IEEE Circuits and Systems Magazine - Q3 2023 - 62

linear periodically time varying (LPTV) system, which
results in (out-of-band) shaped quantization noise folding
into the signal band. In the subsection that follows,
we summarize the key points of shaped-noise aliasing in
CTΔΣMs to motivate the three-stage topology used for
the OTA in the input integrator.
A. Chopping Artifacts
The input integrator of a CTΔΣM processes shaped
quantization noise e as shown in Fig. 11(a). Chopping
the OTA of the integrator at a frequency fc, unfortunately,
causes shaped noise from integral multiples of 2fc
to fold into the signal band, as shown in Fig. 11(b). The
mechanism of shaped-noise aliasing can be understood
with the help of the single-ended equivalent of an activeRC
integrator. For ease of understanding, we explain the
phenomenon using a chopped two-stage OTA. The macromodel
of the OTA is given in Fig. 11(c). Chopping the
first stage can be modeled (as far as chopping artifacts
are concerned) in a single-ended equivalent by connecting
c1 and c2 through choppers to nodes 1 and 2 ,
respectively [6], [27]. Assuming u = 0 and that v is an
NRZ pulse, the current supplied by the OTA will be vR/
after an initial transient following the applied pulse. All
this current will thus be supplied by the second-stage
transconductor gm2, resulting in a voltage vg Rm/
()2
at
its input node 2 . Since gm1 does not supply any current,
the voltage at its input node 1 will be zero. When
a chopping edge occurs, the polarities of c1 and c2 are
instantly flipped. Since the voltage on c1 is zero, flipping
it is of no consequence. Flipping c2, however, is
equivalent to injecting an error charge
− 222 ()cv gRm/
into node 2 at the chopping edge. This error can be referred
to the sequence v to quantify its effect in relation
to the DAC pulse. To summarize, the main consequence
of chopping is to cause an error proportional to the
shaped quantization noise sampled at twice the chopping
frequency. The root cause is the non-zero voltage
across the output parasitic capacitors of the chopped
transconductor when the chopping edge arrives.
From the discussion above, we see that the key to
reducing chopping artifacts is to ensure that the input
and output nodes of the chopped stage are as small as
possible at the chopping instants. A way of achieving
this is to use an integrator with a three-stage feedforward-compensated
OTA, as shown in Fig. 12(a). After an
initial transient that lasts for a duration proportional to
the OTA's bandwidth, the feedback DAC current is completely
sunk by gm3, resulting in its input voltage settling
to − ()
vRgm/
3 . Since gm2 does not supply current,
Figure 10. Input integrator of the CTΔΣM which uses an
OTA with a chopped input stage; the first stage of the OTA
employs current-reuse.
62
IEEE CIRCUITS AND SYSTEMS MAGAZINE
Figure 11. (a) Chopped input integrator excited by shaped
quantization noise e. (b) PSD(e)-the parts in red show the
frequency components that alias into the signal band after
chopping. The chopping frequency fc is assumed to be fc/8.
(c) Time-domain understanding of chopping artifacts using a
two-stage feedforward-compensated OTA.
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IEEE Circuits and Systems Magazine - Q3 2023

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