UNIVERSITE DE LIMOGES ECOLE DOCTORALE Sciences – Technologie - Santé
FACULTE des SCIENCES et TECHNIQUES de LIMOGES Année 2006
N° ordre : - 2006
THESE Pour obtenir le grade de DOCTEUR DE L’UNIVERSITE DE LIMOGES Discipline : Electronique des Hautes fréquences et Optoélectronique Spécialité : "Communications Optiques et Microondes"
Cristiano PALEGO Le Vendredi 19 janvier 2006
Composants MEMS RF pour les têtes de réception RF reconfigurables Thèse dirigée par Pierre BLONDY Roberto SORRENTINO
Professeur à Università di Perugia, Italie
Président
Jean-Louis CAZAUX Nathalie ROLLAND
Ingénieur à ALCATEL ALENIA Space, Toulouse Maître de Conférences à IEMN, Lille
Rapporteur Rapporteur
James C.M. HWANG Pierre BLONDY Valérie MADRANGEAS Thierry MONEDIERE Arnaud POTHIER
Professeur à Lehigh University, Bethlehem, USA Ingénieur de Recherches CNRS, XLIM – Limoges Professeur à l’Université de Limoges – XLIM Professeur à l’Université de Limoges – XLIM Chargé de recherches au CNRS, XLIM – Limoges
Examinateur Examinateur Examinateur Examinateur Examinateur
Christine ZANCHI Xavier GRISON
Ingénieur au CNES – Toulouse Ingénieur à la DGA – Paris
Invitée Invité
Acknowledgements I would like to thank my thesis advisor Pierre Blondy who greatly inspired me throughout my way, with his outstanding insight into research. A very few supervisors are talented in obtaining high quality work in a short time while keeping an extraordinarily liberal attitude and Pierre is one of them. His far-sighted advices often bordering on intellectual temerity, always excited and enriched me. I wonder if he realizes how much I have learned from him in our multiple, virtually zero time consumption discussions. Those discussions were among the factors that made a several years stay away from home worth to be lived and I will miss them inconsolably. I would like to thank the members of my dissertation committee: Roberto Sorrentino, Jean-Louis Cazaux, Nathalie Roland, James Hwang, Pierre Blondy, Valérie Madrangeas, Thierry Monedière, Arnaud Pothier, Christine Zanchi and Xavier Grison for taking the time to attend my defense. A special thanks goes to Professor Roberto Sorrentino who accepted to serve as Chair on my doctoral committee. He remains an unforgettable master of knowledge and style, and I am proud to be numbered among the members of his “offspring”. A special thanks also goes to Jean-Louis Cazaux at Alcatel Alenia Space and Nathalie Roland at IEMN, who dared to serve on the reading committee and to Professor James Hwang at Lehigh University who braved the Atlantic Ocean to attend my defense. I am greatly indebted to Arnaud Pothier for a variety of reasons: for his constant, precious and not owed support, for carefully listening and perceptively replying to any idea of mine and, most important, for giving the impression that everything I undertook was within my capabilities. My appreciation for Arnaud’s technical competences is very deep. My admiration for his human qualities is probably even deeper. I would like to acknowledge the director of Minacom department at XLIM, Professor Serge Verdeyme, for generously accepting me in the group and for his always helpful availability.
I am also very thankful to the Minacom secretary Ms Marie-Laure Guillat for her kind and effective assistance when most needed. There are many people that helped me along the way and I am particularly grateful to those of them who offered hospitality empathy and friendships when I first arrived in Limoges. Finally I would like to express my deepest gratitude to my family, to my friends right here or faraway and to everybody who contributed to make sure that this thesis was not just a thesis.
INTRODUCTION GENERALE
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Introduction générale
Les années 90 ont marqué un profond changement dans l’univers des technologies hyperfréquences qui est en partie imputable aux événements économiques et géopolitiques de la fin du dernier siècle. Notamment l’avènement de l’ère de l’information à crée à la fois un intérêt croissant et un marché à l’échelle mondiale pour les systèmes de communications et les réseaux de données multimédia. L’essor fulgurant vers les dispositifs de communication individuelle et la conséquente démocratisation des technologies électroniques ce sont en général traduites par une reconversion des systèmes de communication classiques, centralisés, encombrants et à fort consommation de puissance, vers une multitude de systèmes distribués de taille et consommation réduites. Les ressources d’énergie étant limitées, les contraintes de consommation de ces nouveaux systèmes deviennent encore plus sévères lorsque aux caractéristiques mentionnées s’ajoute la mobilité ou même la portabilité. C’est pourquoi il existe actuellement un besoin pressant de technologies hyperfréquences à faible consommation de puissance, avec un faible encombrement et capables d’atteindre une fonctionnalité supérieure par unité de volume tout en gardant des performances électriques satisfaisantes jusqu’aux fréquences millimétriques. Dans les 20 dernières années, un important effort de recherche à été mené dans le développement de circuits hyperfréquences intégrés (RFIC) sur Silicium, Silicium-Germanium et Arséniure de Gallium. Les remarquables progrès dans la fabrication de transistors bipolaires CMOS (technologie BiCMOS sur Si et SiGe) et de transistors bipolaires à hétéro-jonction (technologie HBTsur AsGa) ont ainsi abouti à une prolifération de solutions disponibles pour les RFIC avec un faible coût de réalisation. Cependant il semble actuellement difficile de déterminer une technologie hyperfréquence dominante car les contraintes varient énormément suivant les systèmes et les circuits et la plupart des technologies consolidées à l’heure actuelle offrent des capacités de portabilité et modularités modestes. La technologie MEMS (pour “Micro Electro Mechanical Systems”: systèmes micro-électromécaniques) s’est au contraire développée au cours des 3
dernières années et laisse entrevoir des potentialités prometteuses pour le développement de systèmes intégrables à la fois performants et reconfigurables. Cette technologie exploite des techniques de la microélectroniques compatibles avec la fabrication des RFIC classiques pour réaliser une nouvelle classe de microsystèmes qui combinent des propriétés mécaniques et électromagnétiques intéressantes. Ces systèmes sont également caractérisés par une faible consommation de puissance et un comportement en fréquence très linéaire. La possibilité de développer de nouvelles architectures intelligentes avec de très bonnes performances et un coût raisonnable, que ce soit en termes de puissance, de taille ou de complexité de système, a suscité l’effervescence des communautés scientifique et industrielle. Le potentiel de cette technologie à été démontré par un nombre impressionnant de prototypes dans le milieu universitaire/militaire et cela a répandu le sentiment que le saut technologique vers une production à grande échelle est désormais possible ou imminent. Néanmoins il reste encore d’importants progrès à réaliser avant d’achever cette évolution, notamment en ce qui concerne le packaging, la fiabilité à long terme et la tenue en puissance de ces composant MEMS. Le travail de thèse présenté dans ce mémoire s’inscrit dans ce contexte. Notre objectif a été de contribuer au développement de nouvelles topologies de circuits microondes reconfigurables et également d’apporter de solutions pour améliorer la fiabilité et la durée de vie de composant MEMS. L’originalité de ce travail se situe dans la superposition des plans technologiques (optimisation des performances des dispositifs) et théoriques (synthèse de systèmes reconfigurables). En effet notre effort de recherche ne se résume pas à essayer de repousser les limitations techniques des composants MEMS pour égaler (ou améliorer) les prestations et les fonctions hyperfréquences typiquement assurées par les semi-conducteurs. Il se propose aussi de montrer comme l’intégration des composant MEMS directement au niveau de la synthèse offre une nouvelle classe de fonctionnalités autrement inaccessibles. Ce manuscrit se construit de la manière suivante : Dans un premier chapitre, nous proposerons un tour d'horizon des principaux dispositifs issus de l’évolution de la technologie MEMS. Celle-ci c’est en effet avérée très attractive pour les domaines d’applications les plus variés (les accéléromètres et les capteurs en général, l’optique, le biomédical, les systèmes de stockage d’information et très largement, les télécommunications). Les dix dernières années ont connu une prolifération extraordinaire de dispositifs, systèmes ou projets intégrants des composants MEMS, par de nombreux 4
organismes de recherche et groupes industrielles. Nous montrerons ainsi quelques exemples qui ont déjà atteint une importance commerciale (Analog Devices) ou sont en état de développement avancé (NASA, IBM). Nous nous intéresserons plus particulièrement au domaine des hyperfréquences car la contribution de la technologie MEMS à ce secteur est majeure notamment grâce au développement de plusieurs micro-commutateurs très performants. Les applications des commutateurs MEMS aux dispositifs à micro-ondes et millimétriques sont très nombreuses et semblent être parvenue à un stade de maturité relative. Ceci justifie le développement d’un domaine spécifique dit des MEMS pour les radiofréquence (RF MEMS). Nous présenterons les structures les plus répandues, nous analyserons leurs modes de fonctionnement, leurs avantages, leurs inconvénients, et nous comparerons leurs performances à celles de technologies traditionnelles pour les applications hyperfréquences. Cette approche intentionnellement simple et intuitive nous permettra de situer notre travail tout en traçant une prospective pour la suite. Nous verrons enfin quelles sont les caractéristiques actuelles ou potentielles des dispositifs électroniques (tels que les filtres accordables pour les soussystèmes de réception/transmission et les déphaseurs) qui intègrent des composants développés grâce à ces technologies. Dans le second chapitre, nous présenterons la conception, la fabrication, et la caractérisation de filtres accordables en bande passante, en fréquence centrale ou en toutes les deux simultanément, pour des applications en bande L et R. Ce travail vise à dépasser l’ approche traditionnelle de conception de filtres simplement accordables intégrant des composants micro-électromécaniques, et se propose de montrer la possibilité d’une conception “programmable” de filtres reconfigurables. En effet, l’approche traditionnelle consiste à synthétiser une réponse particulière en fréquence, tout en prévoyant une variation des éléments accordables pour en moduler la largeur de bande ou la fréquence centrale. Cela donne une possibilité d’accord qui s’avère en général assez limitée. La méthode proposée au contraire est idéale pour l’implémentation d’un grand nombre de fonctions de filtrage qui atteignent une flexibilité élevée d’accord pour toutes les caractéristiques du gabarit de filtrage. Les outils de synthèse utilisés, ainsi que l’implémentation physique du filtre reconfigurable à l’aide de banques de capacités commutées seront montrées dans ce chapitre. 5
Ce travail s’avère en outre intéressant car il représente un des premiers exemples de circuits hyperfréquences reconfigurables ayant intégré les composants MEMS sur un substrat d’alumine. L’intégration de la technologie MEMS aux substrats céramiques fait actuellement l’objet d’un effort de recherche très important vu la prédominance de ces substrats notamment dans les sous-systèmes de réception sans fil à faible niveau des pertes. Le succès de cette intégration pourrait accélérer l’évolution définitive des MEMS de la dimension prototype/universitaire vers une production en grande échelle et faible coût. La conception électromagnétique des filtres qui font l’objet de ce chapitre est donc consacrée au développement de résonateurs à fort facteur de qualité en technologie micro-ruban sur alumine. Cette étude à fait appel à une approche originale à éléments localisés afin d’obtenir des résonateurs très compacts et compatibles avec la réalisation de filtres miniaturisés. Ceci à demander un effort particulier pour la mise au point d’un procédé de fabrication spécifique dont nous résumerons les étapes principales. Les résultats de mesures seront enfin présentés et discutés montrant un excellent accord avec les performances hyperfréquences visées . Le troisième chapitre sera dédié au développement d’une autre topologie de circuit hyperfréquence reconfigurable. Ce travail s’inscrit dans le cadre du projet ReRaFe (Reconfigurable Radio Front-End) soutenu et financé par le réseau européen AMICOM (Advanced MEMS for RF and Millimeter-wave Communications) pour la réalisation d’un filtre reconfigurable MEMS destiné à un sous-système de réception radio. Ce filtre est basé sur une architecture à résonateurs couplés proche de celle utilisée dans le second chapitre mais il réalise une performance de reconfiguration différente et originale. Le but du filtre ReRaFe sera en effet de reconfigurer la réponse en fréquence sur deux standards préfixés (DCS 1800 et WLAN) complètement hétérogènes. Le défi technologique à relever en ce cas consiste à réaliser un circuit capable de commuter entre deux standards très hétérogènes avec une architecture de filtre unique et compacte. Il sera ainsi montré que cela est possible au prix d’un effort relatif de conception des transformateurs d’impédance en entré et sortie du filtre, qui permettent de parvenir à des éléments LC technologiquement réalisables pour les deux standards. Ce chapitre sera donc en grande partie consacré au développement de solutions spécifiques pour réaliser des transformateurs qui combinent une architecture distribuée avec des capacités localisés et accordables par des commutateurs MEMS. L’architecture obtenue ainsi que les premiers 6
résultats de mesure pour ce filtre reconfigurable bi-standard seront ensuite présentés et discutés. Dans un quatrième et dernier chapitre nous présenterons un nouveau concept de capacité commutée MEMS spécifiquement conçue pour des applications forte puissance. Les capacités variables MEMS présentent un très fort potentiel notamment pour l’application aux filtres reconfigurables et aux systèmes de routage et déphasage électronique. Néanmoins la plupart des exemples disponibles actuellement considère cette intégration en conditions de faible puissance du signal RF injecté. En effet la fiabilité des composants MEMS soumis à un niveau de puissance RF élevé n’a été prouvée qu’en mode “cold switching ”, ce qui signifie que la puissance injectée est coupée avant toute commutation de la capacité MEMS. Il apparaît pourtant primordial d’étudier la tenue en puissance des varactors MEMS lorsque la puissance RF est continuellement injectées dans le dispositif. Ceci revient alors à un étude de fiabilité en mode “hot switching”. Le travail que nous présenterons dans ce chapitre se propose d’une part de développer une varactor de puissance pour des applications hot switching, et de l’autre de caractériser la tenue en puissance du composant réalisé. En ce qui concerne la conception, elle a d’abord fait appel à une étude théorique des principaux mécanismes de défaillance, tels que l’auto-actionnement ou l’auto-maintien, d’une micro-poutre à contact capacitif en condition de forte puissance. Cette étape a essentiellement portée sur la modélisation de la pression électrostatique qui vient s’installer sur la poutre induite par la puissance RF traversant le dispositif. Il a été ainsi montré que la région du contact capacitif est extrêmement sensible à l’influence de la puissance RF et que l’amélioration de la tenue en puissance du dispositif relève du dimensionnement approprié de son impédance capacitive par rapport à sa raideur structurale. Une topologie originale à été mise en place qui se propose de dissocier la performance capacitive du varactor de son comportement mécanique et parvient à limiter efficacement les effets de la puissance. Ensuite une méthode de synthèse/optimisation a été mise au point afin de déterminer exactement la géométrie optimale du dispositif et d’en repousser les limites de tenue en puissance. Cette méthode est basée sur l’optimisation récursive multi-physique des paramètres géométriques de la structure combinant les aspects électrostatique, mécanique et électromagnétique. Les outils de calcul et la démarche suivie dans cette étape afin d’atteindre les performances souhaitées seront décrits dans ce quatrième chapitre. 7
Finalement, les choix de conception seront validés par des caractérisations mécaniques et électromagnétiques des dispositifs réalisés. Cela fait appel à de tests de tenue de puissance maximale ainsi que de tests de durée de vie des composants soumis à divers niveaux de puissance. La fiabilité à long terme est évaluée par de mesures de caractéristiques capacitétension (courbes C(V)) qui sont répétées au bout de plusieurs sessions de cyclage sous un niveau de puissance RF constant. Ce type de tests se propose donc de détecter les éventuelles dégradations de la performance des varactors en fonction de la puissance injectée et de la durée du cycle. L’étude de tenue de puissance maximale consiste à répéter des mesures des tensions d’actionnement et de relâche des dispositifs pour des niveaux de puissance croissants. Ce type de tests se propose ainsi de déterminer le niveaux de puissance à la quelle une défaillance survient par l’auto-actionnement ou l’auto-maintien des micropoutres. Les résultats des tests de fiabilité seront présentés et discutés. Les résultats des tests de fiabilité, qui permettent de valider à la fois la topologie et la méthodologie d’optimisation proposées, seront présentés et discutés. Enfin, nous effectuerons une synthèse des résultats obtenus au cours de ce travail de thèse et nous développerons les perspectives qui en découlent dans la conclusion générale.
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CHAPTER 1
RF MEMS technology for reconfigurable microwave applications
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10
RF MEMS technology for reconfigurable microwave applications
The manuscript introduced with this chapter involves predominantly analysis, design and fabrication of circuits using the technology of micro-electromechanical systems (MEMS) for Radio-Frequency circuits (RF MEMS). This technology has emerged in recent years with a comparable level of interest and even more rapid development than silicon-based RF integrated circuits (RFIC’s). RF MEMS enable a new class of components and subsystems that are electrically reconfigurable, provide new system capabilities and display superior high-frequency performance relative to conventional (usually semiconductor) devices. RF MEMS technology probably represents one of the most interesting and inter-disciplinary research/industry area in microwave engineering. Indeed on one side MEMS devices enable substantial enhancement of microwave designer possibilities by providing almost ideal tunable network transfer functions. On the other side MEMS fabrication represents a challenge for technology engineer that intrinsically conjugates different areas as mechanics, electrostatics, electromagnetics, material science… To a certain extent, the author was given the chance to follow the still ongoing evolution of RF MEMS from the status of latest revolution in microelectronics into one of the major topics in microwave engineering. MEMS technology is growing so fast and in so widespread domains that an exhaustive introduction even limited to RF area would provide sufficient material for a whole Ph.D. thesis. Hence this chapter is not intended as a systematic introduction to MEMS technology. On the other hand it appeared useful to collect some of the subjects, principles and metrics that are commonly employed all over the rest of the manuscript. The main goal is not to achieve completeness in enumerating MEMS components and properties but showing the complete versatility of MEMS technology while providing an insight into MEMS impact on modern RF communication systems.
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I MEMS components
Micro-electromechanical systems include a variety of circuits and devices. These components borrow some consolidated techniques from integrated circuits fabrication processes to realize mechanically deformable devices at micron scale [1] . The most important technique for RF MEMS is surface micromachining which consists of the deposition and lithographic patterning of various thin films, usually on silicon, quartz, or other substrates. Generally, the intent is to make one or more of the sacrificial films freestanding over a selected part of the substrate, later able to undergo the mechanical deformation motion or actuation. This is done by depositing a sacrificial film (or films) underneath the one(s) to be released, which is removed in the last steps of the process using selective etchants. Bulk micromachining involves the creation of mechanical structures directly in silicon, quartz, or other substrates by selectively removing the substrate material. MEMS devices currently collect considerable efforts in multiple research/industry domains including electronics, micromechanics, optics, fluid dynamics, bioengineering and defence. Originally the term MEMS was
strictly employed to designate mechanically
deformable devices, while nowadays it rather includes the totality of devices obtained by micro-fabrication techniques. The first devices that fully demonstrated the potential of this technology were microsensors that exploit the sensibility of special materials and thin film to pressure, acceleration or mechanical deformation. This lead to a variety of monolithically integrated systems where packaged MEMS sensors are integrated to traditional electronic components. A well known example is probably the Analog Devices AD-XL50 automotive airbag accelerometer [2-3]. This is essentially a monolithic surface micromachined accelerometer with capacitive position detection. Beyond crash sensing for airbag control MEMS devices offer interesting solutions for vehicle dynamic control, rollover detection, antitheft systems and electronic parking brake systems. Several examples of these navigation systems are based on MEMS angular-rate sensing gyros.
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Figure 1.1 Analog Devices AD-XL50 automotive airbag accelerometer.
Optics also exploits MEMS technology to realise adaptive micromachined mirrors based on thin reflecting membranes [4] whose position and inclination can be electronically controlled resulting in reconfigurable optic networks. Deformable mirrors were successfully integrated to fibre laser, to control and modulate pulse laser emission (active Q-switched fiber laser), [5].
(a)
(b)
Figure 1.2 Reconfiguralbe mirrors realized at TU Delft (a), and Xlim (b).
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MEMS technology is showing increasing potential for fluidic (inkjet nozzles) and biomedical applications. Indeed miniaturized size exhibited by micromachined devices is strongly attractive for the implementation of non invasive systems for diagnostic or, in more advanced applications, local treatment. In particular, there is a growing trend towards development of complex microsystems (lab on chip) integrating micro-probes, micro-pumps at cell-scale and capable to deal with minimum clusters of cells for on side detection of physiological parameters or micro-injection of reagents.
(a)
(b)
Figure 1.3 (a) Microfabricated silicon neural probe array [6]. (b) Cell-based biosensors with micro-electrode array [7].
Spectroscopy and astronomy take advantage of MEMS technology as well. Microshutter arrays (see Figure 1.4, [8]) are being developed at NASA Goddard Space Flight Center for use in the Near Infrared Spectrograph (NIRSpec) on the James Webb Space Telescope (JWST), which is expected to measure the number and density of young galaxies. The microshutter arrays are designed for the simultaneous observation of a large number of sources in the sky and the transmission of light to the NIRSpec detector with high contrast. Individual shutter cells can be actuated to a fully open position, allowing light to completely pass through the device and reach the NIRSpec detector. A dedicated actuation mechanism allows selecting and controlling single shutters in a matrix of more than 200 objects (Figure1.4 (b)). Shutters are opened by a magnetic field (that allows large displacement actuation), latched by an electrostatic force, and selected to be open or close by addressing the electrostatic force. This allows an arbitrary pattern to be generated as shown in Figure 1.4 (c). 14
(a)
(b)
(c)
Figure 1.4 Frontside (a) and backside (b) of the microshutter array. Arbitrary pattern generation (c).
IBM is also testing a “millipede” high density data storage system based on MEMS components (see Figure 1.5, [9]). This exploits tiny depressions created with an atomic force microscopy (AFM) tip in a polymer medium to write data bits that can be read back and erased by the same tip. This thermodynamical storage technique is capable of achieving data densities exceeding 1 Tb/in2. well beyond the expected limit of magnetic recording. High data rates can also be achieved by making use of massive parallelism.
Cantile ver
Figure 1.5 IBM MEMS millipede high density data storage system.
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Apparently the domains of application of MEMS technology are expanding very quickly. This is mainly due to compatibility with miniaturized size applications and potential for low-cost mass production. However to date there is little doubt that one of the application field that took huge advantage from advent of MEMS era is that of RF communication systems. This justifies the establishment of a branch named RF MEMS and to some extent can be attributed to the success encountered by MEMS switches which are still considered as the paradigm of RF MEMS devices [10]. The tremendous impact that MEMS technology had on microwave systems in the last ten years can be explained by thinking that probably since the dawn of GaAs IC’s no other RF technology had shown so much potential to improve system performance and affordability at the same time.
II RF MEMS
MEMS fabrication techniques developed and differentiated in the last 15 years and result today in a multitude of devices for microwave applications. A survey of RF MEMS current research/industry activities leads to the following main areas [11]. •
RF MEMS switches: based on controlled movement of mechanical small parts to perform almost ideal RF operations from DC-120 GHz.
•
Variable capacitances: as switches move several micrometers when actuated for operations from 0.1 up to100 GHz.
•
Micromachined inductors: relatively high-Q (Q=20-60) inductors (L=2-15 nH) whose parasitic capacitance is reduced by suspending the inductor high above the substrate [12]. They are static and do not move.
•
Micromachined transmission lines, resonators, filters and antennas: they are generally integrated on thin dielectric membranes or use bulk micromachining of silicon to reduce dielectric loss for application from 10 up to 200 GHz. [1316]. They are static.
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•
FBAR (Film Bulk Acoustic Resonators) devices: they use acoustic vibrations in thin piezoelectric films to achieve high-Q (Q>2000) up to 3 GHz with excellent loss and power handling behaviour. The acoustic wave is excited in the vertical plane of the piezoelectric film resulting in extremely compact resonators [17-18].
•
RF micromechanical resonators and filters: they use mechanical vibration of extremely small beams to achieve high-Q (Q>8000) resonance for 0.01-200 MHz operations. They can be used for reference clock circuits [19-20]
RF MEMS switches and variable capacitances are introduced in some more detail since they were crucial for the development of this thesis work.
II.1 RF MEMS switches
RF MEMS switches are miniature devices that use mechanical movement to achieve a short circuit or an open circuit on a RF transmission line [11]. Although they present a wide variety of structure and layout configurations most MEMS switches share large surface to volume ratio so that surface effects such electrostatics, wetting or air damping dominate volume effects such as inertial or gravitational forces. In order to produce mechanical movement and to achieve switching (“actuation”), several kind of forces can be applied as electrostatic, magnetostatic, piezoelectric or thermal. Electrostatic actuation (see Figure 1.6) is the most common technique in use to date and is discussed in some detail because it concerns all MEMS devices presented in this work. This mechanism is easy to implement since it just requires a fixed (“pull-down”) electrode, a movable electrode which is integrated or corresponds to the mechanically deformable part of the switch, and a bias line to apply voltages between the electrodes. Fixed and movable electrode constitute an approximately parallel-plate capacitor and when a voltage is applied between them an electrostatic force is induced on the movable electrode. This force provokes
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deflection of the movable electrode on the pull-down electrode and results in rapid (1-200 µs) actuation of the switch if the applied voltage exceeds a critical Vp “pull-down” voltage.
Non actuated switches Movable electrode V=0
Movable electrode g=g0
g=g0
V=0
Actuated switches RF INPUT
V=Vp
Pull-down eletrode
g=0
Contact eletrode
g=0
V=Vp
RF OUTPUT Pull-down+contact eletrode
Figure 1.6 Electrostatic actuation for different kinds of RF MEMS switches. Therefore electrostatic actuation occurs through the capacitance formed by pull-down and movable electrode and a very small current (~µA) flows into the bias line during the time necessary for this capacitance to charge/discharge. On the other hand, the current is zero in static conditions which means that power is consumed only during commutation from non actuated to actuated state (or vice versa). Hence electrostatic actuation provides very low power consume, small electrode size, relatively short switching time and contact force which is adequate for most applications. However electrostatic actuated switches require actuation voltages from 10-100 V which makes necessary to amplify the typical 3-5 V source voltages. Furthermore due to non linear dependence of electrostatic force with the actuation gap, controlled deflection of the movable electrode gets impossible as it approaches actuation (see section II.1.1). Thus the system collapses in the actuated state rather than gradually achieving it. Such an instable behaviour especially affects MEMS varactors performance because analog controlled variation of capacitance can be only obtained over a limited range. Magnetostatic actuation provides high contact force with no instability phenomena, but requires considerable size and currents to induce a permanent magnetic field. Thermal actuation results in high contact force but requires relatively high switching time and power consumption. Piezoelectric actuation has virtually no power consume and allows control on the release mechanism of the movable membrane, but requires complex and high temperature 18
fabrication process. Finally different actuation mechanisms can be coupled together (ex. thermal actuation with electrostatic hold) resulting in virtually zero power consumption when the switch is actuated. However in practice only electrostatic actuation was tested in a large frequency range and with high reliability. We now summarize some of the characteristics and configurations that allow dividing MEMS switches in different categories. This classification does not intend to be exhaustive and is not the only possible however it turns out to be practical for further developments. Then switches are categorized by the following three characteristics: 1. Mechanical structure 2. RF circuit configuration 3. Form of contact As for the mechanical structure the switches are either fabricated using a fixed-fixed membrane that results in a air bridge (Figure 1.7 (a)), or a floating cantilever (Figure 1.7 (b)).
(a)
(b)
Figure 1.7 Fixed-fixed beam (a )[21] , and floating cantilever (b)[22] configurations.
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As for the RF circuit configuration it should be pointed out that following electrical convention the number of poles is the number of input terminals or ports to the switch, while the number of throws is the number of output terminals or ports. Then the two common circuit configurations are single pole single throw (SPST) shunt (Figure 1.8 (a)) or series (Figure 1.8 (b))connected [10].
(a)
(b)
Figure 1.8 Shunt (a), and series (b) configurations [23].
The two common contact forms are the capacitive (metal-insulator-metal) contact, and the resistive (metal to metal) contact. The air bridge switch in Figure 1.7 (a) also represents an example of capacitive contact while the cantilever switch in Figure 1.7 (b) illustrates a typical metal to metal contact. However it should be noticed that there are several examples of bridge switches with resistive contact [24] as well as cantilever switches with capacitive contact (see Chapter 4). The resistive contact switches use metal-to-metal direct to achieve an Ohmic contact between two electrodes. In the actuated (On) state the switch presents an essentially resistive impedance ROn which allows signal transmission from DC up to very high frequency. The ROn value and evolution with time and usage strongly depend on the metal material used. The reliability of Ohmic switches is limited by contact degradation and hardening due to the impact force or deposit of contaminants and typically allows lifetime in the order of 1012 cycles (in low power conditions) [11,25]. For capacitive contact switches the contact electrode is covered by an insulating dielectric layer. In the On state the metal beam gets in contact with this layer and the switch presents an essentially capacitive COn impedance, which allows high frequency signal transmission across the capacitance through displacement current. Large COn capacitances are 20
required for proper transmission of RF signal. The ratio of capacitance in the actuated state COn to capacitance in the non actuated (Off) state is COn/COff and is a fundamental parameter for capacitive contact switches. Capacitive contact switches experience smaller contact degradation but suffer from “stiction” between the bridge and bottom contact due to dielectric charging [26-27], humidity or contaminants, and are intrinsically unfit for low frequency applications. Capacitive switches have been tested up to 1011 cycles in low-power conditions [28-30]. From an electrical point of view it is easy to realize how MEMS ohmic contact switches approach an ideal 2-state digital behaviour. On the other hand, although capacitive switches are often employed to perform two 2-state operations (see section II.2 and Chapter 4), they can also be used to provide continuous variation of the capacitance, to some extent. An ideal RF switch is a lossless device for which 2 only transmission states are possible: an Off state where the signal is blocked and the output port is disconnected from the input port, and an On state where the two ports are connected and the signal is transmitted with no loss from input to output. An RF MEMS ohmic contact switch is a real device that can be described with good approximation by the 2-state simple circuit model in Figure 1.9.
COff
RF Input
RF Output ROn
Figure 1.9 Two state circuit model for an RF MEMS ohmic contact switch.
In the Off state the MEMS switch is comparable to a small capacitance COFF and the component presents a high impedance condition so that output is practically isolated from input. In the On state the impedance of the switch reduces to a small resistance ROn that connects input and output and allows transmission of the signal with small loss.
21
A generally used figure of merit for such a component is the cut-off frequency fc that is defined as the frequency such that the ratio of the modulus of impedance in the On state to the modulus of impedance in the Off state is 1.
fc =
1 2π COff ROn
(1)
This limits the range of application of the switch since at f= fc it performs no more impedance commutation. The higher the cut-off frequency the better the switch performance as compared to the ideal behaviour. For instance a MEMS switch with typical values of COFF = 10 fF, RON = 1Ω and has an fc =16 THz, which is about 10 times as higher as typical p-i-n switches cutoff frequencies. Switching time is defined as the time necessary for going from Off to On state (and vice versa) and is also an important parameter when defining the switch performances and range of applications. For example typical switching times range between 1-300 µs and are higher than p-i-n diodes and FET transistors typical switching times (1-100 ns). Finally a few conventional RF metrics commonly apply to MEMS switches and are extensively used all along this work. These are all linked to the On/Off ratio and the cut-off frequency parameters introduced above. 1. The insertion loss, i.e. the 1/|S21| parameter in the On state 2. The isolation, i.e. the 1/|S21| parameter in the Off state 3. The return loss i.e. the 1/|S11| parameter in both states
II.1.1 Overview of electromechanical behaviour for electro-statically actuated switches.
Structural analysis of a cantilever beam submitted to electrostatic actuation will be carried out in some detail in Chapter 4; however the following intuitive description is freely summarized from [31] and introduces some general use parameters basing on the analogy 22
with a simple mechanical system. The switches are modelled as mechanical springs with an equivalent spring constant k [N/m] which depends on the geometrical dimensions of the movable electrode and on the Young’s modulus of the material used. k is 5-40 N/m for most switch designs. Also, the switches have very low mass m (≤10-10 Kg) which makes them pretty insensitive to acceleration forces. By assuming an electrostatic actuation force and referring to the structure parameters as reported by Figure 1.7 (a) the force between the top and the bottom electrodes is:
CV 2 F= t 2 g + d εr
=
ε 0 AV 2 t 2 g + d εr
2
(2)
Where V, g, and C are the applied voltage, gap distance and capacitance between the lower (pull-down) and upper electrodes, respectively, and A is the area of the pull-down electrode. The latter is often covered by a dielectric layer with a thickness td and a relative dielectric constant εr to prevent a short circuit between the movable and fixed plates. For a switch with A=100*100 µm2, V= 50 V, g= 3 µm the initial pull-down force is 12 µN which is pretty low. However this force is sufficient to actuate the switch because as the top electrode starts to deflect the gap is reduced and the pull-down force on the beam increases. On the other hand, a pull-up restoring force also applies to the beam due to the spring constant of the switch, so that an equilibrium is achieved when pull-down and pull-up forces are the same:
F=
ε 0 AV 2 t 2 g + d εr
2
= k(g − g0 )
(3)
where g0 is the beam initial height. This equation predicts a stable position of the beam up to ~ g0/3, after what the actuation force is no more balanced by the spring force and the switch collapses to the down state position. The pull-down voltage Vp that causes this collapse is:
Vp ≈
8kg 03 27ε 0 A
(4) 23
For k=10 N/m, and the values above Vp =30 V. The typically applied voltage is 1.21.4Vp so that actuation is achieved rapidly. Once the switch is pulled in the down state, in capacitive switches an intimate contact is achieved between the beam and the dielectric layer, while in resistive switches a 0.3-0.6 m air gap layer can be present between the beam and the pull-down electrode. In both cases the electrostatic voltage can be reduced to a “release” voltage, Vr =8-20 V, while still keeping the switch actuated. This allows reducing the electric field in the dielectric and the possibility of dielectric breakdown or charge injection into the dielectric. Such an hysteretic behaviour is typical of all MEMS switches and is represented in
3
Stability limit
2.5
1
Release
2
0.5
Vr
1.5
0 0
Actuation
Top electrode height (µm)
Figure 1.10.
Vp Hold-down 10
20
30
40
Applied Voltage (V) Figure 1.10 Beam height versus applied voltage.
It should be observed that while the initial force is 12 µN the force at contact increases to hundreds of µN up to 1.5 mN depending on switch configuration and design. This is essentially what allows metal-to-metal contact switches to achieve low contact resistances. Once the bias voltage is removed the pull-up force is approximately given by F=kg0 since the displacement of the electrode is g0. This results in a pull-up force of 30-60 µN for most switches and is quite small. For this reason MEMS switches are very sensitive to surface chemistry (humidity, contaminants, dielectric charging…) and must be packaged in cleanroom conditions [32-33].
24
MEMS switches also follow classical laws of motion and the d’Alembert-Lagrange principle [34]:
m
d 2g dg +b + k ( g − g 0 ) = Fe 2 dt dt
(5)
where m and b are the mass and damping factor of the top electrode and Fe is the electrical force from (2). This is a second order system with a resonant frequency:
ω0 =
k ω 0 = km / b m
(6)
A switch with m= 10-11 Kg and k = 10 N/m results in a resonant frequency of 50 KHz. The damping factor is seen to be inversely proportional to the mechanical quality factor (Q) defined as Q =
km /b which is 0.2-5 for most switch designs. Low Q systems result in slow
switches while high Q systems result in long settling times for both the actuation and the release operations. Switches that operate in vacuum can have a Q as high as 10-1000, while for atmospheric pressure operations it can be shown that a proper condition is reached for Q~1 which assures an appropriate damping factor. An approximated equation that accurately predicts the switching time can be derived [35] by setting b=0 (no damping) and taking the electrical force as the initial force with g=g0.
t ≈ 3.67
Vp Vω 0
(7)
where V is the applied voltage and the accuracy is within 10% for Q>1 and V>1.3Vp. For a switch with ω0=40 KHz and V=1.4Vp the switching time is 10 µs. (7) shows that it is hard to get very low switching times. For instance a switching time lower than 1 µs requires a resonant frequency ω0=190 KHz and a ratio Vp/V ≤3. Such a high resonant frequency could only be achieved using a high spring constant (and a low mass), so that the associated pulldown voltage would be high and the applied voltage V would be really high! [36]. 25
II.2 MEMS variable capacitors
MEMS tunable capacitances are one of the most promising area of RF MEMS technology although they have not progressed at the speed of MEMS switches. This is probably because silicon and GaAs varactors result in excellent performance especially below 5 GHz and do not have special packaging requirements. However MEMS varactors have the potential of very high-Q operations (Q=100-400), they withstand large RF voltage swings and result in high third order intercept point (IP3) tunable networks, they consume low current even in high power application and can be inexpensively fabricated on glass, ceramics or high-resistivity silicon substrates. The capacitive micro-switches based on a parallel plate architecture are intrinsically suitable for realizing MEMS tunable capacitances. Nevertheless it has been observed how difficult is to achieve analog capacitance variation over a large range for this kind of device. Indeed the previous section described the phenomenon of mechanical instability of parallel plate capacitors under an electrostatic force. It was found that the top plate can be moved to a gap height of 2 g0/3 before it collapses on the bottom plate. The maximum capacitance ratio that can be achieved over the stable range of capacitive variation is then:
ε0 A
+Cf C Max C (2 g 0 / 3) (2 g 0 / 3) = = Cr = ε0 A COff C(g 0 ) +Cf g0
(8)
where Cf is the parasitic fringing field capacitance associated with the beam and typically results in 20-40% increase of capacitance in both cases. This leads to degradation of the capacitance ratio which ranges between 1.4 and 1.3 for most designs. Indeed higher capacitance ratios are typically obtained by a pseudo-digital operation which consist of exploiting the capacitance value in the down state. The latter is typically much higher than the CMax value in (8) due to dielectric layer that covers the contact electrode and has relative dielectric constant 4-10 which is higher than the air’s one. This kind of functioning is more
26
compatible with the instable behaviour of electrostatically actuated MEMS capacitances and is widely employed for the varactor presented in Chapter 4. Alternatively MEMS tunable capacitors can be designed with more sophisticated configurations or different kind of switches. Therefore it is essentially possible to distinguish three different kinds of MEMS varactor. The first one is based on the parallel-plate (vertical) approach where the variable capacitance is achieved by changing the gap between the capacitors plates (Figure 1.11). This suitable for capacitances of few pF applications from 150 GHz.
Electroplated membrane
Springs Anchors
m ov
em en
t
Figure 1.11 Two examples of parallel plate analog MEMS varactors [37-38].
Figure 1.12 An example of interdigital analog MEMS varactor [39]. 27
The second approach is based on an interdigital design and a variable capacitance is obtained by exploiting mechanical horizontal movement to change the common interfaced area of two comb-shaped electrodes (Figure 1.12). This allows obtaining large capacitance values (4-10 pF) and ratio (5-10), and is suitable for applications from 0.1 up to 6 GHz . Nevertheless the size and the design complexity are often considerable. The third approach consists of building a fixed capacitance bank and using MEMS switches to select the required total capacitance (Figure 1.13). This approach allows achieving very high capacitance value (up to 35 pF) and large capacitance ratios, but the Q factor can be limited by the series switch contact resistance or by the metal-insulator-metal (MIM) capacitors used.
RF CPW input MEMS Ohmic switch Bias line
Bit2
Variable C bank
MEMS switch1
BIT1
MEMS switch2
BIT2
MEMS switch2
BIT3
Bit1
Bit3
MIM capacitor
Figure 1.13 An example of MEMS switched capacitor [40].
II.3 RF MEMS from a system perspective
Sections II.1-2 have illustrated several intrinsic properties of RF MEMS technology from a device point of view. This section resumes the introduced characteristics in order to evaluate the impact of RF MEMS on current or imminent RF communication systems. For this purpose two specific examples are considered which still are relevant for a variety of RF systems and subsystems. This necessarily implies a comparison with traditional semiconductor technologies that currently dominate the RF applications. 28
Miniaturized size: RF MEMS devices allow the execution of complex functions on a size scale orders-of-magnitude lower and at far less power than discrete circuits. At microwave frequency most MEMS components exhibit very small size to wavelength ratio and make possible short-circuit/opencircuit/tunable-capacitor operations that approach the lumped elements ideal behaviour. The potential for evolution into nano-scale is currently being showed and is compatible with the main trend in electronics. Virtually zero power consumption: most of the RF MEMS devices developed to date achieves electromechanical actuation electrostatically through air (or vacuum). Hence, the power consumption comes from dynamic current flowing to the MEMS only when actuation is occurring (10-100 nJ per switching cycle). Electromechanical isolation: the RF circuit of MEMS component does not leak or couple significantly to the actuation circuit. Excellent RF performances: currently fabricated micro-switches present low contact resistance in the On state, which results in very low insertion loss (<0.2 dB). Furthermore series switches are fabricated with air gaps and have very low Off state capacitances (<10 fF) which means very high isolation in the Off state (>30 dB). Linearity: RF MEMS components are essentially linear devices over a wide input power and frequency range. Typical intermodulation products are about 30 dB lower than p-i-n or FET devices, while third-order intercept point is higher than +66 dBm, and bandwidth is larger than 40 GHz . Fabrication process: MEMS devices are designed and fabricated by techniques similar to those of very large-scale integration (VLSI) circuits, and can be manufactured by traditional batch-processing methods. This last point is expected to allow rapid dissemination of MEMS into the commercial marketplace.
29
Despite these advantages, however, the implementation of RF MEMS does not come with impunity and a number of serious reliability and cost issues remain unanswered: Packaging requirements: micro-mechanical systems are very sensitive to surface chemistry, humidity, contaminants etc. and need specific packaging solutions notably to contrast the phenomenon of “stiction,” whereby parts of the device can bonded together upon physical contact. Low-cost hermetic package that protect MEMS devices does not exist to date, and the optimum gas microenvironment for the reliable operation of MEMS switches is still unknown. Surface wear: long term utilization and cycling of MEMS components results in contact area damage that leads to contact resistance degradation even for relatively low power levels. Power handling: it is particularly difficult to deal with power levels exceeding 500 mW. High power levels affect strongly the reliability of pull-down/release operations. This issue is extensively treated in Chapter 4. Dielectric charging problems: electrostatic actuation over long period of time or with high biasing voltage results in charge trapping in the dielectric layers that can lead to uncontrollable changes of the actuation voltages versus time. Switching time: due to the mechanical actuation, MEMS components are inherently slower than traditional electronic devices. The electromechanical actuation time is typically many microseconds or greater, which is substantially longer than typical electrical time constants in semiconductor devices. Shorter switching time are currently being achieved at the prize of relatively high pull-down voltages for low mass switches.
30
II.3.1 RF MEMS in front-end systems.
The low insertion loss and high isolation of the metal-to metal micro-switches across the common RF bands combined with their low bias power and physical compactness makes them attractive for the function of RF routing in the front-end of many systems
RF Switch BPF Antenna
RF LNA Switch
Ch 1
RF
Ch 2
RF
• • •
Ch n SPnT selector
• • •
Mixer
RF SPnT selector
LO
Figure 1.14 Radio front-end preselector architecture.
A typical example is the radio front-end, as shown in the block diagram of Figure 1.14. This is a type of radio that must operate simultaneously with other RF transmitters at the same physical site. In this case, there is a strong tendency for “cosite” interference, which requires very high dynamic-range receivers, very clean transmitters, and careful attention to the overall electromagnetic compatibility. This generally requires filters on each transmitter and receiver to ensure that cross interference or signal jamming is minimized. The filters must have a narrow instantaneous pass-bandwidth, high rejection out-of-band, wide tunability, and low insertion loss. Due to the great difficulty, if not impossibility, in achieving all of these filter characteristics simultaneously over many radio channels, the practical solution is to decompose the filtering task. The entire spectrum to be covered by the radio is divided into several independent channels, each of which has a filter of achievable instantaneous bandwidth, rejection, tunability, and insertion loss. RF switches are then required at the input of each channel to connect to the antenna. Simultaneously, switches at the output of each 31
channel must connect the output to the receiver or transmitter electronics. Altogether, the network of switches and filters shown in Figure 1.14, which is called a frequency preselector, is often very massive, power consuming, and expensive. A good example of such a front-end is the ARC-210 multimode integrated communication system [10,41], probably the premier radio today for military airborne communications in the VHF and UHF bands between 30–400 MHz. It comprises five independent channels at: 1) 30–88 MHz; 2) 108–136 MHz; 3) 136–156 MHz; 4) 156–174 MHz; and 5) 225–400 MHz, four of which can be scanned. Among other characteristics, it has a front-end noise figure of 4.5 dB, a 1-dB-output compression of 14 dBm, and a 75 µs tuning time over 160-kHz steps. Most of the RF switching in the ARC-210 is done by 27 p-i-n diodes, each of which consumes many milliwatts of power and provides less-than-desirable isolation. The superior isolation of the MEMS switches (in combination) should improve the transmit/receive isolation from 60 to 80 dB, with commensurate reduction in intermodulation distortion. The lower insertion loss of the MEMS should reduce the front-end noise figure from 4.5 to 4.0 dB. Also, the lower power dissipation of the MEMS should reduce the total power consumption from roughly 100 mW to less than 1 mW. The frequency preselector architecture of ARC-210 is rather generic and could apply to a variety of future radio and wireless systems. A related question is the stability of the tunable filters, which is being addressed by the development of high-Q tunable MEMS filters. Very promising solutions have been proposed for the required bands and higher basing on a MEMS LC tank filter in which both the inductor and capacitor are made by surface micromachining techniques [42]. It can be observed that the considerations above neglect the outstanding development of MEMS tuned bandpass filters in the past few years and focus on the series switch application only. Indeed recently demonstrated results [43-48] allow some optimism about even more pushed integration of the MEMS technology in front-end systems, such that different kind of MEMS components are actively used for a direct reconfiguration of the RF bandpass filter frequency response. This would eventually allow to replace the whole preselector by a single MEMS tunable bandpass filter with the consequent circuitry simplification that can be appreciated from Figure 1.15. 32
Antenna
MEMS Tunable BPF
LNA
Mixer
RF
LO Low-noise tunable RF section
Figure 1.15 Front-end circuitry simplification with MEMS based tunable filter.
II.3.2 RF MEMS in phased antenna arrays and phase shifters.
One of the more ubiquitous control functions at microwave and millimeter-wave frequencies is phase shifting. For example, it is essential to the operation of phase-lock loops and phased array antennas in receivers and transmitters. MEMS switches benefit RF phaseshifting technology in a number of ways (Figure 1.16). Traditional solid-state switches such as p-i-n diodes and FET’s introduce cost, performance, or bias-power problems in the typical arrays used for radar and communications (thousands of antenna elements). P-i-n diodes have low insertion loss, but consume great bias power and are not readily integrated with their bias and other RF electronics. Although much more integrable, FET’s have higher insertion loss because they are not very good resistive (on/off) switches. At microwave frequencies, the finite On-state resistance typically leads to an insertion loss of 1 dB and, because at least one switch is required for each bit in the timedelay phase shifter, at least half of the transmit power is lost to the switches alone, not accounting for transmission-line and other losses. RF-MEMS switches are promising because they can simultaneously provide the RF performance (low insertion loss and high isolation) comparable to or better than p-i-n diodes, the circuit integrability of FET’s, and a bias power consumption much less than either. It has been shown that 2 and 4-bit phase shifters can be realized achieving extremely low insertion 33
loss performance (insertion loss <2 dB) at 18 GHz [49]. Distributed MEMS transmission line phase shifters additionally provide high miniaturization and very wideband (0-60 GHz) designs [50-55] with an improved power handling capability.
transceiver
MEMS Switched capacitor Antenna
T/R
T/R • • •
T/R
(a)
(b)
• • •
• • •
MEMS controlled capacitance Z0 ,β ,l
• • •
• • •
Z0 ,β ,l
(c) Figure 1.16 (a) a MEMS phased antenna array. (b) time delay switched line phase shifter [54]. (c) a distributed MEMS transmission line (DMTL) phase shifter [52].
It can be observed that the relatively slow switching speed of the MEMS switches does not necessarily hinder the system performance in such arrays. For example, when used
34
for beam steering in long-range radar or communications systems, the phase shifters are usually adjusted on time scales of microseconds or longer.
III Conclusion
This chapter is intended as an intuitive introduction to micro-electromechanical systems technology for RF and microwave applications. Indeed, the application fields that currently benefit from this relatively young technology are continuously expanding, and some of the most promising examples were presented. MEMS had deep impact on microwave communications since the advent of RF electrostatic micro-switches. Then particular consideration was given to these components by summarizing their common configurations and analysing their electromechanical behaviour. MEMS variable capacitances also represent an important development area and the typical varactor architectures and characteristics were presented. This allowed introducing the RF MEMS components major advantages in terms of miniturization, electric performances, power consumption and linearity. The main drawbacks and concerns about MEMS packaging requirements, switching time, power handling capability and reliability were also discussed. Finally the introduced properties were considered from a system point of view, providing an insight on the integration of MEMS components to recently developed phased antenna arrays, phase shifters and reconfigurable front-end subsystems. Hence, Chapter 1 defines the context of this thesis work that will be essentially oriented in a twofold direction: to exploit the MEMS technology potential for reconfigurable operations in tunable and multiband front-end systems; to develop solutions improving the reliability of MEMS switched capacitors in high power conditions.
35
36
CHAPTER 2
A 2-pole lumped element programmable filter with MEMS digital capacitor banks
37
38
A 2-pole lumped element programmable filter with MEMS digital capacitor banks
Last generation wireless and radar communication systems show increasing interest in reconfigurable networks notably targeting on high sensitivity and low complexity receivers. RF MEMS components offer ideal tuning solutions in front-end subsystem design due to linear, high-Q, low intermodulation behavior and virtually no DC power consummation. Indeed MEMS based filters, reconfigurable both in bandwidth and in central frequency, have been successfully developed relying on capacitive or Ohmic switches [56-59]. Recent researches have been addressed to pseudo-digital frequency tuning [58-59], which increases immunity to noise deriving from electrical noise in the biasing network, reduces temperature sensitivity and allows better performances reproducibility. This is typically based on tunable capacitor banks where MEMS switches are connected in series with metal-air-metal (MAM), or metal-insulator-metal (MIM) capacitors resulting in a discrete capacitance variation (Figure 2.1).
Variable C bank
MEMS switch1
C1 (BIT1)
MEMS switch2
C2 (BIT2)
MEMS switch3
C3 (BIT3)
Intrinsic capacitance C0
air
MAM fixed capacitors or MIM fixed capacitors metal
insulator
Figure 2.1 Principle of MEMS switch digital control over a discrete tunable capacitor bank. 39
Most results available today concern MEMS bandpass filters on silicon, quartz or glass substrate. However considerable research and industry efforts are currently focusing on transfer of MEMS technology to alumina substrates which would allow extremely compact and low loss design. Furthermore this would increase the already remarkable integration potential of MEMS components to microwave subsystems, since a variety of receiver and oscillator subsystems is realized on ceramic substrates.
This chapter deals with the development of a new 2-pole reconfigurable filter on alumina substrate for applications in the L and S bands. Hence a simple and original approach was first followed for fast synthesis of multiple filtering characteristics and is presented in the first part of the chapter. The next section focuses on the design of a microstrip network on alumina that was optimized to implement programmable filtering functions. Finally the reconfigurable filter was fabricated and tested in order to validate the proposed approach, and measurement results are presented and discussed in the last part. The 2-pole reconfigurable filter uses a coupled resonator architecture with lumped tunable LC resonators. The lumped elements approach gives compactness, makes design intuitive and prevents problems with spurious harmonics that typically affect distributed solutions. The multi-coupled resonator architecture exploits ideally the integration potential of MEMS components to planar structures since MEMS tunable capacitances can be easily employed to control the electric coupling and the resonance frequency of multiple microstrip resonators. This generally results in very flexible microstrip networks that can perform complex tuning operations with simple MEMS ohmic switch control [60] and relatively low technological complexity.
I Coupled resonator filters: general principles
Coupled resonator circuits are extensively used in microwave/RF filters design, especially for narrowband filters where microwave resonant structure as waveguide or cavity resonators can be conveniently represented by lumped element circuits. Then a very versatile 40
design is possible since the filter implementation does not depend on the resonator physical structure. General synthesis techniques have been developed based on coupling coefficient of inter-coupled resonators and the external quality factors (Qe) of the input/output resonators [61-64]. The following analysis focuses on a 2-coupled resonator network, although similar relations and principles hold for n-coupled resonator circuits [62]. This results in relatively simple synthesis and implementation of a 2-pole reconfigurable filter, so that the proposed approach can be rapidly validated.
E1·E2
H1·H2
coupling Resonator 1
Resonator 2
E1 H1
E2 H2 ε µ
V
Figure 2.2 Two-coupled microwave resonators in a V volume with ε permittivity and µ permeability [62].
A pair of coupled microwave resonators can be outlined as in Figure 2.2, where the uncoupled resonators can be different in structure and have different self-resonant frequencies. The coupling coefficient is defined as the ratio:
M =
=
coupled energy stored energy in uncoupled resonators
∫
V
∫
V
ε E1 ⋅ E 2 dV 2
2
ε E1 × ∫ ε E 2 dV V
Electric coupling
+
∫
V
∫
V
=
(1)
µ H 1 ⋅ H 2 dV 2
2
µ H 1 × ∫ µ H 2 dV V
Magnetic coupling
From (1) it appears that coupling is mathematically described by the dot product of field vectors. Then it can either be positive or negative sign, depending on the sign of dot products. 41
A positive sign means that coupling enhances the stored energy of uncoupled resonators, whereas a negative sign implies that the stored energy of uncoupled resonators is reduced. It is also clear that coupling coefficient can be computed from (1) only if a solution for the fields in the V space is known. Alternatively it is possible to evaluate the coupling coefficient directly from the circuit frequency response, regardless the structure of physical resonators [62]. This will be shown below for the 2-coupled resonators network.
I.1 2-coupled resonator network
In this section an electrically coupled-resonator circuit is considered, featuring a pair of parallel LC resonators as in Figure 2.3. Electric coupling occurs by means of mutual capacitances between the resonators and is suitable for a physical implementation based on MEMS tunable capacitances. This provides effective and simple control over the network coupling coefficients while magnetic coupling control, that exploits tunable inductors is generally complex, bulky and expensive to implement. The resonators are intended to be identical and hence called synchronously tuned, meaning that they resonate at the same frequency ω0=1/ LC . However similar results are obtained for magnetically coupled resonator circuits, series resonators and even asynchronously tuned circuits [62].
Cm
L1 = L2 = L L
C
C
ω0 =
L
C1 = C2 = C
1 LC
Figure 2.3 Electric coupling of two synchronously tuned resonators.
The mutual interaction between resonators due to electric coupling can be described in terms of loop currents. Thus the jωCVi terms in Figure 2.4 represent the C self-capacitance currents, while the jωCmVi terms are the induced currents resulting from coupling.
42
Cm
I1
I2 I1 = jωCV1 − jωCmV2
C V2
V1 C
jωC [I]= [Y]·[V] [Y ] = − jωC m
I 2 = jωCmV1 − jωCV2
− jωC m jωC
Figure 2.4 Loop currents formulation for the electric coupling of two resonators.
By expressing the currents in matrix form, the associated admittance [Y] matrix can be easily found for the 2-coupled capacitances and the network theory allows deriving an equivalent П–network (Figure 2.5) that represents the electric coupling explicitly:
Cm C
-y12 y11+y12
C
Cm y22+y12
C-Cm
C-Cm
Figure 2.5 Admittance matrix formulation for the electric coupling of two resonators.
In the last circuit on the right, an inner П–network can be isolated which depends on Cm only and is recognized to implement an admittance inverter J=ωCm. These equivalencies can be applied to the 2-coupled resonator network as in Figure 2.6 and a connection to the classical bandpass filter section [65] with parallel resonators and admittance inverters is established. This is often exploited for filter synthesis as explained in section II.
Cm
Cm J=
L
C
C
L
L
L
L
C ωCm C
L
C-Cm Figure 2.6 Coupling equivalent circuit as an admittance inverter.
43
It is also of interest to consider a further equivalent form for the coupled resonator network that exploits its symmetrical configuration. This allows to derive some interesting properties as the circuit characteristic resonance frequencies and the coupling coefficient [62]. Indeed two special kinds of excitation can be considered for such a network, normally referred to as the even mode and the odd mode, and any arbitrary excitation can be reduced to a linear combination of even and odd modes. In the even mode the two resonators undergo purely symmetrical excitation, which corresponds to replacing the symmetry plane by an open circuit or a magnetic wall. The resulting circuit is visible in Figure 2.7, and resonates at the characteristic frequency feven which is higher than resonant frequency for the single resonator, f0. This means that the charge storing capability decreases for the coupled structure when undergoing even excitation.
2Cm 2Cm
+V L
I=0 C-Cm V=0 C+Cm
+V -V
C-Cm C+Cm
L
+V
f even = L
C-Cm C+Cm
f odd =
1 > f0 2π L(C − Cm ) 1 2π L(C + C m )
< f0
Figure 2.7 Even and odd excitation.
In the odd mode the two resonators undergo the same amplitude but opposite sign excitation, that corresponds to replacing the symmetry plane by an electric wall or a short circuit. The resulting circuit is also shown in Figure 2.7, and resonates at the characteristic frequency fodd which is lower than resonant frequency for the single resonator, f0. This means that the charge storing capability increases for the coupled structure when undergoing even excitation. Now the ratio in equation (2):
1 C V2 2 2 coupled electric energy − f odd f even Cm 2 m = = = 2 2 1 C stored energy uncoupled resonator f even + f odd CV 2 2
(2)
44
corresponds exactly to the definition of coupling coefficient (1) so that the electric coupling coefficient is recognized to be:
M =
2 2 − f odd f even C = m 2 2 C f even + f odd
(3)
For practical operations the coupled resonator network is connected to external feeding lines and an equivalent circuit can be considered as in Figure 2.8, where GS=GL=G is the external conductance that is assumed to load the LC lossless resonators. The two resonators are also the Input/Output (I/O) resonators and their external quality factor is:
Qe =
ω0C
(4)
G
Cm
Is
Gs II
L
C
V1 V2
C
L
GL=G
G
Figure 2.8 2-coupled resonator circuit considering feeding .
The resulting Figure 2.8 network is analysed in more detail in section A1, where its admittance and scattering matrix are computed in order to derive the circuit filtering properties. From Figure 2.8 it can be noticed that the conductance G corresponds to the network admittance level that is a key parameter for practical realization of the filter. Indeed gaining physical control over the G level is generally essential to provide physical feasibility for all the reactive components. For example, when dealing with synthesis of multiple filtering 45
functions, it can be convenient to impose a different G level for any different function to implement. This allows to scale the network such that it keeps a constant inductance value regardless the filtering function performed. Therefore no multiple or tunable inductors are needed and the reconfigurable filter can be realized with a single and simple architecture. The L value is additionally chosen relatively large (L>2nH) in order to obtain compact LC resonators with feasible capacitors (C<3.5pF). On the other hand, an impedance transformer is needed to match the variable 1/G impedance at I/O of the filter to the Z0=1/G0=50 Ω typical feeding lines. Tunable impedance transformers can be implemented also relying on MEMS controlled capacitances and are efficiently employed to couple energy from external lines while performing tunable matching. Admittance inverters similar to the one in Figure 2.1 could ideally accomplish the impedance transformation shown in Figure 2.9, where n is the ideal transformer ratio and Cinid = G0/nω0 .
1:n G0
Cm L
C-Cm
n:1 L
G0
Cm J= G0
ω 0Cin
J= L
C-Cm
L
ω0Cin
G0
Figure 2.9 Impedance transforming for the filter in Figure 2.8.
Nevertheless the external negative -Cinid capacitances are unsuitable for practical realization. On the other hand the inverter configuration visible in Figure 2.10 is equivalent to the ideal one around ω0 and is physically realizable, since the -Cp capacitance can be absorbed by C-Cm. The critical coupling condition can be easily computed from network 46
theory such that the Yin admittance seen by the filter looking into the real transformer equals the Yinid admittance seen looking into the ideal transformer and sets:
Cin =
G0
G G0 − G
ω0
Cp =
1
ω0
G(G0 − G)
(5)
Cin
1:n J= G0
G0
G0
ω 0Cin id
-Cp
Yin id
Yin
Figure 2.10 Practical impedance transformer realization.
When the I/O transformers are integrated to the coupled resonator reactive core, a complete and feasible 2-coupled resonator filter is obtained as shown in Figure 2.11, where Cr=C-Cm-Cp is the total resonator capacitance.
Cin
Cin
Cm
Cin1,Cm1,Cr1
IS
G0
L
Cr
Cr
L
G0 Cin2,Cm2,Cr2 Cini,Cmi, Cri
f1 f f2 fi
f f
Figure 2.11 Lumped elements final model for the programmable filter.
It can be noticed that the filter key parameters Qe, M, and G are directly controlled by Cin, Cm and Cr capacitive components that can be implemented by MEMS tunable capacitance in order to provide reconfiguration of the filter frequency response. More precisely, MEMS based capacitor banks will be used to provide discrete capacitance variation for Cin, Cm and Cr components, in a fixed range. This results in different sets of possible 47
values for Cin, Cm and Cr capacitances (see Figure 2.11), that can be selected in order to implement different filtering functions. The sets of capacitive values corresponding to the desired filtering characteristics are synthesized in advance by the simple technique described in the next section. In practice, by properly choosing the associated capacitive values, the filter can be programmed to perform a variety of frequency responses with great degree of flexibility in central frequency and bandwidth parameters. The physical implementation of MEMS capacitor banks providing the synthesized capacitive values will be addressed in section III.
II Synthesis of multiple filtering functions
A synthesis procedure is tailored to the filter of Figure 2.11 considering the assumptions below and a few simple relations. For a matrix formulation of this procedure that is suitable for automatic implementation, the reader is referred to section A1.
The desired response is specified in terms of its central frequency ω0, the fractional bandwidth FBW and the scattering parameters at ω0 (in practice due to the lossless condition it is sufficient to specify either |S11(ω0)| or |S21(ω0)|) . The system unknowns are 3: C, Cm and G. The inductance L =2.6 nH is chosen among commercially available components, while the impedance-scaled filter Cin, Cr parameters are easily derived by (5) from C, Cm, G and G0=1/50 Ω-1.
A first obvious equation is provided by the resonance frequency of the LC shunt resonators ω0=1/ LC . A second relation is found by considering the MQe product from (34), that can be expressed as a function of the S11(ω0) parameter only :
MQe =
ω0Cm G
= f [S11 (ω 0 )] ⇒ C m =
G
ω0
⋅
1 + S11 1 − S11
(5)
48
This is analytically shown in section A1 and is intuitive since at resonance the reactive admittance of shunt LC resonators in Figure 2.8 is zero and the return loss is determined by Cm and G only. Finally, the last relation needed comes from the specified bandwidth. Indeed the system is a second order one and there is a well known relation between the uncoupled resonator external quality factor Qe and the system bandwidth FBW . For example for a Chebyshev 2nd order response:
Qe =
g 0 g1 FBW
(6)
where g0 and g1 are the Chebyshev coefficients that essentially depend on the insertion loss parameter (S21(ω0)). In section A1 a general expression is derived, that relates Qe to FBW through a function of the MQe product:
Qe =
1 1 f ( MQe) = f ( S 21 ) FBW FBW
(7)
Hence, all the filter physical parameter corresponding to the desired filtering function can be now derived. From network theory and (4-5) it is also possible to express directly the external quality factor and the coupling coefficient as a function of the Cin, Cr, Cm parameters in the final filter architecture of Figure 2.11.
Cr + Cm + Qe = ω 0
Cin 2 1 + QIN 2 IN
Q G0 2 1 + QIN
M =
Cm Cin Cr + Cm + 2 1 + QIN
QIN =
ω 0 Cin G0
(8)
where ω0 is a function of Cin, Cr, Cm also, as determined in A1. This allows evaluating how the tunable components affect the 2-pole filter frequency response. For example, if two 49
identical LC resonators are coupled at ω0=2π*2GHz with a FBW=10% and the desired return loss is 15 dB, then from (5-8):
C=
1
ω 02 L
Qe = 17
= 2.436 pF C m = 1.711 pF G = 1 / 557Ω M = 0.0702
Cin = 0.5 pF
Cr = 1.806 pF
and the system frequency response is represented in Figure 2.12 where a comparison with a standard Chebyshev bandpass filter is performed. The influence of Cin, Cr, Cm parameters over the filter frequency response can be inferred from Figure 2.13. 0
S-parameters
-10 ) 1 2 2 ht -20 S s( BB d d -30
FBW=10%
-40
Chebyshev protot Coupled res. filter
-50
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
Frequency (GHz) freq GHz
Figure 2.12 Frequency response for the filter in the example and comparison with a Chebyshev bandpass prototype. 30
20
Coupling coefficient: M
Quality factor: Qe
25
0.2
Critically coupled equiripple responses Over-coupled I/O
Cr=2.48 Cm=0.28 Cr=1.81 Cm =0.17
15 10
(Fig.2.12):
5
Cin=0.5 Qe=17.0
0 0.3
0.4
Under-coupled Cr=1.38 Cm=0.11 I/O 0.5
0.6
Cin (pF)
0.7
0.8
Cin=0.37 Cr=1.38
Critically coupled equiripple responses
0.15
Over-coupled Cin=0.5 Resonators Cr=1.81
0.1
Cin=0.71 Cr=0.17 (Fig.2.12):
0.05
0 0.1
Cm=0.17 M=0.07
Under-coupled Resonators 0.15
0.2
0.25
0.3
0.35
Cm (pF)
Figure 2.13 Qe and M parameters variation as a function of Cin and Cr.
50
TABLE I PROGRAMMABLE FILTERING FUNCTIONS f0 BW (GHz) (GHz) 1.50 0.2 1.60 0.2 1.70 0.2 1.80 0.2 1.90 0.2 2.00 0.2 2.1 0.2 2.2 0.2 2.3 0.2 2.00 0.4 2.00 0.2 2.00 0.1 1.9 0.3 2.0 0.4 2.1 0.5
FBW (%) 13.33 12.50 11.76 11.11 10.53 10.00 9.52 9.09 8.70 20.00 10.00 5.0 15.79 20.00 23.81
1/G (Ω) 313 357 402 451 502 557 614 674 736 278 557 1113 335 278 245
C (pF) 4.33 3.81 3.37 3.01 2.70 2.44 2.21 2.01 1.84 2.44 2.44 2.44 2.70 2.44 2.21
Cm (pF) 0.41 0.33 0.28 0.23 0.20 0.17 0.15 0.13 0.11 0.34 0.17 0.09 0.30 0.34 0.37
L (nH) 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6
Qe
M
12.8 13.63 14.5 15.3 16.1 17.0 17.9 18.7 19.6 8.5 17.0 34.1 10.8 8.5 7.1
0.0937 0.0878 0.0826 0.0780 0.0739 0.0702 0.0669 0.0639 0.0611 0.1405 0.0702 0.0351 0.111 0.1405 0.1672
Cin (pF) 0.91 0.80 0.71 0.62 0.55 0.50 0.45 0.41 0.37 0.74 0.50 0.35 0.70 0.74 0.77
Cr (pF) 3.15 2.78 2.48 2.22 1.99 1.81 1.65 1.50 1.38 1.48 1.81 2.02 1.80 1.48 1.23
The computed parameters are reported as reference in the 6th row of Table I. The presented approach was then employed for synthesis of all the frequency responses shown below. This essentially aims at demonstrating different tuning mechanism for the 2-pole filter frequency response. Therefore several filtering characteristics are synthesized in order to exhibit constant insertion loss/return loss levels at ω0, for different ω0 and/or FBW values. A first set of 9 filtering functions is synthesized to cover uniformly the1.5-2.3 GHz band with constant absolute bandwidth BW=0.2 GHz. Thus FBW=BW/f0 varies as 1/ω0 while Qe increases with ω0 . The resulting responses extend over the frequency axis with invariable insertion loss and return loss profiles, or equivalently frequency tuning of the same response is performed over the chosen band. This can be seen in the first 9 rows of Table I, while the resulting functions are represented in Figure 2.14. 0 -10 )) 3, 3( S( -20 B d -30
S-pram. (dB)
)) 3, 2 4( S( SB Bd
-40 1.3
1.5
1.7
1.9
2.1
2.3
2.5
Frequency (GHz) freq, GHz Figure 2.14 Multiple response synthesis: frequency tuning. 51
Next, 3 different responses are synthesized in order to achieve larger and narrower FBW around the constant ω0 =2π·2GHz reference frequency. Then Qe varies as 1/BW, C keeps constant, and bandwidth is directly controlled by the coupling capacitance Cm value while keeping the other filtering properties unchanged. This implements bandwidth tuning of the response around the chosen frequency. The corresponding parameters are visible in the rows 10-12 of Table 1, while the bandwidth tuned characteristics are represented in Figure 2.15.
0 )) -10 1 2, 2 2( -20 S( B d -30
S-pram. (dB)
)) 1 2, 2 1 2( S S( BB d
-40 1.5
1.7
1.9
2.1
2.3
2.5
Frequency (GHz) freq, GHz Figure 2.15 Multiple response synthesis: bandwidth tuning.
Finally frequency and bandwidth tuning can be combined for example such that ω0 and FBW increase linearly together. This is referred to as mixed tuning and the corresponding curves are reported in the last 3 rows of Table 1 and appear in Figure 2.16.
S-pram. (dB)
0 -10 -20 -30 -40 1.5
1.7
1.9
2.1
Frequency (GHz)
2.3
2.5
Figure 2.16 Multiple response synthesis: mixed tuning.
52
III Lumped tunable resonators microstrip design
The 2-pole reconfigurable filter exploits MEMS series ohmic switches [67] to obtain discrete capacitance values from five lumped capacitor banks. In addition, a couple of surface mounted (SM) inductors combine with two of the capacitor banks, resulting in a pair of tunable lumped high-Q resonators. As a consequence of the lumped elements design approach Cin, Cr, Cm, L circuit parameters find very intuitive implementation in microstrip technology, and there is no need to approximate the LC resonators by transmission line sections. The filter is designed on 256 µm thick alumina substrate, the SM inductors are commercially available and optimized for high-Q performance (Coilcraft, L=2.6 nH, Q=156 @ 1.7 GHz) and the lumped capacitor banks are also designed to achieve a high Q value [60]. MEMS switches are assigned a logical function, either connecting or not several fixed capacitors (bits), to result in different discrete capacitance values (see Figure 2.1). Thus each variable capacitor is based on the series combination of MEMS ohmic switches and MAM capacitors for Cin and Cm banks, or MIM capacitors for Cr banks. The combination between MAM or MIM bits and MEMS ohmic switches is shown in Figure. 2.17. This also illustrates how MEMS switches are regrouped in pairs or triplets to reduce ohmic contact loss.
RF Input RF Input MAM series capacitor MEMS air bridge
MIM capacitor to GND RF Output
Figure 2.17 MEMS ohmic switches control over a series (shunt) MAM (MIM) capacitor.
Capacitor banks with N bits are controlled by N independent pairs or triplets of switches and theoretically provide 2N possible capacitive states if the bits have N different 53
capacitive values or “weights”. This is easily achieved by introducing slight differences in the bits geometrical parameters. For example, in Figure 2.18 the Cm capacitor bank is represented where different weights are achieved by modulating the surface area (Ai) of the lower electrode of MAM series capacitors. When MEMS switch pair controlling the ith bit is activated, the bit combines in parallel with the fixed bit-0 capacitor and a capacitive term is added to the global Cm value, proportionally to the ith bit weight (Ai). The different weights are chosen such that the whole set of bit combinations results in a picewise linear capacitance variation, as visible in Figure 2.18. The achievable capacitance values as well as the capacitor bank quality factors can be extracted by EM simulations of the structure in Figure 2.18 that allow determining the capacitor impedance ZCm. A series contact resistance RDC =1Ω is assumed for the switches and the resulting Q value is higher than 360 at 2GHz for all bit combinations. The EM simulated range of variation for Cm capacitance includes the required 112-405 fF range reported in Table I, although the intermediate values cannot be achieved because the 3 bit bank only provides 23 states. Nevertheless, when the Cm bank is combined with Cin and Cr banks, the effective Cm capacitor impedance is affected by the interaction with other capacitive banks since inter-capacitor connections have non-zero electrical length. Thus the actual Cm value achieved turns out to depend on Cin and Cr values. This eventually provides additional capacitive states that are exploited to implement the whole set of filtering functions. On the other hand the synthesis of the desired capacitive values requires EM global optimization of all banks simultaneously, which is often a hard task. 450
A2
A1
Capacitance (fF)
A3
A0
374
415
330 270
ZCm (2GHz)
228
250
172 135 62 B0 0 1
B1 B0 2
B3 B0
B2 B0
B3 B1 B0
3
4
5
B2 B1 B0
B3 B2 B0
B3 B2 B1 B0
6
7
8
Bit combination
Qe =
Im( Z Cm ) Re al ( Z Cm )
Figure 2.18 Different bit configuration in the Cm capacitor bank and picewise linear capacitance characteristic obtained for the Cim bank when considered separately.
54
Cin: fixed MAM cap.
Cin: BIT1
Cin: BIT2
Cin: BIT3
Cm: BIT3
Cr: BIT3
Cm: BIT2
Cr: BIT 2
Cm: BIT1
Cr: BIT 1
Cr: fixed MIM capacitor
Cm: fixed MAM cap.
Figure 2.19 Different kinds of capacitor banks implementing variable capacitances in the Figure 2.11 model.
Figure 2.20 shows how Cin, Cm and Cr banks, that all combine a fixed capacitor with 3 MEMS controlled capacitive bits, are integrated in the overall microstrip structure. Indeed EM simulations proved that a very large number of capacitive configurations or “states” can be virtually achieved for this network, which is theoretically sufficient to implement all the filtering functions of Table I However, full-wave optimization efforts were addressed at implementing only a limited set of them [12], that still reproduces the 3 tuning mechanisms illustrated in section II. The optimization process essentially consists of tailoring the microstrip stubs for MAM and MIM capacitors in order to achieve the desired capacitive performance while minimizing the inductive parasitic effects and radiation loss. The SM inductors effect is taken into account by hybrid ADS simulations as outlined in Figure 2.20, and some additional optimization is required. It is worth mentioning that the synthesized geometry for the whole filter is strongly affected by the Coilcraft inductors size and shape. Indeed, as can be appreciated from Figure 2.20-21, capacitor banks are tailored to the SM components in order 55
to obtain very compact tunable resonators. Furthermore the inductors bonding pads are exploited as shunt MIM capacitors, which typically provides a large intrinsic capacitance value for Cr. Coilcraft S-param.
P6 P1
P3
P5
P4
P6
P4 P3 P2 P5
P1 Momentum Simulated S-param.
P2
Figure 2.20 Integration of the Coilcraft SM inductors in the global EM simulations.
Cm
Cin
L
Cr
Cin
Cr
L
8mm
Figure 2.21 Micro-photograph of the fabricated filter showing the SM inductors impact on the global size.
Finally, Figure 2.22 reports details of the filter biasing network. The bias line ends in a bias pad and includes an integrated resistor that aims at reducing parasitic coupling between the MEMS switches and the biasing system. Integrated resistors are also employed to apply DC potential between different bits and minimize RF signal leakage in the biasing network. It should be noticed from Figure 2.20-2.22 that the number of components included in such a biasing network is considerable. This results in high sensitivity of the filter electric performance to the biasing resistance value that is actually achieved by the fabrication process and will be later discussed in more detail.
56
Bias pad Bias resistor
MEMS ohmic switches Pull-down electrode
Bias line
BIT DC connection resistor
Figure 2.22 Biasing network in the vicinity of MAM capacitors of Figure 2.17.
0
S11 (dB)
S21 (dB)
0
-20
-20
Frequency tuning
-40 1.3
1.5
1.7
1.9
2.1
Frequency (GHz)
2.3
-40
2.5
1.3
(a)
0
1.7
1.9
2.1
Frequency (GHz)
2.3
2.5
0
-20
S11 (dB)
S21 (dB)
1.5
-20
Mixed tuning BW tuning
-40
-40
1.5
1.7
1.9
2.1
Frequency (GHz)
2.3
2.5
1.5
(b)
1.7
1.9
2.1
Frequency (GHz)
2.3
2.5
Figure 2.23 EM-simulated S-parameters for the reconfigurable filter: (a) Frequency tuning. (b) Bandwidth and mixed tuning.
Hence 9 states between 1.5 and 2.3 GHz are optimized for trying out frequency tuning with constant 10% FBW and are visible in Figure 2.23 (a). This allows achieving 0.1 GHz 57
frequency resolution and 40% overall tunability if the reference state is the 2 GHz one, according to circuit simulations. As for bandwidth tuning an additional state is optimized in order to achieve 20% FBW at 2 GHz and appears in Figure 2.23 (b). Finally this state combines with two more states, at 1.9 and 2.1 GHz in order to reproduce the last 3 states of Table 1 and try out mixed tuning, as in Figure 2.23 (b).
IV Fabrication
The fabrication process main steps are summarized in Figure 2.24. The circuits have been fabricated on a 256µm mirror polished alumina substrate graciously provided by Alcatel Alenia Space. The back side metallization is made with a 3µm thick electroplated gold. Then, 1 kΩ/square SiCr resistors are thermally evaporated on the front side and patterned using a lift-off technique. This is followed by a 200/1000 Å Cr/Au layer evaporation to form the filter biasing network (a). In the next step, a 3500 Å thick PLD (Pulsed Laser Deposition) Alumina insulating layer is deposited and patterned to protect the biasing network (b). Then, a 200/1050 Å Cr/Au layer is evaporated and electroplated to increase the final thickness up to 1 µm, in order to form the filter first metallization layer and the switch contact fingers (c). Next, a 1.8 µm thick polymer is used as a sacrificial layer for the MEMS cantilevers and patterned in two steps to form the dimples (d). The second metal layer used for the MEMS structure is created by first evaporating a seed layer of Ti/Au (100/1500Å) and then electroplating up to 3 µm to obtain stiff cantilevers structures and low loss metalization (e). Once the second metal layer is patterned, each filter is individually diced using a precision wire saw in order to isolate the circuits to be measured (f). Then the sacrificial layer is removed to release MEMS devices (g). Finally the SM inductors are aligned and bonded to their pads by means of a silver epoxy glue. The same epoxy is exploited to place the circuit on a metallic support for measurement and to realize via connections to ground for the inductors and the I/O CPW to microstrip transitions (h).
58
Pull-down electrode
Insulating layer
evaporated Cr/Au
Al2O3
PLD Al2O3
SiCr electroplated Cr/Au
(a) 1st metal layer
(b) Sacrificial layer Dimples
Contact
(c) 2nd metal layer
(d) Circuit cutting evaporated Ti/Au
(f)
(e) Releasing
(g) Grounding
SM inductor Via CPW/microstrip transi tion
conductive epoxy glue
(h)
Metallic support
Via I/O
Figure 2.24 Fabrication process steps.
59
V Measurement results
Measured insertion loss and return loss are shown in Figure 2.25-27 and summarized in Table II. Measurements are performed on wafer by a Single-Open-Load-Thru (SOLT) calibration technique which includes loss due to I/O CPW to microstrip RF transitions.
0
0
-20
S11 (dB)
S21 (dB)
-10
-30 -40 -50 -60
-10 -20 -30 -40
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
Frequency (GHz)
Frequency (GHz)
Figure 2.25 Measured S-parameters: frequency tuning.
q, 0
0
-20
S11 (dB)
S21 (dB)
-10
-30 -40 -50
-10 -20 -30 -40
-60 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
Frequency (GHz)
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
Frequency (GHz)
Figure 2.26 Measured S-parameters: bandwidth tuning.
60
0
0
S11 (dB)
S21 (dB)
-10 -20 -30 -40 -50 -60
-10 -20 -30 -40
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
Frequency (GHz)
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
Frequency (GHz)
Figure 2.27 Measured S-parameters: mixed tuning.
The insertion loss ranges between 2.9 dB, for the broadband state at 2.03 GHz , and 5.9 dB for the lowest frequency state at 1.51 GHz. The reflection loss is always better than 14 dB. Table II compares ideal and measured central frequencies f0 , so that measured states can be directly related to the simulated states of Table I. This shows that the fabricated filter performs correctly the programmed tuning operations. The measured filtering functions distribute over the frequency axis in very good agreement with circuit and EM simulations. The midband frequencies shifts observable from Table II never exceed 2.4 %. The reference state is located at 1.98 GHz with 10.5% FBW which is very close to simulated results. As the frequency tuned states are concerned (Figure 2.25), the measured FBWs are generally close to simulated ones, although a bit broader for higher frequency states. This only provokes moderate drift in the extracted Qe and M values. The highest frequency state turns out to be at 2.26 GHz and sets the overall tunability to 37.5 % which is pretty close to the theoretical value. The bandwidth tuning performance is conform to EM simulations and can be observed from Figure 2.25 where the reference state is compared to the larger 0.4 GHz BW state at 2.03 GHz. As for mixed tuning the measured functions are visible in Figure 2.26 and show particular good agreement with simulated f0, BW, Qe parameters. Next section provides simple interpretation of the measured insertion loss performance by modeling the biasing network influence.
61
TABLE II MEASURED FILTERING FUNCTIONS f0 SIM. (GHz) 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.00 2.00 1.90 2.00 2.10
f0 MEAS. (GHz) 1.51 1.60 1.66 1.81 1.88 1.98 2.14 2.18 2.26 1.98 2.03 1.90 2.03 2.14
BWSIM (GHz) 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.4 0.5
BWMEAS. (GHz) 0.17 0.2 0.21 0.22 0.27 0.20 0.21 0.21 0.22 0.20 0.40 0.33 0.40 0.46
FBW (%) 11.25 12.50 13.00 12.43 14.36 10.52 10.00 9.63 11.28 10.52 19.7 17.63 19.7 21.5
S21(f0) (dB) -5.9 -4.9 -5.1 -4.1 -4.3 -4.3 -5.3 -5.5 -5.5 -4.3 -2.9 -3.2 -2.9 -3.5
S11(f0) (dB) -14.3 -16.0 -15.7 -14.9 -17.4 -15.4 -14.7 -15.5 -14.7 -15.4 -18.1 -19.7 -18.1 -17.3
Qe extr.ed 15.4 13.3 13.25 14.0 11.4 16.7 17.4 17.5 17.2 16.7 8.1 8.9 8.1 7.5
M extr.ed 0.0790 0.0879 0.0889 0.0854 0.1004 0.0710 0.0689 0.0677 0.0699 0.0710 0.1389 0.111 0.1389 0.1514
V.1 Insertion loss performance improvement
This filter exhibits a globally satisfying electrical performance, and demonstrates the capability to implement totally reconfigurable networks on alumina, while keeping a very compact size for the programmable device. However the measured loss level is higher than expected and represents an improvable parameter for an alumina based filter. As observed in section III the filter insertion loss behavior is strongly affected by the biasing resistances performance. Also it has been shown how insertion loss can be generally improved by increasing the resistivity of the bias line integrated resistors [47]. The thin SiCr film process allows rough control over the effective resistivity rb value, however the conductivity measurements performed during fabrication evaluated rb ~1kΩ. Fullwave back-simulations have been performed on the filter including the obtained resistivity value and reproduce accurately the measured loss performance. In Figure 2.28 the measured scattering parameters for the state at 1.51 GHz (worst case) are compared to the simulation of the same state for different rb values. It can be noticed that for 10kΩ/square resistivity the insertion loss performance improves consistently and would be better than 2.1 dB for 100kΩ/square resistivity. This is close to the loss simulated performance (2.0 dB) when no biasing network is applied. 62
S-parameters (dB)
0 -10
(kΩ/square) Sim. : 100 Sim. : 10 Sim. : 1 Meas. i
-20 -30 -40
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
Frequency (GHz)
Figure 2.28 Simulated loss performance for different biasing resistance values at 1.51 GHz.
VI Conclusion
A new kind of reconfigurable filter on alumina has been designed, fabricated and tested. This filter exploits an original synthesis procedure to achieve reconfigurability between multiple filtering functions that combine different tuning mechanisms. Measurement results have validated the principle of reconfiguration and demonstrated 12-state operations with an overall tuning range of 37.5% in the 1.51-2.26 GHz band. The desired filtering functions can be achieved in good agreement with simulations and the device additionally exhibits very compact global size that makes it suitable for miniaturized applications. These encouraging results will allow further development of reconfigurable devices on alumina substrate that will be based on the same principle, while aiming at improved frequency resolution and overall tunability. Also, there seems to be considerable interest in generalizing the presented synthesis technique to n-coupled resonator networks. This would provide acquired control over the outof-band rejection of multiple filtering characteristics and would eventually allow the implementation of totally programmable filters, where central frequency, bandwidth and selectivity can be simultaneously set.
63
64
CHAPTER 3
A multi-band MEMS reconfigurable filter
65
66
A multi-band MEMS reconfigurable filter
The coupled resonator approach adopted for developing the reconfigurable filter in Chapter 2, has proven to allow flexible, compact and low complexity design for relatively narrow-band 2-pole filters. Furthermore the proposed filter architecture has shown to exploit naturally the high integration potential of MEMS technology to planar structures. Indeed MEMS DC contact switches can be easily employed to control the electric coupling of multiple microstrip resonators as well as their resonant frequency, resulting in both frequency and bandwidth tunable networks. On the other hand the encouraging results achieved before arose growing interest for solutions that reduce the technical implementation complexity, as well as the dependence of some of the filter key parameters on the fabrication process. For example the reconfigurable filter in Chapter 2 requires some extra process steps to realize ground connections for the surface mounting (SM) inductors, which essentially depends on the shunt resonator configuration. Hence it can be inferred that a different configuration would allow significant process simplification. Also, the metal-air-metal (MAM) capacitors that implement series input capacitances, are made of MEMS air bridges whose height directly affect the achievable Cin capacitance values. This could provoke dispersion in the external quality factors (Qe) values since the effective bridge height and profile is strongly dependent on the technological process. A superior performance reproducibility could then be obtained by reducing the number, or the influence of MAM capacitors. Therefore it appears that there is considerable advantage in exploiting the principles and techniques consolidated in Chapter 2 while developing a new reconfigurable filter, whose technological dependence can be reduced by careful design. Also, although this filter is still based on 2-electric coupled resonator architecture, both the specifications and the tuning approach are innovated. The filter in Chapter 2 tried to achieve maximum tunability of basically the same frequency response. The new filter rather seeks for reconfigurability between completely different filtering characteristics or “standards”. In this chapter the design principle and optimisation of an original MEMS multi-band reconfigurable filter is presented. 67
This work was carried out in the context of the North Star AMICOM [68] ReRaFE (Reconfigurable Radio Frond-End) project, and the author wishes to acknowledge the support and founding of the AMICOM European Network on RF MEMS and Microsystems.
I The DCS 1800-WLAN filter The Northstar ReRaFE project intends to realize a flexible or reconfigurable radio front-end for multi-frequency or broadband operations which maximally explores the use of RF-MEMS technologies. This essentially implies the development of a new Single-RadioFront-end MEMS based architecture enabling reconfiguration for different standards (GSM, UMTS, WLAN, BLUETOOTH, …), while current solutions rather use different front-ends for different standards. Hence the reconfigurable sub-system potentially offers considerable advantages in terms of size, cost and capability of adaptation to upcoming standards. In this context a demonstrator of the front-end is targeted and will be built as a RF-SiP (Silicon-inPackage for RF applications) module to prove the feasibility of a MEMS-based reconfigurable radio front-end. A draft of the demonstrator architecture can be inspected in Figure 3.1 [69].
B7: TMN3
B4: Tx/Rx B2 : Tunable BPF switch (DCS or WLAN)
B1: TDD/FDD mode DCS1800 switch matrix
WLAN (5.2 GHz) UMTS (2.2 GHz)
Rx LNA
B5: DPST B3: Diplexer UMTS switch
B8: Antenna (DCS, WLAN, UMTS)
Tx PA
B6b: TMN2
B6a: TMN1
TMN=Tunable Matching Network
Figure 3.1 Bulding blocks of the ReRaFe demonstrator circuit.
68
The bandpass filter presented in this chapter is designed to provide reconfiguration of the frequency response between DCS1800 and WLAN standard in the B2 block of Figure 3.1. These two standards exhibit extremely different insertion loss and bandwidth requirements: DCS1800 has its central frequency at 1.84 GHz with a 4% fractional bandwidth (FBW), while WLAN is centred at 5.2 GHz with a 17% FBW. By combining the DCS1800 and WLAN insertion loss requirements together, a global attenuation profile is established in the 0-13 GHz band and is outlined in Figure 3.2 in terms of the S21 parameter. This suggests that implementing a MEMS tunable single-response filter is probably unpractical and MEMS components can be more easily employed to realise a double standard reconfigurable filter. The in-band specifications (Table 1) are the same for both standards and require an in-band loss level <2.5 dB.
S21 (dB)
0
-10
1.84
2.5
DCS 1800 FBW=4%
4.9 5.2
5.8
Frequency (GHz)
7
13
WLAN FBW=17%
-20
-30
Figure 3.2 Required attenuation profile in the 0-13 GHz band.
TABLE I IN BAND SPECIFICATIONS FOR BOTH STANDARDS
PARAMETER
DCS 1800 & WLAN
Insertion Loss
< 2.5 dB
Return Loss
> 10 dB
Ripple
< 1 dB
69
II Design
The strongly heterogeneous and demanding specifications make design particularly challenging. Indeed if a two coupled resonator architecture is assumed, as in Chapter 2, the DCS1800 standard requires to couple resonators around 1.842 GHz with very low intercoupling coefficient, since the FBW is extremely small. On the other hand for the WLAN standard not only the central frequency is about 3 times as higher, but also the FBW is 4 times as larger. This requires a considerable increase in the coupling coefficient which could be difficult to achieve, even though MEMS tunable components are used. Clearly a compact architecture featuring a single filter to be tuned between two different standards is preferable both for design and technical feasibility. Nevertheless the required tuning range could impose a double filter architecture including a distinct filters for each standard and a MEMS control system to switch between them (Figure 3.3). MEMS Log ic Control DCS 50 Ω INPUT
DCS WLAN
50 Ω OUTPUT
50 Ω INPUT
f
50 Ω OUTPUT
WLAN
f
f
Figure 3.3 Single filter versus double filter architecture for the multi-band reconfigurable filter.
A preliminary analysis shows that the two coupled shunt resonator design which was employed in the previous chapter is unfit to meet the DCS standard requirements. Indeed as visible from simulations results reported in Figure 3.4, any attempt to achieve the required selectivity generally suffers by mismatching, high loss, or both of them.
70
0
S parameters (dB)
Qe=12.7 M=0.088 Qe=32.7 M=0.045 Qe=40.4 M=0.027
)) 1, 1( S( B d
-10 )) 1, 2( S( -20 B d -30 -40
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
Frequency (GHz) freq, GHz Figure 3.4 Selectivity versus matching for different Qe/Cm couple values. A three-pole design could provide better in-band characteristics at the price of increasing design and fabrication complexity. The synthesis can be carried out either by the insertion loss method ([65],[69] ), or by the coupling and admittance matrix technique used in Chapter 2. Both the approaches lead to the same lumped equivalent model sketched in Figure 3.5.
Zo Vg
J4
L0
C0
J3
L0
C0
J2
L0
C0
J1
Zo
Figure 3.5 Lumped equivalent model for a three-pole band-pass filter.
A major inconvenience of the parallel resonators configuration in microstrip technology is that a via connection to ground is needed for the shunt inductors. This not only implies some additional steps in the fabrication process developed in the lab (via drilling for each inductor and epoxy glue deposition for grounding them), but also makes EM simulations of the overall structure less accurate. Indeed the MoM tools employed for full-wave simulations are better suited for purely planar networks than for 3-D structures where signal propagation also occurs in the vertical direction.
71
An interesting alternative solution can be investigated by electrically coupling two lumped series resonators as outlined by Figure 3.6.
L C
L
L
Cm C
C-Cm
Cm
L C-Cm
Figure 3.6 Two electrically coupled series resonators.
The idea is to exploit series surface mounting (SM) inductors with a relatively large inductance value to obtain very compact lumped resonators in microstrip technology. L and C represent the uncoupled resonators inductance and capacitance. The two resonators are electric-coupled by means of mutual Cm capacitances, and they are ideally identical to perform a synchronously tuned filter. This configuration turns out to be attractive for several reasons. First it is possible to find a set of feasible values for the reactive components, such that the specifications are respected with good approximation in both bands, as shown below. The circuit in Figure 3.6 performs a band-pass filter while keeping a 2-pole configuration which allows great practical advantage of physical realisation. The two SM inductors combine with two capacitor banks in series configuration, implementing a couple of tunable lumped series resonators. This benefits again process simplicity and low loss compact design, since no via-holes are needed. The completely lumped design is also indicated to prevent problems with spurious harmonics that affect distributed solutions. Finally it is possible to choose a value for the reactive elements such that the inductors keep the same value regardless the standard. This makes possible to achieve two standards with a single filter architecture. From Figure 3.6 it can be noticed that the proposed architecture for this filter is in close and dual relation with the reconfigurable filter presented before. Also the reconfiguration principle is derived from the same filter and is here briefly summarized as following. The 2-pole filter response can be tuned by inducing a variation in the LC loops 72
resonant frequency, as well as in their coupling coefficient. The use of MEMS variable capacitances for Cm and Cr =C-Cm allows achieving both types of variations resulting in a simultaneous control over the filter central frequency and bandwidth. Furthermore two MEMS reconfigurable impedance transformers can be applied to couple input and output of the filter on the external Z0=50Ω access lines. This allows scaling the impedance level of the whole circuit to the proper value for both standards, in order to assure technological feasibility for all components. An equivalent lumped model of the resulting 2-pole filter is provided in Figure 3.7.
Zo
n:1
L
Cm
Cr= C-C m
L Cr= C-C m
1:n Zo
Figure 3.7 Principle of the two electric coupled resonator filter.
Lumped elements circuit synthesis is carried out as in Chapter 2 and a few Agilent ADS simulations are sufficient to obtain frequency responses according to specifications for both standards. The resulting values for the inductors, for the different kind of capacitances and the transformers n ratio are summarized by Table II. The MEMS digital control is thought to allow two combinations only (all the switches are actuated or not) for the capacitor banks which is required to achieve reconfigurability between the specified DCS and WLAN standards. However it should be noticed that a generalisation to multi-standard filters is potentially possible using MEMS multi-state capacitor banks as employed in Chapter 2. The circuit-simulated frequency response can be seen in Figure 3.8, which shows the achievable tunability for the circuit in Figure 3.7.
73
S parameters (dB)
0 )) 1, 1( S( B d
-10
)) 1, -20 2( S( -30 B d -40 -50 DCS 1800
-60 0
1
2
WLAN
3
4
5
Frequency (GHz)
6
7
8
freq, GHz
Figure 3.8 Circuit simulation results in both bands for the circuit model reported in Figure 3.7.
TABLE II FILTER PARAMETERS FOR BOTH STANDARDS LOWER
UPPER
PARAMETER
BAND
BAND
L [nH]
2.6
2.6
Cr [pF]
2.85
0.28
Cm [pF]
0.2
0.045
n
5
1.85
From Table 2, one can observe that tunability between heterogeneous standards relies on the capability to achieve a large drift in the Cr, Cm, and n values when switching from one standard to the other. The variable value for n, which means reconfigurable impedance transformers, is the price to pay for keeping a single inductance value in both bands. From the lumped equivalent model presented it appears that the filter is made of the combination of two distinct parts. The central reactive section, usually referred to as the core, is composed of integrated components as SM inductors (L) and capacitor banks (Cm, Cr) and can be conveniently designed at the desired frequencies, basing on a lumped circuit approach. On the other hand the two input/output impedance transformers are difficult to implement basing on lumped elements, and require some distributed, or hybrid lumped-distributed design, as it will 74
be shown. The design of the filter core design and the input/output matching sections are presented separately in the following two paragraphs.
II.1 Filter core design In order to pursue a low loss design, the filter is to be fabricated on a 525µm thick quartz substrate (εr=3.78, tanδ=0.0001), featuring high Q SM integrated inductors (Coilcraft, L=2.6 nH, Q=156 @ 1.7 GHz) and lumped capacitors equally designed to achieve a high Q value. These present a different configuration whether they implement the Cr capacitor banks to ground, or the series Cm coupling capacitor bank. Indeed the Cm capacitor bank is composed of a single interdigital capacitor (residual capacitance when all switches are in Off state) and two switchable MAM capacitors, controllable by 3 series MEMS relays (Figure 3.9).
MAM series fixed capacitor
MEMS cantilever ohmic switch
C-Cm SM Inductor L pad
L pad
Cm
MIM shunt fixed capacitor
Figure 3.9 Filter core microstrip layout, detailing MEMS Ohmic switch control on MAM series capacitor and on MIM shunt capacitor.
75
The Cr capacitor bank features the intrinsic capacitance to ground associated to the L contact pads (where SM inductors are to be bonded) and two MIM capacitors, switchable by 3 series MEMS micro-relays. The core optimisation can now be carried out by fitting the frequency response from EM Agilent Momentum simulations, with response from ADS simulation of the Figure 3.7 lumped network. The effect of integrated Coilcraft inductors is taken into account by hybrid ADS simulation, as summarized in Figure 3.10 .
Inductor Core S-Parameters EM simu lation (Co ilcraft datasheet) dataset
Inductor S-Parameters (Co ilcraft datasheet)
Figure 3.10 Simulation of the SM inductors interaction on the filter core.
II.2 Input/output impedance transforming sections design Input/output transformers turn out to allow flexibility and simplicity in the overall design although requiring careful and demanding impedance matching operations. The equivalent load seen by the filter core because of the input transformer is readily found from network theory, as outlined in Figure 3.11.
n:1 Input line Zo =50Ω
Filter Core
ZL =
Z0 n2
Filter Core
Figure 3.11 Equivalent circuit from the filter core.
76
Therefore an impedance converting section is required for the 50 Ω feeding line to match such a load. The impedance transition is very abrupt for the lower standard where the large transformer ratio n=5 implies ZL= 2 Ω, which is considerably smaller than Z0 , while for the upper standard n=1.85 implies ZL= 14,6 Ω. Thus the transformer design is basically a double matching problem, involving the Z0=50 Ω input line and the two standard Z0/n² loads. A lumped LC network could theoretically perform proper impedance conversion, as shown in Figure 3.12, provided it is still preferable to keep a series inductor configuration. j1
C
j2
-j0.5
j2
j0.2
L Zo
j0.5
ZL =
Z0 n2
ZL -j0.2
-j1
Figure 3.12 Lumped LC-network matching for resistive loads (smaller than Z0= 50 Ω ).
For example the Figure 3.12 network performs proper matching with Ldwn= 0.864 nH, Cdwn=8.64 pF in the DCS band, and Lup=1.29 nH, Cup=4.85 pF in the WLAN band. Nevertheless this leads to very redundant design because it requires the employment of 3 different inductors: Ldwn, Lrup and Lr (=2.6 nH). On the other hand, since the specified FBW is relatively narrow for both standards, a classical quarter wave transformer could perform the desired impedance matching in each band, with low design and technical complexity. However this generally turns out to exceed the technological size constraints as the lower band is considered. Indeed λ/4>>2cm at 1.84 GHz on a 525µm thick quartz substrate and the resulting circuit, which combines two transformers with the filter core, would be unfit for the 77
integration to the ReRaFe front-end demonstrator. This shows the necessity for more compact solutions. Alternatively a hybrid lumped/distributed network could perform a quarter wave transformer, on narrowband basis, with a shorter length. Indeed by capacitively loading a transmission line it is possible to synthesize a sufficiently compact equivalent transformer, provided the line impedance and the capacitive load are properly chosen. These can be determined analytically, as summarized below, by computing and comparing the ABCD matrix for both the normal quarter wave transformer and the hybrid network to synthesize. Then, at 1.84 GHz, a Z1 characteristic impedance transmission line performs a quarter wave transformer with n=5 if the electrical length θ1=π/2 and Z1=Z0/n (Fig. 3.13). L1 and W1 are the line physical length and width.
θ1 Zo
Z1
ZL =
Z0 n2
L1
w1
Z1
Z1 = Z 0 Z L =
Z0 n
Figure 3.13 Transmission line quarter wave transformer: n=5 .
The associated ABCD [T1] matrix is known from the transmission line theory and is reported below:
0 [T1 ] = 1 j Z1
jZ1 0
(1)
78
As about the equivalent hybrid transformer, the Z2 impedance transmission line capacitively loaded by a normalized b susceptance, is visible on Fig. 3.12. L2 and W2 are the line physical length and width, while θ2 is the electrical length at 1.84 GHz.
θ2 Zo
b =ωCZ2
Z2
ZL =
Z0 n2
w2
L2
Z2
b
Figure 3.14 Lumped/distributed equivalent transformer .
The related [T2] transmission matrix can be calculated, by multiplying the ABCD matrices of the 3 two-ports networks featuring in the cascade connection (Figure 3.14). These include two external θ2/2 lines, and a shunt C capacitance in the middle. All matrices are known from transmission line theory and [T2] is a function of the unknown Z2, θ2 , b:
θ2 cos 2 [T2 ] = 1 θ j sin 2 2 Z 2 = j 1 Z 2
θ2
1 2 ⋅ θ cos 2 jωC 2
jZ 2 sin
b cosθ 2 − sin θ 2 2 b b sin θ 2 + 2 sin θ 2 + 2
θ 0 cos 2 2 ⋅ 1 θ sin 2 1 j 2 Z 2
b b jZ 2 sin θ 2 + sin θ 2 − 2 2 b cosθ 2 − sin θ 2 2
jZ 2 sin
θ2
2= θ cos 2 2
(2)
79
For this network to behave like a quarter wave transformer around 1.84 GHz, [T2] must be equated to [T1] , which leads to the three non linear equation system below, for the unknown θ2, b and Z2 :
b cosθ 2 − sin θ 2 = 0 2 b b Z 2 sin θ 2 + cosθ 2 − = Z1 2 2
(3)
b b 1 sin θ 2 + 2 cosθ 2 + 2 = Z 1
1 Z2
This can be rearranged in a two equation system upon linearly combining the second and the third equation:
b = 2 cot g (θ 2 ) b=
(4)
Z 2 Z1 − Z1 Z 2
From the latter
Z 22 1 2 b ± b2 + 4 − Z1 ⇒ Z 2 − bZ 2 − Z1 = 0 ⇒ Z 2 = Z1 2 Z1 Z1
Z 2b =
100
30 20
Z2
50
b
10 0
0
b
-10 -20
Line Impedance: Z2 (Ω)
Succeptance: b (Ω-1 )
40
(5)
-50
-30 -40
00
0.5
1 π/2
1.5
π2
2.5
3 3π/2
Elec. Length: θ2 (rad)
3.5
2π4
-100 -10
-5
0
5
10
Susceptance: b (Ω-1 )
Figure 3.15 Graphical solution for the equation system (3) . 80
Then from (3), Z2 can be directly expressed as a function of Z1 and θ2 (Figure 3.15):
[
]
Z1 cos 2 (θ 2 ) + sin 2 (θ 2 ) 2 Z2 = cot(θ 2 ) ± 4 cot (θ 2 ) + 1 = Z1 cot(θ 2 ) ± = 2 sin 2 (θ 2 ) =
Z1 [cos(θ 2 ) ± 1] sin(θ 2 )
⇒ Z2 =
(6)
Z1 [1 ± cos(θ 2 )] sin(θ 2 )
Actually from a practical point of view θ2 cannot be considered as completely arbitrary and is more conveniently fixed by technological considerations. Since the upper standard central frequency is about 3 times as bigger as the lower standard one, there is significant advantage in choosing
1 π π = 3 2 6
θ2 = ⋅
(7)
which leads to L2 ~7500µm. This allows synthesizing a very compact hybrid network which is equivalent to the quarter-wave transformer in the lower band with Z1Low=Z0/nLow = 10Ω.
b π = 8.02 pF bLow = 2 cot g = 3.464 Ω −1 ⇒ C Low = ωZ 2 6 Z1Low =
Z0 = 10 Ω n Low
Z 2low =
Z1 π sin 6
π 1 + cos 6 = 37.32 Ω
(8)
81
80
Z2 (θ2 ) b (θ2 )
60
Z2 =37.32 Ω
40
Z2 (Ω)
20 0
-20 -40
θ2 =
-60 -80
0
0.5 π/2
π 6 π1
1.5 3π/2
2
Elec. Length: θ2 (rad) Figure 3.16 Lumped/distributed equivalent transformer .
Now the microstrip structure visible in Figure 3.17 can be optimised such that it performs a hybrid transformer with nLow=5, Z2Low=37.3 Ω , bLow=3.5 Ω-1 and CLow=8 pF according to (8). This provides the required impedance matching for the DCS1800 standard. The equivalence to a quarter-wave transformer in the lower band can be appreciated from Figure 3.18.
W2 Low
L2
Z2 Low
bLow
Figure 3.17 Hybrid transformer for the lower (DCS1800) standard.
82
0
)) -20 1, 1( S( B d -40
S11 (dB)
)) 3, 3( S( B d
S11 λ/4 transf. S11 hybrid transf.
-60 1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
Frequency (GHz) freq, GHz
Figure 3.18 Comparison between quarter wave transformer matching, and hybrid transformer matching .
On the other hand the same network turns out to be 3θ2=π/2 long in the upper band. Then a classical quarter wave transformer could be obtained for the WLAN standard if the CLow capacitive load could be disconnected, and the line impedance switched to Z2up=Z0/nup=27 Ω. For example, the hybrid network in Figure 3.19 presents a very small capacitive load connected to the line and can be optimised to behave as a simple Z2up=27 Ω transmission line with good approximation in the upper band. Therefore it performs a transformer with nup=1.85, Z2up= Z1up =27 Ω . This provides the required impedance matching for the upper WLAN standard.
W2 Low
W2 up
L2
Z2 Low
bLow
bup
Z2 up Figure 3.19 Hybrid transformer for the upper (WLAN) standard.
83
II.2.1 Double stadard MEMS transformers Now MEMS Ohmic switches can be easily employed to implement a control system that allows commuting from the transformer configuration in Figure 3.17 to the one in Figure 3.19, while keeping a single transformer architecture. The resulting double standard transformer can be seen in Figure 3.20 .
L2
Figure 3.20 MEMS double standard transformer .
For the MEMS switches in the ON-state (Figure 3.21), the capacitive load is connected to the transmission line and the system behaves as the lower standard equivalent transformer in Figure 3.17 with WLow =1750µm (Z2Low=37.32 Ω).
CON=8 pF
WON
ON state ZON
Figure 3.21 MEMS switches in the ON state: DCS standard transformer .
84
For the MEMS switches in the OFF-state (load disconnected), the line effective width is Wup =2715 µm (Z2up=27 Ω), the equivalent capacitive load is very low and the system performs a quarter wave transformer in the upper band (Figure 3.22).
CUP<<1 pF
WOFF
OFF state ZOFF
Figure 3.22 MEMS switches in the ON state: WLAN standard transformer .
Some further EM optimisation is needed to achieve proper and simultaneous matching for both standards. This requires accurate tuning of the g1,g2 and W1 geometrical parameters reported in Figure 3.23, which affects the system behaviour in both bands, but not in the same way. Another challenge comes from the (horizontal) width of shunt capacitive stubs which has been increased, as can be noticed comparing Figures 3.17 and 3.20 to Figure 3.14, in order to maximize the achievable capacitive load. This makes the effective impedance control arduous, since higher order modes can be easily excited, and the structure behaviour can differ significantly from that predicted basing on the one-dimensional transmission line model of equation (1-6) [71]. Finally the parasitic effects associated with both MEMS switches imperfect isolation and the peculiar meander shape synthesized are to be taken into account and controlled, also. However the required impedance characteristic can be eventually achieved with good approximation, as shown in Figure 3.23 where frequency S11 responses for different sets of g1,g2 , W1 parameters are represented.
85
0
g2 g1
)) 3 1, 3 1( S( B d
W1
)) 1 1, 1 1( S( B d
WLAN transf. )) 5, 5( S( B d
)) 9, 9( S( B d
)) 3, 3( S( B d
)) 7, 7( S( B d
)) 1, -20 1( S( B d -40
DCS transf.
S11 (dB)
)) 5 1, 5 1( S( B d
g1=192µm, g2=175µm, W 1=780µm g 1=242µm, g 2=175µm, W1=780µm g 1=492µm, g 2=175µm, W1=350µm g 1=492µm, g 2=155µm, W1=350µm
-60
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
Frequency (GHz) freq, GHz Figure 3.23 MEMS double standard transformer optimisation .
II.3 MEMS double standard microstrip filter The final circuit, combining the filter core to the access sections is visible in Figure 3.24. It can be observed how the DCS-WLAN filter exhibits considerably larger size than the filter in Chapter 2. This mainly depends on the lower permittivity of the substrate (quartz with εr=3.78 instead of alumina that has εr=9.6) which makes necessary to exploit big surfaces to implement the MIM capacitances required for the lower standard. Also, the global size is invariably affected by the hybrid distributed/lumped nature of the transformers.
Input matching section
Output matching section
1.4 cm
Filter reactive core
2 cm
Figure 3.24 MEMS double standard filter .
86
As in the core case, full-wave simulations of the whole structure are coupled to circuit simulations aiming at integration of the inductors effect. The resulting frequency response is reported in Figure 3.25, showing fair agreement with Figure 3.8 circuit simulation results. In practice, due to the hybrid nature of the microstip network in Figure 3.24, reproducing the lumped elements circuit responses turns out to be quite demanding and slight variations over the ideal loss and bandwidth performances are invariably present. A more realistic circuit model that takes into account the MEMS switches finite conductivity will be introduced in the next section and will be conveniently used for interpretation of measurement results.
S parameters (dB)
0 )) 1, 1( S( B d
circuit sim. DCS
)) -10 1, 2( S( -20 B d -30
circuit sim. WLAN
-40 0
1
2
3
4
5
6
7
8
Frequency (GHz) freq, GHz Figure 3.25 Microstip filter EM simulated results and comparison with circuitsimulation results .
III Fabrication and measurement results The fabrication process is a standard MEMS process on quartz substrate and presents no conceptual difference with the process reported in Chapter 2. However particular attention was paid in the realization of the biasing system. Indeed, from Figure 3.26 it can be noticed how the biasing resistances length has been considerably increased in order to overcome the lower resistivity achieved with thermal evaporated resistive films. This is expected to provide 4 kΩ/square biasing resistors which is approximately four times as big as the resistivity obtained for the filter of Chapter 2.
87
200µm Figure 3.26 Detail on the biasing system in the core region .
III.1 Measurement results Measurements have been performed by the HP822ES analyser connected to the onmicrostrip Wiltron probing station as in Figure 3.27. Measured EM performances for the first circuit tested are compared to the simulation results in Figure 3.28.
Figure 3.27 Photograph of one of the fabricated DCS-WLAN reconfigurable filters in the microstrip Wiltron probing station.
88
00
0
)) 7, -20 8( S( B d -40
d B ( -10 -10 S 7(, 7 )) -20 -20
dd BB S( S( 5(, 1(, 51 )) ))
S21 (dB)
S11 (dB)
)) 5, 6( S( B d
10
-60
-30 -30 0
1
2
3
4
5
6
7
d B DCS std: S( simulations 3(, 3 measurement )) WLAN std: simulation measurement
8
Frequency (GHz) freq, GHz Figure 3.28 Dual-band filter measured performance and comparison with the EM simulation results.
The filter achieves double-standard reconfiguration of the frequency response and additionally shows good performance reproducibility when switching between WLAN and DCS band operation or vice versa. The measured standards are centred at 1.80 and 4.90GHz, that means 2.3% and 5.8% frequency shift, respectively, from ideal responses. The WLAN standard insertion loss is better than 2 dB and bandwidth is 22%, while the DCS response suffers from exceeding loss (6.5 dB) and bandwidth (13.6%). A simple circuit model is derived as in Figure 3.29, from models in Figure 3.7, 3.14, and turns out to be useful for interpretation of the DCS standard measured response. ADS simulations are then carried out to reproduce both measurement and full-wave simulation performances, resulting in the comparison on Table III.
θ2
L
Rt1
Rr1
Ct1
Cr1
L
Cm Rm1
Rm2
θ2
Rr2
Rt1
Cr2
Ct2
Figure 3.29 Circuit model used for back-simulations. 89
TABLE III IDEAL AND BACK-SIMULATION PARAMETERS FOR DCS &WLAN
STANDARDS
EXTRACTED
DCS from
DCS from
WLAN from
WLAN from
PARAMETER
EM Simul.s
Measurem.s
EM Simul.s
Measurem.s
Cr1 [pF]
3.0
1.64
0.30
0.37
Cr2 [pF]
3.0
3.11
0.30
038
Rr1 [Ω]
0.20
8.8
0.12
4.3
Rr2 [Ω]
0.20
0.7
0.12
3.4
Cm [pF]
0.19
0.77
0.056
0.085
Rm1 [Ω]
0.23
5.3
<0.1
<0.1
Rm2 [Ω]
0.23
5.3
<0.1
<0.1
Θ2 [deg]
30
32
90
94
Ct1 [pF]
8.01
8.21
-
-
Ct2 [pF]
8.01
5.03
-
-
Rt1 [Ω]
0.33
1.6
-
-
Rt2 [Ω]
0.33
0.4
-
-
Back-simulations result in high series resistance(>7Ω) for some of the capacitor banks and suggest that a few of the (54) MEMS switches present high contact resistance or/and do not achieve proper actuation. Thus Cr1 and Ct2 banks only achieve about a half of the expected capacitance in the On-state and exhibit asymmetrical values (Cr1 ~0.5Cr2 , Ct2~0.5 Ct1) for the DCS standard response. This could derive from problems in the biasing network (as bad adherence of biasing resistance to substrate or bias lines) and confirms what inferred by visual inspection during measurements. Indeed, the switches triplet highlighted in Figure 3.30 generally exhibited lower efficiency in the actuation dynamic, meaning that, for the same applied biasing voltage, the apparent deflection during low frequency switching cycles was less evident than in other switches.
Defective MEMS switches
Figure 3.30 Physical interpretation of the extracted parameters in Table III. 90
Furthermore, the extracted Cm coupling capacitance is considerably larger than expected for the DCS response. This actually comes from improper mask design that led to fabrication of MIM coupling capacitors instead of the required MAM ones. Additional measurements were performed after removing the improper capacitors and resulted in the curves in Figure 3.31. These show very good agreement with expected central frequency, bandwidth and return loss performance. 10
0
0
)) -20 7, 8( S( B d -40
d B S( -10 7(, 7 )) -20
d B S( 5(, 5 ))
S21 (dB)
S11 (dB)
)) 5, 6( S( B d
d B S( 1(, 1 ))
-30
-60 0
1
2
3
4
5
6
7
d BDCS std: S( 3(, simulations 3measurement )) WLAN std: simulation measurement
8
Frequency (GHz) freq, GHz Figure 3.31 Measured performance after suppression of the improper MIM capacitors.
The insertion loss performance in the DCS band is still affected by high contact resistance of a few MEMS ohmic switches. This is confirmed by the measured response of a filter fabricated with all switches in the down-state position.
0
0
S21 (dB)
)) 7, -20 8( S( B d -40
d B S( -10 9(, 9 )) -20
DCS std: simulations measurement
-60
d B S( 1(, 1 ))
S11 (dB)
)) 9, 0 1( S( B d
10
-30 0
1
2
3
4
5
6
7
8
Frequency (GHz) freq, GHz
Figure 3.32 DCS-band performance for the filter with all switches in the On-state.
91
The resulting DCS response is visible in Figure 3.32 and shows impressive agreement with the EM simulated results, with insertion loss performance better than 1.9 dB.
IV Conclusion
A new design for a MEMS double standard filter to be employed in a reconfigurable radio front-end has been presented. In order to achieve tunability between two heterogeneous, DCS1800 and WLAN, standards an original architecture has been developed combining a lumped elements reactive core to a couple of lumped/distributed transformers. Both the core and the transformer sections exploit 2-state capacitor banks digitally controlled by MEMS ohmic switches to achieve double standard reconfiguration. It has been shown how careful design of the impedance transforming sections allows low design and technological complexity while keeping a global size which is compatible with the integration of the filter in the demonstrator RF-SiP module. Furthermore, the DCS1800-WLAN filter size could be considerably reduced by implementing it on alumina substrate. The EM optimisation of this filter turns out to be quite demanding due to its hybrid nature and to the difficulty in achieving simultaneous impedance matching in both standard bands. The application of techniques of parametric optimisation appears a viable solution to improve the efficiency of such a process and would be certainly required for the generalisation of the developed topology to multi-standard MEMS reconfigurable filters. Measurement results of the fabricated filter have been presented. The circuit performs double standard operations in good agreement with the specified dual band characteristic. Measured performances allow full validation of the design principle and show potential for low loss operations, although the DCS standard loss performance in the tested circuit is affected by a few high contact resistance MEMS switches.
92
CHAPTER 4
A MEMS switched varactor for high RF power applications
93
94
A MEMS switched varactor for high RF power applications
As outlined in the first chapter RF micro-electro-mechanical systems (MEMS) technology has become increasingly attractive over the past few years, for a large range of wireless and radar communications systems. These include tuners, antenna beam forming networks and reconfigurable filters, which can all benefit from compact, low loss and linear design offered by MEMS components [11, 48, 56, 59]. Co-integration with gallium nitride devices is also very promising due to power and bias voltage compatibility. Finally, very low DC current consumption exhibited by MEMS components is particularly attractive for potential high power applications. Nevertheless the RF power handling capability for most MEMS switched devices typically provides reliable behaviour in the 1mW up to 100mW range. Indeed most high power (P>1W) applications available to date are limited to cold switching conditions. This means that the injected RF power is turned off before closing or opening the contact. Raytheon [72] has demonstrated capacitive shunt switches without self actuation up to 4W under cold switching conditions and 1billion cycles up to 510mW under continuous applied power (hot switching). MIT Lincoln Laboratory [73] has presented a series capacitive switch capable of handling 10W under cold switching conditions and 1.7W under hot switching conditions. On the other hand, continuous wave RF power operation, that is to say hot switching operation, is clearly of interest for a variety of high power microwave devices, as phase shifters and front-end tunable components. It is important to notice that for these applications, it is not necessary to achieve large switching contrast, while power handling capability in the watt range would be a major breakthrough in the integration of MEMS components for high power reliable systems.
95
Analog variation MEMS devices can handle high power [74], but suffer from temperature sensitivity, noise and mechanical instability. Furthermore the large power handling capability is obtained at the price of increased design/process complexity, since these devices present a dual beam/actuation architecture (see Figure 4.1).
Figure 4.1 An example of analog RF MEMS varactor [74].
The work presented in this chapter deals with the development of a cantilever based MEMS tunable capacitor specifically designed to handle RF power exceeding 1W. Although the proposed architecture presents innovative characteristics, the overall configuration intends to be simple and the varactor micro-fabrication relies on completely standard MEMS process. For this purpose, careful design was performed starting from the analysis of typical failure mechanisms in high RF power conditions. Then a multi-domain synthesis was carried out, combining mechanical, electrostatic and electromagnetic simulations. Finally a reliability analysis was conducted on the fabricated devices, including long term cycling tests under continuous RF power, capacitance/voltage (C(V) curves) characterization, and tests of maximum power handling before failure.
96
I Design principles
RF MEMS components relying on electrostatic actuation typically present a small air gap (~µm) between their movable beam and their actuation electrode (see Figure 4.2).
Figure 4.2 An example of MEMS cantilever DC contact switch realised at XLIM lab [60] showing a flat cantilever beam and a uniform air gap (=3 µm) .
Hence the applied voltage Vp, needed to actuate the beam, ranges between 10 and 100V, depending on design and mechanical stiffness of the structure. However, a major drawback of such a configuration for MEMS varactor components is the higher sensitivity to RF power effects on the membrane dynamics, which could cause a temporary device failure. For example, when the membrane is in the up state, a high power RF signal at the device input will induce an electrostatic pressure on the membrane surface that may actuate it whereas no bias signal is applied. In a similar way, in the down state, the induced electrostatic pressure may hold the beam down even once the bias voltage is removed, preventing the membrane from recovering the up state position. The microwave power effects both in the up state and in the down state, can be evaluated in more detail depending on the varactor designed architecture and the associated circuit model. This is summarized later in this section. To overcome the electrostatic pressure induced by the RF signal on the membrane, its stiffness and its power exposed surface must be properly designed. For this purpose, the proposed varactor is based on a specific cantilever structure which consists of two separate 97
beam sections [75] (see Figure 4.3): a large and stiff actuation part and a small capacitive contact part located at the cantilever tip where RF signal is concentrated. A dielectric layer is deposited on the contact electrode under the contact tip preventing full actuation of the cantilever. From a preliminary analysis it can be noticed that the proposed design presents several advantages, as far as the global electromechanical behaviour is considered. First, the smaller gap h2 at the capacitance contact section, compared to the actuation section one h1, allows increasing the tip contact force and improves the capacitance contrast when actuating the membrane. Indeed a small displacement in the actuation region turns out to be a large shift in the capacitive contact region. Therefore a stiff and essentially stable structure can still achieve proper On/Off capacitance ratio. Furthermore the double step profile prevents the cantilever from collapsing on the actuation electrode, which reduces consistently charge injection phenomena in the dielectric [27, 76-77], typical of MEMS capacitive switches. This not only limits stiction failure phenomena due to the dielectric charging, but also provides more reproducible C(V) characteristics for the varactor. Indeed a smaller amount of charges trapped in the dielectric allows a better evaluation of the real DC pull-down voltage. Finally, the small contact area reduces the stiction risks associated to air, humidity and organic contaminants, which makes designing of a package system for the varactor a minor concern. This was experimentally verified by testing the component in room atmosphere for a month with no stiction failure observed.
Actuation section
RF signal propagation (T -line)
h1 Pull -down electrode
Capacitive tip
h2 RF GND
Contact dielectric l
Figure 4.3 The proposed cantilever double step profile .
98
The summarized features essentially aim at decoupling the varactor capacitive performance from the actuation and release mechanisms. The cantilever tip geometrical parameters do not affect directly the beam stiffness, while conditioning the system power handling capability, as shown in the next session.
I.1 Voltage across the capacitive tip due to the RF input signal
A simple model for the MEMS switched varactors can be seen in Figure 4.4, and consists of a lossless transmission line loaded by a lumped variable capacitance C. The RF line parameters are the propagation constant β and the characteristic impedance Z0 and it is assumed that an incident wave of the form VIN =V+ e- jβz is generated at z<0. V(z), I(z) VIN Z0 , β
VTip
C
Z0 , β z
0
Figure 4.4. Circuit model for the RF input signal interaction with the switched varactor.
In the time domain, the input RF signal is then:
v IN (t ) = V0 cos(ωt )
(1)
with V0 = V+ and the associated RF power value is:
1 V0 P= 2 Z0
2
⇒
V0 = 2 PZ 0
(2)
99
Hence, from the transmission line theory [78], the incident wave propagates in the positive direction along the line with V+ amplitude while, at the load (z = 0), a reflected wave is generated with amplitude V- = ΓL V+. The ΓL reflection coefficient is immediately derived:
Y − YL Y0 − ( jωC + Y0 ) ΓL = 0 = = − Y0 + YL Y0 + ( jωC + Y0 )
C Z0 2 C 1 + jω Z 0 2 jω
(3)
At any point of the line, the total voltage can be expressed as sum of the incident and reflected waves. Therefore the voltage due to the input microwave signal across the cantilever tip, VTip , is the total voltage at the z=0 point:
VTip = V (0) = V + (1 + ΓL ) = V0 ⋅
1 C 1 + jω Z 0 2
⇒ VTip =
V0 ωCZ 0 1+ 2
2
(4)
It should be noticed that the analysis above allows computing the VTip voltage by assuming that the RF source is matched, so that no reflections occur at the generator. However for several practical applications, as phase shifters, it is useful to consider the varactor loading a finite length transmission line, so that reflections can occur at input also. In section A5 a more detailed analysis is carried out considering a mismatched generator and finite length transmission lines as in Figure 4.5. θ
Zg
Vg
Z0 , β
θ VTip
C
Z0 , β z
-L
0
L
Figure 4.5 Varactor connected to a mismatched generator through finite length lines.
100
Figure 4.6 shows an example of |VTip| evaluation from equation (4) for a 1W sinusoidal input RF signal at 10 GHz propagating along a 50 Ω transmission line that is loaded by a 500 fF varactor capacitance.
10
|VT ip | (V)
9.9 9.8
|VTip |=9.97
9.7 9.6 9.5 0
5
10
15
Frequency (GHz)
20
Figure 4.6 |VTip| computing for a 10V sinusoidal 10GHz input RF signal on a 500 fF varactor.
As the electrostatic pressure due to the VTip signal on the varactor is considered, the equivalent effective DC voltage, which would induce the same pressure, can be computed from equation (5):
VTip eff =
VTip 2
=
PZ 0 ωCZ 0 1+ 2
2
(5)
Although the tunable capacitance C in (5) undergoes analog variation depending on its applied DC biasing voltage, two major cases are of interest for practical operations. These two situations also corresponds to two possible failure mechanisms in the actuation/release dynamic, as discussed below, and determine a two state pseudo-digital functioning for the switched varactor.
101
I.2 Power handling in the up state: self actuation phenomenon
When a zero or low biasing voltage is applied between the cantilever and the actuation electrode, the beam stands in the up state position and the capacitance loading the line is minimum. The small up state capacitance C~Cup=C(0V) provides negligible reflection at z=0 and the resulting equivalent DC voltage is, from (5) with ωCZ0<<1:
VTip eff = PZ 0
(6)
Self actuation failure can occur if VTip_eff exceeds the pull-down voltage Vp of the cantilever, which sets a critical power value in the up state:
VP2 Pup = Z0
(7)
The designed double step cantilevers typically exhibit large actuation voltages. Theoretical values were evaluated as explained later, around 70V, while measurements demonstrated even larger values, due to an imperfect control on the beam gold thickness and residual stress. Then the critical value in the up state is larger than several tens of Watt and will not affect power handling in the watt range.
I.3 Power handling in the down state: hold down phenomenon
When the applied DC voltage exceeds the actuation voltage the cantilever lowers in the down state position where the tip collapses on the contact electrode. The latter is covered with a 0.3µm thick alumina layer whose permittivity is significantly larger (εr=9.6) than the air one. Then the actuated state capacitance value, Cdwn, undergoes a strong increase and the incoming microwave signal may hold the cantilever down with much higher force. Hold
102
down failure can occur if the effective voltage across the tip exceeds the release voltage, Vr of the cantilever. Then from (5):
Pdwn
2 Vr2 ωCZ 0 = 1 + Z 0 2
(8)
Now the influence of cantilevers tip surface on the down state power handling can be considered. On the one hand, the larger the tip surface, the bigger the associated capacitance and the stronger the load holding the beam in the down state. On the other hand, equation (8) shows that larger capacitances at higher frequencies, that is larger value ωC values, perform a more efficient short-circuit for the RF signal, resulting in a lower VTip value. This shows that for equal release voltages, bigger capacitances (i.e. larger tip surfaces) perform better power handling in the down state. Consequently, the capacitive tip geometrical parameters affect the structure power handling capability in a complex manner. As summarized below, such an influence required finite elements method simulations for accurate modelling.
I.4 Varactor multi-domain recursive synthesis.
The varactor design optimisation consists of the iteration of several specific steps regarding the different physical aspects discussed above. Starting from a first guess design, the initial varactor geometry undergoes electromagnetic simulations by Agilent MoM software (MOMENTUM). A second EM simulation is performed on the RF line only (see Figure 4.7), in order to deembed the effects of the access lines on the varactor. Now a circuit model integrating the lines can be derived as in Figure 4.7 to characterize the current structure, and a few ADS circuit simulation/refinement cycles are sufficient to achieve good fitting between fullwave and circuit simulations. This allows characterizing the capacitance values both in the up and in the down state.
103
Cs L RF Line [S]
Varactor
RF Line
L C
RF Line [S]
(Momentum simulation)
Figure 4.7 Circuit model for a simple varactor in CPW technology.
It can be noticed that although some additional reactive components are introduced to properly characterize both MEMS component and the interaction with transmission lines, this model is basically similar to the one used to compute the voltage induced across the cantilever tip by the microwave signal. Although the qualitative results derived with the first simple model hold valid, the second model is actually employed for fine evaluation of |VTip| versus power and frequency, since it provides better interpretation of the varactor electromagnetic performance as long as the geometry of the RF line gets elaborated (see Figure 4.7). Then the |VTip| signal time evolution is determined by ADS simulations which perform an harmonic balance analysis of the circuit in Figure 4.7, for different input power levels, and the peak |VTip| value is retained (worst case). The |VTip| evaluation by means of ADS circuit simulations is discussed in more detail in the A5 section. The model of Figure 4.7 turns out to be very efficient in phase response computing. It is worth mentioning that the phase response is particularly important in measurement operations since the varactor actuation can be readily inferred from the phase response variations, while the other measurable parameters generally exhibit lower sensitivity to state commutations (see S11 and S21 parameters in Figure 4.8).
104
0 )) 7, 8( S( es hpa
)) 11 , 21 ( S( es a ph
)) -50 9, 01 ( S( -100 es hpa -150
Phase (deg)
)) 5, 6( S( es hpa
S21 Up State:Model S21 Up State: Measure S21 Dwn State: Model S21Dwn State: Measure
-200 0
5
10
15
20
Frequency (GHz)
25
30
freq, GHz
0
S11 Up State:Model S11 Up State: Measure S11 Dwn State: Model S11Dwn State: Measure
-3 10
12
14
16
Frequency (GHz) freq GHz
18
)) 5, 5( S( B d
)) 7, 7( S( B d
S21 Up State: Model S21 Up State: Measure
-10 )) 1 )) 1, 9, 1 9( -20 1( S S( ( B B d -30 d -40
S11 (d B)
)) 9, -1 0 1( S( B d -2
S21 (d B)
5 6 S B d
)) 1 1, 2 1( S( B d
S21 Dwn State: Model S21Dwn State: Measure
-50
20
4
6
8
10
12
14
16
Frequency freq, GHz(GHz)
18
20
Amplitude (dB)
0
Figure 4.8 Comparison of frequency response from Figure 4.6 model simulations and measurements in both states for the CPW varactor designed.
Finally, the VTip value is entered in a coupled electromechanical FEM simulation (ANSYS) that allows determining the complete mechanical behaviour of the structure. Now the pull-down/release voltages Vp,Vr can be computed leading to the critical power values Pup, Pdwn in both states. If these provide insufficient power handling capability the varactor geometry can be refined consequently, notably by modifying the size of cantilever tip, and the synthesis process is summarized. The Vp,Vr, Pup, Pdwn values are listed as a function of frequency and input power in the following paragraph, after a brief description of how the release voltage is determined from Ansys simulations. This section also gathers some of the principles that have largely benefited the author’s comprehension of the varactor dynamic.
105
I.4.1 An outline on MEMS cantilever beams mechanical behaviour
The deflection of a cantilever beam when a vertical force P (N) concentrated in the a point is applied as in Figure 4.9 is derived from the Euler-Bernoulli beam equation [79]:
y a
P
0
x
Figure 4.9 Application of a concentrated load to a cantilever beam.
Px − Pa ∂2 EI 2 y ( x, a) = ∂x 0
x
x≥a
where E is the Young’s modulus of the beam, I is the area moment of inertia of the beam’s cross section, and the fixed end conditions holds at the left end extremity:
y=0 ;
∂y =0 x=0 ∂x
(10)
Also, using the step function u-1(x) from the theory of distribution:
0 u −1 ( x) = 1
x<0 ⇒ x≥0
∂ 2 y ( x) = Px − P( x − a)u −1 ( x − a) − Pa ∂x 2
(11)
106
which is a very compact form suitable for automatic computations. By integrating twice the equation (11) the beam deflection as a function of the (concentrated) load position is derived. As an example Figure 4.10 shows the deflection computed for a 16.5 µN concentrated load at
y’’(x) (µm)
a=100 µm on a typical MEMS cantilever (gold, 160*100*3 µm3):
a
0
L
-50
-100
0
20
40
60
80
100
120
140
160
0
20
40
60
80
100
120
140
160
0
20
40
60
80
100
120
140
160
0 *10
y’(x) (µm)
-3
-2 -4 -6
y(x) (µm)
0
-0.5 -1
x (µm)
Figure 4.10 Double integration of the (12) equation to derive the deflection.
Px 2 (3a − x) − 6 EI y ( x, a ) = Pa 2 (3x − a) − 6 EI
0< x
a≤x≤L
When a uniformly distributed load is applied between the a1 and a2 points (Figure 4.11):
107
y
P
a2
a1
0
x
Figure 4.11 Application of a uniformly distributed load to a cantilever beam.
(9) is still valid upon considering P as a load per unit length and deflection can be computed by the superposition effect. This has been implemented by a Matlab routine that integrates numerically the (12) solution to equation (11):
y ( x) =
a2
N pitch
a1
n =1
∫ y( x, a)da ≅
∑
y (n ⋅ pitch)
(13)
where the numerical integration pitch is conveniently chosen in the micron range so that Npitch = L/pitch is typically smaller than 1000. Now the electrostatic actuation of MEMS cantilever beams rather involves considering a distributed non-uniform load. Indeed the electrostatic force applied at any point between a1 and a2 depends on the gap between the cantilever and the pull down electrode at that point (Figure 4.12), which in turn depends on the deflection in the same point (14).
y
P a1
a2
0
Air gap ε0 g (a1)
x g (a2)
Pull down electrode
Figure 4.12 Application of a non uniform load to a cantilever beam.
108
1 ε 0 AV 2 1 ε 0 AV 2 Fe ( x) = − =− 2 [g ( x)] 2 2 [ y ( x )] 2
(14)
V is the applied voltage, A is the area of cantilever exposed to the electrostatic actuation and a parallel plates capacitor model is assumed to compute Fe. Even with such a simple model for the electrostatic actuation it can be noticed that the expression for Fe introduces in the deflection equation a non-linear dependence from itself. Still a numeric evaluation of deflection is possible and some results for calculations on cantilevers as the one in Figure 4.3 are summarized in Figure 4.13 while the Matlab code is reported in section A6. 0
0
Vp = 0 V y(L) =-1.3 µm
Cantilever deflection: y(x) (µm)
-0.5 -1
-1
-1.5
-1.5
Contact dielectric level: -2.6 µm
-2
-3
-2
Pull-down electrode level: -2.9 µm
-2.5
0
40
80
120
160
-2.5
200
-3
0
0
-0.5
-0.5
Vp = 60 V y(L) =-1.97 µm
-1
-1.5
-2
-2
-2.5
-2.5
0
40
80
120
160
200
0
40
80
120
160
200
-1
-1.5
-3
Vp = 20 V y(L) =-1.36 µm
-0.5
-3
Vp = 78 V y(L) =-2.6 µm
0
40
80
120
160
200
Distance from anchorage: x (µm) Figure 4.13 Pull-down voltage evaluation for a typical cantilever (see Table 4.2 for dimensions).
109
It could be objected that the double step profile proposed for the switched varactor is sensibly different from the flat cantilever geometries considered in this section and that the relations (9-14) do not take into account the dielectric layer which prevents full actuation of cantilever. Nevertheless, as explained in section I, the double step architecture decouples the global mechanical behaviour from the capacitive tip influence. This is especially true in the up state (biasing voltage applied <50 V), where the effective dielectric constant is dominated by the air’s one [11]. Therefore the behaviour of the double step cantilever shows poor sensitivity to the capacitive tip effects as far as there is no contact, and the double step beam is comparable to a flat beam with no tip. The equations (9-14) can then be employed to describe the dynamic of the system in Figure 4.1 with good approximation. For instance the beam pulldown voltage Vp has been estimated by computing the minimum voltage for the cantilever tip to touch the contact electrode. This leads to fair agreement with measured results. On the other hand in the down state the capacitive tip effect on the overall dynamic is not anymore negligible due to the electrodes proximity and the abrupt increase in the effective dielectric constant. Therefore equations (11-14) become too simplistic to describe the mechanical behavior in the proximity of contact and Ansys FEM simulations were more conveniently employed to evaluate the release voltage Vr. For this purpose the structure is modelled starting from his contact state, a constant voltage is imposed across the cantilever tip and a simulation is performed to check if the up state can be recovered. The release voltage is assumed as the minimum voltage such that the beam fails to recover the up state. It is worth mentioning that a precise theoretical estimation of Vr would require accurate modelling of the intimate contact between the cantilever tip and the dielectric surface which is actually a not understood issue to date [11]. The calculated pull-down and release voltage corresponding to different cantilever geometries, as well as the resulting power affordable level in both states are reported on Tables I and II ; the geometrical parameters refer to Figure 4.14.
110
L1 th1 RF signal propagation (T-line)
L2
th2 h1 h2
W2
W1
Contact dielectric layer
Figure 4.14 Geometrical parameters referred in Table I and II.
TABLE I CANTILEVER GEOMETRICAL PARAMETERS
Act. section
L1
(µm)
W1
h1
th1
145 100
2.6
3
Cap. section
L2
W2
h2
th2
(µm)
20
50
1.3
3
TABLE II
THEORETICAL PULL-DOWN/RELEASE VOLTAGES AND CRITICAL POWER VALUES
L2*W2
Vp
Pup
Vr
Cdwn
Pdwn (W)
(µm²)
(V)
(W)
(V)
(fF)
3 GHz
5 GHz
10GHz
20*50
<80
>50
20
142
1.7
2.9
9.6
20*30
<80
>50
44
86
6.2
8.2
19.0
20*20
<80
>50
49
49
6.6
7.9
13.8
111
II Fabrication
Evaporated gold
SiO2 Si
(a)
(b) Al2 O3
Photoresist (Step2)
Photoresist (Step1)
(c)
(d) Electroplated gold
(e)
(f)
Figure 4.15 Fabrication steps.
The fabrication process steps are summarized in Figure 4.15. In order to validate the MEMS varactor design, several test structures for RF power characterization have been fabricated on 500µm thick high resistivity silicon substrate, using standard MEMS process. Exploiting the substrate conductivity, silicon is used in this case as a global pull down electrode for each MEMS varactor, which allows to simplify the fabrication reducing the number of process steps [80]. Moreover the silicon surface has been covered with a 1µm thick thermally grown SiO2 as insulated layer (a). The contact areas under the cantilever tip are 0.15µm thick (b) and covered with a 0.3µm alumina layer as contact dielectric (c). The 112
sacrificial layer profile is obtained using a double deposition and patterning of a PMGI SF13 resist from MICROCHEM (d). The RF lines as well as MEMS cantilevers have been patterned using a 3µm thick gold metallization (e) At the end of the process, the sacrificial layer is removed and the component is dried with CO2 critical point system (f). It can be noticed from Figure 4.16 that the fabricated varactors do not present any protecting package against air and humidity, as announced in section 1.
PMGI SF13 photoresist
Alumina contact layer
Figure 4.16 One of the fabricated varactors.
III RF measurements and reliability
A first set of MEMS varactor test structures has been submitted to several RF power characterizations in order to study their reliability in high power operations and measure the maximum power level that they can handle in hot switching conditions.
III.1 Lifetime and reliability under RF power
The varactors have been submitted to a 100V magnitude bipolar cycling biasing actuation waveform, under a constant RF power in order to monitor the number of cycles performed without a failure occurs. Hot switching tests have been done at 10GHz up to a maximum of 1W power available and at 3GHz up to 15W (limitation of our amplifiers).
113
HP 8722ES
1
Bias T
2
30dB coupler
actuation
Bi polar
RF probe
LF function generator
LF Amplifier +100V
RF detector
R&S FSEK 20-40 spectrum analyser
-30dB
RF probe
Attenuator
2
DUT
Load
Load
Power Circulator divider
0.5V applied 1
Power meter
Load
Bias T
DC power supply
PA
Circulator
10dB coupler
VNA
Attenuator
scope
Agilent 33220A Agilent 54622A -100V
Figure 4.17 Experimental setup for RF power reliability testing.
The used cycling test setup is shown in Fig. 4.17 . The microwave signal is produced by the internal source of an HP 8722ES network analyser and amplified through a TWT PA. This high power signal is applied across the MEMS device loaded on 50 Ohm impedance. The output signal is then split to be simultaneously directed to the VNA (which tracks the transmitted signal phase change when varactors are actuated ), and to a power detector connected to a digital oscilloscope (that monitors the signal magnitude time variation as a function of the biasing waveform). Moreover, during all tests, a small electrostatic force (0.5V DC voltage) is applied between cantilevers and contact electrodes in order to obtain a more reproducible contact in the actuated state. A slightly different setup was used to measure the varactors RF performance (Figure 4.18). Then cycling was periodically stopped in order to measure the calibrated capacitance variation as a function of the applied DC voltage, under low power. The calibrated reflection coefficient is measured at the input of the test device when the output is left in open circuit.
114
HP 8722ES VNA Calibrated S22
Attenuator Bias T
30dB coupler
Power divider
actuation
Only DC
R&S FSEK 20-40 spectrum analyser
RF probe
DC Amplifier 0-120V
LF function generator
RF detector
Open circuit
2
Attenuator
DUT
-30dB
Load
Load
Bias T
0.5V applied 1
Power meter
2
DC power supply
PA Circulator
1
10dB coupler
scope
Agilent 33220A Agilent 54622A
Figure 4.18 Experimental setup for capacitance monitoring.
The circuit model employed to extract the capacitance value is shown in Figure 4.19:
a1
a1 f=f0
DUT
Y0
O. C.
Y0
CEQ
G EQ
b1
b1 measured YEQ @
f=f0
Figure 4.19 Circuit model for deriving the capacitance value.
115
Then the measured complex S22 parameter available from the VNA is:
Γ ≡ S 22 =
YEQ
Y0 − YEQ Y0 + YEQ
=
1 − YEQ / Y0 1 + YEQ / Y0
=
1 − YEQ 1 + YEQ
⇒
ωC EQ 1 − S 22 1 − S 22 G EQ 1 Im = = +j ⇒ C EQ = 1 + S 22 Y0 2π f 0 Z 0 1 + S 22 Y0
(15)
and since S22=Re(S22)+ Im(S22)= r+ji , CEQ can be extracted as in (18):
C EQ =
(1 − ji ) 2 − r 2 1 − r − ji 1 1 Im Im = = 2π f 0 Z 0 1 + r + ji 2π f 0 Z 0 (1 + r ) 2 + i 2
(1 − r − i − j 2i 2 Im{S 22 } 1 1 Im ⇒ C EQ = − 2 2 2π f 0 Z 0 (1 + r ) + i 2π f 0 Z 0 (1 + Re{S 22 }) 2 + (Im{S 22 }) 2 2
(16)
2
116
The following results were achieved on varactors made with 20*30µm² cantilever tip surface. These devices have exhibited pull down and release voltages respectively in the 8590V and 65-70V range for most components, which is a bit larger than expected and was attributed to a thicker gold metallization occurred during the fabrication process. The measured results are summarized in Figure 4.20.
Intrinsic capacitance (f F)
450 400
500E6 cycles
350
50E6 cycles 10E6 cycles
300 250 200
5E6 cycles
Cdown
1E6 cycles
Cup
0E6 cycles
=7-8
150 100 50 0
20
40 60 80 Applied voltage (V)
100
120
Figure 4.20 Capacitance monitoring as a function of the applied static voltage during cycling test under a 1W, 10 GHz RF power signal.
At 10GHz varactors have been cycled with 2.5kHz bipolar square actuation waveform under 1 Watt and have reached 1 billion cycles in hot switching mode. Tests have been stopped before any observed failure occurred. The C(V) curves are obtained after deembedding the parasitic capacitance of the input RF lines and suggest no evident electrical or mechanical degradation due to the applied power. Indeed completely similar characteristics were obtained during cycling tests with no power. As shown in Figure 4.20, the resulting switched varactor capacitance ratio ranges between 7 and 8. The small variations of pull down voltage can be attributed to residual SiO2 dielectric charging phenomenon during the C(V) testing (120V maximum DC voltage applied). Moreover the slight change in the measured down state capacitance mainly relies on the difficulty to keep a perfect constant calibration on reflection coefficient measurement after switching between two different setups. 117
In the same way similar devices were tested at 3 GHz under a 4W continuous power and C(V) curves have been measured up to 0.5 billion cycles with no failure observed (Figure 4.21). Again the obtained curves do not show any significant degradation due to high power signal; the down state capacitance increase between 0 and several cycles is attributed to an initial cleaning or polishing of the contact surface, generally observed after a few cycles, that improves the contact efficiency.
Intrinsic capacitance (f F)
450 Contact cleaning
500E6 cycles 50E6 cycles 1E6 cycles 0E6 cycles
400 350 300 250 200 150 100 50 0
20
40 60 80 Applied voltage (V)
100
120
Figure 4.21 Capacitance monitoring as a function of the applied static voltage during cycling test under a 4W, 3 GHz RF power signal.
Additional experiments are presented in Figure 4.22 6 for a 5W level (which is close to the theoretical power handling limit of these devices) and 0.25 billion cycles have been reached showing behavior similar to the 4W one.
118
Intrinsic capacitance (f F)
500 450
1E6 cycles 0E6 cycles
400 350 300 250 200 150 100 50 0
20
40 60 80 Applied voltage (V)
100
120
Figure 4.22 Capacitance monitoring as a function of the applied static voltage during cycling test under a 5W, 3 GHz RF power signal.
A slightly different test was performed by measuring the C(V) curve at 0 cycles, continuously cycling the varactor under 1W up to 1 billion cycles and then measuring again the capacitance characteristic. The comparison between C(V) curves at 0 and 1 billion cycles is reported on Fig. 4.23. Similar conclusions can be drawn to the step by step test.
Intrinsic capacitance (f F)
600 1E9 cycles 0E6 cycles
500 400 300 200 100 0
0
20
40 60 80 100 Applied voltage (V)
120
Figure 4.23 Capacitance monitoring as a function of the applied static voltage during cycling test under a 1W, 3 GHz RF power signal.
119
III.2 RF power handling static testing
The power handling of tested MEMS varactors is measured by plotting the pull down voltage Vp and the release voltage Vr evolution as a function of RF power level. For this purpose, a continuous input RF power is injected in the device and the applied biasing voltage is slowly increased until actuating the varactor, this voltage is then reduced until all cantilevers release. The measured results are reported in Figure 4.24. The pull down voltage shows almost no sensitivity to power in the 0-10W range, as mechanical simulations predicted. Regarding the release voltage, the maximum affordable power is measured at 37dBm (5W) close to FEM simulations results. Above this limit, the cantilever stiffness is not anymore sufficient to recover the up state and the varactor fails.
100
Voltage (V)
80 60 40 20 0 0
Vrelease Vpull down 5
10
15
20
25
Input power (dBm)
30
35
40
Figure 4.24 Vp and Vr evolution as a function of the input power level at 3 GHz for standard 20*30µm ²tip structure.
Cantilevers with smaller tips (20x20µm²) have been fabricated and tested. The metal thickness turned out to be little larger in these circuits and the pull in voltage is 116V. The measured characteristics are shown in Figure 4.25 and the corresponding maximum handled power is about 40 dBm (10W). 120
120
Voltage (V)
100 80 60 40 Vrelease Vpull down
20 0 0
5
10 15 20 25 30 35 40 45
Input power (dBm)
Figure 4.25 Vp and Vr evolution as a function of the input power level at 3 GHz for standard 20*20µm ²tip structure.
IV Conclusion This chapter focused on the design, fabrication and characterization of original MEMS switched varactors. The presented experimental results validate our approach and allow demonstrating the ability to handle large RF power in hot switching conditions. Varactors capable of handling power up to 10Watt CW have been demonstrated and reliability results have shown 1 billion cycle operations under 1Watt @ 10GHz, and 250 million at 4 & 5Watt @ 3GHz, with on-off ratio between 7 and 8. The proposed double step profile structure is shown to be an efficient solution to overcome RF power failure while keeping simple and compact design. This makes the developed device particularly attractive, compared to previous solutions based, for example, on counter-electrode approaches. These promising results will allow further developing high power MEMS components such as phase shifters, tuners and tunable devices. However, there is still room for improvement in the switched varactor performances. A considerable amelioration could be obtained by integrating a real pull-down electrode as in Figure 4.2. This is expected to reduce the device pull-down voltage with no decrease of the 121
cantilever stiffness then providing higher immunity to dielectric charging problems and better reproducibility of the C(V) curves. Another concern which must be given attention is the improvement of synchronisation of the cantilevers deflection. Measurement operations have shown that the different beams of a same varactor collapse in the down state for slightly different pull-down voltages. The release mechanism neither is perfectly synchronous. This makes hard defining the varactor pull-down and release voltages. Although the synchronisation issue is strongly correlated to the achieved control over the fabrication process, simple design solutions are currently being investigated that can dramatically improve the synchronism of deflection/release operations, with no increased fabrication complexity.
122
CONCLUSION GENERALE
123
Conclusion générale et perspectives
Le travail de recherche présenté dans ce mémoire a été consacré à la conception, la réalisation et la caractérisation de composants micro-électromécaniques pour l’intégration aux systèmes de communication hyperfréquences reconfigurables. Dans un premier chapitre, nous avons tout d'abord défini le contexte de notre étude, à partir de la multitude de dispositifs et de domaines d’application actuels des systèmes microélectromécaniques. Nous nous sommes plus précisément intéressés au fonctionnement des micro-commutateurs pour les applications en hyperfréquence, car la contribution de la technologie MEMS à ce domaine est particulièrement importante et porteuse. Nous avons décrit les structures les plus répandues ainsi que leurs caractéristiques générales. Ce chapitre nous a permis de résumer les principales propriétés électriques et mécaniques des composants micro-électromécaniques et de montrer les améliorations qu’ils pourront apporter aux systèmes hyperfréquences en terme de pertes et de modularité. Nous avons également défini les propriétés actuelles et potentielles des dispositifs électroniques qui intègrent cette technologie. Dans un second chapitre, nous avons présenté la conception, la fabrication, et la caractérisation d’un filtre entièrement reconfigurable, réalisé en technologie microruban sur un substrat d’alumine. L’alumine est en effet très utilisée dans les modules de réception/ émission hyperfréquences, et l’intégration de la technologie MEMS aux substrats céramiques fait actuellement l’objet d’un effort de recherche important. Ce filtre est basé sur l’utilisation de banques de capacités contrôlées par des micro-commutateurs MEMS ohmiques permettant de programmer différentes fonctions de filtrage. Nous avons développé une méthode spécifique pour la synthèse automatique d’un grand nombre de fonctions avec une possibilité d’accord discret pour certains paramètres du gabarit. Nous avons ensuite conçu des résonateurs à fort facteur de qualité en technologie micro-ruban et avec une approche à éléments localisés afin d’implémenter physiquement les fonctions synthétisées. Dans ce chapitre nous avons également présenté les principales étapes du procédé de micro-fabrication et notamment les solutions utilisées pour l’intégration d’inductances montables en surface de commerce. Le filtre mesuré présente de très bonnes performances avec une adaptation 124
supérieure à 15 dB et des pertes meilleures que 5.9 dB pour chacune de fonctions réalisées. En effet, toutes les modalités d’accord sont reproduites correctement et un accord global de 37.5% a été montré autour de 2 GHz. Nous avons également démontré que le réseau de polarisation présente une forte influence sur les pertes du filtre, qui peuvent donc être minimisées grâce à l’intégration de fortes résistances au sein des lignes de polarisation. Dans un troisième chapitre, nous avons présenté une nouvelle topologie de filtre hyperfréquence multistandard, dans le cadre du projet « ReRaFe» du réseau d’excellence AMICOM [68] pour le développement d’un front-end reconfigurable. Nous avons cherché à réaliser un dispositif simple et compact qui exploite une topologie similaire à celle du filtre précédent pour atteindre une reconfiguration complètement différente. En effet, le but du filtre ReRaFe est de reconfigurer la réponse en fréquence sur deux standards préfixés (DCS 1800 et WLAN) complètement hétérogènes. Nous avons montré que cela requiert la mise en place de solutions innovantes pour la réalisation des transformateurs d’impédance d’entrée et sortie qui combinent une architecture distribuée avec des capacités localisées et accordables par des commutateurs MEMS. Les résultats expérimentaux présentés ont validé le principe de reconfiguration bi-standard et ont montré un très bon accord avec les performances hyperfréquences visées. Dans un quatrième et dernier chapitre nous avons présenté un nouveau concept de capacité variable pour des applications forte puissance. Nous avons tout d’abord situé le contexte de ce travail en soulignent la nécessité pressante de composants MEMS capables d’opérer en “hot switching” lorsque la puissance véhiculée par le signal RF qui traverse le dispositif est relativement élevée (P>1W). Le but de ce travail était donc à la fois de développer un composant de puissance pour des applications hot switching, et de caractériser la tenue en puissance du composant fabriqué. Pour cela nous avons étudié théoriquement les principaux mécanismes de défaillance, tels que l’auto-actionnement ou l’auto-maintien à l’état actionné, d’une micro-poutre à contact capacitif en condition de forte puissance. La compréhension de ces mécanismes nous a permis d’élaborer une architecture qui parvient à limiter efficacement les effets de la puissance grâce à un dimensionnement adapté de l’impédance capacitive par rapport à la raideur de la structure. Ensuite nous nous sommes consacrés à l’optimisation de la tenue en puissance du dispositif en développant une procédure d’optimisation récursive multi-physique qui combine les aspects électrostatique, 125
mécaniques et électromagnétique à l’aide de différents logiciels de calcul. Nous avons présenté les principales étapes du procédé de réalisation des varactors optimisées sur un substrat de silicium. Finalement, les choix de conception ont été validés par une caractérisation mécanique et électromagnétique des dispositifs fabriqués comprenant des tests de tenue en puissance maximale ainsi que de tests de durée de vie des composants soumis à divers niveaux de puissance. Les dispositifs ainsi caractérisés ont présenté les propriétés attendues en très bon accord avec le résultats théoriques permettant de valider à la fois la topologie et la méthodologie d’optimisation. Les caractéristiques C(V)) mesurées au cours de plusieurs sessions de cyclage en fonctionnement “hot switching” n’ont montré pratiquement aucun signe de dégradation liée à la puissance transmise au travers des composants. Le contraste d’impédance présenté par les varactor est pour le moment limité à 7-8, ce qui est déjà suffisent pour certaines applications telles que les déphaseurs. La puissance maximale de fonctionnement voisine les 5W pour la plupart des structures et presque à 10W pour un certain nombre de dispositifs qui ont été fabriqués de façon à présenter des constantes de raideur plus importantes. Les résultats obtenus au cours de ce travail de recherche sont intéressants pour la suite et permettent de mettre en evidence de nombreuses perspectives qui en partie inspirent déjà les travaux futurs. Nous avons démontré, sur quelques cas particuliers, que l’intégration de composants MEMS peut accroître le potentiel et la flexibilité des systèmes hyperfréquences classiques. En ce qui concerne les filtres reconfigurables, il nous semble tout a fait envisageable d’intégrer à la structure développée pour le filtre du second chapitre un nombre plus important de bit capacitifs, de façon à améliorer la résolution fréquentielle et l’accord discret global du filtre. On peut également imaginer de généraliser notre étude à la synthèse de filtres multipôles tout en prévoyant une possibilité de réglage de la réjection hors bande. Pour les filtres multistandards il serait également intéressant de généraliser notre technique à un nombre de standards supérieurs. Pour cela, il nous semble fondamental d’envisager la réalisation de ce type de filtre sur alumine, ce qui permettrait d’atteindre une fonctionnalité plus complexe sans augmenter la taille des dispositifs.
126
En ce qui concerne les varactors de puissance, il est naturel d’entrevoir un axe de recherche portant sur l’application de ces dispositifs aux systèmes de déphasage électronique. Néanmoins il nous semble qu’il existe encore un potentiel d’amélioration du composant de base sur les aspects de fiabilité. Par exemple, l’intégration d’une vraie electrode d’actionnement au dispositif (qui actuellement exploite le silicium comme electrode globale) se traduirait en une réduction de la tension d’actionnement et pourrait donc limiter ultérieurement les phénomènes de chargement du dielectrique. Il reste aussi du travail concernant le contrôle de la déflection simultanée des différentes micro-poutre d’un même varactor, celle ci n’étant pas en général parfaitement synchronisée lors de nos expérimentations.
127
128
Appendix A1
2-coupled resonator network: admittance matrix, scattering matrix and multiple filtering function automatic synthesis
129
130
A1.I Filtering properties of the 2-coupled resonator network
For the system on Figure 2.8, from the Kirchhoff’s current law:
1 GS + jωC + V1 − jωC12V2 = I S jωL
(A1)
1 V2 = 0 − jωC 21V1 + G L + jωC + jωL
or in matrix form:
1 − jωC12 GS + jωC + jωL V1 I S = 1 V2 0 − jωC 21 G L + jωC + jωL
⇒ [Y ][V ] = [I ]
(A2)
where GS=GL=G and C12=C21=Cm .Then [Y] can be expressed as the product of the filter central frequency ω0, the fractional bandwidth FBW= ∆ω/ω0 and the resonator capacitance C, for the normalized admittance matrix [Ŷ]:
[Y ] = ω 0 CFBW ⋅ [Yˆ ] ω Cm 1 1 ω ω0 G −j +j − ω 0 CFBW ω 0 C FBW FBW ω 0 ω ˆ [Y ] = G ω Cm 1 1 ω ω 0 −j +j − ω 0 C FBW ω 0 CFBW FBW ω 0 ω
(A3)
Now, from Chapter 2 definitions:
q=
ω 0 CFBW G
= Qe ⋅ FBW
(A4) 131
is the normalized external quality factors, and
m=
Cm 1 M = C FBW FBW
(A5)
is the normalized coupling coefficient, while
ωp = j
1 ω ω0 − FBW ω 0 ω
(A6)
is the complex bandpass frequency. Furthermore for narrowband operations the approximation ω/ω0 ~1 holds. This leads to the compact form:
1 q +ωp ˆ [Y ] = − jm
− jm 1 +ωp q
1 q +ωp = 0
0 ωp + 1 0 q
0 0 − jm + 0 ω p − jm
= (A7)
= [Q] + [Ω] + j[ M ]
where the normalized admittance matrix is decomposed into the sum of 3 terms accounting for the quality factor, [Q], the bandpass complex frequency variable, [Ω] and coupling between resonators, [M]. [M] is referred to as the generalized coupling matrix. It can be noticed that [M] has 0 entries on the diagonal (as suitable for synchronously tuned resonator systems [63]) and is real and symmetrical. Then a canonical diagonal form for [Ŷ] can be found and is useful when computing the inverse [Ŷ]-1 which is in turn required for the network scattering parameters determination. General formulas for deriving [Ŷ]-1 are reported in section A2, however due to the limited number of resonators, [Ŷ]-1 can be conveniently computed by elementary matrix algebra and is shown in equation (A8).
132
1/ q + ω p (1 / q + ω p ) 2 + m 2 [Yˆ ]−1 = jm 2 2 (1 / q + ω p ) + m
jm (1 / q + ω p ) 2 + m 2 1/ q + ω p (1 / q + ω p ) 2 + m 2
(A8)
Now, by considering the 2-coupled resonator filter as a 2-port network, the system scattering parameters can be derived leading to the determination of the circuit filtering properties.
a1
Is
I1
I2
2-P
V1
Gs II
a2
V2
GL=G
G b1
I 1 = I S − G S V1 = I S − GV I 2 = −G LV2 = −GV2
b2
Figure A1.1 2-port representation for the 2-coupled resonator filter.
The incident and reflected waves can be written for this network:
a1 = b1 = a2 = b2 =
V1 + Z S I 1 2 ZS V1 − Z S I 1 2 ZS V2 + Z L I 2 2 ZL V2 − Z L I 2 2 ZL
=
V1 + I 1 / G
=
V1 − I 1 / G
2 1/ G
2 1/ G
= =
IS 2 G 2V1G − I S 2 G (A9)
=0 =
V2 − I 2 / G 2 1/ G
= V2 G
Now the 2-port network voltage parameters can be expressed from the [I]= [Y] [V]:
133
[V ] =
1 [Yˆ ]−1 [ I ] ω 0 CFBW
V 1 ⇒ 1 = V2 ω 0 CFBW
[Yˆ ]−111 [Yˆ ]−112 I S 1 = ˆ −1 ˆ −1 [Y ] 21 [Y ] 22 0 ω 0 CFBW
[Yˆ ] −111 I S ˆ −1 [Y ] 21 I S
(A10)
and from the scattering parameters definition:
S11 =
S 21 =
b1 a1
b2 a1
= a 2 =0
= a 2 =0
1 +ωp q
2G 2 2 −1 [Yˆ ] −111 − 1 = [Yˆ ]−111 − 1 = 2 q q 1 ω 0 CFBW 2 + ω p + m q
(A11)
2G 2 2 jm [Yˆ ]−1 21 = [Yˆ ]−1 21 = 2 ω 0 CFBW q q 1 + ω p + m 2 q
where the equation (A8) has been used for the inverse [Ŷ]-1 matrix. Equations (16) provide a very useful approximated expression for the scattering parameters around central frequency in terms of the external quality factor and coupling between resonators. This essentially represents an implicit relation between the scattering [S] matrix, which accounts for the network transfer function and the admittance [Y] matrix, which accounts for the circuit physical structure. In the following section it will be shown that starting from (A11) it is possible to derive a flexible and fast approach for synthesis of multiple frequency responses. The example presented in Chapter 2 allows evaluating the precision of the approximated expression for the scattering parameters, as computed from (A11). Hence the exact (Chebyshev) frequency response for a 2-pole filter at 2GHz with FBW=10% is compared to the approximated response provided by (A11). The same comparison is also performade for a FBW=20% response, as visible on Figure A1.2.
134
0
-40 -50
FBW=10% ) )) )) ) 21 1 1, 11 ht 1( s( S B B( dd
1 1, 2 1( S( B d
S-param: e xact S-param: approx.
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
Frequency (GHz) freq, GHz (a)
S-parameters
S-parameters
-10 ) 1 2 2 ht -20 S s( BB d d -30
0 -10
2 1 -20 2 ht s( B -30 d
FBW=20%
-40
S-param: e xact S-param: approx.
-50
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
Frequency (GHz) freq, GHz (b)
Figure A1.2 S-Comparison between exact and narrowband approximated response for a 10% FBW filter (a), and a 20% FBW filter (b).
A1.II Fast synthesis of multiple filtering functions
It can be noticed that filter synthesis is exactly the inverse problem of the one faced in equations (A11), since it involves determining the resonators coupling coefficients and quality factors once the filter frequency response is assigned. In matrix term, this is equivalent to computing the admittance matrices [Y], [Ŷ] from the scattering matrix [S], which essentially is an inverse eigenmatrix problem. Although established synthesis procedures exist for ncoupled resonator filters ([61-66]), in the n=2 case an intuitive and flexible approach can be derived directly from equations (A11). This method only requires to specify the desired frequency response in terms of scattering parameters at central frequency. Indeed as a consequence of the narrowband approach, around ω0 the [Ŷ] matrix can be simply derived from (A11) as a function of the S21(ω0) and S11(ω0), and no additional assumption is required about the [S] matrix at different frequencies. Therefore for a given filtering characteristic the corresponding circuit parameters can be found directly in a single step procedure from the equations (A3-A6). Finally due to the lossless network approximation the scattering parameters are mutually dependent. Then the filter can be eventually synthesized basing on S21 (or S11) at ω=ω0 and BW only, which typically results in proper control over
135
central frequency, bandwidth and selectivity performances with minimum computational effort. Hence when (A11) are evaluated ω=ω0 , where ωp=0 and the scattering parameters are assigned, it is easy to extract the mq product:
mq =
1 + S11 C mω 0 C 1 − ( S11 + S 21 ) G 1 + S11 = j = ⇒ m = ⋅ G 1 + S11 + S 21 1 − S11 G ω 0 1 − S11
(A12)
Then the Cm/G ratio is determined unless a constant conductance. This typically allows the designer to scale the network to the proper impedance level in order to assure technological feasibility for all the reactive components. Then the G parameter is generally chosen by technological considerations, as explained soon, and the coupling capacitance Cm is determined. On the other hand when (16) are considered around ω0, it can be seen that S21(∆ω) performs a 2nd order response with conjugate poles, damping factor ζ and resonant frequency ωn that are functions of the mq product( see Figure A1.3):
S 21(ω ) ω ≈ω0 ≅ j j
2mq 1 + (mq) 2
2mq ≅ (1 + pq + jmq)(1 + pq − jmq) 1
∆ω 1 1 + j2 1 + (mq) 2 ω 0 1 + (mq) 2 2Qe
∆ω − 2 ω 0 1 + (mq) 2Qe
∆ω = ω − ω 0 = jG ⋅
G=
1 ∆ω ∆ω − 1 + j 2ζ ωn ωn
2
ζ =
1 1 + (mq) 2
ωn =
2
=
(A13)
2mq 1 + (mq) 2
ω 0 1 + (mq) 2 2Qe
136
10
1.00
3
0
0
S21 (deg)
ζ=0.1 ζ=0.4 ζ=0.707 -1
mq =1.19 Qe =17 ζ =0.676 ω n =1.046 ω0
0.75 0.70
1
-200 -1 10
exact 2nd order approx
S21 (Magnitude)
0.95 )) ) 1, 1 2 0.90 2( ht S( s( 0.85 g g a a m m 0.80
ζ=0.1 ζ=0.4 ζ=0.707
10 -1 0 10
-50-500 -100 -50 -90 -150 -100 -150 -200 -150 -200 10
S21 (dB)
|G|
1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5
∆ω/ωn (rad/s)
Frequency (GHz) freq GHz
Figure A1.3 S21 response as a 2nd order system around ω0.
Then control system theory provides a useful expression relating the system absolute bandwidth BW to the resonator external quality factor Qe :
BW = 2ω n (1 − 2ζ ) + 4ζ − 4ζ + 2 = ω 0 2
4
2
1 + (mq) 2 ⋅ f (ζ ) Qe
(A14)
and the C/G ratio, or the resonator Qe, is determined once the desired bandwidth is specified. Now the system [Y] matrix corresponding to the specified filtering response is completely determined. It can be noticed that from (A12-14):
Qe =
ω0 BW
⋅ 1 + (mq) 2 ⋅ f (ζ ) =
1 f (ζ ) ⋅ FBW ζ
⇒
q = Qe ⋅ FBW =
f (ζ )
ζ
(A15)
where the last term is a function of the mq product (or S11(ω0)) only. This shows that q can be found directly from (A15) with no dependence from FBW. Indeed the q (and m) dependence on FBW in equation (A4-5) is apparent because it is compensated by the Qe dependence, so that m and q can be found directly as a function of S11(ω0).
137
In practice the proposed method allows determining [Ŷ] and [Y] matrices with low computational effort and is suitable for iterative synthesis of multiple filtering functions. The [Ŷ] matrix turns out to be a powerful tool for programming the system to perform a response with arbitrary insertion loss (or return loss) level at ω0. The [Ŷ] parameters m and q are univocally determined from the assigned scattering parameter at midband frequency and do not depend on the system bandwidth. On the other hand the [Y] matrix is derived from [Ŷ] by specifying the response bandwidth and provides information about the resonators quality factor. The corresponding circuit physical parameters can be finally derived from (A3-6). In this sense [Ŷ] and [Y] allow programmable synthesis of multiple filtering functions, meaning that for a given frequency response, determining [Ŷ] and [Y] leads systematically to the circuit components that implement that response. Very fast synthesis of multiple filtering characteristics is obtained by integrating the [Ŷ], [Y] and circuit parameters computation in a single automatic procedure. The resulting Matlab program can be inspected in section A3 and was employed for synthesis of all the frequency responses shown below.
A1.III Qe and M parameters extracting for the impedance transformed filter
Equation (8) in Chapter 2 for Qe and M are determined from the elementary network equivalence of Figure A.3 that allow to derive the 2-coupled resonator filter capacitance C if only the realisable filter parameters Cin, Cr, Cm are known. Cin G0
Cin
Cm L
Cr
Cr
L
G0
Cm J= G0
Cin ωCm
J=
L ωCm Cin G0
L Cr+ Cin
Figure A1.4 Network theory equivalence used for determination of Qe and M.
138
The admittance inverters in Figure A1.4 can be then used to absorb the Cin external capacitances and a filter of the Figure 2.8 kind is obtained. This also leads to the relation (8) in Chapter 2 and the 2nd degree equation in (A16) that provides the realisable filter resonance frequency:
ω 02 =
1 Cr + Cm + Cin
(A16)
1 ω Cin 1 + 0 G 0
2
139
140
Appendix A2
Canonical form of the normalized admittance matrix
141
142
The [M] coupling matrix featuring in equation (12) of Chapter 2 has 0 entries on the diagonal (as suitable for synchronously tuned resonator systems [52]) and is real and symmetrical. Then an orthogonal [T] matrix exists such that:
[ M ] = [T ][Λ][T t ] [Λ] = diag (λ1 , λ2 )
(A17)
[T ][T t ] = [T t ][T ] = [U ]
with λ1,λ2 the eigenvalues of [M] which are –m and m respectively. [T] is easily computed from the[M] eigenvectors:
[T ] =
2 2 2 2
−
2 2 2 2
(A18)
and diagonalization of the whole normalized admittance matrix can be finally accomplished:
[Yˆ ] = (1 / q + ω p )[U ] + j[T ][Λ][T t ] = [T ] {(1 / q + ω p )[U ] + j[Λ]} [T t ] = [T ][YˆD ][T t ] = =
2 2 2 2
−
2 1 + ω − jm p 2 q 2 0 2
2 2 1 + ω p + jm − 2 2 q 0
2 2 2 2 (A19)
where [ŶD] is the diagonalized and normalized admittance matrix. The matrix decomposition to its canonical diagonal form turns out to be useful when computing [Ŷ]-1 matrix for ncoupled resonator problems with n>2, which is generally required for scattering parameters determination. However even in the n=2 case:
143
{
}
[Yˆ ]−1 = [T ][YˆD ][T t ] =
2 2 2 2
−
−1
= [T ][YˆD ]−1 [T t ] =
1 2 2 0 1 / q + ω p − jm 2 2 1 2 2 0 − + + 1 / q ω jm 2 p 2
2 2 2 2
(A20)
and from (A19) it is interesting to obtain a well known general form [52] for the [Ŷ]-1 matrix:
1/ q + ω p 2 2 2 (1 / q + ω p ) + m −1 ˆ [Y ] = jm q 2 2 (1 / q + ω p ) + m
jm 2 2 r −1 (1 / q + ω p ) + m T T ⇒ [Yˆ ] −1 nm = ∑ nk mk [T ][YˆD ][T t ] 1/ q + ω p k =1 δ + jλ k 2 2 (1 / q + ω p ) + m (A21)
{
}
where [Ŷ]-1nm is the n-th row, m-th column element of [Ŷ]-1, r =2 is the number of resonators , and δ= (1/q)+ωp .
144
Appendix A3
Exact expression for the scattering parameters of a 2-coupled resonator network
145
146
The exact frequency response for a 2-coupled resonator network can be derived by the principle of superposition of an even and an odd mode, as explained in Chapter 2. When the system undergoes an even excitation, referring to the convention and schematic of Figure 2.6 the reflection coefficient can be written as:
S11even
2 ω even G0 − jω (C − Cm)1 − 2 ω =− ω2 G0 + jω (C − Cm)1 − even ω 2
(A22)
When the system undergoes an odd excitation, referring to the convention and schematic of Figure 2.7 the reflection coefficient can be written as:
S11odd
ω2 G0 − jω (C + Cm)1 − odd ω2 =− ω2 G0 + jω (C + Cm)1 − odd ω2
(A23)
Furthermore when the modes are linearly combined from network theory [55] the network scattering matrix is given by:
S11 =
1 [S11EVEN + S11ODD ] 2
(A24)
1 S11 = [S11ODD + S11EVEN ] 2
This leads to the exact scattering parameters expression that features in the comparison of Figure 2.9.
147
148
Appendix A4
Matlab code for the multiple filtering characteristics synthesis program
149
150
This is the Matlab code developed and employed for synthesizing the whole set of frequency responses in Chapter 2.
151
152
Appendix A5
VTip evaluation for a mismatched generator and finite lengths transmission lines
153
154
The model for the MEMS switched varactor connected to an arbitrary RF source through a finite length transmission line was introduced in Chapter 4 and is reported in Figure A.1. The RF line parameters are now the electrical length 2θ, the propagation constant β and the characteristic impedance Z0. The time domain applied RF signal is vg(t)=V0 sin(ωt) θ
Zg VIN Vg
Z0 , β
θ VTip
C
Z0 , β z
-L
0
L
Figure A5.1. Circuit model for the RF input signal interaction with the switched varactor.
Following the conventions of Chapter 4 the input RF signal can be expressed as:
VIN = V (− L) = V g
Z IN = V + (e jβL + ΓL e − jβL ) Z IN + Z g
Z IN 1 ⇒ V + = Vg jβL Z IN + Z g (e + ΓL e − jβL )
(A25)
where ZIN is the input impedance looking into the transmission line from the generator:
Z IN
1 + ΓL e − j 2 βL = 1 − ΓL e − j 2 βL
(A26)
Thus the V+ expression can be algebraically manipulated, leading to [78]:
V + = Vg
Z0 e − jβ L Z 0 + Z g (1 − ΓL Γg e − j 2 βL )
(A27)
155
where Γg is the reflection coefficient seen looking into the generator:
Γg =
Z g − Z0
(A28)
Z g + Z0
The voltage across the cantilever capacitive tip is the total voltage at the z=0 point:
VTip = V (0) = V + (1 + ΓL ) = V g
Z0 e − jβL (1 + ΓL ) Z 0 + Z g (1 − ΓL Γg e − j 2 βL )
(A29)
Therefore, due to multiple reflections in the line, the resulting voltage across the varactor tip and in general the efficiency of the power transfer to the capacitive load depend on the Zg , Z0 and θ=βl parameters according equation (A29). For example Figure A5.2 reports the ADS simulated |Vtip| signals for a sinusoidal input signal of P=2.2 W RF power, at 10 GHz and a 5 degrees line with Z0=50 Ω line. The |Vtip| function as computed from (A29) is also reported, showing perfect agreement with simulation. The schematic for ADS circuit simulation is shown in Figure A5.2.
Figure A5.2 |VTip| evaluation by ADS harmonic balance analysis and the circuit model of Figure A5.1.
156
15
|VTip | (Model)
Vo ltage (V)
10
|VTip | (ADS )
5
|VIN |
0 -5
-10 -15 0
20
40
60
80
100
120
140
160
180
200
Time (ps)
Figure A5.2 |VTip| computing for a 2.2W sinusoidal 10GHz applied RF signal over a 500 fF varactor loading a 5 deg 50Ω line.
It can be noticed that for some practical applications the loaded line impedance can be different from the source reference impedance which is typically 50 Ω. For example, DMTL phase shifters usually consist of a high impedance (>50Ω) transmission line periodically loaded by a the periodic placement of discrete capacitors [35]. Indeed, the RF line meander shape the for the varactor presented in Chapter 4 is purposely designed to provide such a high impedance behaviour (Z0~67Ω). This is thought to allow potential integration of the device in a DMTL phase shifter. The circuit model of Figure A5.1 can be properly employed for analytical determination of the |Vtip| signal by considering the effective RF lines impedance and computing the reflection coefficient consequently. However, ADS circuit simulations based on the circuit model presented in Chapter 4 (Figure 4.7) are actually employed as in Figure A5.5, because they provide better deembedding of the RF lines effect. This allowed computing the critical power values in the down state reported by Table II in Chapter 4.
157
RF lines MOMENTUM [S]
Figure A5.5 |VTip| evaluation by ADS harmonic balance analysis and the circuit model of Figure 4.7.
.
158
Appendix A6
Matlab code for the cantilever beam deflection simulation and pull-down voltage evaluation program
159
160
This is the Matlab code developed and employed to simulate the cantilever beam deflection and to predict the pull-down voltages in Chapter 4.
161
162
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PUBLICATIONS
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Publications Reviews [1]
C. Palego, A. Pothier, A. Crunteanu and P. Blondy, “A 2-pole lumped programmable filter with digital MEMS digital capacitor banks”,
submitted to IEEE Transactions on Microwave Theory and Techniques, December 2006. [2]
C. Palego, A. Pothier, A. Crunteanu and P. Blondy, “High power reliability aspects on RF MEMS varactor design”, Microelectronics and
Reliability, Volume 46, issues 9-11, pp.1705-1710, September-November 2006.
Conferences [1]
P. Blondy, C. Palego, A. Pothier, and A. Crunteanu “High Power Applications of RF-MEMS”, invited paper at 7th topical meeting on
Silicon Monolithic Integrated Circuits in RF Systems, Long Beach, USA, January 2007. [2]
C. Palego, A. Pothier, A. Crunteanu, P. Blondy “High power reliability aspects on RF MEMS varactor design”, European Symposium
Reliability of Electron Devices Dig., October 2006, Wuppertal, Germany. [3]
C. Palego, A. Pothier, T. Gasseling, A. Crunteanu, C. Cibert, C. Champeaux, P.
Tristant, A. Catherinot and P. Blondy “RF-MEMS Switched Varactor for High Power Applications”, MTT-S Int Symp. Dig., San Francisco, USA, June 2006. [4]
C. Palego, A. Pothier, P. Blondy “Double Standard MEMS Tunable Filter for a Reconfigurable Front-End”,
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