Loop equation formulation for switched capacitor networks containing nullors

A method is given for determining the loop equations of an ideal active switched capacitance (SC) network containing switches, capacitors and nullors. These equations are obtained directly by row-column operations on the passive unswitched loop elastance matrix. the results are extended for the P- phase case. It is shown that the loop charges can be solved for and that the branch voltages can be obtained from the loop charges.     

Synthesis of voltage-transfer matrices with active RC networks embedding nullors

Realizability conditions for the synthesis of multiport voltage-transfer matrices by means of RC transformerless networks embedding either balanced or grounded nullors are systematically described. The results obtained are summarized in two theorems concerning the minimum number of nullors necessary and sufficient to synthesize a given voltage-transfer matrix.     

Using the superposition method to formulate the state variablematrix for linear networks

This paper proposes a systematic method for writing the state variable matrix for nondegenerate linear electrical networks by using the superposition principle and also extends the procedure to cover degenerate networks. To use the proposed method, all inductances and capacitances in a network are replaced by ideal independent sources; the state variable equations are then written, often by inspection with nondegenerate networks, utilizing the superposition principle in conjunction with the resulting simplified electrical network     

On the realization of gyrators by nullors and resistors

It is proved that for the realization of a gyrator by nullors and resistors, at least two nullors and at least two resistors are needed. A generalization is the result that any n-port network possessing both an impedance and an admittance matrix and consisting of nullors and resistors must contain at least n resistors. It is conjectured that a realization of a gyrator with only two nullors requires four resistors and a realization of a gyrator with only two resistors requires three nullors.     

Using neural networks to select wavelet features for breast cancerdiagnosis

This study focuses on improving microcalcification classification by establishing an efficient computer-aided diagnosis system that extracts Daubechies-4 and biorthogonal wavelet features. These wavelets were chosen because they have been used in military target recognition and fingerprint recognition research with images characterized by low contrast, similar to mammography. Feature selection techniques are employed to further increase classification performance. The artificial neural network feature selection techniques are complemented by a conventional decision boundary-based feature selection method. The results using the wavelet features are compared to more conventional measures of image texture, angular second moment, and Karhunen Loeve coefficients. The use of alternative signal processing to compare wavelet and neural techniques allows for a measure of the problem difficulty. It is concluded that advances and contributions have been made with the introduction of two novel feature extraction methods for breast cancer diagnosis, wavelets and eigenmasses. Additionally, feature selection techniques are demonstrated, compared, and validated, transforming adequate discrimination power into promising classification results     

On the existence of solutions to linear active networks: A state-space approach

In recent literature, several alternative conditions for the existence of solutions to active networks are given. In this paper, yet another condition is given which is both necessary and sufficient for the existence of a unique solution to the network. Based on this new condition a precise upper bound for the order of complexity of an active network is established which differs from published results. A Fortran coded program is also available.     

Electrical characterization of linear and non‐linear random networks and mixtures

A material composed of a mixture of distinct homogeneous media can be considered as a homogeneous one at a sufficiently large observation scale. The problem of mixture characterization has been exactly solved in case of linear random mixtures, that is, materials for which the various components are isotropic, linear and mixed together as an ensemble of particles having random shapes and positions. In the present work the authors briefly review the linear theory and then consider mixtures of non‐linear media. In particular they give formulas for obtaining their constitutive equations for current density, electrical displacement, and magnetic induction. These relations have been derived by means of heuristic considerations on random networks and they have been verified with simulations obtaining a high degree of accuracy. Copyright © 2003 John Wiley & Sons, Ltd.     

Some topologico-dynamical properties of linear passive reciprocal networks

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

A linear approach to study the influence of asynchronous wind parks on isolated networks

This paper deals with the study of power quality in an isolated system with high wind energy penetration level. An induction wind plant, a synchronous power plant and a network constitute the analysed system. The work focuses on studying the effect of mechanical power from wind on load voltage and network frequency fluctuations. A linear model for the complete system is proposed in order to use eigenfrequencies and Bode plots to carry out this study.     

Topological conditions for the solvability of linear active networks

The solvability problem of a linear active network is approached from a purely topological point of view using the two-graph method. It can be said that a topological condition for the solvability is the existence of a common tree of the voltage and current graphs. A few conditions for the existence of a common tree are derived. If there exists no common tree, subgraphs which cause the nonexistence can be distinguished, and a partition of two-graphs can be introduced. The partition has similar properties to the principal partition of a graph or the canonical form of a bipartite graph, and a structure of two-graphs represented by a partial ordering of sets of edges can be defined. An algorithm to find the partition and a common tree, if one exists, or if no common tree exists, a tree of one of the graphs which has as many common edges as possible with a tree of the other graph, is given. The decomposition of the coefficient matrix accompanying the structure is discussed, and algorithms to determine the decomposition is given.     

Some considerations on state equations of linear active networks

It is shown that if there equivalently exist the virtual resistive elements in parallel with the inductive elements of the over-normal tree of a given linear active network or in series with the capacitive elements of the corresponding co-tree, an increase in the number of state variables arises. It is also shown that when a virtual resistor equivalently appears in parallel with the distinct resistor in a tree or in series with the distinct resistor in the co-tree, a decrease in the number of state variables may arise. This is, however, a rare case in the usual types of network. Two algebraic methods for obtaining the state equation of linear active networks are presented. One is useful for the networks in which the decrease in the number of state variables does not arise. From the other, the output equation for the required variables is obtained at the same time as the state equation. Further, the initial values are simply determined without iteration in many cases.     

On the minimal realization of the gyrator by means of nullors and resistors

This paper is a second step in the proof of the conjecture that it is impossible to synthesize a gyrator by means of nullors and linear resistors with fewer than four resistors if only two nullors are permitted, or with fewer than three nullors if only two resistors are permitted. It is proved that a gyrator cannot be realized with only two nullors and two resistors. In a forthcoming paper (third step) it will be proved that a two-nullor, three-resistor gyrator realization cannot be obtained. The proofs are presented in such a way that at the same time a synthesis procedure for minimal nullor-resistor networks is demonstrated.     

Natural gradient algorithm for neural networks applied to non‐linear high power amplifiers

This paper investigates the processing techniques for non‐linear high power amplifiers (HPA) using neural networks (NNs). Several applications are presented: Identification and Predistortion of the HPA. Various Neural Network structures are proposed to identify and predistort the HPA. Since a few decades, NNs have shown excellent performance in solving complex problems (like classification, recognition, etc.) but usually they suffer from slow convergence speed. Here, we propose to use the natural gradient instead of the classical ordinary gradient in order to enhance the convergence properties. Results are presented concerning identification and predistortion using classical and natural gradient. Practical implementations issues are given at the end of the paper. Copyright © 2002 John Wiley & Sons, Ltd.     

The realization of inverse system for circuits containing nullors with applications in chaos synchronization

A very simple method for synthesizing the inverse system of a non-linear non-autonomous circuit containing nullors is proposed. The main application of the procedure is the synchronization of chaos by the inverse system approach. This is illustrated with two examples: the synchronization of a Duffing circuit and a communication scheme by direct chaotic modulation using Chua's circuit. © 1998 John Wiley & Sons, Ltd.     

The equidistant linear phase polynomial for distributed and digital networks

A closed form expression for the recurrence formula for the generation of polynomials whose phase interpolates to linear characteristics at equidistant frequencies is presented. This polynomial may be used directly in the design of both distributed and digital networks and, due to the recurrence formula, readily generated. Since the complete proof of this formula is extensive and not required for normal use of this polynomial, it has been outlined in an Appendix.     

On complete stability of linear and quadratic programming neural networks

The paper addresses complete stability (CS) of the important class of neural networks to solve linear and quadratic programming problems introduced by Kennedy and Chua (IEEE Trans. Circuits Syst., 1988; 35 : 554). By CS it is meant that each trajectory converges to a stationary state, i.e. an equilibrium point of the neural network. It is shown that the neural networks in (IEEE Trans. Circuits Syst., 1988; 35 : 554) enjoy the property of CS even in the most general case where there are infinite non‐isolated equilibrium points. This result, which is proved by exploiting a new method to analyse CS (Int. J. Bifurcation Chaos 2001; 11 : 655), extends the stability analysis by Kennedy and Chua (IEEE Trans. Circuits Syst., 1988; 35 : 554) to situations of interest where the optimization problems have infinite solutions. Copyright © 2002 John Wiley & Sons, Ltd.     

A method for acceptability region representation in analogue linear networks

A new simple approach to acceptability region representation in analogue linear circuit design is presented. The proposed method is also able to characterize non‐convex and disjoint acceptability regions with low computational effort. In fact, the developed procedure is based on the use of symbolic analysis techniques, which permit one to perform only one simulation of the circuit under consideration, thus reducing the computational efforts. The theoretical basis and the algorithm implementing the technique are presented. A circuital example is also included. Copyright © 2008 John Wiley & Sons, Ltd.     

The generalized tree for state variables in linear active networks

A tree for the association of state variables in linear active networks is presented. This tree is selected in such a manner that the voltages across the capacitors contained in it and the currents through the inductors contained in its cotree may be chosen as state variables of a linear network. An algorithm for finding such a tree is given, and the association of state variables with this tree are demonstrated by examples.     

Robustness of convergence in finite time for linear programming neural networks

A recent work has introduced a class of neural networks for solving linear programming problems, where all trajectories converge toward the global optimal solution in finite time. In this paper, it is shown that global convergence in finite time is robust with respect to tolerances in the electronic implementation, and an estimate of the allowed perturbations preserving convergence is obtained. Copyright © 2006 John Wiley & Sons, Ltd.