Derivation of Digital-to-Analog Converter Architectures Based on Number Theory

This paper investigates possibilities of deriving new Digitalt toAnalog Converter (DAC) architectures based on polygonal and prime number theories. As the result, configurations of polygonal number DACs and prime number DACs are obtained; each consists of a few current sources, a resistor network, switch arrays and a decoder circuit. Whole circuits are designed and their operations are confirmed with simulation; they work as DAC in principle, and most of their circuits consist of digital circuit, which is suitable for implementation with nano-CMOS process. In many cases, analog/mixed-signal circuit architecture design relies on intuitions and experiences of the designer, but here we demonstrate that it is feasible to derive different DAC architectures from conventional ones based on mathematical theory.