Some open issues associated with the new type of component: digital-to-frequency converter [Open Column]

This paper presents seven unsolved mathematical problems which all relate to a new type of electronic component: digital-to-frequency converter. These problems are parts of the theoretical foundation of this new component. Even though theoretical in nature, these problems will have profound impact on future real electronic system design. These problems present themselves as an excellent example of demonstrating the significance of mathematical analysis in circuit design applications. They show the importance of fundamental research on directing the real world work.

The Background

This open column paper is closely tied to the reference [1], which appears in the same issue of CAS Magazine as this one. The goal of this paper is to provide further detailed description on the issues raised in that accompanying paper. As described in Section II.E of [1], the Flying-Adder frequency synthesizer's operation depends heavily on the fractional number used in that system. When a fractional number is used in the frequency control word of a Flying-Adder synthe sizer, the synthesizer's output is in the fashion of time-average-frequency. In other words, in the output clock waveform, there is a prolonged cycle every once in a while. These prolonged cycles are caused by the fractional carry-in overflows. Table 1 of [1] lists the resulting patterns from some commonly used fractions. For convenience, this table is presented in here (Table 1) as well. The left column is the fraction number, while the right column is the corresponding pattern of the cycles. Letter A represents the normal cycle, letter is the prolonged cycles caused by the accumulation of the fraction. The pattern repeats forever.