Advanced Frequency Synthesis by Phase Lock

CHAPTER 7

DIOPHANTINE SYNTHESIZER

Another method that has long been used to achieve fine frequency resolution simultaneously with wide loop bandwidth is the combining of two synthesizer PLLs. One method for doing this, which we discussed in Section F.8.2.3, is an architecture that we called Offset Reference after Smith [1996]. It has an advantage over other dual loops (Section F.8.2.2) in which the output frequency of one loop is divided before that output is mixed with the other, because the output frequencies of these individual loops tend to be more commensurate and, therefore, more easily mixed. (When one frequency is much smaller than the other, it is difficult to separate the mixing products from each other.) We found that developing a tuning algorithm for the Offset Reference loop can require some effort. A synthesis method [Sotiriadis, 2006] called diophantine, after the mathematics that has been applied to it, includes Offset Reference as a subset. It provides a mathematical basis that expands the design possibilities and facilitates the specification of design parameters and of a tuning algorithm. In addition, it has been applied to synthesizer architectures for more than two loops [Sotiriadis, 2008a].

Figure 7.1 shows one loop of a diophantine synthesizer. Other loops would be fed by the same basic reference frequency F_ref,0 and their output frequencies would all be added or subtracted in frequency mixers.

FIGURE 7.1   One synthesizer loop in a diophantine synthesizer. ...