Study of analog-to-digital mixed integrated circuit configuration using number theory

Abstract

Electronic circuits form the basis of much of the technology we use today. Professor Haruo Kobayashi and Assistant Professor Anna Kuwana, Division of Electronics and Informatics, Gunma University, Japan, are utilising classical mathematics, including theorems such as number theory and control theory in their design of circuits that contain elements of analogue signalling. Analogue circuit planning is regarded as an art as these circuits are typically designed based on mature designers' intuition and experiences in a process that is less systematic for coming up with new architectures and more designing than digital circuit design and Kobayashi and Kuwana firmly believe that 'beautiful' mathematics can facilitate truly great circuit design. Additional mathematics techniques employed by Kobayashi and the team are statistics, coding theory, modulation and signal processing algorithms and pairing pure mathematics theorems with electrical engineering is a key feature of the researchers' work. The team utilises theoretical analysis and simulations such as the circuit simulator (SPICE) and system simulator (MATLAB) to test its work and collaborates with semiconductor companies and electronic measurement instrument companies in Japan for smart circuit design and effective circuit testing. So far, results include that using SAR ADC configurations with Fibonacci sequence weights can improve the speeds and reliability of the SAR ADC. Also several new DAC architecutures and waveform sampling methods are derived based on mathematics.