IEEE Circuits and Systems Magazine - Q3 2023 - 59

problems associated with reference-switched resistor
DACs (see Fig. 5) are the following [22]:
■ Parasitic Resistance in the Reference Path: The
data-dependent switching current drawn from the
references due to the parasitic capacitance of the
switches and distributed capacitance of the resistors
creates a second-harmonic voltage drop in
the reference path. This results in third-harmonic
distortion in the CTΔΣM output.
■ Inter-Symbol Interference: ISI, caused by rise-fall
asymmetry in the feedback DAC pulse, is another
problem with the conventional switched-resistor
DAC of Fig. 5(a). The root cause of ISI is the unequal
resistance of the PMOS and NMOS switches,
resulting in even-harmonic distortion and an increased
in-band noise floor.
It turns out that the problems listed above are " dealbreakers "
when low-noise, and distortion levels below
100 dB are desired. In the discussion that follows, we
describe potential solutions to these problems.
A. The Virtual-Ground-Switched Resistive NRZ DAC
The virtual-ground-switched DAC [12] is an attempt to
address the problems with a conventional switchedresistor
DAC. The principle of operation is shown in
Fig. 6. For the time being, disregard the
dummy element enclosed in the grey
box. The switch parasitic capacitance
is denoted by cp1. The resistors are
associated with a distributed capacitance
to ground, denoted by cp2. As
the name suggests, the switches are at
the " virtual-ground ends " of Rdac. The
other ends of Rdac are simply tied to
Vref and ground, respectively. Notice
that all the switches are realized using
n-channel devices. Thanks to the
virtual ground of the OTA, the voltage
across cp1 does not change when the
data-bit D makes a transition. Consequently,
the current drawn from Vref
has no switching component, and the
parasitic resistance in the reference
path, which was problematic in the
conventional switched-resistor DAC,
is no longer an issue. Unfortunately, it
turns out that the virtual-ground voltage
of the OTA is effectively sampled
onto cp1 and cp2 at every transition
of D. The resulting data-dependent error
causes distortion at the output of
the modulator. This error is eliminated
by adding a dummy element (shown in
THIRD QUARTER 2023
the grey box in Fig. 6) as discussed below. The capacitance
of the dummy is nominally identical to the parasitic
capacitance of the main DAC element. Furthermore,
the dummy is excited by a data-sequence Dx which
makes a transition when D does not and vice versa. Consequently,
the error charge injected by the DAC element
is independent of the data sequence D.
Another important attribute of the virtual-groundswitched
resistor DAC is its inherently lower ISI. This
is because both the rising- and falling-edges of the
single-ended current waveform are controlled by NMOS
devices.
A potential source of distortion in the virtual-groundswitched
resistive NRZ DAC is the imbalance between
the differential inputs and/or mismatch in the input resistors.
This is illustrated using Fig. 7(a). For the time being,
ignore the CMFB block at the virtual ground nodes
drawn in red. Ideally, the voltages at ip and im should
be perfectly balanced about a dc common-mode voltage
05
()Vref
.. In practice, the source driving the CTΔΣM
will be imbalanced; the inputs will not have the same
amplitude, and their phase difference, which should
be π radians, will be πφ+()∆ . As a consequence, the
OTA's virtual-ground nodes have a small common-mode
component proportional to the input. This will in turn
Figure 6. (a) Feedback DAC with dummy element identical to that of main DAC.
(b) Example drive waveforms of main DAC and the dummy.
IEEE CIRCUITS AND SYSTEMS MAGAZINE
59
IEEE Circuits and Systems Magazine - Q3 2023

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