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.

On the mass determination of super-Earths orbiting active stars: the CoRoT-7 system

Context. Star activity makes the mass determination of CoRoT-7b and CoRoT 7c uncertain. Investigators of the CoRoT team proposed several solutions, but all but one of them are larger than the initial determinations of 4.8 +/- 0.8 M(Earth) for CoRoT-7b and 8.4 +/- 0.9 M(Earth) for CoRoT 7c. Aims. This investigation uses the excellent HARPS radial velocity measurements of CoRoT-7 to redetermine the planet masses and to explore techniques for determining mass and orbital elements of planets discovered around active stars when the relative variation in the radial velocity due to the star activity cannot be considered as just noise and can exceed the variation due to the planets. Methods. The main technique used here is a self-consistent version of the high-pass filter used by Queloz et al. (2009, A&A, 506, 303) in the first mass determination of CoRoT-7b and CoRoT-7c. The results are compared to those given by two alternative techniques: (1) the approach proposed by Hatzes et al. (2010, A&A, 520, A93) using only those nights in which two or three observations were done; (2) a pure Fourier analysis. In all cases, the eccentricities are taken equal to zero as indicated by the study of the tidal evolution of the system. The periods are also kept fixed at the values given by Queloz et al. Only the observations done in the time interval BJD 2 454 847-873 are used because they include many nights with multiple observations; otherwise, it is not possible to separate the effects of the rotation fourth harmonic (5.91 d = P(rot)/4) from the alias of the orbital period of CoRoT-7b (0.853585 d). Results. The results of the various approaches are combined to give planet mass values 8.0 +/- 1.2 M(Earth) for CoRoT-7b and 13.6 +/- 1.4 M(Earth) for CoRoT 7c. An estimation of the variation of the radial velocity of the star due to its activity is also given. Conclusions. The results obtained with three different approaches agree to give higher masses than those in previous determinations. From the existing internal structure models they indicate that CoRoT-7b is a much denser super-Earth. The bulk density is 11 +/- 3.5 g cm(-3), so CoRoT-7b may be rocky with a large iron core.

SSSPM J1102-3431 brown dwarf characterization from accurate proper motion and trigonometric parallax

Context. In 2005, Scholz and collaborators discovered, in a proper motion survey, a young brown dwarf SSSPM J1102-3431 (SSSPM J1102) of spectral type M8.5, probable member of the TW Hydrae Association and possible companion of the T Tauri star TWHya. The physical characterization of SSSPM J1102 was based on the hypothesis that it forms a binary system with TWHya. The recent discovery of a probable giant planet with a very short-period inside the TW Hya protoplanetary disk, as well as a disk around SSSPM J1102, make it especially interesting and important to measure well the physical parameters of SSSPM J1102. Aims. Trigonometric parallax and proper motion measurements of SSSPM J1102 are necessary to test for TWA membership and, thus, to determine the mass and age of this young brown dwarf and the possibility that it forms a wide binary system with TW Hya. Methods. Two years of regular observations at the ESO NTT/SUSI2 telescope have enabled us to determine the trigonometric parallax and proper motion of SSSPM J1102. Results. With our accurate distance determination of 55.2(-1.4)(+1.6) pc and proper motions of (-67.2, -14.0) +/- 0.6 mas/yr, we could confirm SSSPM J1102 as a very probable member of TWA. Assuming the TW Hydrae association age of 5-10 Myr, the evolutionary models compared to the photometry of this young brown dwarf indicate a mass of M = 25 +/- 5 M(Jup) and an effective temperature T(eff) = 2550 +/- 100 K. Conclusions. Our parallax and proper motion determination allow us to precisely describe the physical properties of this low mass object and to confirm its TWA membership. Our results indicate that SSSPMJ1102 may be a very wide separation companion of the star TW Hya.

The stellar content of obscured Galactic giant H II regions. VI. W51A

We present K-band spectra of newly born OB stars in the obscured Galactic giant H II region W51A and approximate to 0.8 '' angular resolution images in the J, H, and K(S)-bands. Four objects have been spectroscopically classified as O-type stars. The mean spectroscopic parallax of the four stars gives a distance of 2.0 +/- 0.3 kpc (error in the mean), significantly smaller than the radio recombination line kinematic value of 5.5 kpc or the values derived from maser proper motion observations (6-8 kpc). The number of Lyman continuum photons from the contribution of all massive stars (NLyc approximate to 1.5 x 10(50) s(-1)) is in good agreement with that inferred from radio recombination lines (NLyc = 1.3 x 10(50) s(-1)) after accounting for the smaller distance derived here. We present analysis of archival high angular resolution images (NAOS CONICA at VLT and T-ReCS at Gemini) of the compact region W51 IRS 2. The K(S)-band images resolve the infrared source IRS 2 indicating that it is a very young compact H II region. Sources IRS 2E was resolved into compact cluster (within 660 AU of projected distance) of three objects, but one of them is just bright extended emission. W51d1 and W51d2 were identified with compact clusters of three objects (maybe four in the case of W51d1) each one. Although IRS 2E is the brightest source in the K-band and at 12.6 mu m, it is not clearly associated with a radio continuum source. Our spectrum of IRS 2E shows, similar to previous work, strong emission in Br gamma and He I, as well as three forbidden emission lines of Fe III and emission lines of molecular hydrogen (H(2)) marking it as a massive young stellar object.

PARALLAXES OF SOUTHERN EXTREMELY COOL OBJECTS. I. TARGETS, PROPER MOTIONS, AND FIRST RESULTS

We present results from the PARallaxes of Southern Extremely Cool objects ( PARSEC) program, an observational program begun in 2007 April to determine parallaxes for 122 L and 28 T southern hemisphere dwarfs using the Wide Field Imager on the ESO 2.2 m telescope. The results presented here include parallaxes of 10 targets from observations over 18 months and a first version proper motion catalog. The proper motions were obtained by combining PARSEC observations astrometrically reduced with respect to the Second US Naval Observatory CCD Astrograph Catalog, and the Two Micron All Sky Survey Point Source Catalog. The resulting median proper motion precision is 5 mas yr(-1) for 195,700 sources. The 140 0.3 deg(2) fields sample the southern hemisphere in an unbiased fashion with the exception of the galactic plane due to the small number of targets in that region. The proper motion distributions are shown to be statistically well behaved. External comparisons are also fully consistent. We will continue to update this catalog until the end of the program, and we plan to improve it including also observations from the GSC2.3 database. We present preliminary parallaxes with a 4.2 mas median precision for 10 brown dwarfs, two of which are within 10 pc. These increase the present number of L dwarfs by 20% with published parallaxes. Of the 10 targets, seven have been previously discussed in the literature: two were thought to be binary, but the PARSEC observations show them to be single; one has been confirmed as a binary companion and another has been found to be part of a binary system, both of which will make good benchmark systems. These results confirm that the foreseen precision of PARSEC can be achieved and that the large field of view will allow us to identify wide binary systems. Observations for the PARSEC program will end in early 2011 providing three to four years of coverage for all targets. The main expected outputs are: more than a 100% increase in the number of L dwarfs with parallaxes, increment in the number of objects per spectral subclass up to L9-in conjunction with published results-to at least 10, and to put sensible limits on the general binary fraction of brown dwarfs. We aim to contribute significantly to the understanding of the faint end of the H-R diagram and of the L/T transition region.

Solar twins in M 67: evolutionary status and lithium abundance

Aims. We determine the age and mass of the three best solar twin candidates in open cluster M 67 through lithium evolutionary models. Methods. We computed a grid of evolutionary models with non-standard mixing at metallicity [Fe/H] = 0.01 with the Toulouse-Geneva evolution code for a range of stellar masses. We estimated the mass and age of 10 solar analogs belonging to the open cluster M 67. We made a detailed study of the three solar twins of the sample, YPB637, YPB1194, and YPB1787. Results. We obtained a very accurate estimation of the mass of our solar analogs in M 67 by interpolating in the grid of evolutionary models. The three solar twins allowed us to estimate the age of the open cluster, which is 3.87(-0.66)(+0.55) Gyr, which is better constrained than former estimates. Conclusions. Our results show that the 3 solar twin candidates have one solar mass within the errors and that M 67 has a solar age within the errors, validating its use as a solar proxy. M 67 is an important cluster when searching for solar twins.

Spectroscopic variabilities in lambda Pavonis

Aims. We investigate the time-varying patterns in line profiles, V/R, and radial velocity of the Be star HD 173948 (lambda Pavonis). Methods. Time series analyses of radial velocity, V/R, and line profiles of He I, Fe II, and Si II were performed with the Cleanest algorithm. An estimate of the stellar rotation frequency was derived from the stellar mass and radius in the Roche limit by adopting an aspect angle i derived from the fittings of non-LTE model spectra affected by rotation. The projected rotation velocity, necessary as input for the spectral synthesis procedure, was evaluated from the Fourier transform of the rotation profiles of all neutral helium lines in the optical range. Results. Emission episodes in Balmer and He i lines, as well as V/R cyclic variations, are reported for spectra observed in year 1999, followed by a relatively quiescent phase (2000) and then again a new active epoch (2001). From time series analyses of line profiles, radial velocities, and V/R ratios, four signals with high confidence levels are detected: nu(1) = 0.17 +/- 0.02, nu(2) = 0.49 +/- 0.05, nu(3) = 0.82 +/- 0.03, and nu(4) = 1.63 +/- 0.04 c/d. We interpret nu 4 as a non-radial pulsation g-mode, nu 3 as a signal related to the orbital timescale of ejected material, which is near the theoretical rotation frequency 0.81 c/d inferred from the fitting of the models taken into account for gravity darkening. The signals nu(1) and nu(2) are viewed as aliases of nu(3) and nu(4).

Transiting exoplanets from the CoRoT space mission X. CoRoT-10b: a giant planet in a 13.24 day eccentric orbit

Context. The space telescope CoRoT searches for transiting extrasolar planets by continuously monitoring the optical flux of thousands of stars in several fields of view. Aims. We report the discovery of CoRoT-10b, a giant planet on a highly eccentric orbit (e = 0.53 +/- 0.04) revolving in 13.24 days around a faint (V = 15.22) metal-rich K1V star. Methods. We used CoRoT photometry, radial velocity observations taken with the HARPS spectrograph, and UVES spectra of the parent star to derive the orbital, stellar, and planetary parameters. Results. We derive a radius of the planet of 0.97 +/- 0.07 R(Jup) and a mass of 2.75 +/- 0.16 M(Jup). The bulk density,rho(p) = 3.70 +/- 0.83 g cm(-3), is similar to 2.8 that of Jupiter. The core of CoRoT-10b could contain up to 240 M(circle plus) of heavy elements. Moving along its eccentric orbit, the planet experiences a 10.6-fold variation in insolation. Owing to the long circularisation time, tau(circ) > 7 Gyr, a resonant perturber is not required to excite and maintain the high eccentricity of CoRoT-10b.

Transiting exoplanets from the CoRoT space mission XI. CoRoT-8b: a hot and dense sub-Saturn around a K1 dwarf

Aims. We report the discovery of CoRoT-8b, a dense small Saturn-class exoplanet that orbits a K1 dwarf in 6.2 days, and we derive its orbital parameters, mass, and radius. Methods. We analyzed two complementary data sets: the photometric transit curve of CoRoT-8b as measured by CoRoT and the radial velocity curve of CoRoT-8 as measured by the HARPS spectrometer**. Results. We find that CoRoT-8b is on a circular orbit with a semi-major axis of 0.063 +/- 0.001 AU. It has a radius of 0.57 +/- 0.02 R(J), a mass of 0.22 +/- 0.03 M(J), and therefore a mean density of 1.6 +/- 0.1 g cm(-3). Conclusions. With 67% of the size of Saturn and 72% of its mass, CoRoT-8b has a density comparable to that of Neptune (1.76 g cm(-3)). We estimate its content in heavy elements to be 47-63 M(circle plus), and the mass of its hydrogen-helium envelope to be 7-23 M(circle plus). At 0.063 AU, the thermal loss of hydrogen of CoRoT-8b should be no more than similar to 0.1% over an assumed integrated lifetime of 3 Ga.

Age and metallicity of star clusters in the Small Magellanic Cloud from integrated spectroscopy

Context. Analysis of ages and metallicities of star clusters in the Magellanic Clouds provide information for studies on the chemical evolution of the Clouds and other dwarf irregular galaxies. Aims. The aim is to derive ages and metallicities from integrated spectra of 14 star clusters in the Small Magellanic Cloud, including a few intermediate/old age star clusters. Methods. Making use of a full-spectrum fitting technique, we compared the integrated spectra of the sample clusters to three different sets of single stellar population models, using two fitting codes available in the literature. Results. We derive the ages and metallicities of 9 intermediate/old age clusters, some of them previously unstudied, and 5 young clusters. Conclusions. We point out the interest of the newly identified as intermediate/old age clusters HW1, NGC 152, Lindsay 3, Lindsay 11, and Lindsay 113. We also confirm the old ages of NGC 361, NGC 419, Kron 3, and of the very well-known oldest SMC cluster, NGC 121.

THE STELLAR CONTENT OF OBSCURED GALACTIC GIANT H II REGIONS. VII. W3

Spectrophotometric distances in the K band have been reported by different authors for a number of obscured Galactic H II regions. Almost 50% of them show large discrepancies compared to the classical method using radial velocities measured in the radio spectral region. In order to provide a crucial test of both methods, we selected a target that does not present particular difficulty for any method and which has been measured by as many techniques as possible. The W3 star-forming complex, located in the Perseus arm, offers a splendid opportunity for such a task. We used the Near-Infrared Integral Field Spectrograph on the Frederick C. Gillett Gemini North telescope to classify candidate ""naked photosphere"" OB stars based on Two Micron All Sky Survey photometry. Two of the targets are revealed to be mid-O-type main-sequence stars leading to a distance of d = 2.20 kpc. This is in excellent agreement with the spectrophotometric distance derived in the optical band (d = 2.18 pc) and with a measurement of the W3 trigonometric parallax (d = 1.95 kpc). Such results confirm that the spectrophotometric distances in the K band are reliable. The radio-derived kinematic distance, on the contrary, gives a distance twice as large (d = 4.2 kpc). This indicates that this region of the Perseus arm does not follow the Galactic rotation curve, and this may also be the case for other H II regions for which discrepancies have been found.

ANALYSIS OF THE PICO DOS DIAS SURVEY HERBIG Ae/Be CANDIDATES

A large sample of Herbig Ae/Be (HAeBe) candidates, distributed in different Galactic regions south to declination +30 degrees, were identified by the Pico dos Dias Survey (a search for young stellar objects based on IRAS colors). Most of the candidates are nearby or associated with star-forming clouds, but several others are considered isolated objects. Aiming to verify the young nature of 93 HAeBe candidates, we searched for additional information that could be useful to confirm if they are pre-main-sequence (PMS) stars or evolved objects, which coincidentally show similar IRAS colors. By adopting a spectral index that is related to the amount of infrared excess and the shape of the spectral energy distribution, we have classified the sample according to three groups, which are analyzed on the basis of (1) circumstellar luminosity; (2) spatial distribution; (3) optical polarization; (4) near-infrared colors; (5) stellar parameters (mass, age, effective temperature); and (5) intensity of emission lines. Our analysis indicates that only 76% of the studied sample, mainly the group with intermediate to low levels of circumstellar emission, can be more confidently considered PMS stars. The nature of the remaining stars, which are in the other group that contains the highest levels of infrared excess, remains to be confirmed. They share the same characteristics of evolved objects, requiring complementary studies in order to correctly classify them. At least seven objects show characteristics typical of post-asymptotic giant branch or proto-planetary nebulae.

The young, tight, and low-mass binary TWA22AB: a new calibrator for evolutionary models? Orbit, spectral types, and temperature

Context. Tight binaries discovered in young, nearby associations are ideal targets for providing dynamical mass measurements to test the physics of evolutionary models at young ages and very low masses. Aims. We report the binarity of TWA22 for the first time. We aim at monitoring the orbit of this young and tight system to determine its total dynamical mass using an accurate distance determination. We also intend to characterize the physical properties (luminosity, effective temperature, and surface gravity) of each component based on near-infrared photometric and spectroscopic observations. Methods. We used the adaptive-optics assisted imager NACO to resolve the components, to monitor the complete orbit and to obtain the relative near-infrared photometry of TWA22 AB. The adaptive-optics assisted integral field spectrometer SINFONI was also used to obtain medium-resolution (R(lambda) = 1500-2000) spectra in JHK bands. Comparison with empirical and synthetic librairies were necessary for deriving the spectral type, the effective temperature, and the surface gravity for each component of the system. Results. Based on an accurate trigonometric distance (17.5 +/- 0.2 pc) determination, we infer a total dynamical mass of 220 +/- 21 M(Jup) for the system. From the complete set of spectra, we find an effective temperature T(eff) = 2900(-200)(+200) K for TWA22A and T(eff) = 2900(-100)(+200) for TWA22 B and surface gravities between 4.0 and 5.5 dex. From our photometry and an M6 +/- 1 spectral type for both components, we find luminosities of log(L/L(circle dot)) = -2.11 +/- 0.13 dex and log(L/L(circle dot)) = -2.30 +/- 0.16 dex for TWA22 A and B, respectively. By comparing these parameters with evolutionary models, we question the age and the multiplicity of this system. We also discuss a possible underestimation of the mass predicted by evolutionary models for young stars close to the substellar boundary.

Pulsations in the late-type Be star HD 50 209 detected by CoRoT

Context. The presence of pulsations in late-type Be stars is still a matter of controversy. It constitutes an important issue to establish the relationship between non-radial pulsations and the mass-loss mechanism in Be stars. Aims. To contribute to this discussion, we analyse the photometric time series of the B8IVe star HD 50 209 observed by the CoRoT mission in the seismology field. Methods. We use standard Fourier techniques and linear and non-linear least squares fitting methods to analyse the CoRoT light curve. In addition, we applied detailed modelling of high-resolution spectra to obtain the fundamental physical parameters of the star. Results. We have found four frequencies which correspond to gravity modes with azimuthal order m = 0,-1,-2,-3 with the same pulsational frequency in the co-rotating frame. We also found a rotational period with a frequency of 0.679 cd(-1) (7.754 mu Hz). Conclusions. HD 50 209 is a pulsating Be star as expected from its position in the HR diagram, close to the SPB instability strip.

Low-amplitude variations detected by CoRoT in the B8IIIe star HD 175869

Context. The origin of the short-term variability in Be stars remains a matter of controversy. Pulsations and rotational modulation are the components of the favored hypothesis. Aims. We present our analysis of CoRoT data of the B8IIIe star HD 175869 observed during the first short run in the center direction (SRC1). Methods. We review both the instrumental effects visible in the CoRoT light curve and the analysis methods used by the CoRoT Be team. We applied these methods to the CoRoT light curve of the star HD 175869. A search for line-profile variations in the spectroscopic data was also performed. We also searched for a magnetic field, by applying the LSD technique to spectropolarimetric data. Results. The light curve exhibits low-amplitude variations of the order of 300 mu mag with a double wave shape. A frequency within the range determined for the rotational frequency and 6 of its harmonics are detected. The main frequency and its first harmonic exhibit amplitude variations of a few days. Other significant frequencies of low-amplitude from 25 to a few mu mag are also found. The analysis of line profiles from ground-based spectroscopic data does not detect any variation. In addition, no Zeeman signature was found. Conclusions. Inhomogeneities caused by stellar activity in or just above the photosphere are proposed to produce the photometric variability detected by CoRoT in the Be star HD 175869. The hypothesis that non-radial pulsations are the origin of these variations cannot be excluded.