With the advancement of CMOS process and fabrication, it has been a trend to maximize digital design while minimize analog correspondents in mixed-signal system designs. So is the case for PLL. PLL has always been a traditional mixed-signal system limited by analog part performance. Around 2000, there emerged ADPLL of which all the blocks besides oscillator are implemented in digital circuits. There have been successful examples in application of Bluetooth, and it is moving to improve results for application of WiMax and ad-hoc frequency hopping communication link. Based on the theoretic and measurement results of existing materials, ADPLL has shown advantages such as fast time-to-market, low area, low cost and better system integration; but it also showed disadvantages in frequency resolution and phase noise, etc. Also this new topic still opens questions in many researching points important to PLL such as tracking behavior and quantization effect. In this thesis, a non-linear phase domain model for all digital phase-locked loop (ADPLL) was established and validated. Based on that, we analyzed that ADPLL phase noise prediction derived from traditional linear quantization model became inaccurate in non-linear cases because its probability density of quantization error did not meet the premise assumption of linear model. The phenomena of bandwidth expansion and in-band phase noise decreasing peculiar to integer-N ADPLL were demonstrated and explained by matlab and verilog behavior level simulation test bench. The expression of threshold quantization step was defined and derived as the method to distinguish whether an integer-N ADPLL was in non-linear cases or not, and the results conformed to those of matlab simulation. A simplified approximation model for non-linear integer-N ADPLL with noise sources was established to predict in-band phase noise, and the trends of the results conformed to those of matlab simulation. Other basic analysis serving for the conclusions above covered: ADPLL loop dynamics, traditional linear theory and its quantitative limitations and numerical analysis of random number. Finally, a present measurement setup was demonstrated and the results were analyzed for future work.

Un microscope à force atomique (AFM) est utilisé pour caractériser des matériaux isolant ou semi-conducteur avec une résolution pouvant atteindre l'échelle atomique. Ce microscope est constitué d'un capteur de force couplé à une électronique de contrôle pour pouvoir correctement caractériser ces matériaux. Parmi les différents modes (statique et dynamique), nous nous focalisons essentiellement sur le mode dynamique et plus particulièrement sur le fonctionnement sans contact à modulation de fréquence (FM-AFM). Dans ce mode, le capteur de force est maintenu comme un oscillateur harmonique par le système d'asservissement. Le projet ANR Pnano2008 intitulé : ”Cantilevers en carbure de silicium à piézorésistivité métallique pour AFM dynamique à très haute fréquence" a pour objectif d'augmenter significativement les performances d'un FM-AFM en développant un nouveau capteur de force très haute fréquence. Le but est d'augmenter la sensibilité du capteur et de diminuer le temps nécessaire à l'obtention d'une image de la surface du matériau. Le système de contrôle associé doit être capable de détecter des variations de fréquence de 100mHz pour une fréquence de résonance de 50MHz. Etant donné que les systèmes présents dans l'état de l'art ne permettent pas d'atteindre ces performances, l'objectif de cette thèse fut de développer un nouveau système de contrôle. Celui-ci est entièrement numérique et il est implémenté sur une carte de prototypage basée sur un FPGA. Dans ce mémoire, nous présentons le fonctionnement global du système ainsi que ses caractéristiques principales. Elles portent sur la détection de l'écart de fréquence de résonance du capteur de force. / An atomic force microscope (AFM) is used to characterize insulating materials or semiconductors with a resolution up to the atomic length scale. The microscope includes a force sensor linked to a control electronic in order to properly characterize these materials. Among the various modes (static and dynamic), we focus mainly on the dynamic mode and especially on the frequency modulation mode (FM-AFM). In this mode, the force sensor is maintained as a harmonic oscillator by the servo system. The research project ANR Pnano2008 entitled: "metal piezoresistivity silicon carbide cantilever for very high frequency dynamic AFM" aims to significantly increase the performance of a FM-AFM by developing new very high frequency force sensors. The goal is to increase the sensitivity of the sensor and to decrease the time necessary to obtain topography images of the material. The control system of this new sensor must be able to detect frequency variations as small as 100mHz for cantilevers with resonance frequencies up to 50MHz. Since the state-of-the-art systems doe not present these performances, the objective of this thesis was to develop a new control system. It is fully digital and it is implemented on a FPGA based prototyping board. In this report, we present the system overall functioning and its main features which are related to the cantilever resonant frequency detection. This detection is managed by a phase locked loop (PLL) which is the key element of the system.