonstrated that limitation by the slew rate yields zero first‐order frequency sensitivity with respect to changes in the op amp gain‐bandwidth product (GB). Design procedures are then outlined for each of the structures comprising the complete set of canonical RC oscillators. Sensitivity figures providing criteria for comparison between the different structures are also included. Finally, experimental results are shown illustrating the validity of the proposed techniques.
Design of recursive digital filters with variable characteristics
Authors: Mitra Sanjit K. , Neuvo Yrjö , Roivainen Hannu
Published: July 2007

A new method for changing the cut‐off frequency of infinite impulse response (IIR) digital filters with a single parameter is derived. the method is based on the use of the Taylor series expansion of the lowpass‐to‐lowpass frequency transformation. the filter structure is a parallel connection of real or complex allpass sections. the tuning range is several octaves for narrowband filters. By taking also the complementary output, a power‐complementary filter pair with tunable crossover frequency is readily obtained. Tunable centre frequency and bandwidth are obtained by incorporating a special lowpass‐to‐bandpass transformation into the structure. Design examples and a description of a signal processor implementation are included.
Linear frequency networks with applications to ‘frequency set‐on oscillators’ and ‘self‐adaptive bandpass filters’
Authors: Rhodes J. D.
Published: July 2007

A ‘linear frequency network’ is a network system which consists of an arbitrary connection of devices, each of which performs a linear transformation on the instantaneous frequency of a signal. Thus a transfer function may be defined relating the output to input instantaneous frequency.

Particular networks are investigated. the first is a basic section, producing a ‘self‐adaptive bandpass filter’ which is then applied to a ‘frequency set‐on oscillator’. Such an oscillator is a multimode oscillator where any mode will be stable when excited by a sample of an RF pulse adjacent to the mode. Cascading these basic sections results in an nth‐degree ‘self‐adaptive bandpass filter’ producing a bandpass characteristic which tracks a carrier frequency.

Experimental devices in the 400‐600 MHz band are shown to have excellent agreement with theory, and applications to digital RF memories, ESM receivers and frequency memory loops are discussed.
A pole‐zero pairing strategy for minimum‐gain‐sensitivity nth‐order biquadratic filter cascades
Authors: Hiltgen Alaln , Moschytz G. S.
Published: July 2007

In attempting to use the pole‐zero assignment for gain sensitivity minimization in biquadratic filter cascades, a new expression for the total gain error is derived. In this result the logarithmic gain slope appears as a weighting factor to a second term depending on the structure and the parameter or component inaccuracies. On the basis of this partitioning, a pairing method for minimum gain sensitivity is developed which uses the ‘modified bottleneck algorithm’. Additional investigations finally show that minimum gain sensitivity and optimum dynamic range lead to similar constraints which can be achieved simultaneously in most applications.
A method for finding bounds on the location of all the solutions of dc piecewise‐linear circuits
Authors: Tadeusiewicz Michal
Published: July 2007

In this paper a method is developed for rapidly finding bounds on the location of all the solutions of a broad class of DC piecewise‐linear circuits. the class includes diode‐transistor circuits as well as circuits containing locally active resistors and controlled sources. the method can be useful as a preliminary stage of the computation process in which the well‐known Chua‐Ying algorithm is used for finding all solutions. It improves the efficiency of the Chua‐Ying algorithm. the convergence of the computation process is discussed in detail and numerical examples are given.
An improved macromodel for operational amplifiers
Authors: Hu Chenmin , Leach Donald P. , Chan Shu‐Park
Published: July 2007

The proposed macromodel in this paper precisely simulates almost all performance characteristics of integrated circuit operational amplifiers. It is shown by an example that the model bears very strong resemblance to actual circuits, A detailed comparison with other existing models demonstrates the great advantages of the proposed model. the simplicity and accuracy together with the employment of the most popular circuit simulator SPICE2 enable design engineers to use the macromodel on CAE workstations for all general purpose applications.
Generating randomness from chaos and constructing chaos with desired randomness
Authors: Chua Leon O. , Yao Yong , Yang Qing
Published: July 2007

We have designed, built and tested a switched‐capacitor circuit for generating pseudo‐random signals. the circuit is an electronic implementation of a one‐dimensional discrete map, which has been fully understood mathematically. the time series of the circuit has extremely rich dynamics, e.g. aperiodicity, non‐asymptoticity, ergodicity and fractal dimension. That is, the circuit is indeed chaotic. Furthermore, a general method for designing chaotic circuits with prescribed random properties is proposed. Numerous examples are given to illustrate the theory and methods developed in this paper.
Chaos and fractals from third‐order digital filters
Authors: Chua L. O. , Lin T.
Published: July 2007

It is observed that the third‐order digital filter with an overflow non‐linearity has a much richer dynamics than the second‐order digital filter. Computer simulations show that the third‐order non‐linear system can exhibit incredibly complicated fractal geometrical patterns. A three‐dimensional trajectory of the non‐linear system always lies on several parallel planes, but reaches these planes at different points to create the chaotic behaviour and the fractal geometrical patterns. the number and location of the planes are determined by the parameters of the system and the starting point of the trajectory. In general, a seven‐value symbolic dynamics is developed to explain the complex dynamics observed in the non‐linear digital filter.