bluuebunny/crossref_metadata_2025 huggingface dataset:
Complete stability of autonomous reciprocal nonlinear networks
Authors: Chua Leon O. , Wang Niantsu N.
Published: July 2007

Several sufficient conditions are presented which guarantee that an autonomous nonlinear reciprocal network having multiple equilibrium states is completely stable in the sense that every trajectory of the network tends to an equilibrium state and hence no oscillation of other exotic mode of spurious behaviour can occur. Stability criteria are derived with the help of the concept of the generalized inverse of a maxtrix for both complete and noncomplete networks. The results on noncomplete networks depend crucially on the introduction of a pseudopotential function called pseudo‐hybrid content and on the imposition of a local solvability condition. Most of the hypotheses are algorithmic in the sense that either explicit bounds are provided for computation purposes, or equivalent topological tests are given for checking the nonquantitative conditions.

Most results presented are applicable to networks containing multiport and multi‐terminal elements which are represented by coupled two‐terminal elements. Examples are given which demonstrate that some of our results on complete stability are the best possible that can be obtained for the class of networks under consideration.
Multiport converters and inverters
Authors: Silva Manuel M.
Published: July 2007

Two‐port immittance converters and inverters are well known active‐network ‘components’. In this paper the concepts of conversion and inversion are generalized so as to apply to multiports. A definition of multiport hybrid converter is proposed, and the necessary and sufficient conditions that the matrix description of this multiport must satisfy are derived from the definition. Multiport admittance and impedance converters and inverters are introduced as special cases of hybrid converters, and it is pointed out that, whereas 2‐port admittance converters or inverters are always also impedance converters or inverters, and vice‐versa, this is not generally true for the multiport converters or inverters proposed here.

Multiwinding transformers, multiport gyrators, and most of the circuits that can be used for the simulation of floating inductors are shown to be special cases of multiport converters or inverters. It is believed that the theory of multiport conversion and inversion presented here provides a better understanding of these special cases and is also useful as a contribution to multiport theory in general.
(n +p)‐node realizability of Y‐matrices of (n + 1)‐node resistance n‐port networks
Authors: Thulasiraman K. , Swamy M. N. S. , Reddy P. S.
Published: July 2007

Sufficient conditions are established for the (n +p)‐node, p>2, realizability of Y‐matrices of (n + 1)‐node resistance n‐port networks. It is shown that these conditions are a generalization of the previous known results for p = 2 and p =n.
A new result in negative‐feedback theory, and its application to audio power amplifiers
Authors: Cherry E. M.
Published: July 2007

A nest of differentiating loops is described by means of which a very large amount of negative feedback can be applied to a specified stage in an amplifier (normally the output stage) with progresively less being applied to other stages. The effects of nonlinearity (other than hard limiting) in the specified stage can be virtually eliminated. The structure enables Bode's limit for loop‐gain roll‐off to be exceeded for the specified stage; both the frequency up to which loop gain is maintained constant and the frequency at which loop gain falls through unity are free design variables. As a result, practical difficulties associated with excess phase shift in low‐frequency power transistors are minimized. The structure does not increase the susceptibility to transient overload and the resulting intermodulation. A practical amplifier using output transistors with fT∼2 MHz has an output‐stage loop gain of 25,000 (88 dB) at 20 kHz and 0.002 per cent harmonic distortion.
On second‐order cofactors and null return difference in feedback amplifier theory
Authors: Chen Wai‐Kai
Published: July 2007

Like the general return difference, the general null return difference is defined as the ratio of the two functional values assumed by the second‐order cofactor of the elements associated with the input and output terminals of the indefinite‐admittance matrix of a feedback amplifier under the condition that the element of interest assumes its nominal value and the condition that the element assumes its reference value. It is shown that this algebraic definition is entirely consistent with the classical physical formulation of the null return difference.
Application of the mixed potential for formulating normal form equations for nonlinear rlc‐networks with ideal transformers
Authors: Horneber E.‐H.
Published: July 2007

For the class of complete nonlinear RLC‐networks the normal form equations can be established by a method given in Brayton and Moser1 using the mixed potential. Before applying this approach it is a crucial point to investigate whether a network is complete. To this end in the present paper an algorithm is given which additionally leads to a partitioning of the network under consideration. Two theorems are given enabling the direct construction of the mixed potential starting from the obtained subnetworks. It is shown that complete nonlinear RLC‐networks with ideal two‐port transformers (RLCT‐networks) can be remodelled into complete RLC‐networks using a new approach to model non‐hybrid transformers. Noncomplete RLCT‐networks often can be remodelled into complete RLCT‐networks by inserting additional branches containing controlled sources which do not affect the mixed potential. Further simplifications are possible using the rules given to derive the so‐called ‘potential‐equivalent’ networks which contain less controlled sources but lead to the same normal form equations. Finally some theorems are given concerning the existence and uniqueness of solutions of a complete network where the conditions can be examined directly at the network before establishing the network equations.
A nonlinear lumped circuit model for gunn diodes
Authors: Chua L. O. , Sing Y. W.
Published: July 2007

A nonlinear lumped circuit model for Gunn diodes which includes the effects due to domain extinction and nucleation phenomena is presented. The model is based upon physical principles and allows an arbitrary nonlinear drift velocity curve v(E) and a nonlinear diffusion curve D(E) to be specified by the user. It is valid for simulating arbitrary Gunn‐diode circuits operating in any matured high‐field domain mode, or in the LSA mode. Under additional assumptions, the model simplifies to other existing models. Several computer‐simulated examples of Gunn‐diode circuits operating under both steady‐state and transient regimes are presented. Finally, a rigorous definition of a ‘DC’ I‐V curve for Gunn diodes is offered and shown to be rather useful for predicting the qualitative behaviour of Gunn‐diode circuits during all time intervals where a matured domain exists.
A class of nonrealizable paramount matrices
Authors: Loughlin Timothy A. , Slepian Paul
Published: July 2007

Although paramountcy1 is a necessary and sufficient condition for the realizability of a 3 by 3 matrix as either an open‐circuit impedance matrix or a short‐circuit admittance matrix of a resistive 3‐port,2 Weinberg's 4 by 4 example3,5 shows that paramountcy, although necessary for open‐circuit impedance realization, is not sufficient. Here we exhibit a class of 4 by 4 completely irreducible paramount matrices, including Weinberg's example, no member of which is realizable as an open‐circuit impedance matrix. This is accomplished by examining those topological constraints inherited by a realizing network when algebraic conditions are imposed on the paramount matrix which the network realizes. Our development deals with an n‐port network, for arbitrary n, and also provides new criteria guaranteeing nonrealizability of an irreducible1 paramount matrix.
Transfer functions with arbitrary phase characteristics
Authors: Fahmy M. F.
Published: July 2007

A simplified method—based on Thiele's continued fraction—is proposed for the derivation of transfer functions whose phase responses interpolate a desired phase characteristics at a set of prescribed frequencies, the maximally flat delay aproximation being recovered as a degenerate one. Illustrative examples showing the application of this procedure in the design of linear delay networks are also given.
Unique solvability and order of complexity of linear networks containing memoryless n‐ports
Authors: Recski András
Published: July 2007

Essentially combinatorial necessary and sufficient conditions are given for the unique solvability of linear networks containing memoryless n‐ports, and for the existence of a hybrid immittance description of the interconnection of such n‐ports. Formulae for the maximum number of independent state variables and order of complexity are also presented.

The essential tool for obtaining the results is the theory of matroids. The conditions can be effectively checked by matroid partition or intersection algorithms.

Throughout, the ‘general’ approach is considered, i.e., no cancellation among the nonzero terms is allowed. The results are illustrated by several examples.
Synthesis of n‐port networks by a matrix‐continuant
Authors: Cichocki A. , Osowski S.
Published: July 2007

A general RC active network synthesis procedure for the realization of the multiport is proposed in this paper. The method is developed and based on using matrix‐continuants and simple matrix manipulations. A numerical example of the realization is also given.
Microwave filters with nonperiodic transmission characteristic
Authors: Arndt F. , Saulich G.
Published: July 2007

A microwave filter with nonuniform‐coupled transmission lines is suggested. In contrast to known transmission‐line microwave filters the transmission characteristic does not change periodically with frequency. The synthesis procedure shown reduces the design problem to the known synthesis of directional couplers with nonuniform coupling factor. A table of calculated coupling factor values of the microwave filter with an equi‐ripple passband of 0.05 dB up to 1 dB and an equi‐ripple stopband of 60 dB is given. A practical design example shows good agreement with theoretical results.
Elimination of zero‐input limit cycles by bounding the state transition matrix
Authors: Turner L. E. , Bruton L. T.
Published: July 2007

A method of eliminating zero‐input granularity limit cycles in digital filters using the state transition matrix is presented. Further, for a particular class of digital filters, it is shown that bounding the transition matrix is sufficient to eliminate limit cycles of length n > 1.
Computer‐aided design of stable recursive digital filters from magnitude specifications
Authors: Prasad K. P. , Reddy P. S.
Published: July 2007

This paper presents a method of designing one‐ and two‐dimensional recursive digital filters making use of the properties of bilinear transformation of strictly Hurwitz polynomials. The result is a stable digital filter in both one‐ and two‐dimensional cases, which requires no further testing for stability. The well known unconstrained minimization technique of Fletcher—Powell is used, making use of a transformation of optimization parameters to satisfy the mild constraints of stability. This method is considered to be more efficient on an overall basis than the existing lp design technique of Maria and Fahmy. Nor does it rely on Deczky's theorem to ensure a stable filter which may sometimes lead to unstable solutions in the two‐dimensional case. An example is provided illustrating the method.
A refined classification of single amplifier filters
Authors: Sedra Adel S. , Brown Les
Published: July 2007

It is shown that Single Amplifier Biquads (SAB's) may be grouped into two major categories, the Enhanced Negative Feedback (ENF) and the Enhanced Positive Feedback (EPF). These two major classes of circuit are related by the complementary transformation and hence exhibit identical sensitivity performance. In the extreme, the ENF class degenerates to the familiar Negative Feedback (NF) class while the EPF class reduces to the Positive Feedback (PF) case where the op amp is connected in a unity‐gain configuration. Depending on the order of the RC feedback network, each class includes two subclasses with different sensitivity performance. The paper examines in detail the ‘enhanced feedback’ mechanism, and investigates the optimum design of the Deliyannis—Friend circuit and its complement the Sallen and Key positive feedback configuration.
On the interchanging of the second‐order network with high Q‐factor poles by low Q‐factor stages
Authors: Filanovsky I. M. , Stromsmoe K. A.
Published: July 2007

This article presents a method for the interchange of a second‐order network with high Q‐factor poles by a more complicated network that consists of several low Q‐factor stages. The transfer function square modulus of this new network approximates in a Chebyshev manner the square modulus of a given transfer function if the zeros of a given network are complex conjugate and not located on the α‐axis. In the other cases an error of the square modulus approximation is a Chebyshev kind also, but with the weight that depends on the zero locations of the given second‐order network and given maximum Q‐factor. It is shown that all low Q‐factor pairs of the poles must coincide when we apply the proposed method directly. The approximation error decreases in a geometric progression with the growth of the number of low Q‐factor stages. A method for determination of the numerator zeros of the approximating transfer function is described and examples of interchanging are given.
Selective, constant delay wave digital filters
Authors: Denton G. , Carlin H. J.
Published: July 2007

A wave digital filter design method is discussed which produces good selectivity and flat delay characteristics. The filter is designed in the microwave domain with monotonic stopband response using Carlin and Wu's technique for minimum‐phase linear phase commensurate line transducers, then realized in the digital domain with Fettweis relations. A comparison is made of frequency response sensitivity to multiplier coefficient truncation between this wave filter and some FIR's, all with approximately the same number of multipliers. The cascade realizations of the FIR's show considerable passband amplitude response deterioration due to coefficient truncation, whereas the direct realizations for the FIR's show significant deterioration of stopband amplitude response owing to coefficient truncation. Coefficient truncation for the wave digital filter caused relatively small deterioration of both passband and stopband amplitude responses as well as small distortion of the flat delay characteristic in the passband.
Synthesis of active RC‐biquads using generalized immittance converters
Authors: Nenov Georgi A.
Published: July 2007

This paper considers a new nullor structure of a current‐inversion generalized immittance converter and its application. On the base of generalized continuants a method for synthesis of active RC‐sections with biquadratic voltage transfer functions (biquads) is developed. The structures obtained contain current‐inversion generalized immittance converters and passive RC‐elements. The synthesis procedure is illustrated by examples and experimental results.
Critical element analysis for the transfer, gain and phase functions in linear active filters
Authors: Acar Cevdet
Published: July 2007

In linear active filters, the element criticalness, the most and the least critical elements, and also optimum tolerances have been defined for transfer, gain and phase functions. Simple and systematic procedures for computing their values, thus determining the ordered hierarchy of critical elements, are provided. Moreover, as an example, the element criticalness, the most and the least critical elements, and the optimum tolerances have been evaluated for Gopal's network realizing the third‐order Butterworth characteristic and using equal‐valued capacitors and resistors.
Third order oscillators with independently adjustable frequency, amplitude and transient response
Authors: Owen Earle W.
Published: July 2007

A class of third order harmonic oscillators with frequency, amplitude and transient response controlled by three separate sets of parameters is derived. A simplified group of oscillators is described in which there are only three parameters, one which controls the frequency, another the amplitude, and the third the transient response. Each oscillator contains a single nonlinearity, which can be either of the saturation or the dead space type. The mathematical analysis is based on linearizing the nonlinearity by means of the sinusoidal describing function. The transient response is studied by considering small amplitude perturbations away from the oscillator's limit cycle. The results of analogue computer simulations are presented with emphasis on the relationship between transient response and the gain controlling it.
Optimal printed circuit board ordering via hart‐nilsson‐raphael‐algorithm
Authors: Sangiovanni‐Vincentelli Alberto L. , Santomauro Mauro
Published: July 2007

A layout problem, the optimal ordering of printed circuit boards equally spaced on a straight line, is investigated. An optimal algorithm whose structure is based on the Hart, Nilsson and Raphael algorithm is presented and its complexity evaluated. Since the intrinsic complexity of the problem is shown to be very high, an approximated algorithm is introduced and its performances are evaluated. Experimental results are discussed to emphasize the efficiency of the approximated algorithm.
A tableau approach to power system analysis and design
Authors: Director S. W. , Sullivan R. L.
Published: July 2007

The tableau formulation of electronic circuit equations has been shown to be an efficient and useful formulation for circuit optimization. In this paper a tableau based formulation of the static power‐flow equations for a power system is presented. Because of the explicit appearance of all quantities of interest the tableau formulation allows the general statement, and solution, of a variety of power system optimization and design problems without the need to resort to restrictive assumptions.
On obtaining of a transfer function with complex‐conjugate poles of the same Q‐factor by fourier approximation
Authors: Filanovsky I. M. , Stromsmoe K. A.
Published: July 2007

This communication presents a method for obtaining a transfer function with multiple complex conjugate poles. The procedure is based on a special frequency transformation. The function derived from those to be approximated is expanded in a Fourier series with a finite number of terms. The application of the inverse transformation to this truncated series gives an algebraic ratio from which the transfer function with chosen poles can be obtained with known methods.
A theory of Q‐reciprocal and quasi‐reciprocal multiports
Authors: Osiowski Jerzy , Morawski Tadeusz
Published: July 2007

Two notions: quasi‐reciprocity and Q‐reciprocity as generalizations of classical reciprocity are introduced and examined for the multiport case. A number of theorems and properties characterizing a class of Q‐reciprocal multiports are stated. A way of extending to quasi‐reciprocal networks some results proved under the assumption of reciprocity is presented as an example of application.
Effect of operational amplifier imperfections on single amplifier filters
Authors: Soundararajan K. , Ramakrishna K.
Published: July 2007

A general method is given for the analysis of single amplifier RC‐active filters using nonideal operational amplifiers (OA). It is shown that the output resistance of the OA has a significant effect in the passband and stopband in addition to the known deviations due to the finite gain—bandwidth product. The nonideal transfer functions in the factorized form, giving clearer concept of the effects of the nonideal OA, are obtained using some realistic approximations based on the typical specifications of modern general purpose OA. Expressions thus obtained closely follow the exact transfer functions, as demonstrated in the illustrative examples given, and their validity is confirmed by the experimental results.
Narrow‐band stripline filters with transmission zeros at finite frequencies
Authors: Jokela Kari
Published: July 2007

A design method is described to realize narrow‐band stripline or microstrip bandpass filters having one transmission zero near to the upper and lower bandedge. The filters utilize capacitively coupled open half‐wave TEM‐line resonators. Two nonadjacent resonators are also inductively coupled. No short circuits are needed.

The design is based on the approximate or exact synthesis of the lowpass protoype presented by Levy. The transmission line parameters are obtained easily from the design formulae which have been derived using the susceptance (or reactance) slope parameter technique. The filter performance is good up to 12 per cent bandwidth. Measured results show good agreement with the theoretical ones.
Frequency‐dependent OP‐AMP gain influence on parameters of the single amplifier biquad filters
Authors: Reljin Branimir D.
Published: July 2007

The influence of the finite gain and gain‐bandwidth product of the operational amplifier on the parameters of the active RC filter has been investigated in the present paper. Single amplifier biquad filters were analysed for the case when the central frequency in the pole pair does not depend on the amplifier gain, i.e. when S = 0. The general results were obtained for such filters, describing well the filter behaviour at low as well as at high frequencies. On the basis of the results obtained, the deviation of the realized parameters from the desired values can be determined, and thereby the necessary correction of the filter calculation can be made. The experimental results agree well with the theoretical ones.
Notch filter based on identical building‐blocks with arbitrary transfer function
Authors: Plotkin E.
Published: July 2007

A new design formula for the Multiple Frequency Notch Filter is proposed. The filter can be constructed from a finite set of identical linear sections with arbitrary transfer functions. The general transversal structure and the cascade connection of the identical linear section are considered. In contrast to the general structure, there are found three configurations which have only one adjustable element. An example illustrating the use of the proposed technique is included.
Sufficient conditions for the unique solvability of linear networks containing memoryless 2‐ports
Authors: Recski András
Published: July 2007

Combinatorial necessary and sufficient conditions for the unique solvability of linear networks containing n‐ports are well known for the ‘general’ case. They are only necessary if relations among n‐port parameters are also taken into consideration.

In the present paper combinatorial sufficient conditions are presented for linear networks containing RLC elements and memoryless 2‐ports. The somewhat surprising result is proved that whether a 2‐port can cause certain types of singularities can be predicted before the interconnection.

A concept, similar to the normal tree (which intersects ideal transformers by one, gyrators by two or no edges) is introduced for arbitrary 2‐ports. Its existence implies unique solvability.

Relations to previous results and algorithmical aspects are also discussed.
Propagation of constraints applied to circuit synthesis
Authors: De Kleer Johan , Sussman Gerald Jay
Published: July 2007

A major component in the process of design is synthesis, the determination of the parameters of the parts of a network given desiderata for the behaviour of the network as a whole. Traditional automated synthesis techniques are either restricted to small, precisely defined classes of circuit functions for which exact mathematical methods exist or they depend upon numerical optimization methods in which it is difficult to determine the basis for any of the answers generated and their relations to the design desiderata and constraints. We are developing a symbolic computer‐aided design tool, SYN, which can be of assistance to an engineer in the synthesis of a large class of circuits. The symbolic methods produce solutions which are clear and insightful. The dependence of each parameter on the individual design desiderata and circuit constraints can be easily traced.
On the sensitivity analysis of digital filters
Authors: Liberatore A. , Manetti S.
Published: July 2007

A very quick and simple algorithm for the overall evaluation of the sensitivity performance of a digital filter is introduced.

To this end, it is shown that the sensitivity of the system function with respect to a given coefficient comes out equal to the output of a special digital network with unitary input. Having defined, then, an ‘overall sensitivity index’ as the sum of the various network sensitivities, it is shown that such an index can still be considered as the output of a digital network with unitary input. This network is composed of two subnetworks, identical to the original circuit, connected by a special set of branches.
Maximum flow in probabilistic communication networks
Authors: Nawathe S. P. , Rao B. V.
Published: July 2007

The purpose of this paper is to provide a general approach for the problems of analysis and synthesis of probabilistic communication networks. The flows in the branches of a network may be interdependent random variables having any arbitrary distribution.

A simple technique, based on the theory of best linear prediction, enables Monte Carlo simulation of such a network. The simulation results suggest that the distribution of the maximum flow (that can be established in the network) can be approximated by a normal distribution despite the inapplicability of the central limit theorem. The results of Monte Carlo simulation are consistent with those obtained through an alternative analytical procedure.

The synthesis problem considered in this paper is that of finding the branch capacities of a network so that a given demand for flow (specified in terms of its mean and variance), between a pair of vertices of interest, is satisfied. A direct search method (to find out the optimal branch capacity vector) enables simultaneous consideration of the first two moments of the maximum flow as against the existing ones which consider only the first moment.
Selective constant delay filters with chebyshev passband amplitude response
Authors: Fahmy M. F. , Sobhy M. I.
Published: July 2007

The aim of this letter is to show that the principle of least squares norm can be utilized to offer flexibility in the design of selective linear phase filters.
The use of Padé approximants in the derivation of distributed low‐pass filters with simultaneous flat amplitude and delay characteristics
Authors: Fahmy M. F.
Published: July 2007

A unified approach—based on Padé Approximants—is presented for the design of simultaneous equal constraints non‐minimum phase distributed filters. The results obtained indicate that this method is more general than previous methods, and allow considerable freedom for the control of both amplitude and delay. The procedure outlined can apply for any transfer function with arbitrary characteristics.
The existence and the determination of terminal equations for hybrid connected N‐ports
Authors: Sen A. Esref , Tokad Yilmaz
Published: July 2007

A new procedure for the existence and the determination of terminal equations for the hybrid interconnection of two n‐port networks is given. It is shown that this procedure generalizes the previous works of Duffin, Trapp and Mitra for the hybrid sum of terminal impedance matrices which are either Hermitian positive semi‐definite (HSD) or arbitrary matrices with complex entries. For the application of the new procedure it is shown that each n‐port need not be terminal solvable or well defined. In fact, even in the case of active RLC n‐ports considered in sinusoidal steady‐state, the previous results of Duffin, Mitra and Trapp established for HSD matrices or arbitrary complex matrices can still be utilized with the use of modified terminal equations, to obtain the terminal equations of the resulting n‐port networks. It is also noted that the method introduced in this paper is independent of the choice of generalized inverses.
Synthesis of some non‐reciprocal filters employing the Jacobi polynomials
Authors: Jarry P.
Published: July 2007

In this paper, we establish that some of the generalized linear phase polynomials defined in Reference 1 are Hurwitz. The demonstration consists in showing that the ratio of two linear phase polynomials is a positive real function. The corresponding network interpretation with closed‐form element values is then given, which yields at the same time the reflection‐filter synthesis of the non‐minimum phase, non‐reciprocal transfer functions introduced in Reference 1.
D–T adaptor: Applications to the design of non‐linear N‐ports
Authors: Huertas J. L.
Published: July 2007

A new network element is presented which can be of interest for synthesizing non‐linear n‐ports. It is shown that the use of n D–T adaptors reduces the problem to the synthesis of a multidimensional transfer‐characteristic (TC) plot. Some examples are given to show the applicability of the procedure and its ability to make a convenient use of integrated technology.
Compensation of frequency‐dependent amplifier non‐idealities in tunable RC‐active networks
Authors: Ferling Heinz‐Dieter
Published: July 2007

A structure‐independent synthesis procedure for RC‐active networks, which performs the synthesis process by successive matrix expansion steps, allows the straightforward realization of networks with arbitrary tunable parameters. Since the desired behaviour of the realized circuit may be strongly affected by the frequency‐dependent imperfections of the active devices used for practical circuit construction, a compensation of the resulting root displacements of the network's characteristic equation is needed.

The particular properties of the synthesis technique lead to an immediate relation between the root displacement caused by a single matrix transformation step and the information being available when this step is executed. Following a brief description of the synthesis process, this relation is derived and then used to establish a compensating circuitry which has to be added to the synthesized network structure in order to achieve the compensation effect required above.
Realizability conditions on short‐circuit conductance matrix by means of grounded active resistive networks embedding grounded VCVSs
Authors: Stamenković Borivoje B.
Published: July 2007

The proof is given of a new theorem concerning the minimum number of ideal grounded voltage‐controlled voltage sources (VCVSs) necessary and sufficient to realize an arbitrary real square matrix as the short‐circuit conductance matrix of a grounded transformerless active resistive multiport network embedding grounded VCVSs.
What does duality really mean?
Authors: Iri Masao , Recski András
Published: July 2007

The average network theorist answers this question by speaking about the interchange of the roles of voltage and current, while the average mathematician uses orthogonal vector spaces for his definition (as in mathematical programming, matroid theory, etc.). What is even worse, both of them believe that the two definitions are essentially the same. The main aim of the present paper is to show that this is the case for reciprocal networks only. Hence, in the theory of non‐reciprocal networks, two entirely different voltage‐current symmetries exist. We also show that both concepts are naturally related to the same, well known, duality principle of graph theory which also explains why nobody seems to have observed this phenomenon till now.
Modelling considerations and mean square error analysis for PSK data transmission
Authors: Henk Tamás
Published: July 2007

Coherent PSK data transmission systems are modelled using matrices and non‐linear co‐ordinate transformations. A polyphase multiplier type demodulator with a new structure is suggested. A mean square error (MSE) analysis is carried out in the frequency domain for small perturbations which are linear distortions and static imperfections of the carrier and timing recovery, without any other restrictions for the bandwidth and the distortions. General and explicit expressions are given for the optimal carrier phase and timing delay, for their sensitivity and for the minimal MSE value. Using these expressions, filter design as well as carrier and timing recovery considerations are presented.
Realization of tunable RC‐active oscillators using grounded capacitors and voltage amplifiers
Authors: Bhattacharyya B. B. , Sundaramurthy M. , Swamy M. N. S.
Published: July 2007

A systematic procedure is given to generate a set of tunable RC oscillators, each using two finite gain voltage controlled voltage sources, three resistors and two grounded capacitors. These realizations are shown to be minimal with respect to passive and active elements under the constraint that (one end of) all the capacitors remain grounded. The set consists of four oscillators and is shown to be complete, that is, no additional oscillator circuit can be generated under the given assumptions. A simple approach is then introduced for testing the structures for latch up behaviour. This approach also suggests a way of redesigning the oscillator circuits to render them free of latch up problems, if they exist. Experimental results are found to be in good agreement with the theory.
An analogue filter synthesis package based upon vector space operations
Authors: Marshall T. G. , Liu F. C.
Published: July 2007

A complete APL analogue filter synthesis package is described which includes provisions for avoiding ill‐conditioning when polynomials with clustered roots are considered. The solution to the numerical problem that is employed in this package is the introduction of a change in representation in a linear manner by a change of basis. This is accomplished by the reformulation of the polynomial problem as a vector space problem. This results in a set of vector space synthesis algorithms which are conveniently implemented in APL. The conventional polynomial operations of filter synthesis such as polynomial division, zero shifting, and removal of a known factor lead to interesting and challenging vector space algorithms. These algorithms and their APL implementations are discussed. An advantage of this approach for APL implementations is that complex arithmetic can be avoided by selecting an appropriate basis for the vector space.
The design of low noise digital filters with controlled dynamic range
Authors: Bonsaver E. , Szczupak J. , Mitra S. K.
Published: July 2007

A novel digital filter structure, that allows proper positioning of the zeros of the noise transfer functions to reduce the output roundoff noise, is introduced. Relations between zero locations, roundoff noise and dynamic range are derived and are then utilized in an heuristic optimization method for synthesizing a low noise scaled digital filter structure. Illustrative examples supporting the proposed approach are included.
Formulation of equations in terms of scalar functions for lumped non‐linear networks
Authors: Milič Mirko M. , Novak Ladislav A.
Published: July 2007

A general method is presented of formulating the Lagrangian and anti‐Lagrangian equations for networks consisting of non‐linear RLCM (M = memristor) multiports with hybrid representation.

The formulation is obtained with no restriction on the network topology. An explicit procedure is given to construct the scalar functions needed. This procedure is based on the concept of L and H functions introduced. The Brayton‐Moser equations in a generalized form can be directly obtained from the anti‐Lagrangian equations. From these equations, new equations of Brayton‐Moser type can also be derived.

The invariance property of Lagrangian and anti‐Lagrangian equations under a transformation of variables is also discussed.
Experimental noise effects on transfer function—phase evaluations via Hilbert transforms: Application to optical fibres
Authors: Bassi Paolo , Zoboli Maurizio
Published: July 2007

The effect of measurement noise on the phase of a linear network‐transfer‐function, computed as the Hilbert transform of the modulus, is investigated experimentally. As a typical example, the case of an optical fibre is dealt with. It is shown that, when noise is present, theoretically equivalent methods of performing this transform lead to results affected by uncertainties strongly depending on the chosen algorithm.
Initial vertex partitioning and testing isomorphism of graphs and digraphs
Authors: Bhat Kabekode V. S. , Rahnavard M. H.
Published: July 2007

In this paper, we present a new method for initial vertex partitioning of graphs (digraphs) using the notion of a vertex label that includes several parameters of the graph for each vertex of the graph (digraph). Our method provides a more refined initial vertex partitioning for graphs (digraphs) than any of the known methods in O(nE) time for a graph withnvertices andEedges. Several examples are given as illustrations of the method. A computational comparison of our method with the Schmidt‐Druffel algorithm is presented. The method can be coupled with any existing good back‐tracking method for testing isomorphism of graphs and digraphs.
Principles of complex wave digital filters
Authors: Fettweis Alfred
Published: July 2007

The theory of real wave digital filters (WDFs) is extended to complex WDFs. A fundamental requirement turns out to be that of one‐realness, a complex impedance in the reference filter being called one‐real if it is real for Ψ = 1, where Ψ is the equivalent complex frequency. The only new components then required are complex multipliers with unimodular coefficients, but the adaptors are just as in the real case. The stability properties known for real WDFs can, in this way, also be extended.
Optimal selection of IC fabrication parameters
Authors: Karmokolias C. , Portnoy W. M. , Saeks R. E.
Published: July 2007

A procedure is described in which the output characteristics of an integrated circuit are optimized with respect to a set of variable fabrication parameters. A simple RC coupled audio amplifier is used as an example. The gain–bandwidth product is obtained as a function of oxidation and diffusion times and temperatures, and the optimization is performed by way of a line search using these variables as the parameters of the optimization. The values established for the process parameters are consistent with those employed for conventional fabrication, and desired changes in performance can be obtained, in general, by a straightforward readjustment of the values of the process variables. Although limited by certain assumptions and a relatively primitive circuit, the results demonstrate the validity of the procedure.
Necessary and sufficient conditions for absolute stability of linear n‐ports
Authors: Zeheb Ezra , Walach Eugene
Published: July 2007

A set of necessary and sufficient conditions is stated and proved for the absolute stability (under any passive terminations), in the ‘bibo’ sense, of a linear n‐port characterized by its open‐circuit impedance matrix. A more explicit set of such conditions is derived for the special case n = 3. In the process of deriving this set of conditions, some results and theorems concerning finding the zero sets of two and three parameter functions, are stated and proved. Also derived is a set of necessary and sufficient conditions for the absolute stability of two‐ports characterized by the scattering parameters. Such sets have already been derived previously, but the present set is considerably simpler.
Biquadratic n‐dimensional impedances
Authors: Gregor J.
Published: July 2007

A discussion of n‐dimensional quadratic Hurwitz polynomials and biquadratic positive real functions is given. The formulated necessary and sufficient conditions are easily verifiable and make the discussion of the influence of coefficient changes possible. Some more general results and examples are included.
A possibility of filling the gap between local and global passivity of non‐linear networks and some of its consequences
Authors: Roska Tamás
Published: July 2007

In the qualitative theory of non‐linear networks the non‐linear n‐ports are generally considered either locally passive or globally passive even eventually globally passive (the most restrictive or the least restrictive properties respectively). Moreover the reciprocity condition in many cases (e.g. complete stability) restricts the area of applications. In the area of economics and other fields, basically motivated by Sandberg's results, the role of the off‐diagonally monotone and antitone mappings is crucial.

In this paper, based on the above facts and results, it is shown that partly similar classes of mappings could have a role in non‐linear network theory. More precisely, the off‐diagonally locally active (passive) n‐ports, defined in the paper, could represent an important new class of n‐ports.

As an application of the features of this new class of n‐ports two Theorems are given showing conditions under which in case of a network consisting of off‐diagonally locally active n‐ports the DC solution can be uniquely calculated using the standard iterative methods and an autonomous network is asymptotically stable in a given domain. Hence, this paper partially overcomes the so called ‘curse of non‐reciprocity’.
A comparative study of multiple amplifier active RC biquadratic sections
Authors: Padukone Pradeep R. , Ghausi Mohammed S.
Published: July 2007

Biquadratic sections play an important role in the design of high order active filters. This paper compares a number of popular multiple amplifier active RC biquads on the basis of their sensitivities as well as ω0 and Q enhancement effects due to finite amplifier gain–bandwidth products (GB). For sensitivity comparison, statistical sensitivity measures, which take into account the tolerances of various passive and active elements, are used. Simple expressions for gain, phase and transfer function sensitivities are derived for the case of uncorrelated element variations. Graphic illustrations of the effects of increasing ω0 and Q on the sensitivity measures are presented. In addition, root‐loci, which show the effects of GB on the network poles are included. To further facilitate the comparison, graphs demonstrating changes in ω0 and Q due to GB are also presented.
The generation of arbitrary‐phase polynomials by recurrence formulae
Authors: Henk Tamás
Published: July 2007

A filter‐design oriented theory is presented for polynomials with prescribed phase properties. The phase function is specified by its values and/or higher derivative values at a set of given frequencies. The polynomials are generated by recurrence formulae whose coefficients are calculated by a recursive algorithm. Formulae are presented to calculate the higher derivatives of some composite functions of the phase which are utilized in the process of flat phase approximations.
Sensitivity minimization in signal‐flow graphs
Authors: Tan M. Ali , Acar Cevdet
Published: July 2007

In this work, the sensitivity minimization is studied for the signal‐flow graph of the state equations realizing a general biquadratic transfer function. The sensitivity measures are defined for the poles, the pole Q and the pole frequency. The formulae are derived for their evaluations. Branch transmittances minimizing each of these measures are found. Finally, it is shown that there exists a very simple relation between the measures. The results obtained in this study can be used in active filter realizations with minimum sensitivity.
On the parametrization of linear memoryless 2‐ports
Authors: Recski Andras , Zoller Vilmos
Published: July 2007

A parametric description of all homogeneous linear memoryless 2‐ports is given using the Grassmann‐Plücker co‐ordinates of algebraic geometry. Unlike the usual (impedance, scattering, chain, etc.) descriptions, this one presents a 1–1 correspondence between the set of all 2‐ports and certain 4‐tuples. The physical meaning of these parameters is related to reciprocity, passivity and losslessness, hence every important transformation of the 2‐port (not only negative and inverse but dual and adjoint as well) can directly be obtained.

A remark on linear network solvability is included.
An analysis of slew‐induced distortion in single‐amplifier active filters using the volterra‐wiener series technique
Authors: Borys Andrzej
Published: July 2007

A model of an operational amplifier suitable for small‐signal non‐linear analysis is developed in the present paper. The model, based on the Volterra‐Wiener functional series expansion, contains the slew‐rate non‐linearity. By performing an accuracy analysis, the limits of its validity are also given. The stability of the single‐amplifier basic structure considered as a non‐linear network is studied. On the basis of the results obtained, the field on an amplitude‐frequency plane for a small‐signal non‐linear case (FAF) is introduced for single‐amplifier active filters containing operational amplifiers. It is shown that this FAF is simply related to the threshold of the input‐signal amplitude at which slew‐induced distortion (SID) begins.
On the dynamic spaces and on the equations of motion of non‐linear
Authors: Szatkowski Andrzej
Published: July 2007

The problems of the qualitative theory of non‐linear RLC networks are considered from a geometric point of view. Several general properties of the dynamic space of the network are presented. The concept of the vector field generated by the network on its dynamic space is introduced and discussed. The equations of motion are formulated in the forms which are useful in the qualitative analysis of the solutions.
Approximation method for decomposable filter pairs
Authors: Carlin Charles‐Henri
Published: July 2007

The decomposable filter pair is presented, starting from the general form of the scattering matrix of a lossless reciprocal 3‐port. The restrictions with respect to the general case are discussed. The two general categories of requirements imposed to a filter pair are presented and their incompatibility is established. An algorithm is described, allowing one to approximate simultaneously the two main transfer functions of a filter pair.
Sensitivity analysis of RLC nullor networks
Authors: Svoboda J. A. , Wojcik R. J.
Published: July 2007

Linear active networks can be represented either as RLC‐dependent source networks or as RLC nullor networks. The calculation of the sensitivities of the transfer functions of active networks modelled by RLC nullor networks is considered. Three methods for calculating sensitivity are applied to the class of RLC‐nullor networks. Some simplifications resulting from the absence of coupled elements in such networks are observed. The resulting algorithms are implemented as FORTRAN programs and the execution times are compared.
Sensitivity analysis and dynamic range of quad filters and some comparative results
Authors: Nur Gönüleren Ali
Published: July 2007

The paper considers general sensitivity analysis and dynamic range of quad filters. The use of quad structures in the design of symmetrical and/or unsymmetrical active filters is studied from the sensitivity and dynamic range points of view and these are compared with other design methods. Determination of gain constants of biquadratic blocks either according to overloading or noise immunity or both for quad realization are also considered. It is shown that, especially for symmetrical transfer functions, the design equations are simple and that the sensitivity performance is as good as the FLF and LF configurations and better than GFLF. Furthermore, it is shown with an example that quad realization also yields better dynamic range as compared to GFLF.