Reactance extraction at the ports of the general reciprocal three-port

The following theorems are derived:

• I By means of suitable lossless, reciprocal two-ports, any reciprocal three-port with complex parameters can be transformed into a real three-port.
• II Any desired reciprocal three-port can be synthesized as a real three-port with lossless, reciprocal two-ports connected to its ports.

     

The jaumann structure in wave-digital filters

This paper deals with an extension of the wave-digital filter structures introduced by Fettweis. A new structure is introduced, viz, the digital translation of the Jaumann structure. The Jaumann structure is a well-known canonical realization of analogue, symmetric, grounded lossless two-port networks. With this structure, transfer functions with complex transmission zeros can be obtained in a wave-digital realization, which is not possible by means of a wave-digital ladder filter. Two examples are given, one of which has been implemented using TTL digital integrated circuits showing excellent properties.     

Lossless 2-ports between non-reactive terminations

Lossless reciprocal 2-ports between terminations with even impedance functions are considered. They are the unifying concept for the synthesis of FDNR and leapfrog RC-active filters in their most general form. The scattering matrix of lossless reciprocal 2-ports with respect to such terminations is defined, its canonic form deduced and the transfer of active power discussed. This scattering matrix is related to the usual scattering matrix of the same 2-port but with respect to unit resistance terminations. In such a way the precise structure of the 2-port as an LC ladder can be deduced from properties of the original transfer function and the termination impedances and the LC synthesis can be performed by conventional methods and programs. An exhaustive enumeration of the different cases that may arise is given. It can give a general outlook on the different RC-active filters that may be obtained.     

Darlington's theorem and complex normalization

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

Negative resistance devices: Part II

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.     

Adaptive Optimal Kernel Time–Frequency Representation Technique for Partial Discharge Ultra-high-frequency Signals Classification

An intelligent system for automatic partial discharge pattern recognition is proposed using adaptive optimal kernel time-frequency representation and a fuzzy k-nearest neighbor classifier. The adaptive optimal kernel technique is employed to acquire the joint time-frequency information for partial discharge signals, which is characterized by the adaptive optimal kernel amplitude matrix. A new feature extraction algorithm, i.e., non-negative matrix factorization aided principal component analysis, is proposed to solve the difficulties of principal component analysis for feature extraction of partial discharge adaptive optimal kernel amplitude matrices due to the high dimensionality. Using an ultra-high frequency detector, 600 partial discharge signals sampled from 4 categories of typical artificial defect models in the laboratory are employed for testing. It is shown that the maximum classification accuracy of 94.33% is obtained considering different non-negative matrix factorization parameter r and various non-negative matrix factorization iterations T. Also, the classification performance of the non-negative matrix factorization–principal component analysis features is superior to that of principal component analysis features extracted from original partial discharge signals, two-dimensional non-negative matrix factorization features and phase-resolved partial discharge statistical operators. The proposed technique can be used for partial discharge pattern recognition based on ultra-high-frequency detection arrangements.     

An approach to digital implementation of continuous backstepping adaptive control for linear systems

This paper presents a solution to the problem of digitally implementing backstepping adaptive control for linear systems. The continuous‐time system to be controlled is given a discrete‐time representation in the δ‐operator. A discrete adaptive backstepping controller is then designed for such a discrete‐time model. The effect of the modelling error, generated by the sampling process, is accounted for in the parameter update law by a σ‐modification. It is shown that all the signals (discrete and continuous) of the closed loop are uniformly bounded, with a region of attraction which is a K_∞ function of the sampling rate. An upper bound on the asymptotic tracking error is then given, and shown to be proportional to the sampling period. Copyright © 1999 John Wiley & Sons, Ltd.     

Necessary and sufficient conditions for absolute stability of linear n-ports

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.     

A‐map representations and asymptotically almost periodic responses

It was recently shown that for each member G of a large class of causal time‐invariant non‐linear input–output maps, with inputs and outputs defined on the non‐negative integers, there is a functional A on the input set such that (Gs) (k) has the representation A(F_ks) for all k and each input s, in which F_k is a simple linear map that does not depend on G. In this paper, we consider non‐linear maps G that have such ‘A‐map representations’. We observe that these Gs have extensions to a domain of inputs defined on the set of all integers. We show that these extensions possess some interesting properties including a certain important uniqueness property. As an application, we show that under the (very often satisfied) conditions of time invariance, causality, and approximately finite memory, and under typically mild boundedness and continuity conditions, the response of G to a discrete‐time asymptotically almost periodic input is an output that is always an asymptotically almost periodic function, and that the almost periodic part of the output is independent of the transient part of the input. We also give corresponding results for a continuous‐time case. Copyright © 2001 John Wiley & Sons, Ltd.     

A Rule-Based Approach for Second Order Model Formulation of Linear Time Invariant Multivariable Systems

A Rule-based approach for formulating a second order MIMO model for a given absolutely stable higher order MIMO system in transfer function matrix form is proposed. The Rule base has been built based on the performance characteristics of general second order systems. An initial second order approximant is constructed for each of the transfer functions in the matrix, based upon a set of guidelines that reflects the characteristics of the corresponding higher order systems. This is taken as input for the Rule based algorithm. Rules are iteratively applied so that a better second order approximant is evolved. Cumulative error index computed from the integral square error is used as the indicator for selecting the best second order model. An algebraic scheme has been proposed for commonizing the denominators of the individual second order models so that a second order MIMO model can be declared in the transfer function matrix form. The analysis is carried out in the s-domain. For discrete systems, a linear transformation of z=s+1 is used to obtain an equivalent continuous model in the s-domain. The proposed methodology is illustrated with two concrete examples taken from the literature.     

The role of lossless systems in modern digital signal processing: atutorial

A self-contained discussion of discrete-time lossless systems and their properties and relevance in digital signal processing is presented. The basic concept of losslessness is introduced, and several algebraic properties of lossless systems are studied. An understanding of these properties is crucial in order to exploit the rich usefulness of lossless systems in digital signal processing. Since lossless systems typically have many input and output terminals, a brief review of multiinput multioutput systems is included. The most general form of a rational lossless transfer matrix is presented along with synthesis procedures for the FIR (finite impulse response) case. Some applications of lossless systems in signal processing are presented     

Parameter determination of a nonsinusoidal periodic signal harmonic based on the modified sine transform

An algorithm is presented for determining the amplitude and the initial phase of the oscillations of the kth harmonic included in the structure of the nonsinusoidal periodic signal. The algorithm differs from the well-known Euler–Fourier method based on sine and cosine transforms. The qualitative difference of the proposed method consists in the use of the cosine function, which is an analytic solution of a modified sine transform, the structure of which includes a sinusoidal factor with a complex argument that contains a variable phase angle. The coordinates of the maximum of this functional dependence, which is raised to a positive integer power to improve the accuracy of determining the parameters, are uniquely associated with the amplitude and the initial phase of oscillations of the kth harmonic of the nonsinusoidal signal. The considered method minimizes the use of nonlinear operations and at its core has the element inherent in the selective filter. The possibility of obtaining information on the parameters of the first voltage and current harmonics with the required accuracy enhances the reliability of the evaluation of processes occurring in the power system in the conditions of interference in the form of higher harmonics. An example problem is solved in the MS Excel environment.     

Use of lossless transmission‐line segments and shunt resistors for TLM diffusion modelling

In diffusion modelling by means of the transmission‐line matrix (TLM) method, a nodal arrangement of using lossless transmission‐line segments and series resistors is almost exclusively adopted and is currently considered as a standard approach. In this paper, the use of shunt resistors instead of series resistors is shown to represent an equally valid configuration. As a starting point, we have derived the telegrapher's equation in its most general form for TLM modelling of diffusion processes. A general algorithm based on the shunt‐resistor TLM model for implementing a numerical solution of the diffusion equation in multiple dimensions is given. Fundamental analysis and calculated examples confirm that the alternative shunt‐resistor configuration does not exhibit the unwanted absorption effects suggested by a recent paper (Internat. J. Numerical Model.: Electronic Networks, Devices and Fields 2002; 15 :261). Copyright © 2003 John Wiley & Sons, Ltd.     

Parallel VLSI design for the fast 3-D DWT core algorithm

By studying the core algorithm of a three-dimensional discrete wavelet transform (3-D DWT) in depth, this paper divides it into three one-dimensional discrete wavelet transforms (1-D DWTs). Based on the implementation of a 3-D DWT software, a parallel architecture design of a very large-scale integration (VLSI) is produced. It needs three dual-port random-access memory (RAM) to store the temporary results and transpose the matrix, then builds up a pipeline model composed of the three 1-D DWTs. In the design, the finite state machine (FSM) is used well to control the flow. Compared with the serial mode, the experimental results of the post synthesized simulation show that the design method is correct and effective. It can increase the processing speed by about 66%, work at 59 MHz, and meet the real-time needs of the video encoder. Translated from Transactions of Beijing Institute of Technology, 2006, 26(3): 211–215 [译自: 北京理工大学学报]     

Transfer functions interpolating an ideal amplitude with arbitrary phase and delay

A method is presented to generate polynomials with phase values and delay (first derivative) specified at given frequencies. Then a closed form solution is described for the scattering transfer function S₁₂(p) of a resistively terminated lossless reciprocal two-port network with ideal amplitude and arbitrary phase and delay.     

A note on passivity and losslessness

This note gives new necessary and sufficient conditions for a linear system to be passive or lossless. It will be shown that, by using the theory of operators on an indefinite J(t)-Hilbert space, both the passivity and isometric conditions for an operator to be lossless can be combined into a single condition—namely an operator is lossless if and only if it is J(t)-contractive.     

考虑不确定性和主动性的配电网柔性协调评估

柔性评估是适应未来电网发展需要的综合评价方法。文中提出被动柔性和主动柔性的概念研究配电网中的不确定性和主动性要素,形成柔性评估的计算模型。同时,提出基于改进离散化隐枚举(DIEM)方法的计算流程。通过柔性指标的评估与匹配,结合节点的柔性水平计算与线路N-k校验,发掘配电网的薄弱环节。结合算例分析表明,所提出的方法能够提高系统的可靠性与安全性。     

A theory of nonenergic N-ports

A circuit element is nonenergic if the instantaneous power flow into it is always zero. Well-known examples include the ideal diode, transformer, gyrator and circulator. Most of the interesting nonenergic elements are nonlinear N-ports with N ? 2, and many of their properties are quite counterintuitive. For example, there exists a surprisingly large class of nonenergic multiport capacitors and inductors, all of which, it turns out, are nonlinear and reciprocal. Nonenergic linear N-ports, on the other hand, are necessarily resistive and antireciprocal. In this paper, we present a rigorous fundamental theory of nonenergic N-ports that results in a general canonical representation. Special canonical forms are developed for nonenergic resistors, capacitors and inductors, and numerous examples are given.