Advanced Frequency Synthesis by Phase Lock

CHAPTER 5

OTHER ΣΔ ARCHITECTURES

There are a large number of possible architectures other than MASH-11…. We will consider a few of these here.

5.1   STABILITY

One issue that we have not had to be concerned with in MASH configurations is the stability of the modulator. This is an issue for the more general ΣΔ modulator, where well-behaved performance is limited to a finite range of input values.

It should be apparent, with a little consideration, that the MASH modulator also has a limited range of input values. Fortunately, the allowed range is the range we require. Consider, however, what would happen if we input a number larger than 1. The first accumulator cannot output an average value larger than its maximum output, which is 1, and the outputs from the other accumulators are passed through difference functions (1 − z⁻¹), so their average contribution is 0.

The limits are not so obvious in more complex structures, where a single quantizer must output more than 1 bit. When their output ranges are restricted, they will perform properly only over a finite input range, which may not encompass the required range. We could observe the unrestricted output range over the full input range and provide for this in the design, but there may be reasons to restrict the output to a somewhat smaller range. For instance, increasing the range of the quantizer requires that the pulse swallower also be designed for a larger range. If the quantizer range is smaller than the range that occurs without ...