High‐order sensitivity invariants

The aim of the research reported in this paper is to extend the notion of invariant sensitivity sum, widely known for electrical networks, from first‐order sensitivities to high‐order sensitivities. The results are high‐order invariant sums of sensitivities of the first and the second kind, formulated for nonlinear lumped circuit, which consists of one‐port and two‐ports only. One‐ports are generalized resistances, capacitances, inductances, voltages, and current sources, whereas two‐ports are nonlinear generalizations of four types of controlled sources. It is observed that the invariant sums actually found for nonlinear lumped networks are generalizations of sums given earlier by authors for linear lumped networks. The article is illustrated by numerical sensitivity analysis of simple linear and nonlinear circuits. Copyright © 2010 John Wiley & Sons, Ltd.     

Differential equation description and Chebyshev approximation of linear time‐invariant circuits

The approximation technology of analogue circuit functions is crucial to the computer‐aided simulation, analysis, and design automation of electronic circuits. Chebyshev polynomials and various differential equations are proposed in this paper to approximate the functions of linear time‐invariant circuits. The coefficient calculation methods of the Chebyshev expansion and the differential equation matrices are thoroughly deduced, and the construction methods employed in the functions and the actual time mapping of the linear time‐invariant circuits are presented in this paper. An example of an analogue filter verifies the effectiveness and accuracy of the proposed approximation algorithm and elaborates on the selection process of the order number and the time step length of the Chebyshev expansion according to the demanded truncation error.     

A study on higher‐order disturbance observer and robust stability

In earlier papers, it has been reported that a fast and precise servo system, which has low sensitivity to parameter variation and disturbance, can be realized with simple structure by using a high‐order disturbance observer. However, no clear and simple design method satisfying specifications for robust stability, the influence of measurement noise, and relative stability (damping characteristics) for large parameter variation has been proposed. In this paper, we clarify the class of robust servo systems realized by adjusting the order of the disturbance observer and the control parameters. We apply this strategy to the design of a second delay system, such as a position servo system, and realize a high‐performance robust servo system using a high‐order disturbance observer. © 1999 Scripta Technica, Electr Eng Jpn, 128(1): 37–44, 1999     

Uniform approximation of time‐invariant non‐linear systems

An Erratum has been published for this article in International Journal of Circuit Theory and Applications 2004; 32(6):633. It is shown that the elements of a large class of time‐invariant non‐linear input–output maps can be uniformly approximated arbitrarily well, over infinite time intervals, using a certain structure that can be implemented in many ways using, for example, radial basis functions, polynomial functions, piecewise linear functions, sigmoids, or combinations of these functions. For the special case in which these functions are taken to be certain polynomial functions, the input–output map of our structure is a generalized finite Volterra series. Results are given for the case in which inputs and outputs are defined on ?. The case in which inputs and outputs are defined on the half‐line ?₊ is also addressed, and in both cases inputs need not be functions that are continuous. Copyright © 2004 John Wiley & Sons, Ltd.     

Explicit design formulas for current‐mode leap‐frog OTA‐C filters and 300 MHz CMOS seventh‐order linear phase filter

The leap‐frog (LF) configuration is an important structure in analogue filter design. Voltage‐mode LF OTA‐C filters have recently been studied in the literature; however, general explicit formulas do not exist for current‐mode LF OTA‐C filters and there is also need for current‐mode LF‐based OTA‐C structures for realization of arbitrary transmission zeros. Three current‐mode OTA‐C structures are presented, including the basic LF structure and LF filters with an input distributor or an output summer. They can realize all‐pole characteristics and functions with arbitrary transmission zeros. Explicit design formulas are derived directly from these structures for the synthesis of, respectively, all‐pole and arbitrary zero filter characteristics of up to the sixth order. The filter structures are regular and the design formulas are straightforward to use. As an illustrative example, a 300 MHz seventh‐order linear phase low‐pass filter with zeros is presented. The filter is implemented using a fully differential linear operational transconductance amplifier (OTA) based on a source degeneration topology. Simulations in a standard TSMC 0.18µm CMOS process with 2.5 V power supply have shown that the cutoff frequency of the filter ranges from 260 to 320 MHz, group delay ripple is about 4.5% over the whole tuning range, noise of the filter is 420nA/√Hz, dynamic range is 66 dB and power consumption is 200 mW. Copyright © 2008 John Wiley & Sons, Ltd.     

Time–frequency higher‐order spectra with adjustment to the instantaneous frequency variation

Novel time–frequency techniques are proposed: the short time instantaneous higher‐order spectra (HOS) with adjustment to measured or known a priori time variation of the instantaneous frequency of transient signals. It is shown that the proposed transforms are more effective than the non‐instantaneous HOS (i.e. without adjustment to time variation of the instantaneous frequency) in recognizing a non‐stationary nonlinearity. Copyright © 2008 John Wiley & Sons, Ltd.     

An expression for the voltage response of a current‐excited fractance device based on fractional‐order trigonometric identities

We report a closed‐form expression of the voltage response of a current‐excited fractance device. The derived simple expression is made possible following the introduction of the generalized sine and cosine functions (rmsin_α(t) and cos_α(t)), which are valid on any fractional‐order surface and tend to the normal sin(t) and cos(t) at α = 1 or asymptotically as t→∞. Copyright © 2011 John Wiley & Sons, Ltd.     

Design equations for fractional‐order sinusoidal oscillators: Four practical circuit examples

Four practical sinusoidal oscillators are studied in the general form where fractional‐order energy storage elements are considered. A fractional‐order element is one whose complex impedance is given by Z = a(jω)^±α, where a is a constant and α is not necessarily an integer. As a result, these oscillators are described by sets of fractional‐order differential equations. The integer‐order oscillation condition and oscillation frequency formulae are verified as special cases. Numerical and PSpice simulation results are given. Experimental results are also reported for a selected Wien‐bridge oscillator. Copyright © 2007 John Wiley & Sons, Ltd.     

Efficient estimation of adjoint‐variable S‐parameter sensitivities with time domain TLM

We present a novel algorithm for efficient estimation of S‐parameter sensitivities with the time‐domain transmission line modelling (TLM) method. The original electromagnetic structure is simulated using TLM to obtain the S‐parameters in the desired frequency band. For each port, an adjoint TLM simulation that runs backward in time is derived and solved. The sensitivities of the S‐parameters in the desired frequency band are estimated using only the original and adjoint simulations. For a structure with N_p ports and n designable parameters, our approach requires only N_p additional simulations regardless of n. This can be easily contrasted with the 2nN_p additional simulations required by the central difference approximation. Our algorithm is illustrated through the estimation of S‐parameter sensitivities with respect to the dimensions of waveguide discontinuities. Very good match is obtained between our sensitivity estimates and those obtained using central difference approximation. Copyright © 2005 John Wiley & Sons, Ltd.     

An unconditionally sound algorithm for testability analysis in linear time‐invariant electrical networks

The issue of testability, intended as a measure of solvability of the parametric fault diagnosis problem in analog linear time‐invariant electrical networks, is addressed in this paper. Independently of the considered fault location method, such important metric provides information as to how many and which components can be diagnosed. For the reader's convenience and to set up an appropriate framework for our main achievements, our first concern is to rederive fundamental results concerning analog linear time‐invariant electrical network testability hinging on multifrequency measurements. Then a novel algorithm for testability analysis is proposed, which is straightforward and able to circumvent the main drawbacks of formerly proposed methods, such as computational and conceptual complexities, proneness to roundoff errors, and vulnerability to particular cases. A computer program that implements such algorithm is also described. Moreover, the possibility of employing further simplified versions of the latter and their links with a previously proposed approach are discussed on rigorous bases. Finally, examples are provided, which show the effectiveness and robustness of the new algorithms, also by means of a comparison with the old ones. Copyright © 2015 John Wiley & Sons, Ltd.     

State‐space equations of regular and strictly topologically degenerate linear lumped time‐invariant networks: the multiport method

A new complete approach to the multiport formulation of the state‐space equations of uniquely solvable regular or strictly topologically degenerate linear lumped time‐invariant networks is presented. It is based on a Gedankenexperiment during which the topological structure of the original network is manipulated in various ways. The final method requires one to calculate the describing matrices of three homogeneous multiports (i.e. a capacitive, an inductive and a resistive one), which are obtained from the network of interest in a very simple manner. As a by‐product, the equivalent partitioned network is also derived. As an example of application, the state‐space equations of a fourth‐order strictly topologically degenerate network are provided. Copyright © 2001 John Wiley & Sons. Ltd.     

Second order mem‐circuits

This paper presents a comprehensive taxonomy of so‐called second‐order memory devices, which include charge‐controlled memcapacitors and flux‐controlled meminductors, among other novel circuit elements. These devices, which are classified according to their differential and state orders, are necessary to get a complete extension of the family of classical nonlinear circuit elements (resistors, capacitors, and inductors) for all possible controlling variables. Using a fully nonlinear formalism, we obtain nondegeneracy conditions for a broad class of second‐order mem‐circuits. This class of circuits is expected to yield a rich dynamic behavior; in this regard, we explore certain bifurcation phenomena exhibited by a family of circuits including a charge‐controlled memcapacitor and a flux‐controlled meminductor, providing some directions for future research. Copyright © 2014 John Wiley & Sons, Ltd.     

Design for testability of high‐order OTA‐C filters

A study of oscillation‐based test for high‐order Operational Transconductance Amplifier‐C (OTA‐C) filters is presented. The method is based on partition of a high‐order filter into second‐order filter functions. The opening Q‐loop and adding positive feedback techniques are developed to convert the second‐order filter section into a quadrature oscillator. These techniques are based on an open‐loop configuration and an additional positive feedback configuration. Implementation of the two testability design methods for nth‐order cascade, IFLF and leapfrog (LF) filters is presented, and the area overhead of the modified circuits is also discussed. The performances of the presented techniques are investigated. Fourth‐order cascade, inverse follow‐the‐leader feedback (IFLF) and LF OTA‐C filters were designed and simulated for analysis of fault coverage using the adding positive feedback method based on an analogue multiplexer. Simulation results show that the oscillation‐based test method using positive feedback provides high fault coverage of around 97%, 96% and 95% for the cascade, IFLF and LF OTA‐C filters, respectively. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust adaptive consensus tracking for higher‐order multi‐agent uncertain systems with nonlinear dynamics via distributed intermittent communication protocol

This paper considers the robust adaptive consensus tracking for higher‐order multi‐agent uncertain systems with nonlinear dynamics via distributed intermittent communication protocol. The main contribution of this work is solving the robust consensus tracking problem without the assumption that the topology among followers is strongly connected and fixed. The focus is the problem of actuator with occasional failure inputs and communication resources constraints. A novel distributed intermittent communication framework is proposed via adaptive approach. In this framework, the underlying communication topologies switch among several directed graphs with a limited directed spanning tree rooted at a leader agent. Furthermore, by introducing a strategy of actuator fault compensation inputs, a combination of robust consensus tracking protocol is designed by the different adaptive feedback controllers. It is proved that the robust adaptive consensus tracking can be achieved by using local states information of neighboring agents if the communication retention rate condition is satisfied. Two examples are presented to demonstrate the effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Fractional‐order mutual inductance: analysis and design

This paper introduces for the first time the generalized concept of the mutual inductance in the fractional‐order domain where the symmetrical and unsymmetrical behaviors of the fractional‐order mutual inductance are studied. To use the fractional mutual inductance in circuit design and simulation, an equivalent circuit is presented with its different conditions of operation. Also, simulations for the impedance matrix parameters of the fractional mutual inductance equivalent circuit using Advanced Design System and MATLAB are illustrated. The Advanced Design System and MATLAB simulations of the double‐tuned filter based on the fractional mutual inductance are discussed. A great matching between the numerical analysis and the circuit simulation appears, which confirms the reliability of the concept of the fractional mutual inductance. Also, the analysis of the impedance matching using the fractional‐order mutual inductance is introduced. Copyright © 2015 John Wiley & Sons, Ltd.     

On the existence of common quadratic Lyapunov functions for second‐order linear time‐invariant discrete‐time systems

Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function (CQLF) are given for two second‐order linear time‐invariant discrete‐time systems. These conditions are later extended to an arbitrary number of systems. The conditions are readily verifiable both analytically and graphically. The paper also provides a constructive procedure for computing a CQLF when it exists. Copyright © 2002 John Wiley & Sons, Ltd.     

Higher‐order differentiation of network functions using signal flow graphs

This paper presents the application of signal flow graphs (SFG) in the calculation of higher‐order derivatives (sensitivities) of the linear circuit functions. The idea of exact differentiation of the circuit functions is based on the adjoint networks, translated into SFG language. Thanks to its application, it is possible to calculate the exact value of any order derivative of circuit function without knowing this function in explicit form. Moreover, these derivatives can be determined on the basis of analysis of only two graphs (circuits): the original and adjoint one. We show that the SFG approach to the sensitivity calculation allows to reduce greatly the complexity of calculations. Copyright © 2011 John Wiley & Sons, Ltd.     

Almost invariant manifold approach for adaptive estimation of periodic and aperiodic unknown time‐varying parameters

This paper provides a novel identification technique for the estimation of time‐varying parameters in a class of nonlinear dynamical systems. The concept of almost invariant manifold is used to find an implicit mapping from known variables of the system to the unknown variables. A parameter estimation update law is generated from the proposed mapping. The exponential convergence of parameter estimation error to a small neighbourhood of the origin is achieved. The algorithm is extended to estimate the uncertain periodic parameters. An upper bound estimation of the unknown periodic parameters and their time derivatives are obtained. Unlike most periodic time‐varying parameter estimation techniques, only the knowledge of the number of distinctive frequencies is assumed. The effectiveness of the proposed method is illustrated with two simulation examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Analytical synthesis and comparison of voltage‐mode Nth‐order OTA‐C universal filter structures

Complementary single‐ended‐input operational transconductance amplifier (OTA)‐based filter structures are introduced in this paper. Through two analytical synthesis methods and two transformations, one of which is to convert a differential‐input OTA to two complementary single‐ended‐input OTAs, and the other to convert a single‐ended‐input OTA and grounded capacitor‐based one to a fully differential OTA‐based one, four distinct kinds of voltage‐mode nth‐order OTA‐C universal filter structures are proposed. TSMC H‐Spice simulations with 0.35µm process validate that the new complementary single‐ended‐input OTA‐based one holds the superiority in output precision, dynamic and linear ranges than other kinds of filter structures. Moreover, the new voltage‐mode band‐pass, band‐reject and all‐pass (except the fully differential one) biquad structures, all enjoy very low sensitivities. Both direct sixth‐order universal filter structures and their equivalent three biquad stage ones are also simulated and validated that the former is not absolutely larger in sensitivity than the latter. Finally, a very sharp increment of the transconductance of an OTA is discovered as the operating frequency is very high and leads to a modified frequency‐dependent transconductance. Copyright © 2010 John Wiley & Sons, Ltd.     

Higher‐order CN‐FETD method for analysis of microwave circuit structures

In this paper, the hierarchical high‐order basis functions on tetrahedrons are introduced to the Crank–Nicolson (CN) finite‐element time‐domain (FETD) with the 3D Maxwell equations for analysis of the microwave circuit structures. Whitney 1‐form high‐order hierarchical basis functions are used to expand the electric field and Whitney 2‐form high‐order hierarchical basis functions for the magnetic field. The CN scheme is employed in the FETD method to lead to an unconditionally stable algorithm. Numerical results were presented to demonstrate the accuracy and efficiency of the proposed high‐order CN‐FETD method. Copyright © 2012 John Wiley & Sons, Ltd.