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Matrix Methods for the Dynamic Range Optimization of Continuous-TimeGm-CFilters

This paper presents a synthesis procedure for the optimization of the dynamic range of continuous-time fully differential G m - C filters. Such procedure builds up on a general extended state-space system representation which provides simple matrix algebra mechanisms to evaluate the noise and distortion performances of filters, as well as, the effect of amplitude and impedance scaling operations. Using these methods, an analytical technique for the dynamic range optimization of weakly nonlinear G m - C filters under power dissipation constraints is presented. The procedure is first explained for general filter structures and then illustrated with a simple biquadratic section

A 0.18 μm CMOS low noise, highly linear continuous-time seventh-order elliptic low-pass filter

This paper presents a fast procedure for the system-level evaluation of noise and distortion in continuous-time integrated filters. The presented approach is based on Volterra's series theory and matrix algebra manipulation. This procedure has been integrated in a constrained optimization routine to improve the dynamic range of the filter while keeping the area and power consumption at a minimum. The proposed approach is demonstrated with the design, from system- to physical-level, of a seventh-order low-pass continuous-time elliptic filter for a high-performance broadband power-line communication receiver. The filter shows a nominal cut-off frequency of fc = 34MHz, less than 1dB ripple in the pass-band, and a maximum stop-band rejection of 65dB. Additionally, the filter features 12dB programmable boost in the pass-band to counteract high frequency components attenuation. Taking into account its wideband transfer characteristic, the filter has been implemented using G m-C techniques. The basic building block of its structure, the transconductor, uses a source degeneration topology with local feedback for linearity improving and shows a worst-case intermodulation distortion of -70 dB for two tones close to the passband edge, separated by 1MHz, with 70mV of amplitude. The filter combines very low noise (peak root spectral noise density below 56nV/√Hz) and high linearity (more than 64dB of MTPR for a DMT signal of 0.5Vpp amplitude) properties. The filter has been designed in a 0.18μm CMOS technology and it is compliant with industrial operation conditions (-40 to 85°C temperature variation and ±5% power supply deviation). The filter occupies 13mm2 and exhibits a typical power consumption of 450 mW from a 1.8V voltage supply.Ministerio de Ciencia y Tecnología TIC2003-0235

System-level optimization of baseband filters for communication applications

In this paper, a design approach for the high-level synthesis of programmable continuous-time baseband filters able to achieve optimum trade-off among dynamic range, distortion behavior, mismatch tolerance and power area consumptions is presented. The proposed approach relies on building programming circuit elements as arrays of switchable unit cells and defines the synthesis as a constrained optimization problem with both continuous and discrete variables, this last representing the number of enabled cells of the arrays at each configuration. The cost function under optimization is, then, defined as a weighted combination of performance indices which are estimated from macromodels of the circuit elements. The methodology has been implemented in MATLAB™ and C++, and covers all the classical approximation techniques for filters, most common circuit topologies (namely, ladder simulation and cascaded biquad realizations) and both transconductance-C (Gm-C) and active-RC implementation approaches. The proposed synthesis strategy is illustrated with a programmable equal-ripple ladder Gm-C filter for a multi-band power-line communication modem.P.R.O.F.I.T. FIT-070000-2001-84

A 0.18μm CMOS low-noise elliptic low-pass continuous-time filter

This paper presents a seventh order low-pass continuous-time elliptic filter for use in a high-performance wireline communication receiver. As an additional attribute, the filter provides programmable boost in the pass-band to counteract high frequency components attenuation. The filter shows a nominal cutoff frequency of fc=34 MHz , less than 1dB ripple in the pass-band, and a maximum stop-band rejection of 65dB. The filter also exhibits low noise feature (peak root spectral noise density below 56nV√Hz) and high linearity (more than 64dB of MTPR for a DMT signal of 0.5Vpp amplitude). It has been designed in a 0.18μm CMOS technology and it is compliant with industrial operation conditions (-40 to 85° C temperature variation and ± 5% power supply deviation). Simulations show a typical power consumption of 450 mW @ 1.8V supply.Ministerio de Ciencia y Tecnología TIC2003-0235

Study of the optimal harvesting control and the optimality system for an elliptic problem

An optimal harvesting problem with concave non-quadratic cost functional and a diffusive degenerate elliptic logistic state equation type is investigated. Under certain assumptions, we prove the existence and uniqueness of an optimal control. A characterization of the optimal control via the optimality system is also derived, which leads to approximate the optimal control.Ministerio de Ciencia y TecnologíaJunta de AndalucíaDirección General de Enseñanza Superior e Investigación Científic

Optimal control for the degenerate elliptic logistic equation

We consider the optimal control of the harvesting of the diffusive degenerate elliptic logistic equation. Under certain assumptions, we prove the existence and uniqueness of an optimal control. Moreover, the optimality system and a characterization of the optimal control are also derived. Sub-supersolution method, singular eigenvalue problem and differentiability with respect to the positive cone are the techniques used to get our results.Comisión Interministerial de Ciencia y TecnologíaJunta de AndalucíaDirección General de Enseñanza Superior e Investigación Científic

Revisión de la literatura en el marco de un proyecto para la validación de estrategias de aprendizaje de la Geometría en ambientes apoyados con TIC

Este artículo tiene el propósito de mostrar algunos elementos que constituyen una propuesta de acercamiento al estado del arte, como marco de referencia para un proyecto de investigación enfocado al estudio de las condiciones bajo las cuales una herramienta informática permite que los estudiantes obtengan aprendizajes significativos en Geometría

A two-layer shallow flow model with two axes of integration, well-balanced discretization and application to submarine avalanches

We propose a two-layer model with two different axes of integration and a well-balanced finite volume method. The purpose is to study submarine avalanches and generated tsunamis by a depth-averaged model with different averaged directions for the fluid and the granular layers. Two-layer shallow depth-averaged models usually consider either Cartesian or local coordinates for both layers. However, the motion characteristics of the granular layer and the water wave are different: the granular flow velocity is mainly oriented downslope while water motion related to tsunami wave propagation is mostly horizontal. As a result, the shallow approximation and depth-averaging have to be imposed (i) in the direction normal to the topography for the granular flow and (ii) in the vertical direction for the water layer. To deal with this problem, we define a reference plane related to topography variations and use the associated local coordinates to derive the granular layer equations whereas Cartesian coordinates are used for the fluid layer. Depthaveraging is done orthogonally to that reference plane for the granular layer equations and in the vertical direction for the fluid layer equations. Then, a finite volume method is defined based on an extension of the hydrostatic reconstruction. The proposed method is exactly well-balanced for two kind of stationary solutions: the classical one, when both water and granular masses are at rest; the second one, when only the granular mass is at rest. Several tests are presented to get insight into the sensitivity of the granular flow, deposit and generated water waves to the choice of the coordinate systems. Our results show that even for moderate slopes (up to 30◦), strong relative errors on the avalanche dynamics and deposit (up to 60%) and on the generated water waves (up to 120%) are made when using Cartesian coordinates for both layers instead of an appropriate local coordinate system as proposed here.Ministerio de Economía y Competitividad (MINECO). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Agence Nationale de la Recherche. FranceEuropean Research Council (ERC