X-parameters based analytical design of non-linear microwave circuits Application to oscillator design

Resumen El diseño clásico de circuitos de microondas se basa fundamentalmente en el uso de los parámetros s, debido a su capacidad para caracterizar de forma exitosa el comportamiento de cualquier circuito lineal. La relación existente entre los parámetros s con los sistemas de medida actuales y con las herramientas de simulación lineal han facilitado su éxito y su uso extensivo tanto en el diseño como en la caracterización de circuitos y subsistemas de microondas. Sin embargo, a pesar de la gran aceptación de los parámetros s en la comunidad de microondas, el principal inconveniente de esta formulación reside en su limitación para predecir el comportamiento de sistemas no lineales reales. En la actualidad, uno de los principales retos de los diseñadores de microondas es el desarrollo de un contexto análogo que permita integrar tanto el modelado no lineal, como los sistemas de medidas de gran señal y los entornos de simulación no lineal, con el objetivo de extender las capacidades de los parámetros s a regímenes de operación en gran señal y por tanto, obtener una infraestructura que permita tanto la caracterización como el diseño de circuitos no lineales de forma fiable y eficiente. De acuerdo a esta filosofía, en los últimos años se han desarrollado diferentes propuestas como los parámetros X, de Agilent Technologies, o el modelo de Cardiff que tratan de proporcionar esta plataforma común en el ámbito de gran señal. Dentro de este contexto, uno de los objetivos de la presente Tesis es el análisis de la viabilidad del uso de los parámetros X en el diseño y simulación de osciladores para transceptores de microondas. Otro aspecto relevante en el análisis y diseño de circuitos lineales de microondas es la disposición de métodos analíticos sencillos, basados en los parámetros s del transistor, que permitan la obtención directa y rápida de las impedancias de carga y fuente necesarias para cumplir las especificaciones de diseño requeridas en cuanto a ganancia, potencia de salida, eficiencia o adaptación de entrada y salida, así como la determinación analítica de parámetros de diseño clave como el factor de estabilidad o los contornos de ganancia de potencia. Por lo tanto, el desarrollo de una formulación de diseño analítico, basada en los parámetros X y similar a la existente en pequeña señal, permitiría su uso en aplicaciones no lineales y supone un nuevo reto que se va a afrontar en este trabajo. Por tanto, el principal objetivo de la presente Tesis consistiría en la elaboración de una metodología analítica basada en el uso de los parámetros X para el diseño de circuitos no lineales que jugaría un papel similar al que juegan los parámetros s en el diseño de circuitos lineales de microondas. Dichos métodos de diseño analíticos permitirían una mejora significativa en los actuales procedimientos de diseño disponibles en gran señal, así como una reducción considerable en el tiempo de diseño, lo que permitiría la obtención de técnicas mucho más eficientes. Abstract In linear world, classical microwave circuit design relies on the s-parameters due to its capability to successfully characterize the behavior of any linear circuit. Thus the direct use of s-parameters in measurement systems and in linear simulation analysis tools, has facilitated its extensive use and success in the design and characterization of microwave circuits and subsystems. Nevertheless, despite the great success of s-parameters in the microwave community, the main drawback of this formulation is its limitation in the behavior prediction of real non-linear systems. Nowadays, the challenge of microwave designers is the development of an analogue framework that allows to integrate non-linear modeling, large-signal measurement hardware and non-linear simulation environment in order to extend s-parameters capabilities to non-linear regimen and thus, provide the infrastructure for non-linear design and test in a reliable and efficient way. Recently, different attempts with the aim to provide this common platform have been introduced, as the Cardiff approach and the Agilent X-parameters. Hence, this Thesis aims to demonstrate the X-parameter capability to provide this non-linear design and test framework in CAD-based oscillator context. Furthermore, the classical analysis and design of linear microwave transistorbased circuits is based on the development of simple analytical approaches, involving the transistor s-parameters, that are able to quickly provide an analytical solution for the input/output transistor loading conditions as well as analytically determine fundamental parameters as the stability factor, the power gain contours or the input/ output match. Hence, the development of similar analytical design tools that are able to extend s-parameters capabilities in small-signal design to non-linear ap- v plications means a new challenge that is going to be faced in the present work. Therefore, the development of an analytical design framework, based on loadindependent X-parameters, constitutes the core of this Thesis. These analytical nonlinear design approaches would enable to significantly improve current large-signal design processes as well as dramatically decrease the required design time and thus, obtain more efficient approaches.

Non-linear Control of an Autonomous Ground Vehicle

In this paper, in order to select a speed controller for a specific non-linear autonomous ground vehicle, proportional-integral-derivative (PID), Fuzzy, and linear quadratic regulator (LQR) controllers were designed. Here, in order to carry out the tuning of the above controllers, a multicomputer genetic algorithm (MGA) was designed. Then, the results of the MGA were used to parameterize the PID, Fuzzy and LQR controllers and to test them under laboratory conditions. Finally, a comparative analysis of the performance of the three controllers was conducted.

Non-linear gain - look-up table based approach for modeling a family of DC to DC converters based on transient response analysis

The purpose of this work is to propose a structure for simulating power systems using behavioral models of nonlinear DC to DC converters implemented through a look-up table of gains. This structure is specially designed for converters whose output impedance depends on the load current level, e.g. quasi-resonant converters. The proposed model is a generic one whose parameters can be obtained by direct measuring the transient response at different operating points. It also includes optional functionalities for modeling converters with current limitation and current sharing in paralleling characteristics. The pusposed structured also allows including aditional characteristics of the DC to DC converter as the efficency as a function of the input voltage and the output current or overvoltage and undervoltage protections. In addition, this proposed model is valid for overdamped and underdamped situations.

Comparing linear and non linear wind flow models

Assessing wind conditions on complex terrain has become a hard task as terrain complexity increases. That is why there is a need to extrapolate in a reliable manner some wind parameters that determine wind farms viability such as annual average wind speed at all hub heights as well as turbulence intensities. The development of these tasks began in the early 90´s with the widely used linear model WAsP and WAsP Engineering especially designed for simple terrain with remarkable results on them but not so good on complex orographies. Simultaneously non-linearized Navier Stokes solvers have been rapidly developed in the last decade through CFD (Computational Fluid Dynamics) codes allowing simulating atmospheric boundary layer flows over steep complex terrain more accurately reducing uncertainties. This paper describes the features of these models by validating them through meteorological masts installed in a highly complex terrain. The study compares the results of the mentioned models in terms of wind speed and turbulence intensity.

The Cohesive Crack Model Applied To Notched PMMA Specimens Obeying a Non Linear Behaviour Under Torsion Loading

This article presents a new material model developed with the aim of analyzing failure of blunt notched components made of nonlinear brittle materials. The model, which combines the cohesive crack model with Hencky's theory of total deformations, is used to simulate an experimental benchmark carried out previously by the authors. Such combination is achieved through the embedded crack approach concept. In spite of the unavailability of precise material data, the numerical predictions obtained show good agreement with the experimental results.

Numerical study of ultrasound induced non-linear shape and size bubble oscillations in viscoelastic media

The theoretical study of forced bubble oscillations is motivated by the importance of cavitation bubbles and oscillating encapsulated microbubbles (i.e. contrast agents) in medical sciences. In more details,theoretical studies on bubble dynamics addressing the sound-bubble interaction phenomenon provide the basis for understanding the dynamics of contrast agent microbubbles used in medical diagnosis and of non-linearly oscillating cavitation bubbles in the case of high-intensity ultrasound therapy. Moreover, the inclusion of viscoelasticity is of vital importance for an accurate theoretical analysis since most biological tissues and fluids exhibit non-Newtonian behavior.

Efficient PGD-based dynamic calculation of non-linear soil behavior

Non-linear behavior of soils during a seismic event has a predominant role in current site response analysis. Soil response analysis consistently indicates that the stress-strain relationship of soils is nonlinear and shows hysteresis. When focusing in forced response simulations, time integrations based on modal analysis are widely considered, however parametric analysis, non-linear behavior and complex damping functions make difficult the online use of standard discretization strategies, e.g. those based on the use of finite element. In this paper we propose a new harmonic analysis formulation, able to address forced response simulation of soils exhibiting their characteristic nonlinear behavior. The solution can be evaluated in real-time from the offline construction of a parametric solution of the associated linearized problem within the Proper Generalized Decomposition framework.

A study of the mechanical behaviour of the human aortic artery by means of non-linear finite element models

En la presente tesis desarrollamos una estrategia para la simulación numérica del comportamiento mecánico de la aorta humana usando modelos de elementos finitos no lineales. Prestamos especial atención a tres aspectos claves relacionados con la biomecánica de los tejidos blandos. Primero, el análisis del comportamiento anisótropo característico de los tejidos blandos debido a las familias de fibras de colágeno. Segundo, el análisis del ablandamiento presentado por los vasos sanguíneos cuando estos soportan cargas fuera del rango de funcionamiento fisiológico. Y finalmente, la inclusión de las tensiones residuales en las simulaciones en concordancia con el experimento de apertura de ángulo. El análisis del daño se aborda mediante dos aproximaciones diferentes. En la primera aproximación se presenta una formulación de daño local con regularización. Esta formulación tiene dos ingredientes principales. Por una parte, usa los principios de la teoría de la fisura difusa para garantizar la objetividad de los resultados con diferentes mallas. Por otra parte, usa el modelo bidimensional de Hodge-Petruska para describir el comportamiento mesoscópico de los fibriles. Partiendo de este modelo mesoscópico, las propiedades macroscópicas de las fibras de colágeno son obtenidas a través de un proceso de homogenización. En la segunda aproximación se presenta un modelo de daño no-local enriquecido con el gradiente de la variable de daño. El modelo se construye a partir del enriquecimiento de la función de energía con un término que contiene el gradiente material de la variable de daño no-local. La inclusión de este término asegura una regularización implícita de la implementación por elementos finitos, dando lugar a resultados de las simulaciones que no dependen de la malla. La aplicabilidad de este último modelo a problemas de biomecánica se estudia por medio de una simulación de un procedimiento quirúrgico típico conocido como angioplastia de balón. In the present thesis we develop a framework for the numerical simulation of the mechanical behaviour of the human aorta using non-linear finite element models. Special attention is paid to three key aspects related to the biomechanics of soft tissues. First, the modelling of the characteristic anisotropic behaviour of the softue due to the collagen fibre families. Secondly, the modelling of damage-related softening that blood vessels exhibit when subjected to loads beyond their physiological range. And finally, the inclusion of the residual stresses in the simulations in accordance with the opening-angle experiment The modelling of damage is addressed with two major and different approaches. In the first approach a continuum local damage formulation with regularisation is presented. This formulation has two principal ingredients. On the one hand, it makes use of the principles of the smeared crack theory to avoid the mesh size dependence of the structural response in softening. On the other hand, it uses a Hodge-Petruska bidimensional model to describe the fibrils as staggered arrays of tropocollagen molecules, and from this mesoscopic model the macroscopic material properties of the collagen fibres are obtained using an homogenisation process. In the second approach a non-local gradient-enhanced damage formulation is introduced. The model is built around the enhancement of the free energy function by means of a term that contains the referential gradient of the non-local damage variable. The inclusion of this term ensures an implicit regularisation of the finite element implementation, yielding mesh-objective results of the simulations. The applicability of the later model to biomechanically-related problems is studied by means of the simulation of a typical surgical procedure, namely, the balloon angioplasty.

Some recent applications of non-linear models to the engineering practice

The Department of Structural Analysis of the University of Santander has been for a longtime involved in the solution of the country´s practical engineering problems. Some of these have required the use of non-conventional methods of analysis, in order to achieve adequate engineering answers. As an example of the increasing application of non-linear computer codes in the nowadays engineering practice, some cases will be briefly presented. In each case, only the main features of the problem involved and the solution used to solve it will be shown

A non-linear analysis of lying a floating pipeline on the seabed

In this article, a model for the determination of displacements, deformations and tensions of a submarine pipeline during the construction is presented. The process is carried out from an initial floating situation to the final laying position on the seabed. The existence of currents and small waves are also considered. Firstly, this technique, usually applied to polyethylene pipelines, is described in this paper as well as some real world examples, as well as the variables that can be modified to control the behavior of the structure. A detailed description of the actions in this process is considered, specially the ones related to marine environment, as Archimedes force, current and sea waves. The behavior of the pipeline is modeled with a non linear elasto dynamic model where geometric non linearities are taken into account. A 3-D beam model, without cross section deformation effects, is developed. Special care is taken in the numerical analysis, developed within an updated lagrangian formulation framework, with the sea bed contact, the follower forces due to the external water pressures and the dynamic actions. Finally, some subroutines are implemented into ANSYS to simulate the two dimensional case, where the whole construction process is achieved. With this software, a sensibility analysis of the bending moments, axial forces and stresses obtained with different values of the control variables in order to optimize the construction steps. These control variables are, the axial load in the pipe, the inundated inner length and the distance of the control barge from the coast.

Seminar on non-linear elasticity,

Reproduced from typewritten copy.

A non-linear dynamic model for primates. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

CRASH: a computer simulator of non-linear transient response of structures, basis for car crash simulation. Research report.

National Highway Traffic Safety Administration, Washington, D.C.

Fabrication, installation, test and evaluation of motorcycle controls and displays; gear position, indicator, non-linear throttle, tactile indicator of neutral position. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Study of stability for non-linear ordinary differential equations.

"C00-1469-0118."