It is well known that real op-amps do not share most of the desirable characteristics of an ideal one, particularly those of gain and output impedance. When presented with a capacitive load, such as a MOSFET or ADC, feedback in an op-amp circuit can quickly become unstable. This thesis studies and characterizes an op-amp’s output impedance and how its interaction with this type of load creates a parasitic pole which leads to instability. Applying ideas from feedback control theory, a model for studying the problem is developed from which a generalized method for compensating the undesirable circumstance is formulated. Even in a zero-input state, many real op-amps driving capacitive loads can experience unforced oscillations. A case study is performed with three commonly used devices. First, the output impedance is determined by its dependence on the unity-gain bandwidth, load capacitance, and oscillation frequency. It is fitted into a second-order feedback control model that allows for an analytical study of the problem. It is then shown that a carefully designed passive network can be introduced between the load and op-amp to obtain a properly damped system free of oscillation and well-behaved. Using a shunt resistor is a known and commonly used method for lowering an op-amp’s output impedance to gain stability. This work considers the converse addition of a series capacitor to instead lower the load capacitance seen by the op-amp, a seemingly complementary method that achieves the same goal. A generalized, composite compensation method is developed that uses both the shunt resistor and series capacitor– a strategy not yet found in literature. Relevant formulas for damping ratio and natural frequency are derived that allow the design of a passive compensation network. Furthermore, tradeoffs between compensation, voltage swing, current consumption, and power usage are considered. An emphasis is placed on comparing simulated versus real circuits to highlight the fact that any problem is much worse in real-life than in a simulation. SPICE models and programs aim to de-idealize certain device characteristics, but often cannot account for environmental conditions and manufacturing variance. Thus, an importance is placed on experimental verification guided by simulations.

Cette thèse a pour but d’étudier les activités humaines à travers l’analyse du flux de signalisation du réseau cellulaire de données (GTP). Pour ce faire, nous avons mis en place un ensemble d’outils nous permettant de collecter, stocker et analyser ces données de signalisation. Ceci en se basant sur une architecture indépendante au maximum des constructeurs de matériel. À partir des données extraites par cette plateforme nous avons fait trois contributions.Dans une première contribution, nous présentons l’architecture de la plateforme de capture et d’analyse de la signalisation GTP dans un réseau d’opérateur. Ce travail a pour but de faire l’inventaire des différents éléments déclenchant des mises à jour et aussi d’estimer la précision temporelle et spatiale des données collectées. Ensuite, nous présentons une série de mesures, mettant en avant les caractéristiques principales de la mobilité humaine observées au travers de la signalisation mobile (le temps inter-arrivées des messages de mise à jour, la distance observée des sauts entre cellules lors des déplacements des clients). Finalement, nous présentons l’analyse des compromis qui ont été faits entre la rapidité d’écriture/de lecture et la facilité d’usage du format de fichier utilisé lors de l’échange d’informations entre les sondes de capture et le système stockage. Deuxièmement, nous avons été capables de mettre en place un algorithme de reconstitution de trajets. Cet algorithme permet, à partir de données éparses issues du réseau cellulaire, de forger des trajets sur les voies de transport. Il se base sur les données des trajets sous-échantillonnées et en déduit les positions du client sur les voies de communication. Nous avons mis en place un graphe de transport intermodal. Celui-ci porte sur le métro, le train et le réseau routier. Il connecte les différents points entre eux dans chacune des couches de transport et interconnecte les modes de transport entre eux, aux intersections. Notre algorithme se base sur un modèle de chaîne de Markov cachée pour placer sur le graphe les positions probables des individus entre les différentes observations. L’apport de ce travail est l’utilisation des propriétés topologiques du réseau de transport afin de renseigner les probabilités d’émission et de transition dans un modèle non supervisé. Ces travaux ont donné lieu à une publication et à un brevet. Finalement, notre dernière contribution utilise les données issues de la signalisation à des fins de dimensionnement du réseau mobile d’opérateur. Il s’agit de dimensionner dynamiquement un réseau mobile en utilisant les bandes de fréquences dites vTV-Whitespace. Ces bandes de fréquences sont libérées sous certaines conditions aux USA et soumises à vente aux enchères. Ce que nous proposons est un système basé sur un algorithme de qualité d’expérience (QoE) et sur le coût de la ressource radio afin de choisir où déployer des femtocells supplémentaires et où en supprimer en fonction des variations de population par unité d’espace. En conclusion, cette thèse offre un aperçu du potentiel de l’analyse des metadata de signalisation d’un réseau dans un contexte plus général que la simple supervision d’un réseau d’opérateur / The aim of this thesis is to study human activities through the analysis of the signaling flow in cellular data network (GTP). In order to achieve this goal, we implemented a set of tools allowing us to collect, store and analyze this signaling data. We created an architecture independent at most of hardware manufacturers and network operators. Using data extracted by this platform we made three main contributions. In our first contribution, we present the GTP capture and analysis platform in a mobile operator network. This work intends to list the different elements triggering updates and to estimate the temporal and spatial accuracy of the data collected. Next, we present a set of measures that represent the main characteristics of human mobility observed through the mobile signaling data (the inter-arrival time of update messages, the observed distances of hops from cell to cell made by moving users). Finally, we present the analysis of the compromise that was made between the writing/reading performances and the ease of use of the file format for the data storage. In our second contribution, we propose CT-Mapper, an unsupervised algorithm that enables the mapping of mobile phone traces over a multimodal transport network. One of the main strengths of CT-Mapper is its capability to map noisy sparse cellular multimodal trajectories over a multilayer transportation network where the layers have different physical properties and not only to map trajectories associated with a single layer. Such a network is modeled by a large multilayer graph in which the nodes correspond to metro/train stations or road intersections and edges correspond to connections between them. The mapping problem is modeled by an unsupervised HMM where the observations correspond to sparse user mobile trajectories and the hidden states to the multilayer graph nodes. The HMM is unsupervised as the transition and emission probabilities are inferred using respectively the physical transportation properties and the information on the spatial coverage of antenna base stations. Finally, in our last contribution we propose a method for cellular resource planning taking into account user mobility. Since users move, the bandwidth resource should move accordingly. We design a score based method using TV Whitespace, and user experience, to determine from which cell resource should be removed and to which one it should be added. Combined with traffic history it calculates scores for each cell. Bandwidth is reallocated on a half-day basis. Before that, real traces of cellular networks in urban districts are presented which confirm that static network planning is no longer optimal. A dynamic femtocell architecture is then presented. It is based on mesh interconnected elements and designed to serve the score based bandwidth allocation algorithm. The score method along with the architecture are simulated and results are presented. They confirm the expected improvement in bandwidth and delay per user while maintaining a low operation cost at the operator side. In conclusion, this thesis provides an overview of the potential of analyzing the signaling metadata of a network in a broader context that supervision of an operator network