Distribution in TLM models for diffusion (Part II: multi‐dimensional treatment)

The signals obtained at each time step of a transmission line matrix (TLM) simulation of Gaussian diffusion are analysed for two‐ and three‐dimensional cases. A combinatorial formula is derived to provide the signal magnitude at any spatial position and any time step after a single‐shot excitation in the two‐dimensional link‐line model. Formulae for the expectation and variance of the axial positions of a particle are determined for two‐ and three‐dimensional link‐line and link‐resistor models. A generalization of these formulae is proposed for higher dimensions, and an entirely numerical proving scheme is devised. Finally, we briefly compare the resulting variances and that of the underlying diffusion process. Copyright © 2003 John Wiley & Sons, Ltd.     

TLM nodal state estimator: An alternative method of initializing a two‐dimensional diffusion model

The transmission line matrix (TLM) method is an established technique for modelling thermal transients in heat transfer systems. However, initial and boundary conditions have always been slightly problematic, particularly when the boundary condition is specified as a temperature (Transmission Line Matrix (TLM) Techniques for Diffusion Applications. Gordon & Breach: London, 1998), for example, when the body of interest is suddenly exposed to a different temperature on its surface. In such a case the modelled solution contains additional dynamics that are associated with the two sub‐meshes in the TLM network and the two timesteps necessary for the temperature change to be fully communicated. These initialization problems are related to the fact that the boundary temperature in merely imposed as a fixed value on the network; the fundamental information‐carrying quantity, on the other hand, is the pulse, the thermal state of the body being represented by the distribution of pulses. Here, we aim to provide an alternative initialization approach, using nodal state estimation to derive pulse distributions from boundary and initial conditions specified by temperature. Consideration is given to the accuracy of the estimator by comparison with the first timestep solution proposed by Enders (Int. J. Numer. Model. 2002; 15 :251–259). Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Distribution in TLM models for diffusion (Part I: one-dimensional treatment)

The signal obtained at each time step of a TLM simulation for one-dimensional diffusion is analysed for single shot injections. A combinatorial formula is provided to predict the signal value at any given spatial positions. Formulas for expectation and variance are obtained using a technique based on generating functions. We briefly compare the resulting variance and that of the underlying diffusion process. Copyright © 2002 John Wiley & Sons, Ltd.     

On the dispersion of a non‐orthogonal TLM cell

The numerical dispersion of a non‐orthogonal transmission line matrix (TLM) algorithm is for the first time investigated. First of all, the dispersion relation is derived in the most general possible case. Then, the validation is carried out in the analysis of a simple one‐dimensional example. Results show that the theory is in excellent agreement with the numerical simulation. Numerical results concerning various cell shape dispersion characteristics are presented and show some relatively weak numerical dispersion even for rather highly distorted cells. Finally, some indications concerning cell shape selection to minimize the non‐orthogonal TLM cell are proposed. 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.     

Self‐adjoint S‐parameter sensitivities for lossless homogeneous TLM problems

We present a novel efficient algorithm for the estimation of S‐parameter sensitivities in homogeneous and lossless transmission line modelling (TLM) problems. Our approach estimates S‐parameter adjoint‐based sensitivities without actually carrying out any adjoint simulation. By applying a transformation to the original TLM simulation we establish an isomorphism between the original and the adjoint problem. The unique properties of the TLM node in a lossless and homogeneous problem are also exploited in establishing the isomorphism. For an electromagnetic structure with N_p ports, only the N_p original simulations utilized in evaluating the S‐parameters are required to estimate their sensitivities as well. Our novel approach is illustrated through estimating S‐parameter sensitivities with respect to waveguide discontinuities. Good match is obtained between our sensitivity estimates and those calculated using finite differences at the response level. Copyright © 2005 John Wiley & Sons, Ltd.     

Transmission‐line matrix models for solving transient problems of diffusion with recombination

Starting from the general telegrapher's equation, we investigate two nodal network constructions for modelling diffusion with recombination by means of the transmission‐line matrix (TLM) method. The diffusion effect is modelled by the series and shunt capacitance in one approach, and by the series inductance and shunt resistance in the other. Both approaches use the series and shunt resistances to model the recombination effect. The constraint of using both TLM networks for solving transient problems of diffusion with recombination is found to be identical in terms of the physics behind the numerical routines. A practical way of determining the spatial resolution and iteration time step for accurate TLM numerical computations is suggested based on a simple frequency analysis. Copyright © 2003 John Wiley & Sons, Ltd.     

Absorbing boundary conditions for the FD‐TLM method : the perfectly matched layer and the one‐way equation technique

This paper investigates the absorbing boundary conditions for the frequency domain transmission line matrix method. Two approaches are presented, namely the perfectly matched layer (PML) technique and the one‐way wave equation. Concerning the PML technique, two‐dimensional and three‐dimensional transmission line matrix (TLM) nodes, already used in time domain, are exploited in frequency domain where a rigorous formulation of these PML–TLM nodes is presented. In addition, two types of one‐way wave operators are also transposed from time to frequency domain TLM approach: Taylor expansion and Higdon's boundary conditions. The simulation of a wideband matched load WR‐28 rectangular waveguide is presented for validation. Excellent results are obtained with a very thin PML layer. Results concerning one‐way operator techniques also show very good return loss performances. For instance, Higdon's boundary condition was extended beyond third‐order approximation, and a return loss better than 160 dB was obtained. Copyright © 2013 John Wiley & Sons, Ltd.     

Development of Identification Unit for Two‐dimensional RFID‐Tag with UHF Band

Recently, the system for massed tag management (at 13.56 MHz) and the system for the long distance identification (at 920 MHz) have been carried out to practical use. For continuous logistics, it is desired that those be integrated seamlessly. However, integration into the system, which uses the frequency band of 13.56 MHz, is disadvantageous to keep the feature of the long distance identification. In this paper, the system that identifies nearby cluttered tags by the frequency band for the long distance identification is described.     

A step‐by‐step approach to compute a consistent initialization for the MNA

One of the difficulties of the numerical integration methods for differential–algebraic equations (DAEs) is the computation of consistent initial values before starting the integration, i.e. calculating values that satisfy the given algebraic constraints as well as the hidden constraints if higher index problems are considered. This paper presents an approach to calculate consistent initial values for index‐2 DAEs starting up from possibly inconsistent ones for systems arising from modified nodal analysis (MNA) in circuit simulation. This article is based on the results from Estévez Schwarz and Tischendorf, International Journal of Circuit Theory and Applications 2000; 28 : 131–162. Several of the denotations and results that we use were introduced there in more detail. Copyright © 2001 John Wiley & Sons, Ltd.     

Adaptive internal model control: the discrete‐time case

This paper considers the design and analysis of a discrete‐time H₂ optimal robust adaptive controller based on the internal model control structure. The certainty equivalence principle of adaptive control is used to combine a discrete‐time robust adaptive law with a discrete‐time H₂ internal model controller to obtain a discrete‐time adaptive H₂ internal model control scheme with provable guarantees of stability and robustness. The approach used parallels the earlier results obtained for the continuous‐time case. Nevertheless, there are some differences which, together with the widespread use of digital computers for controls applications, justifies a separate exposition. Copyright © 2001 John Wiley & Sons, Ltd.     

filtering for switched discrete‐time systems under asynchronous switching: A dwell‐time dependent Lyapunov functional method

In this article, the filtering problem for switched discrete‐time linear systems under asynchronous switching is addressed in the framework of dwell time, where ‘asynchronous switching’ covers more general and practical cases, for example, the switching lags caused by mode identification process are taken into consideration. Firstly, a novel dwell‐time dependent Lyapunov function (DTDLF) is introduced to solve stability and ?₂ gain analysis problems. The main advantage of DTDLF approach is that the derived conditions are all convex in system matrices, so it is convenient to be applied into filter design with performance instead of weighted performance as many other previous results. Thus, on the basis of DTLDF, a dwell‐time dependent filter with time‐varying structure is proposed to achieve the desirable non‐weighted filtering performance. It is notable that the proposed approach can also easily characterize the relationships among filtering performance, dwell time, and asynchronous time. Two examples are provided to validate the theoretical findings in this paper. Copyright © 2014 John Wiley & Sons, Ltd.     

Filter & hold: a mixed continuous‐/discrete‐time technique for time‐constant scaling

The work reported in this paper introduces a periodic switching technique applied to continuous‐time filters, whose outcome is an equivalent filter with scaled time‐constants. The principle behind the method is based on a procedure that extends the integration time by periodically interrupting the normal integration of the filter. The net result is an up scaling of the time constant, inversely proportional to the switching duty‐cycle. This is particularly suitable for reducing the area occupied by passive devices in integrated circuits, as well as to accurately calibrate the filter dynamics. Previous works have been following this concept in an entirely continuous‐time perspective, either focusing on specific circuits or using approximations to provide an extended analysis. This paper includes input/output sampling to derive a closed‐form representation for the scaling technique herein coined as ‘Filter & Hold’ (F&H). A detailed mathematical analysis is described, demonstrating that the F&H concept represents an exact filtering solution. Simulation results and experimental measurements are provided to further validate the theoretical analysis for an F&H vector‐filter prototype. Copyright © 2014 John Wiley & Sons, Ltd.     

A comparative design study of continuous‐time incremental sigma‐delta ADC architectures

This paper presents a comparative design study of continuous‐time (CT) incremental sigma‐delta (IΣΔ) ADCs, which can expand another dimension of the IΣΔ ADC world that is dominated by discrete‐time implementations. Several CT IΣΔ ADC architectures are introduced and analyzed aiming to reduce the modulator's sampling frequency and consequently the power dissipation. Based on the analytical results, three CT IΣΔ ADCs are selected to be examined, implemented, and tested. The three ADC prototypes, fabricated in a standard 0.18‐m CMOS technology, demonstrate competitive figure‐of‐merits in terms of power efficiency compared to the state‐of‐the‐art counterparts. Copyright © 2016 John Wiley & Sons, Ltd.     

Fault detection for discrete‐time switched singular time‐delay systems: an average dwell time approach

In this paper, the fault detection problem is investigated for a class of discrete‐time switched singular systems with time‐varying state delays. The residual generator is firstly constructed based on a switched filter, and the design of fault detection filter is formulated as an H _∞ filtering problem, that is, minimizing the error between residual and fault in the H _∞ sense. Then, by constructing an appropriate decay‐rate‐dependent piecewise Lyapunov function and using the average dwell time scheme, a sufficient condition for the residual system to be regular, causal, and exponential stable while satisfying a prescribed H _∞ performance is derived in terms of linear matrix inequalities (LMIs). The corresponding solvability condition for the desired fault detection filters is also established via LMI approach. Finally, a numerical example is presented to show the effectiveness of the developed theoretical results.Copyright © 2012 John Wiley & Sons, Ltd.     

A new method for solving non‐linear carrier diffusion equation in axial direction of broad‐area lasers

The solution of non‐linear carrier diffusion equation associated with the axial direction of broad‐area laser has been achieved by a hybrid asymptotic‐numerical method that combines WKB approximation and the variation of constants method. The non‐linearity has been taken into account by using an iterative scheme: carrier lifetime has been linearized and calculated as a function of carrier density known from the previous iteration. Non‐uniform photon density has been taken into account. As the new method is based on analytical solutions, it is very fast and not vulnerable to large gradients of carrier concentration usually occurring in the vicinity of laser facets. Therefore, it can be useful in complicated self‐consistent thermal models of broad‐area lasers. The obtained results are compared with two simplified cases: solution of linear diffusion equation with constant coefficients and calculations neglecting the diffusion. Copyright © 2010 John Wiley & Sons, Ltd.     

An oscillatory noise‐shaped quantizer for time‐based continuous‐time sigma‐delta modulators

In this paper, a new type of an oscillatory noise‐shaped quantizer (NSQ) for time‐based continuous‐time sigma‐delta modulators is presented. The proposed NSQ is composed of an oscillatory voltage‐to‐time converter and a polyphase sampler. Using Tustin's transformation method and through the approximation of the comparator gain, a linearized model of the NSQ is introduced. This way, a novel realization of the first‐ and second‐order NSQ is presented. Its implementation is based on fully passive continuous‐time filters without needing any amplifier or power consuming element. The ploy‐phase sampler inside the NSQ is based on the combination of a time‐to‐digital and a digital‐to‐time converter. The layout of the proposed NSQ is provided in Taiwan Semiconductor Manufacturing Company 0.18 μm complementary metal‐oxide‐semiconductor 1P6M technology. The verification of the proposed NSQ is done via investigating both the system level and postlayout simulation results. Leveraging the proposed NSQ in an Lth‐order time‐based continuous‐time sigma‐delta modulator enhances the noise‐shaping order up to L + 2, confirming its superior effectiveness. This makes it possible to design high performance and wideband continuous‐time SDMs with low power consumption and relaxed design complexity.     

Dead‐time assignment for single‐phase half‐bridge PWM inverters

A new dead‐time assignment technique for single‐phase half‐bridge PWM inverters is presented. Three modulating signals, including the original one and two auxiliary modulating signals with calculated offset voltages are, respectively, compared to the high‐frequency carrier signal. The suitable switching functions without dead‐time degradation effects are determined by sensing the load current polarity. The proposed method can be applied to both online and off‐line PWM schemes as well. Copyright © 2007 John Wiley & Sons, Ltd.     

Delay‐dependent model reduction for continuous‐time switched state‐delayed systems

This paper studies the problem of exponential H_∞ model reduction for continuous‐time switched delay system under average dwell time (ADT) switching signals. Time delay under consideration is interval time varying. Our attention is focused on the construction of the desired reduced order models, which guarantee that the resulting error systems under ADT switching signals are exponentially stable with an H_∞ norm bound. By introducing a block matrix and making use of the ADT approach, delay‐dependent sufficient conditions for the existence of reduced order models are derived and formulated in terms of strict linear matrix inequalities (LMIs). Owing to the absence of non‐convex constraints, it is tractable to construct an admissible reduced order model. The effectiveness of the proposed methods is illustrated via two numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.