Design Techniques for High-Performance SAR A/D Converters

The design of electronics needs to account for the non-ideal characteristics of the device technologies used to realize practical circuits. This is particularly important in mixed analog-digital design since the best device technologies are very different for digital compared to analog circuits. One solution for this problem is to use a calibration correction approach to remove the errors introduced by devices, but this adds complexity and power dissipation, as well as reducing operation speed, and so must be optimised. This thesis addresses such an approach to improve the performance of certain types of analog-to-digital converter (ADC) used in advanced telecommunications, where speed, accuracy and power dissipation currently limit applications. The thesis specifically focuses on the design of compensation circuits for use in successive approximation register (SAR) ADCs. ADCs are crucial building blocks in communication systems, in general, and for mobile networks, in particular. The recently launched fifth generation of mobile networks (5G) has required new ADC circuit techniques to meet the higher speed and lower power dissipation requirements for 5G technology. The SAR has become one of the most favoured architectures for designing high-performance ADCs, but the successive nature of the circuit operation makes it difficult to reach ∼GS/s sampling rates at reasonable power consumption. Here, two calibration techniques for high-performance SAR ADCs are presented. The first uses an on-chip stochastic-based mismatch calibration technique that is able to accurately compute and compensate for the mismatch of a capacitive DAC in a SAR ADC. The stochastic nature of the proposed calibration method enables determination of the mismatch of the CAPDAC with a resolution much better than that of the DAC. This allows the unit capacitor to scale down to as low as 280aF for a 9-bit DAC. Since the CAP-DAC causes a large part of the overall dynamic power consumption and directly determines both the sizes of the driving and sampling switches and the size of the input capacitive load of the ADC and the kT/C noise power, a small CAP-DAC helps the power efficiency. To validate the proposed calibration idea, a 10-bit asynchronous SAR ADC was fabricated in 28-nm CMOS. Measurement results show that the proposed stochastic calibration improves the ADC’s SFDR and SNDR by 14.9 dB, 11.5 dB, respectively. After calibration, the fabricated SAR ADC achieves an ENOB of 9.14 bit at a sampling rate of 85 MS/s, resulting in a Walden FoM of 10.9 fJ/c-s. The second calibration technique is a timing-skew calibration for a time-interleaved (TI) SAR ADC that calibrates/computes the inter-channel timing and offset mismatch simultaneously. Simulation results show the effectiveness of this calibration method. When used together, the proposed mismatch calibration technique and the timing-skew calibration technique enables a TI SAR ADC to be designed that can achieve a sampling rate of ∼GS/s with 10-bit resolution and a power consumption as low as ∼10mW; specifications that satisfy the requirements of 5G technology

On time, time synchronization and noise in time measurement systems

Time plays an important role in our modern lives. Especially having accurate time, which in turn depends on having clocks being synchronized to each other. This thesis is split into three distinct parts. The first part deals with the mathematical description of noise that is required to model clocks and electronics accurately. In particular we will address the problem that the generally used tools from signal theory fail for noise signals which are neither of finite energy nor periodic in nature. For this we will introduce a new function space based on the Pp-seminorm that is an extension of the Lp-norm for functions of potentially infinite energy but limited power. Using this new semi-norm we will modify the Fourier transform to work on signals from this P p-space. And last but not least, we will introduce, based on the above, a new mathematical model of noise that captures all the properties associated with 1/f -noise. In the second part, we will look at how noise propagates in a few classes of electronics, especially how the non-linear behavior of electronics leads to an amplification of noise and how it could be miti-gated. Lastly, in the third part we will look at one approach of fault-tolerant clock synchronization. After explaining its working principle and showing an implementation in an FPGA we will focus on meta-stability, the problems it can cause and how to handle them on two different circuit levels.Zeit spielt eine wichtige Rolle in unserem Leben. Insbesondere die Verfügbarkeit einer genauen Zeit. Welches wiederum davon abhängt, dass man Uhren hat die auf einander synchronisiert laufen. Diese Arbeit ist in drei Teile aufgeteilt: Im ersten Teil betrachten wir die mathematische Beschreibung von Rauschen um elektronische Systeme und Uhren korrekt beschreiben zu können. Im Besonderen betrachten wir die Probleme die die generell benutzten Methoden der Signalverarbeitung beim Umgang mit Rauschsignalen haben, die weder energiebegrenzt noch periodisch sind. Dafür erweitern wir den Funktionenraum der Lp-Norm auf leistungslimiterte Funktionene und führen die Pp-Halbnorm ein und modifizieren die Fouriertransformation zur Verwendung auf diesen Raum. Und letztlich führen wir ein neues mathematisches Model zur Beschreibung von Rauschen ein, welches alle üblicherweise angenommenen Eigenschaften gleichzeitig erfüllt. Im zweiten Teil analysieren wir wie sich einige Klassen von elektronischen Schaltungem im Bezug auf Rauschen verhalten. Insbesondere im Bezug auf das nicht-lineare Verhalten der elektronischen Elemente, welches zu einer Verstärkung des Rauschens führt. Im dritten Teil betrachten wir eine Möglichkeit um fehlertolerante Synchronization von Uhren zu erreichen. Nach einem Überblick über den verwendeten Algorithmus und wie dieser einem FPGA implementiert werden kann, schauen wir uns den Einfluss von Metastabilität an und wie dieser eingedämmt werden kann