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.

Optimización de los procesos de medida e interpretación de la tomografía geoeléctrica en la prospección superficial

Debido al carácter innovador de los objetivos científico-tecnológicos planteados al inicio de la presente Tesis doctoral, además de la primera recopilación bibliográfica, a lo largo del desarrollo de la misma se ha realizado una actualización bibliográfica continua centrada en los desarrollos relativos a la instrumentación, las aplicaciones y los procesos de interpretación de las técnicas de tomografía eléctrica. Durante el desarrollo del presente trabajo, se han realizado una serie de campañas diferenciadas, tanto por los ambientes geológicos y las condiciones antrópicas en los que se han efectuado los perfiles geoeléctricos, como por la profundidad y los objetivos de la prospección. En esas campañas se han obtenido, mediante el programa Res2DInv, las secciones tomográficas con la configuración de variables por defecto y se ha realizado una interpretación estructural de las mismas. Como parte central del desarrollo de esta investigación se han efectuado varios procesos de optimización: Comparación y optimización de los dispositivos empleados para la medición de perfiles de resistividad de cara a la obtención de secciones tomográficas que presenten la mayor resolución en distintos ambientes geológicos. Selección de los rangos de representación (lineales y logarítmicos) y de la gradación cromática que, pudiendo adoptarse de forma generalizada, permita la mejor interpretación gráfica para usuarios no avanzados. Diseño de criterios para la selección del factor de amortiguamiento, como parámetro crítico en los procesos de inversión tomográfica de perfiles geoeléctricos de superficie, de forma que los modelos resultantes alcancen la mejor relación entre fiabilidad y error respecto a los valores medidos. Paralelamente a los procesos anteriores se ha definido un índice de calidad de la inversión, que es directamente normalizado y que permite evaluar el grado en el que pueden considerarse fiables tanto los valores de resistividad obtenidos como su distribución espacial. El índice desarrollado (IRI) está basado en la influencia que tiene la resistividad inicial del modelo de inversión en los valores de cada una de las celdas de la malla de inversión. Tras un exhaustivo análisis estadístico se ha verificado que, a diferencia de otros índices utilizados hasta la fecha, dicho índice no está afectado ni por la profundidad de investigación y la resolución de los dispositivos, ni por la distribución de resistividades que presente el subsuelo. ABSTRACT Due to the innovative character of the scientific and technological objectives proposed at the beginning of this thesis, in addition to preparatory bibliographic reference, a constant bibliographic update on developments related to instrumentation, applications and interpretation processes for electric tomography has been performed all through the development of the work. Several measuring campaigns were performed during the development of the thesis. These campaigns, in which the geoelectric profiles were measured, varied in several aspects, both in the geological and anthropic conditions, and also in the depth and objectives of the prospection. Tomographic sections were obtained and interpretated by making use of the Res2DInv software configured with the default variables. As part of the core development in this research, several optimization processes have been done: Comparison and optimization of the devices used in the measurement of resistivity profiles. This optimization allows increasing the resolution of tomographic sections in different geological conditions. Selection of the best visual representation for the tomographic sections. This involves the selection of the range of values and type of scale (linear vs. logarithmic) as well as the chromatic graduation. This selection allows improving the interpretation of tomographic sections for the non-expert eye. Devising of criteria for the selection of the damping factor, as the critical parameter in processes of tomographic inversion of superficial geoelectrical profiles. The use of these criteria allows selecting the best factors to obtain the best ratio between reliability and error (in relation to the mean values) for the resulting model. In addition to the aforementioned processes, and as part of the work within this thesis, it has been defined a normalized quality index for inversion. This index allows evaluating the degree of reliability of the obtained resistivity values and spatial distribution. The developed index, termed IRI in the thesis, is based on the influence shown by the initial resistivity of the inversion model on the values of each of the cells of the inversion mesh. After an exhaustive statistical analysis it was verified that the IRI index is neither affected by the investigation depth, nor the resolution of the devices, nor the resistivity’s distribution of the sub soil. This independency is a unique characteristic of the IRI index, not present in other indexes developed and used till date.

Efeito da geometria do implante dentário e do protocolo de fresagem óssea na estabilidade primária e na osseointegração inicial: estudo experimental em cães

CHAPTER 1 - This study histologically evaluated two implant designs: a classic thread design versus another specifically designed for healing chamber formation placed with two drilling protocols. Forty dental implants (4.1 mm diameter) with two different macrogeometries were inserted in the tibia of 10 Beagle dogs, and maximum insertion torque was recorded. Drilling techniques were: until 3.75 mm (regular-group); and until 4.0 mm diameter (overdrillinggroup) for both implant designs. At 2 and 4 weeks, samples were retrieved and processed for histomorphometric analysis. For torque and BIC (bone-to-implant contact) and BAFO (bone area fraction occupied), a general-linear model was employed including instrumentation technique and time in vivo as independent. The insertion torque recorded for each implant design and drilling group significantly decreased as a function of increasing drilling diameter for both implant designs (p<0.001). No significant differences were detected between implant designs for each drilling technique (p>0.18). A significant increase in BIC was observed from 2 to 4 weeks for both implants placed with the overdrilling technique (p<0.03) only, but not for those placed in the 3.75 mm drilling sites (p>0.32). Despite the differences between implant designs and drilling technique an intramembranous-like healing mode with newly formed woven bone prevailed. CHAPTER 2 - The objective of this preliminary histologic study was to determine whether the alteration of drilling protocols (oversized, intermediate, undersized drilling) present different biologic responses at early healing periods of 2 weeks in vivo in a beagle dog model. Ten beagle dogs were acquired and subjected to surgeries in the tibia 2 weeks before euthanasia. During surgery, 3 implants, 4 mm in diameter by 10 mm in length, were placed in bone sites drilled to 3.5 mm, 3.75 mm, and 4.0 mm in final diameter. The insertion and removal torque was recorded for all samples. Statistical significance was set to 95% level of confidence and the number of dogs was considered as the statistical unit for all comparisons. For the torque and BIC and BAFO, a general linear model was employed including instrumentation technique and time in vivo as independent. Overall, the insertion torque increased as a function of drilling diameter from 4.0 mm, to 3.75 mm, to 3.5 mm, with a significant difference in torque levels between all groups (p<0.001). Statistical assessment of BIC and BAFO showed significantly higher values for the 3.75 mm (recommended) drilling group was observed relative to the other two groups (p<0.001). Different drilling dimensions resulted in variations in insertion torque values (primary stability) and different pattern of healing and interfacial remodeling was observed for the different groups. CHAPTER 3 - The present study evaluated the effect of different drilling dimensions (undersized, regular, and oversized) in the insertion and removal torques of dental implants in a beagle dog model. Six beagle dogs were acquired and subjected to bilateral surgeries in the radii 1 and 3 weeks before euthanasia. During surgery, 3 implants, 4 mm in diameter by 10 mm in length, were placed in bone sites drilled to 3.2 mm, 3.5 mm, and 3.8 mm in final diameter. The insertion and removal torque was recorded for all samples. Statistical analysis was performed by paired t tests for repeated measures and by t tests assuming unequal variances (all at the 95% level of significance). Overall, the insertion torque and removal torque levels obtained were inversely proportional to the drilling dimension, with a significant difference detected between the 3.2 mm and 3.5 mm relative to the 3.8 mm groups (P < 0.03). Although insertion torque–removal torque paired observations was statis- tically maintained for the 3.5 mm and 3.8 mm groups, a significant decrease in removal torque values relative to insertion torque levels was observed for the 3.2 mm group. A different pattern of healing and interfacial remodeling was observed for the different groups. Different drilling dimensions resulted in variations in insertion torque values (primary stability) and stability maintenance over the first weeks of bone healing.

Avaliação comparativa da remodelação óssea periimplantar em implantes com junção cone-morse e hexágono externo: estudo clínico randomizado controlado, duplo cego, boca dividida

Background: Several theories, such as the biological width formation, the inflammatory reactions due to the implant-abutment microgap contamination, and the periimplant stress/strain concentration causing bone microdamage accumulation, have been suggested to explain early periimplant bone loss. However, it is yet not well understood to which extent the implant-abutment connection type may influence the remodeling process around dental implants. Aim: to evaluate clinical, bacteriological, and biomechanical parameters related to periimplant bone loss at the crestal region, comparing external hexagon (EH) and Morse-taper (MT) connections. Materials and methods: Twelve patients with totally edentulous mandibles received four custom made Ø 3.8 x 13 mm implants in the interforaminal region of the mandible, with the same design, but different prosthetic connections (two of them EH or MT, randomly placed based on a split-mouth design), and a immediate implant- supported prosthesis. Clinical parameters (periimplant probing pocket depth, modified gingival index and mucosal thickness) were evaluated at 6 sites around the implants, at a 12 month follow-up. The distance from the top of the implant to the first bone-to-implant contact – IT-FBIC was evaluated on standardized digital peri-apical radiographs acquired at 1, 3, 6 and 12 months follow-up. Samples of the subgingival microbiota were collected 1, 3 and 6 months after implant loading. DNA were extracted and used for the quantification of Tanerella forsythia, Porphyromonas gingivalis, Aggragatibacter actinomycetemcomitans, Prevotella intermedia and Fusobacterium nucleatum. Comparison among multiple periods of observation were performed using repeated-measures Analysis of Variance (ANOVA), followed by a Tukey post-hoc test, while two-period based comparisons were made using paired t- test. Further, 36 computer-tomographic based finite element (FE) models were accomplished, simulating each patient in 3 loading conditions. The results for the peak EQV strain in periimplant bone were interpreted by means of a general linear model (ANOVA). Results: The variation in periimplant bone loss assessed by means of radiographs was significantly different between the connection types (P<0.001). Mean IT-FBIC was 1.17±0.44 mm for EH, and 0.17±0.54 mm for MT, considering all evaluated time periods. All clinical parameters presented not significant differences. No significant microbiological differences could be observed between both connection types. Most of the collected samples had very few pathogens, meaning that these regions were healthy from a microbiological point of view. In FE analysis, a significantly higher peak of EQV strain (P=0.005) was found for EH (mean 3438.65 µ∑) compared to MT (mean 840.98 µ∑) connection. Conclusions: Varying implant-abutment connection type will result in diverse periimplant bone remodeling, regardless of clinical and microbiological conditions. This fact is more likely attributed to the singular loading transmission through different implant-abutment connections to the periimplant bone. The present findings suggest that Morse-taper connection is more efficient to prevent periimplant bone loss, compared to an external hexagon connection.

Components of learning and assessment in linear algebra

Linear algebra provides theory and technology that are the cornerstones of a range of cutting edge mathematical applications, from designing computer games to complex industrial problems, as well as more traditional applications in statistics and mathematical modelling. Once past introductions to matrices and vectors, the challenges of balancing theory, applications and computational work across mathematical and statistical topics and problems are considerable, particularly given the diversity of abilities and interests in typical cohorts. This paper considers two such cohorts in a second level linear algebra course in different years. The course objectives and materials were almost the same, but some changes were made in the assessment package. In addition to considering effects of these changes, the links with achievement in first year courses are analysed, together with achievement in a following computational mathematics course. Some results that may initially appear surprising provide insight into the components of student learning in linear algebra.