Isnt
the KD1S in Fig. 9.4 simply a multi-bit modulator, Sec.
7.3.4?

No, for
several reasons.

·
First
the ideal *SNR* for a first-order
multi-bit
DS modulator is 6.02*N* + 1.76 5.17 + 30log*K* where *K* is
the oversampling ratio and *N* is
the number of bits used in the
multi-bit quantizer (ADC)
and DAC. The key
thing to note is that the *SNR* increases
linearly with
increases in *N*. For the KD1S modulator
the *SNR* (using
1-bit quantizers and
DACs) is 6.02 + 1.76
5.17 + 30log*K* + 30log*K _{path}* where

o
For a
3-bit multi-bit DS (seven comparators and eight
resistors), *f _{s}* =
100 MHz and

o
For an
8-path KD1S (eight comparators), *f _{s}* =
100 MHz,

o
The
power dissipation is higher for the multi-bit DS

·
Second,
the gain, *G _{c}*,
of a 1-bit quantizer (a
comparator) can
vary from 1 to infinity (actually, the gain of the comparator) as seen
in Fig.
7.15 of the book. The gain of a multi-bit quantizer is
very limited, Fig. 7.16, and close to 1. This later limitation severely
limits
the robustness of the resulting feedback system. Perhaps more important
than
this is that 1-bit quantizers are
inherently linear!

·
Finally,
the sampling rate in the KD1S modulator is *K _{path}* times
larger than the sampling rate in the ordinary DS modulator resulting in
benefits from less aliasing to the ability to use differing digital
filters
that result in wider conversion bandwidths.