Control-Bounded Converters

Abstract

The need for A/D and D/A conversion is a ubiquitous part of many of today's practical applications. The research fields of A/D and D/A conversion are multi-disciplinary, involving topics such as discrete- and continuous-time signal processing, circuit theory, and circuit design. State-of-the-art achievements have refined the practical aspects of traditional converter architectures to a point where performance is reaching its physical limits and progress is stagnating. In this thesis, we present an alternative perspective of analog-to-digital and digital-to-analog conversion called control-bounded conversion. This new perspective utilizes standard circuit components to build up unconventional circuit architectures through a novel theoretical framework between analog and digital. Ultimately, this versatile design principle allows less constrained analog and digital circuit architectures at the expense of a digital post-processing step. We demonstrate the control-bounded conversion principle by a selection of converter examples. First we consider the chain-of-integrators and the leapfrog analog-to-digital converters, which emphasize the division of the analog and digital parts of a control-bounded analog-to-digital converter. In particular, these examples reveal the global nature of the analog design task compared to the local digital part, which can be decomposed into independently operated, sub-circuits. Next, the chain-of-oscillators analog-to-digital converter shows how the control-bounded converter can be adapted for the problem of converting non-baseband signals as is common in communication systems. Specifically, the modulation task (frequency shifting) is incorporated into the digital part of the circuit, removing the need for a pre-processing step. To suppress the influence of circuit imperfections, we introduce the Hadamard analog-to-digital converter that separates the physical and the logical signal dimensions of a control-bounded converter. This separation enables circuit architectures where the sensitivity to component mismatch and thermal noise can be distributed equally throughout the circuit architecture components, thereby minimizing its impact on conversion performance. The overcomplete digital control shows how the digital part's complexity can be increased, resulting in better conversion performance, without substantially increasing the sensitivity to circuit imperfections. This idea relates to using higher-order quantization but partitions the analog part of the circuit in a novel way. We demonstrate that the control-bounded analog-to-digital conversion concept can provide improved conversion performance when converting multiple signals jointly as opposed to independent conversion. Finally, we show how the control-bounded conversion principle can be adopted for digital-to-analog conversion.