IEEE Solid-States Circuits Magazine - Summer 2020 - 25

scheme for the auxiliary inverters
[49], [53]-[55]. Note that this is still a
nearly digital circuit.
Other applications may benefit
from using other (be it less digital)
types of oscillators or ring stages.
For example, the authors in [27] use
a relaxation oscillator as the second
stage to avoid a power-consuming
level shifter, while Marin et al. [13]
use a six-stage ring oscillator with
coupled sawtooth stages for higher
line a r it y in t heir r esist ive sen sor readout.

is one extreme of the spectrum: a
Nyquist-rate design with neither
noise shaping nor oversampling;
w it h its s a mpling f r equenc y of
5 GHz, it has the highest-bandwidth
VCO published to date. A close second is the work in [20], which is a
true oversampling converter with
an effective application bandwidth
of 800 MHz and approximately 10
effective bits resolution. Also, the
design reported in [25] pushes the
bandwidth far in the hundreds of
megahertz region. It is noteworthy
that none of these ultrahigh-speed
desig ns use a globa l feedback
loop, so their noise shaping is only
first order, but they all have digital calibration.
At the other side of the spectrum,
there are the extremely efficient
designs of [38] and [9] with audio (or
near-audio) bandwidth, achieving
high figure of merit (FOM) numbers.
In the near-megahertz range up to
roughly 40 MHz, several efficient
designs have been proposed. Here,
a much wider variety of the techniques discussed in this section
were deployed successfully: some
designs use analog techniques such

A Bird's-Eye View of the
State of the Art
There is a very wide variety in published VCO -based A DC desig ns,
even when limited to highly digital designs that do not require
analog blocks such as opamps. A
bird's-eye view sampling of relevant published designs is listed
in Table 1. Apart from their wide
variety, an important observation
based from this table is that all of
the designs are very compact and
occupy a very small silicon area.
If we rank the designs based on
bandwidth, then the work in [55]

as closed-loop operation [8], [9], [34]
or input feedforward [19], whereas
others use digital calibration to
obtain adequate linearity [10]. In
addition, higher-order noise-shaping structures have successfully
been demonstrated, such as the 1+1
MASH structure in [34] or the thirdorder structure in [10].
Sensor applications are a category of their own. They have low
bandwidth and, when incorporating
the sensor directly in the converter,
typically also higher power; yet they
av o i d a n y b u f fe r o r p r e a m p l i fier. The following are some recent
VCO-based examples. The authors
in [5] target neuron readouts, and,
notwithstanding their low FOM1 of
146 dB, they have an excellent sensitivity with a full-scale input of
8 mVpp. Sacco et al. [35] present a
highly d ig ital, 1−1 sturdy-M A SH
second- order converter for resistive sensor bridge readouts with up
to 16.1 bits of resolution and a very
good FOM1 of 163.5 dB.

Takeaway Points
The following key points can be
observed:

TABLE 1. A REVIEW OF STATE-OF-THE-ART VCO-ONLY ADC CIRCUITS.
REFERENCE

[55]

[20]

[25]

[41]

[19]

[10]

[8]

[34]

[38]

[9]

Year

2020

2020

2019

2020

2015

2017

2020

2020

2020

2020

Noise transfer
function order

0

0 + 1

1

1

0 + 1

3

2

1 + 1

1

1

Analog correction†

no

FF

no

no

FF

FB

FB

FB

no

FB

Digital calibration

yes

yes

yes

yes

no

yes

no

no

no

no

Process [nm]

28

16

65

28

40

65

40

65

130

40

2

Area [mm ]

0.023

0.34

0.244

0.023

0.017

0.01

0.086

0.26

0.04

0.025

Vdd [V]

1

1/1.8

1.05

1.2

0.9

1.2

1.1

0.9

1.2/1.5

0.8

BW [MHz]

2,500

800

200

40

40

10

5.2

2

0.02

0.01

SNDR [dB]

45.2

58

57

77.8

59.5

65.7

69.4

79.7

73.8

78.5

DR [dB]

50.3

60

60

79.5

62

71

72.3

82.7

97

79

22.7

280

49.7

10.9

2.57

3.7

0.86

1.25

0.24

0.0047

FOM1 (SNDR) [dB]

155.6

153

153

171.4

161.4

160

167.2

171.7

153

172

FOM2 (DR) [dB]*

160.7

155

156

173.1

163.9

165.3

170.1

174.7

176.2

172.5

Power [mW]
#

†
FF: input feedforward technique, as explained in the "Input Feedforward Architectures" section; FB: analog feedback; BW: bandwidth; SNDR: signalto-noise and distortion ratio; FOM: figure of merit.
#
FOM1 = SNDR + 10 * log10(BW/Power).
*FOM2 = DR + 10 * log10(BW/Power).

	

	 IEEE SOLID-STATE CIRCUITS MAGAZINE	

SU M M E R 2 0 2 0	

25
IEEE Solid-States Circuits Magazine - Summer 2020

Table of Contents for the Digital Edition of IEEE Solid-States Circuits Magazine - Summer 2020
