A hysteresis is a widely employed solution to mitigate the effect of noise on comparators. This paper presents a very simple technique, applicable to any topology of MOS differential comparator. It ...consists of imposing different bulk-source voltage to the input MOS differential pair. Depending on the polarity of the input signal, one substrate is connected to the rail voltage and the other to a reference control voltage. So, when the slope inverts, the connections are switched through pMOS switches. Simulation results show that the hysteresis up to 302,6 mV can be linearly controlled for bulk voltages ranging from 0 to 500 mV, for XFAB 0.35XH technology. Finally, an approximation for the control rule is proposed.
This paper introduces a new design method of fractional-order proportional-derivative (FOPD) and fractional-order proportional-integral-derivative (FOPID) controllers. A biquadratic approximation of ...a fractional-order differential operator is used to introduce a new structure of finite-order FOPID controllers. Using the new FOPD controllers, the controlled systems can achieve the desired phase margins without migrating the gain crossover frequency of the uncontrolled system. This may not be guaranteed when using FOPID controllers. The proposed FOPID controller has a smaller number of parameters to tune than its existing counterparts. A systematic design procedure is identified in terms of the desired phase and the gain margins of the controlled systems. The viability of the design methods is verified using a simple numerical example.
In this paper, we present a nested splitting conjugate gradient (NSCG) iteration method for solving a class of matrix equations with nonsymmetric coefficient matrices. This method is actually ...inner/outer iterations, which employs a CG-like method as inner iteration to approximate each outer iterate, while each outer iteration is induced by a convergent and symmetric positive definite splitting of the coefficient matrices. Convergence conditions of this method are studied in depth and numerical experiments show the efficiency of this method. Moreover, we show that the use of the quasi-Hermitian splitting as a preconditioner can induce an accurate, robust and effective preconditioned Krylov subspace method.
In this paper, the best linear approximations of addition modulo 2n are studied. Let x = (xn−1, xn−2,…,x0) and y = (yn−1, yn−2,…,y0) be any two n-bit integers, and let z = x + y (mod 2n). Firstly, ...all the correlations of a single bit zi approximated by xj’s and yj’s (0 ≤ i, j ≤ n − 1) are characterized, and similar results are obtained for the linear approximation of the xoring of the neighboring bits of zi’s. Then the maximum correlations and the best linear approximations are presented when these zj’s (0 ≤ j ≤ n − 1) are xored in any given means.
This paper is focused on the numerical solution of elliptic equations with discontinuous coefficients. In particular, the design of efficient geometric multigrid methods for cell-centered finite ...volume schemes for this kind of problems is dealt with. In this work we propose a block-wise multigrid algorithm on semistructured triangular grids for solving piecewise constant diffusivity problems on relatively complex domains. Appropriate novel smoothers for cell-centered discretizations are considered on each structured patch of the mesh. The difficulties appearing when highly varying coefficients occur are overcome by the use of a modified Galerkin coarse grid approximation. Numerical experiments are presented to illustrate the good behavior of the proposed multigrid method which achieves an hindependent convergence rate.
Using the concept of strong summation process, we give a Korovkin type approximation theorem for a sequence of positive linear operators acting from Lpa,bLpa,b into itself. We also study some ...quantitative estimates for LpLp approximation and give the rate of convergence of these operators.
In this paper, we first introduce a novel generalized derivative and obtain the generalized first-order Taylor expansion of the nonsmooth functions. Then we derive the generalized EuleraLagrange ...equation for the nonsmooth calculus of variations and solve this equation by using Chebyshev pseudospectral method, approximately. Finally, the optimal solutions of some problems in the nonsmooth calculus of variations are approximated.
The theory of chaos is applied to the construction of substitution boxes used in encryption applications. The synthesis process of the proposed substitution boxes is presented, which is based on ...chaotic Bakeras map and TDERC chaotic sequences. The objectives of the new substitution box are to provide enhanced resistance against differential and linear cryptanalysis. The constructed substitution boxes uses Galois field elements and relies on discrete chaotic maps while keeping differential and linear approximation probabilities to desired levels.
This paper deals with the study and analysis of several rational approximations to approach the behavior of arbitrary-order differentiators and integrators in the frequency domain. From the ...Riemann–Liouville, Grünwald–Letnikov and Caputo basic definitions of arbitrary-order calculus until the reviewed approximation methods, each of them is coded in a Maple 18 environment and their behaviors are compared. For each approximation method, an application example is explained in detail. The advantages and disadvantages of each approximation method are discussed. Afterwards, two model order reduction methods are applied to each rational approximation and assist a posteriori during the synthesis process using analog electronic design or reconfigurable hardware. Examples for each reduction method are discussed, showing the drawbacks and benefits. To wrap up, this survey is very useful for beginners to get started quickly and learn arbitrary-order calculus and then to select and tune the best approximation method for a specific application in the frequency domain. Once the approximation method is selected and the rational transfer function is generated, the order can be reduced by applying a model order reduction method, with the target of facilitating the electronic synthesis.
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