bluuebunny/crossref_metadata_2025 huggingface dataset:
Selective linear phase filters possessing a pair of J‐axis transmission zeros
Authors: Rhodes J. D. , Zabalawi I. H.
Published: July 2007

A design technique is developed for prototype selective linear phase filters which have an equiripple passband amplitude response and a pair of j‐axis transmission zeros in the stopband while maintaining a linear phase characteristic in the passband. Since the basic technique requires numerical optimization techniques, the element values for several cases have been tabulated together with detailed response characteristics.

One important result is that for certain characteristics, one internal cross‐coupling element may be designed to be zero. As a result, in the sixth degree case with only one extra cross‐coupling element between elements 1 and 6 a significant improvement in both the amplitude and group delay performance can be achieved as compared to the Chebyshev case. Owing to its importance, this case is investigated in detail and a 2.6 GHz post decoupled combline filter has been constructed based upon this prototype.
Differential transforms and circuit theory
Authors: Ev Pukhov Georgii G.
Published: July 2007

The function and equation transformations are presented where the transfer to images is made by means of differentiation. The application of these differential transforms for the design of linear and non‐linear circuits is also discussed.
The (p+q)‐port transformer
Authors: Chua L. O. , Lin G. N. , Lum J. J.
Published: July 2007

Two approaches for realizing a (p+q)‐port transformer using operational amplifiers are presented. Unlike iron‐core transformers, our realization is valid from d.c. to a relatively high frequency limited only by the op amp's frequency response. The stability and limitation of the two approaches are analysed and compared. Examples are given to illustrate two unique and indispensible applications of the (p+q)‐port transformer: Synthesis of non‐linear n‐ports and non‐linear programming.
Unique solvability of RLC nullor networks
Authors: Svoboda J. A.
Published: July 2007

Sufficient conditions for the unique solvability of linear active networks modelled as RLC nullor networks are given. an interpretation of these sufficient conditions in terms of subnetworks of the network being studied is also given. A simple procedure for calculating the matrices involved in these sufficient conditions is described and illustrated by example.
On hilbert space design of least‐weighted‐squares digital filters
Authors: Bromba Manfred U. A. , Ziegler Horst
Published: July 2007

Numerical convolution operations, executed on noise contaminated signals, are approximated by FIR digital filters in such a way that the effect of random coloured noise is minimized. Using elementary Hilbert space techniques, the filter functions of certain least‐weighted‐squares digital filters are derived explicitly by the use of discrete orthogonal functions (e.g. Hahn polynomials). the approach is suitable especially for narrowband operations such as smoothing, narrowband differentiation, and narrowband deconvolution (resolution enhancement). Examples of linear‐phase lowpasses with monotone passband, obtained with the aid of Hahn polynomials, are discussed in detail. Also the well‐known maximally flat digital lowpasses which can be derived with the aid of Krawtchouk polynomials, and narrowband differentiators are considered. In the case of least‐weighted‐squares approximation by Hahn polynomials, powerful recursive realizations can be developed to reduce computational requirements.
Scaling techniques for switched‐capacitor filters employing voltage inverter switches
Authors: Pandel Jürgen
Published: July 2007

Some realizations of scaling elements in cascade connection with unit elements and gyro‐elements will be described. It will be shown that the voltage distribution inside the filter and the spread of capacitor values can be optimized in two steps using two independent parameters for each scaling element. the influence of these scaling elements is such that the very low sensitivity of the attenuation characteristic with respect to element variations is fully retained despite the fact that according to the usual definition the losslessness of the reference filter is not preserved. the SC circuits described in this paper are insensitive to ‘bottom plate’ parasitic capacitances. Top plate parasitics correspond largely to element variations in the reference filter so that also their influence is strongly reduced. A numerical example of a 14th‐order unit element bandpass filter is given.
Non‐linear optimization with constraints: A cook‐book approach
Authors: Chua L. O. , Lin G. N.
Published: July 2007

Based on the stationary co‐content theorem in non‐linear circuit theory and the penalty function approach in non‐linear programming theory, a canonical circuit for simulating general non‐linear programming problems with equality and/or inequality constraints has been developed. the task of solving a non‐linear optimization problem with constraints reduces to that of finding the solution of the associated canonical circuit using a circuit simulation program, such as SPICE.

A catalogue of canonical circuits is given for each class of non‐linear programming problem. Using this catalogue, an engineer can solve non‐linear optimization problems by a cook‐book approach without learning any theory on non‐linear programming. Several examples are given which demonstrate how SPICE can be used, without modification, for solving linear programming problems, quadratic programming problems, and polynomial programming problems.
Stray capacitance eliminating transformations for switched capacitor circuits
Authors: Hasler Martin , Saghafi Morad
Published: July 2007

Transformations are given that eliminate the influence of part or all of the stray capacitances to ground in a switched capacitor circuit, while leaving the transfer functions and, conditionally, their sensitivities to nominal capacitor ratios invariant. the transformations increase the number of operational amplifiers to the minimum that is required, as we prove, for stray capacitance insensitive circuits. the number of capacitors usually also increases, giving rise to constraint equations.
The calculation of transfer matrices of linear systems with continuous and sampled‐data signals by signal flow graphs
Authors: Vágó István
Published: July 2007

The paper presents a method based on the concept of signal flow graphs which is suitable for the determination of transfer matrices of linear systems excited by continuous or by continuous and sampled‐data signals. the method is valid in case of several excitations and responses.
Design of wave‐sc filters using building blocks
Authors: Kleine U.
Published: July 2007

Besides switched‐capacitor (SC) filters developed for high volume production, e.g. the PCM‐codec lowpass filter, numerous low volume applications exist in the area of solid‐state filtering. to open up this application field for SC filters, a novel wave‐SC filter structure is presented. the filter design using this concept requires only moderate design and layout skills since only a limited library of highly modular building blocks is required. It is also suitable for analogue gate array applications. As will be shown, the wave equations which are known from the theory of wave digital filters can be realized using stray‐insensitive SC integrators and SC amplifiers only. Exemplary designs of a lowpass, a highpass, and a bandpass filter will be carried out with the building blocks presented. the theoretical results are verified by measurements at the breadboarded lowpass filter.
On the stability of non‐linear two‐port amplifiers
Authors: Baranyi A. , Ladvanszky J.
Published: July 2007

Based on the two‐port describing function characterization, frequency domain stability conditions are derived for non‐linear two‐port amplifiers. the conditions are applied to the case of a turned transistor amplifier with saturated class‐C type transfer characteristic. the theoretical considerations and the experimental results are in close agreement.
Non‐linear op‐amp circuits: Existence and uniqueness of solution by inspection
Authors: Nishi Tetsuo , Chua Leon O.
Published: July 2007

Even simple circuits containing only one op amp and linear resistors can have multiple d.c. operating points. Using a realistic non‐linear d.c. op‐amp model which includes the saturation characteristics, this paper gives the necessary and sufficient conditions for an arbitrary op‐amp circuit (containing op amps, linear resistors, strictly‐increasing non‐linear resistors and independent sources) to have a unique solution for all values of circuit parameters. These conditions are remarkable because they are couched strictly in topological terms. For many op‐amp circuits (e.g. those containing only one op amp), the necessary and sufficient conditions can be checked by inspection.
Active RC realization of high‐order bandpass filter functions by cascading biquartic sections
Authors: Fotopoulos S. , Deliyannis T.
Published: July 2007

High‐order bandpass filter functions are realized by cascading active RC biquartic sections. A design procedure is proposed, which leads to an optimized circuit with regard to sensitivity, signal distortion and noise. It is shown that the resulting filters have low sensitivity, similar to that of the multiple‐loop feedback (MF) filter and better noise performance than the shifted‐companion‐form and cascade filters.
Maximum power transfer in non‐linear source‐load systems
Authors: Vachtsevanos G. J. , Kalaitzakis K. C.
Published: July 2007

This paper is concerned with the conceptual design and realization of matching networks for the continuous transfer of maximum power from a non‐linear source with randomly varying characteristics to a load. Such sources are commonly encountered in the use of photovoltaic arrays or wind energy conversion systems for the production of electric power. Experimental studies as well as computer simulation results verify the validity of the design and point to methods for its practical implementation.
Multiple‐critical‐pole coupled active filters
Authors: Mijat N. , Moschytz G. S.
Published: July 2007

In this paper realizations of low sensitivity narrow BP active filters implementing multiple‐critical‐pole (MCP) approximation methods and coupled filter structures are studied. In the first part of the paper, a synthesis procedure particularly developed for the realization of MCP transfer functions is described. According to that procedure the portion of the MCP transfer function containing multiple poles is realized as a follow‐the‐leader feedback (FLF) network, and the remaining part as a cascade. It is shown that the lower sensitivities of MCP functions in comparison with standard approximating functions (Butterworth, Chebyshev, etc.) can be further decreased by applying the FLF configuration instead of the cascade. the synthesis procedure is straightforward and in some cases it can be performed using identical second‐order BP blocks. the final circuit sensitivities can be optimized according to given filter specifications and a user selected optimization criterion.

In the second part of the paper, the MCP transfer functions are combined with the cascaded biquarts (CBQ), the shifted companion form (SCF), and the leap‐frog (LF) structures, and sensitivity analysis is performed. It is shown that applications of the above mentioned structures can improve the filter sensitivites in a way similar to that of the given FLF configuration.
Double broadband matching and the problem of reciprocal reactance 2n‐port cascade decomposition
Authors: Youla D. C. , Carlin H. J. , Yarman B. S.
Published: July 2007

Let N, N1, N2 and N3 be prescribed reciprocal reactance 2n‐ports. Then, under certain mild restrictions, this paper supplies answers to the following two related problems:.

P1. Find the necessary and sufficient conditions for the physical extractability of N1 from the front‐end of N. P2. Given that N2 and N3 are individually physically extractable from the back and front‐ends of N. respectively, find a set of sharp sufficient conditions for their simulations physical extractability from N.

The criteria are formulated in terms of the associated scattering matrices and are reasonably simple to apply. Moreover, they also have a clear‐cut network significance involving transmission zeros. to illustrate their use, a recent result for the design of non‐degenerate double broadband‐matching equalizers6 is generalized to a 2n‐port setting in Theorem 2, corollary 2.

Lastly, to round out the development, impedance versions of both Theorem 1 and Theorem 2, corollary 2, are presented in Section 2. This restatement is accomplished with the aid of a new Darlington 2n‐port embedding for passive reciprocal n‐ports that is phrased entirely in the language of impedance matrices.
Integral manifolds for non‐linear circuits
Authors: Odyniec M. , Chua L. O.
Published: July 2007

Although the theory of integral manifolds is well known among applied mathematicians as a powerful tool in non‐linear oscillations, it is relatively unknown, let alone applied, among circuit engineers. the purpose of this mostly tutorial paper is to illustrate the applications of integral manifolds to explain various non‐linear phenomena widely observed in non‐linear circuits. Numerous examples and graphical illustrations are included in order to present the theory with a minimum amount of mathematics.
Negative resistance devices: Part II
Authors: Chua L. O. , Deng An‐Chang
Published: July 2007

As a sequel to Reference 1, this paper presents new analytical and topological guidelines for synthesizing negative‐resistance devices. Among other things, these guidelines can be used to tune the devices by varying the magnitude and dynamic range of the negative (small‐signal) resistance.

Necessary and sufficient conditions are given for a circuit containing only one bipolar transistor and linear reciprocal passive two‐ports (e.g. ideal transformers) to exhibit a negative resistance. In the special case where the circuit contains only one ideal transformer, one transistor and linear positive 2‐terminal resistors, an equivalent topological criterion which can be checked by inspection is given.

Finally, three canonical negative‐resistance one‐ports containing two identical bipolar transistors, linear positive 2‐terminal resistors and batteries are synthesized to exhibit an odd‐symmetric (hence active) voltage‐controlled or current‐controlled v‐i curve.
Uniqueness of the steady state for small source amplitudes in non‐linear non‐autonomous circuitsc
Authors: Hasler Martin , Verburgh Philippe
Published: July 2007

The purpose of this paper is to give a sufficient condition for the uniqueness of the steady state for circuits that are composed of strictly locally passive capacitors and inductors, of time‐dependent bounded voltage and current sources and of a resistive N‐port that is strictly locally passive and eventually strictly passive. It is an extension of previously obtained results by the same authors, where strong local passivity was required. the new condition allows one to give a bound on the source amplitudes below which passive elements. It also gives a more explicit content to a theorem by Chua and Green which states that for sufficiently small source amplitudes the steady state is unique. the new condition is obtained by giving explicit uniform eventual bounds on the solutions as t → ∞, which are of independent interest. Two examples illustrate that the various explicit bounds can easily be computed in concrete examples.
Lowpass approximations of a constant amplitude with arbitrary phase and delay
Authors: Jarry B. , Verdier A. , Jarry P.
Published: July 2007

A review is made of recent developments to the simultaneous lowpass approximation problem of amplitude, phase and delay. the closed from solutions (reciprocal and non‐reciprocal) are expressed in terms of the arbitrary phase and delay polynomials (APD).
Static global models for linear n‐port networks realized with operational amplifiers
Authors: Hueratas J. L. , Rueda A. , Rodriguez‐Vazquez A.
Published: July 2007

This paper is addressed to obtaining global models for the circuit realization of a given linear multiport implemented using operational amplifiers. It is conventional to consider a linear characterization for such multiports, the consequence being a restricted validity for the model. In other words, this model is meaningful only for inputs that do not lead any operational amplifier into saturation. It is a serious drawback, mainly when the linear n‐port has to be embedded of the actual circuit can be very inaccurate leading to problems that cannot be explained by a linear model.

In the work reported herein, two main results must be remarked. One is the procedure for developing explicit global descriptions for two general circuit topologies. the other is concerned with the dependence existing between the circuit topology and the type of model to be deprived. In that sense, it is interesting to note the close relation of our global models with the canonical piecewise‐linear descriptions derived in Reference 12. Extension to piecewise polynomial models is also considered in some detail.
Modelling non‐linear devices exhibiting frequency‐dependent capacitances and inductances
Authors: Dervişoǧlu A. , Chua L. O.
Published: July 2007

The incremental capacitance and inductance of many electronic devices are frequency‐dependent. This paper presents a systematic method for modelling such devices using only positive and/or negative linear time‐imvariant capacitances and inductances.

Modelling of a frequency‐dependent capacitor or inductor is reduced to the realization of an odd rational function. It has been shown that any odd rational function can be realized as the driving‐point function of a ± L, ± C one‐port. It has also been shown that a linear higher‐order capacitor or inductor of order 2k + 1 can be realized by a ± L, ± C one‐port which contains 2k + 2 elements.
Analogue circuits fault dictionary—new approaches and implementation
Authors: Lin P. M. , Elcherif Y. S.
Published: July 2007

The d.c. fault dictionary approach has been found very useful for diagnosing hard failures (open circuits and short circuits) in non‐linear analogue circuits. In this paper we present the use of several techniques to enhance the capability of the d.c. fault dictionary. These include (1) modelling all non‐linearities by piecewise linear characteristics, (2) solving the piecewise linear resistive network by Lemke's complementary pivot algorithm, (3) using multilevel logic operation to compile an integer‐code fault dictionary which totally eliminates any post‐test calculations. the automatic generation of a fault dictionary for a video amplifier by the use of the computer program HAFDIC is described.
A systematic approach to the realization and design of actively compensated two OA voltage amplifiers
Authors: Lopes Paulo B. , Bhattacharyya B. B.
Published: July 2007

Several actively compensated voltage amplifiers (ACVAs) employing two operational amplifiers have been reported separately in the recent literature. In this article, the results of a systematic and comprehensive study of both non‐inverting and inverting such ACVAs are presented. Using a combination of practical and theoretical considerations, ACVAs are first divided into classess. Each class is further divided into types. Realizability conditions are then derived for each of the different types. These conditions lead directly to a set of useful realizations. the performance of each realization is considered in detail with respect to several practical considerations of interest, such as magnitude and phase errors, effect of the second pole of the operational amplifiers (OAs), tunability, maximum signal handling capability, etc. the results of practical experiments are also given. Experimental results agree closely with the theoretical predictions.
Smoothing over the intervals of orthogonally sampled signals
Authors: Halpern Peter H. , Mallory Peter E.
Published: July 2007

A method for smoothing and interpolating a Fourier sine series representation of a continuous signal is developed to take advantage of the relative ease with which since pulse forming networks can be built. With this method it is possible both to accurately approximate the signal at the points where the sine harmonics are all zero and to smooth the signal. A method is also developed to combat round‐off error in the extraction of the harmonic coefficients, and an expression is derived for the maximum error in the representation. Finally, examples are presented to show the effectiveness of this method.
Canonical piecewise‐linear analysis: Generalized breakpoint hopping algorithm
Authors: Chua Leon O. , Deng An‐Cheng
Published: July 2007

As an extension to the breakpoint hopping algorithm developed in reference 1, the algorithm presented in this paper efficiently solves the d.c. problem for finding the d.c. operating point(s) and for tracing the driving‐point and transfer characteristics of an extremely broad class of non‐linear resistive circuits. In particular, bipolar and MOS transistor circuits are included. A user‐friendly C program has been written to implement this algorithm where the input format for describing the circuit is compatible with the SPICE program.
Exact sensitivity analysis for optimization of multi‐coupled cavity filters
Authors: Bandler J. W. , Chen S. H. , Daijavad S.
Published: July 2007

This paper describes an efficient approach to the simulation and exact sensitivity evaluation of multi‐coupled cavity filters. The approach uses sensitivity formulae for such responses as input or output reflectron coefficient, return loss, insertion loss, transducer loss, gain slope and group delay, which are derived for a two‐port equivalent of a general network described by its symmetrical impedance matrix. The formulae are specialized to the case of multi‐coupled cavity filters, using a filter model which takes into account many non‐ideal factors such as losses, frequency dependent coupling parameters and stray couplings. The formulation also treats synchronously or asynchronously tuned structures in a unified manner. Explicit tables of first‐ and second‐order sensitivities w.r.t. all variables of interest, including frequency, are presented. Three problems of significant practical value in manufacturing of multi‐cavity filters are solved with the direct application of our formulae. A 10th‐order filter is considered for all three cases. The first case is simultaneous optimization of the amplitude and delay responses to obtain a self‐equalized filter. The second case is accurate prediction of the responses for a lossy filter by simulating a lossless filter. The third case involves parameter identification of the filter from simulated measurements on its responses.
Theory of perturbed negative conductance oscillators
Authors: Thirup G.
Published: July 2007

An oscillator is considered as a mixing circuit where the voltage of the oscillator is the local oscillator voltage. A sinusoidal perturbation is applied to the oscillator, exciting current and voltage components at frequencies equivalent to signal, intermediate and image frequencies in a normal mixing circuit. The relationship between the components can be described by three linear equations whose determinant is zero for a d.c. perturbation and for perturbations having the oscillator frequency. By means of the three linear equations the stability, mixing, modulation and demodulation of an oscillator are treated (Section 2). The stability conditions are shown to be the same as those derived by Kurokawa in another way (Section 3). Perturbations of a Van der Pol oscillator are investigated in detail. It is shown that the oscillator obtains a high dynamic Q at small oscillator voltages, and that the sensitivity of a self‐detecting oscillator to load perturbations is independent of the oscillator voltage (Section 4). The signal‐to‐noise ratio of a perturbed oscillator is considered and the conditions for the highest signal‐to‐noise ratio are given (Section 5). Finally, some of the difficulties encountered in making perturbed oscillators for microwave spectrometers are mentioned (Section 6).
The double scroll bifurcations
Authors: Matsumoto T. , Chua L. O. , Komuro M.
Published: July 2007

This paper describes the dynamics of the simplest physical system known to date whose chaotic dynamics and rich bifurcation phenomena have been observed not only in the laboratory, but also reconfirmed by extensive computer simulation of its associated mathematical model: a 3rd‐order autonomous ordinary differential equation. The physical system is a 5‐element electrical circuit whose only non‐linearity is a non‐linear resistor characterized by a 3‐segment piecewise‐linear voltage‐current characteristic.

Despite the simplicity of the circuit, however, it is imbued with an extremely rich variety of bifurcation phenomena. By changing the capacitance values, many phenomena, including Hopf bifurcation, period‐doubling cascades, Rössler's spiral‐type and screw‐type attractors,4 periodic windows, ‘double‐scroll’ attractor,1 boundary crisis,5 Shilnikov‐type phenomenon,6 etc. have been observed experimentally and confirmed by computer simulation. Other attractors and periodic windows have also been observed by varying the conductance values.

In addition, Rössler's spiral‐type and screw‐type attractors have been observed from the same circuit, where the non‐linear resistor has only one break point, i.e. it is described by a 2‐segment piecewise‐linear v‐i characteristic. This means that extremely complicated non‐periodic (chaotic) waveforms can arise in the simplest third‐order uncoupled electrical circuit in which all elements except one (a resistor) are linear and passive, and in which the constitutive relation of the non‐linear resistor is made of the simplest conceivable non‐linearity, namely 2 straight‐line segments.
Block parallel processing of 2‐D digital signals
Authors: Mertzios B. G.
Published: July 2007

A structure is presented for the processing of two‐dimensional digital signals, based on a block state‐space model. Specifically the proposed structure exhibits high inherent parallelism since the state‐space model is properly split into a number of parallel subfilters. A detailed analysis is done to achieve a balanced distribution of the necessary non‐trivial multiplications in the subfilters. The optimal block dimensions are determined in order to minimize the critical number of non‐trivial multiplications per output sample. Finally an estimation of the data throughput delay, based on the number of necessary multiplications and additions, is given for the proposed structure. It is shown that the data throughput delay, estimated in the case of optimal block dimensions, is increased almost linearly with the filter's order and is substantially reduced relative to that which has been estimated with the canonical state‐space model. Also the data throughput delay for suboptimal block dimensions are considered. The proposed model is ideally suited to computer use and VLSI implementation.
Solutions for a three‐dimensional non‐linear stabilized oscillator
Authors: Daboul J. , Kaplan B. Z.
Published: July 2007

A system of coupled non‐linear equations, describing a three‐phase stabilized oscillator, is analysed by introducing ‘cyclotomic’ co‐ordinates. We show that this system, under certain conditions, approaches asymptotically non‐conservative linear systems; and yet it does have stabilized solutions (limit cycles). The non‐linear system is solved analytically for an important class of stabilizing functions. We show that the frequency ω of our oscillator responds instantaneously to changes of certain parameters. This result has useful applications in building quickly responding novel electronic voltage‐controlled oscillators.
Efficient realization of pulse‐shaping networks by employing asymmetric reference wave‐forms with fixed spectral envelopes
Authors: Kishi Genya , Sakaniwa Kohichi , Takei Yoshiyuki
Published: July 2007

This paper considers the application of an asymmetric trapezoidal wave‐form to the realization of pulse‐shaping networks.

The first part of the paper shows that a trapezoidal wave‐form can be asymmetrized, keeping its spectral upper bound invariant. More precisely, we have proved that the upper bound of the spectral envelope does not change if the average of the leading and trailing slopes of a trapezoidal wave‐form is kept constant.

In the remaining part of the paper, it is shown that an asymmetric reference wave‐form is very effective in designing pulse‐shaping networks, i.e. in many time‐domain synthesis methods a better approximation is obtained by using an asymmetric reference wave‐form with a compressed leading edge.
Successive approximation logarithmic A/D conversion using charge redistribution techniques
Authors: Lefas C. C.
Published: July 2007

The present paper describes a logarithmic A/D converter (LADC) working with the charge redistribution principle. the LADC uses a serial and a parallel capacitive attenuator and is suitable for manufacturing on a single chip. Formulae for the values of the capacitors are given in terms of the base of logarithm used. This LADC uses logarithmically spaced voltage comparison levels and therefore eliminates the use of logarithmic analogue signal conditioning circuits.
Generalized ladder synthesis by subnetwork removal
Authors: Mou‐Yan Zou , Unbehauen R.
Published: July 2007

A general procedure is presented to realize a two‐port impedance matrix by a generalized transformerless LC ladder network including the classical LC ladder structure as a special case. the realization process consists of repeatedly applying a subnetwork removal cycle for which six different cases are to be considered. the feasibility of the various subnetwork removals is characterized by formulating necessary and sufficient conditions on the impedance matrix. the application of the procedure is illustrated by a numerical example.
Fully integrated active‐Rc filters using mos and non‐balanced structure
Authors: Acar C. , Ghausi M. S.
Published: July 2007

A technique for implementing fully integrated continuous time non‐switched capacitor filter has been recently reported in the literature. the technique uses a balanced structure using op‐amps, capacitors and MOS transistors operated in the non‐saturated region as voltage‐controlled resistors. In order to eliminate the non‐linearity of the MOS transistors over an extended voltage range the current techniques use fully balanced circuits. This paper provides a simple technique for cancellation of non‐linearities, thereby reducing the number of elements, and proposes several simple circuits. the technique is then used in the design of high‐order filters.
Design of testability for analogue fault diagnosis
Authors: Wey Chin‐Long
Published: July 2007

With the rapidly increasing complexity of circuits and systems, the ability adequately to design a diagnosable circuit or system is a prime requisite for rapid fault location. In the present paper, a necessary and sufficient condition for pseudo‐circuit generation is presented for the use of the pseudo‐circuit in the self‐test algorithm. to determine the diagnosability of a designed circuit, a testability condition is presented with examples. the unique feature of these conditions is that they depend only on the topological structure of a given circuit, not on the component values; therefore, these conditions can be implemented in both linear and non‐linear circuits or systems. With the aid of a computer, the test points may be generated automatically by the proposed algorithm. Based on the proposed algorithm, the design of testability can be established.
A simple dynamic circuit model for mos structure
Authors: Chua Leon O. , Chang Chwen‐Cher
Published: July 2007

A new simple circuit model for the MOS (metal‐oxide‐semiconductor) structure is presented. the model consists of three elements, namely, a linear capacitor, a non‐linear capacitor and a C‐dynamic element. Each component bears a simple relationship to the physical operating mechanism inside the MOS structure. the model can be used for simulating arbitrary MOS structure circuits under all operating conditions. In particular, it is capable of reproducing the structure's frequency‐dependent small‐signal characteristics. the model is also shown to exhibit many important and interesting dynamic behaviours under forward, reverse and sinusoidal operating modes.

The model is based mainly upon the device's physical operating principles. But perhaps the most significant implication of this model is that it is the first ever to use a dynamic element to model the MOS structure from a physical approach.
Topological conditions for a resistive circuit containing negative non‐linear resistors to have a unique solution
Authors: Nishi Tetsuo , Chua Leon O.
Published: July 2007

Necessary and sufficient conditions are given for resistive circuits containing both monotone‐increasing non‐linear resistors and monotone‐decreasing non‐linear resistors (called negative non‐linear resistors), in addition to controlled sources and op‐amps, to have a unique solution for all circuit parameters. Several theorems are given for various classes of circuits containing different combinations of active circuit elements. the theorems are couched mostly in topological terms and can therefore be checked by inspection.
Simple proofs of some discrete domain stability related properties of multidimensional polynomials
Authors: Basu S. , Fettweis A.
Published: July 2007

Simple and rigorous proofs of results due to various authors on tests for the property that a multivariable polynomial be devoid of zeros in the closed unit polydisc are given. the proof technique rests largely on a correct and complete formulation of the fact that the zeros of a polynomial are continuous functions of its coefficients. It is shown that almost all other related results can be derived in this manner.
Generation of causal and semicausal 2‐D IIR structures from fir structures via state feedback
Authors: Lehner D. , Unbehauen R.
Published: July 2007

A method is presented to realize a class of 2‐D IIR digital filters by extension of 2‐D FIR structures through feedback paths. Most features of the initial FIR structures remain unchanged (e.g. parallelism, number of delay elements). the approach described is applied to a class of 2‐D FIR filter structures owning several advantages. the method is generalized to semicausal filters.
The set of lagrange and routh formulations for non‐linear networks
Authors: Shragowitz Eugene , Gerlovin Emmanuel
Published: July 2007

Formulations of systems of Lagrange and Routh equations for arbitrary non‐linear electrical circuits are given. the use of Routh equations for this purpose is new. It is proved that these formulations are equivalent to the complete system of Kirchhoff equations (instead of only a part of it as in prior works). the vector of generalized coordinates for the system of Lagrange equations consists of four subvectors (loop charges for fundamental loops, cut‐set fluxes for fundamental cut‐sets, branch fluxes for voltage and flux controlled elements and branch charges for current and charge controlled elements).

For the defined set of Lagrange formulations, the uniqueness of a parametric representation is proved. the structure of the Lagrange (Hamilton, Routh) formulation set is then studied and it is proved that this set is an Abelian group. A duality of Lagrange triples for electrically and topologically dual circuits is established and it is proved that this relation between the sets of Lagrange triples is an isomorphism. It is also shown that the Brayton‐Moser equations and the anti‐Lagrangian equations similar to those of M. Milić and L. Novak represent partial cases of the formulated set.
A network model for the diffusion‐convection equation
Authors: Wong Chi Chung
Published: July 2007

In the past network models have been used frequently to simulate the Laplace's, wave and diffusion equations. In this paper the application of the network model is further extended to include the diffusion‐convection equation. the time‐dependent diffusion‐convection equation is first modelled by an RC electric network from which a set of ODEs is derived. Numerical experiments are then performed to compare the network model and the method of lines in solving the one‐dimensional linear diffusion‐convection equation and the Burgers' equation where highly non‐linear network components are required. It is shown that, for the former problem, the network method has improved accuracy for low Peclet numbers. At high Peclet numbers the behaviour of the network method resembles that of the method of lines (MOL) with upstream‐differencing. Spurious oscillations are absent. Computing time required to solve the network is slightly less than that for the MOL. For the Burgers' equation, the network method shows a substantial improvement over the MOL in terms of accuracy with no oscillations but requires longer computing time.
Computer‐aided design and optimization of control units for VLSI processors
Authors: de Micheli Giovanni
Published: July 2007

This review presents the models, methods and algorithms for synthesis and optimization of control units for VLSI processors. First, circuit structures used for control in the state‐of‐the‐art processors are described. the control synthesis methods are then presented as well as the algorithms for optimizing the control unit representation. Among these techniques, the symbolic design methodology is described that can be applied to optimize the silicon area taken by some particular structures of control units.
Waveform relaxation on parallel processors
Authors: Smart David W. , Trick Timothy N.
Published: July 2007

Waveform relaxation algorithms for the simulation of digital MOS circuits exhibit natural parallelism which can be exploited on parallel processors. This paper addressed the question of how much the circuit simulation run‐time can be reduced by using this natural parallelism. the parallel waveform relaxation methods examined in this paper are based on the Gauss‐Seidel and Gauss‐Jacobi relaxation methods, and window‐level and time‐point level parallelization strategies. the different methods are evaluated using an actual multiprocessor implementation of the algorithms, and by using a program which estimates speed‐ups, neglecting overhead. the method giving the best performance is a function of the circuit being simulated and the number of processors used. When sufficiently many processors are available, the Gauss‐Jacobi method with time‐point pipelining offers the best speed‐up potential. Speed‐ups close to one order of magnitude should be possible using this method for 1000‐node for 32 processors.
Non‐reciprocal network synthesis using the generalized richards transformation
Authors: Unbehauen Rolf , Zimmer Gerhard
Published: July 2007

A generalization of the Richards transformation is presented and its properties are derived. the new transformation is appropriate for the canonic synthesis of non‐reciprocal network sections based on the transformation of an impedance, and it is shown that under certain constraints a transformerless realization is possible. the generalized Richards transformation can also be applied to the synthesis of network sections without degree reduction of the impedance to be transformed. This kind of application is important for the realization of transfer functions. A dual transformation for an admittance is established. Finally, it is shown how to use the generalized Richards transformation for the synthesis of transfer functions by doubly terminated lossless two‐ports.
Measuring volterra kernels (II)
Authors: Chua Leo N. O. , Liao Youlin
Published: July 2007

Accurate measurement of Volterra kernels is an essential step in the modelling of weakly non‐linear physical systems via the block box approach, and in model validation. This paper is a sequel to an earlier paper,1 where practical methods for measuring Volterra kernels were presented along with a quick method for measuring the second‐order Volterra kernels. This paper extends that quick method for measuring higher‐order frequency‐domain Volterra kernels of weakly non‐linear systems. We further developed the quick method to measure directly the points of the Volterra kernels which are located along one or more axes in the frequency domain, thus making our method complete and more accurate than that presented in Reference 1. We illustrate our method by actually measuring a weakly non‐linear circuit whose Volterra kernels can be accurately calculated. the experimentally measured and the theoretically predicted results agree remarkably well.
Impasse points. Part I: Numerical aspects
Authors: Chua Ieon O. , Deng An‐Chang
Published: July 2007

Impasse point is an important phenomenon found in many non‐linear circuits and systems. Among other things, the presence of an impasse point Q implies that the circuit model is defective and must be remodelled by augmenting it with parasitic inductances and/or capacitances at appropriate locations in order to predict the bifurcation from slow to rapid motions (jump phenomenon) widely observed in practice. the presence of an impasse point Q also implies that a numerical simulation of the associated system of implicit differential‐algebraic equations would give rise to an extraneous and random small‐amplitude oscillation in the vicinity of Q. the wave‐form associated with this ‘fake’ oscillatory phenomenon depends on the error‐controlled mechanism of the integration routine and can be detected using the results from this paper.

Impasse points in high‐order circuits (n > 2) need not be isolated. In fact, they often form an impasse set made of impasse curves, impasse surfaces, impasse manifolds, etc. In order to detect the impasse set associated with the implicit differential‐algebraic system.

An analytical characterization of an impasse point (X0,y0) is derived and proved to be equivalent to that of solving for the limit‐points of an associated static bifurcation problem.

Interpreting this as the parametric equation of a space curve in the y‐space, an impasse point (X0,y0) is simply a ‘turning point’ of this curve.
Impasse points. Part II: Analytical aspects
Authors: Chua Leon O. , Deng An‐Chang
Published: July 2007

An impasse point of the implicit differential‐algebraic system

equation image
.

Has been characterized in Part I of this paper as a limit point of an induced solution curve

equation image

In this paper we use the Liapunov‐Schmidt procedure to derive an analytical test for identifying impasse points. We also invoke the transversality theory from differential topology to show that almost all singular points (Xo, yo) of S, which occur when the Jacobian matrix

equation image

is singular, are in fact impasse points.
A new general method to model signal timing of E/D NMOS logic
Authors: Wu Chung‐Yu , Lin Yen‐Tai
Published: July 2007

A new general modelling method for E/D NMOS logic is proposed and applied to the case of inverters. In this model, non‐linear device currents in the large‐signal equivalent circuit are reformulated by the curve‐fitting technique. Then output voltage wave‐forms are analytically solved region by region from the equivalent circuit. From the derived formulae, the rise/fall time and delay time can be calculated. Wide‐range comparisons with SPICE simulation results were performed to verify the accuracy and the general applicability of the developed model. Two examples are given to demonstrate the applications of the developed timing model to timing analysis. It is shown that the model has a good accuracy for E/D inverters with a wide range of beta ratios, gate sizes, capacitive loads, input voltage wave‐forms and device parameters. Moreover, the required CPU time and memory are small. These make the proposed modelling method an interesting approach to model E/D NMOS gates for CAD applications.
Limitations and complexity of digital hardware simulators used for large‐scale analogue circuit and system dynamics
Authors: Roska Tamás
Published: July 2007

Large‐scale electronic circuits and systems are considered with increasing complexity measured in terms of the number of circuit or system elements. the dynamics will be calculated by a digital prototype hardware simulator exploiting parallelism, pipelining and look‐up table techniques to realize minimum solution time. Our ‘canonical’ conceptual prototype digital simulator (PDS) is given and its parts are analysed in detail, including a minimal memory realization of a multivariable non‐linear mapping (look‐up table). It is shown that if the increase of the complexity of the simulator does not exceed the increase of the complexity of the circuit or system to be simulated, then the simulation complexity (measured in terms of the accumulated time of basic calculation steps) will not decrease, but instead will increase. Hence there is an inherent limitation in the digital simulation of analogue operators. This result suggests at the same time that the digital method of data and signal processing has some inherent limitations, a striking example of overcoming it being the neural circuit. the speeding up of the digital hardware due to the scaling down of feature sizes in integrated circuits and the reduction of the time step due to the increase in system size are also taken into account.
A transformation method for the solution of power switching circuits based on network topological concepts
Authors: Milias‐Argitis J. , Zacharias Th.
Published: July 2007

In this paper, a general and systematic method for the analysis of varying topology power semiconductor circuits is presented. the changes of the conduction state of the semiconductor switching devices are handled by successive modifications of the tree of the circuit graph. These tree modifications are systematically reflected on a square transformation tensor. On the basis of well known network topological concepts, this generalized transformation tensor can be constructed in a relatively simple way. This tensor constitutes a flexible and powerful tool to assemble automatically the necessary on‐switch current and off‐switch voltage equations required for any conduction pattern. These manipulations are accomplished with a step‐by‐step modification procedure of the equations describing the circuit in the most previous conduction state. the basic steps of an algorithm suitable for the practical implementation of the analysis of any power switching network on a digital computer are described, and an example is used to demonstrate the effectiveness of the proposed method.
Development of a symmetrically stabilized four‐phase oscillator and some implications
Authors: Kaplan B. Z. , Yardeni D.
Published: July 2007

This paper treats the development of a non‐linearly stabilized oscillator model which generates four sine waves in quadrature. This system is dealt with in spite of the fact that quadrature signals can be generated by a simple two‐phase oscillator. the latter generates only two of the signals needed in a four‐phase system. the rest of the phases signals could nevertheless be obtained by inventing the originally existing signals. It appears, however, that for certain applications the generation of all four signals in a completely cyclic and symmetrical manner (the one described here) is preferable. It is envisaged that one such application is related to recent methods of actively feeding phased array antennas, where each element in the array is connected to an appropriate oscillator phase stage.

Most of the paper deals with the development of an appropriate generator model. the non‐linear oscillator dynamics is treated comprehensively. the peculiar behaviour associated with the limit cycle dynamics and with other manifestations of the system dynamics is investigated. It appears from the detailed simulation work that there exist regions of initial conditions where the system solutions are expected to be relatively sensitive to initial conditions. As a result, it is believed that the system with certain additions may reveal chaotic dynamic behaviour. the realization of the system in electronic hardware is also discussed.