IEEE Solid-States Circuits Magazine - Summer 2020 - 21

A final way to tackle VCO nonlinearity is to apply a calibration technique.
A straightforward approach for this
is to apply the calibration in the digital domain after the VCO-based ADC
[21]-[25]. The principle is shown in
Figure 5 and consists of inverting
the VCO nonlinearity by operating on
the digital output signal of the core
VCO-based ADC. There are two challenges with this technique. First, an
accurate estimation of the VCO nonlinearity must be extracted, making it
available in the digital domain. Most
recently published designs extract
this nonlinearity curve in a lab environment [10], [21]; -h owever, a few
designs using continuous adaptive calibration have been published
[22]-[24]. Second, because the VCO
output signal also contains shaped
quantization noise, applying the digital nonlinearity correction to the VCO
output may make this noise partially
fold into the baseband. A potential
solution for this problem consists of
first removing a large amount of the
quantization noise before doing the
nonlinearity correction [10].

Architectures for Improved
Noise Suppression
Architectures for Reducing
-Quantization Noise
All of the architectures described previously exhibit first-order quantization noise shaping. In many cases, the
oversampling ratio of VCO-based ADCs
is sufficiently large so that this is sufficient. Also, polyphase sampling
techniques have been attempted to
increase the oversampling [25]. However, when going for a higher bandwidth
or higher resolution of say, 16 bits or
greater, a higher order of noise shaping
is beneficial to more efficiently exploit
the advantages of oversampling. To do
this, additional VCOs can be cascaded
and a feedback loop built around the
cascade [10], [26]-[29]. The core mechanism used here exploits the VCO as
an integrating block. Figure 6 shows a
second-order noise-shaping example
where the first VCO is outside the loop.

	

The phase readout can be done with a differential
sense amplifier, combining excellent sensitivity
with very low power consumption.
The disadvantage of this setup is that
the nonlinearity of the first VCO directly couples to the output. To solve
this problem, one of the techniques
described previously (input feedforward or calibration) can be added to
the structure. Also, higher-order examples [10] and structures where the VCO
is inside the loop [8], [28], [29] have
been presented. Although promising, currently the bandwidths of most
published high-order designs do not
exceed that of first-order designs with

similar resolutions, such as in [22], [23],
and [25].
Additionally, the idea of increasing the quantization noise-shaping
order of VCO-based ADCs by cascading multiple units in a multistage
noise-shaping (MASH) structure (see
Figure 7) has been around for some
time [30]-[33]. Recently, successful
silicon implementations have been
presented, such as the 1−1 cascade
w ith second- order qua ntization
noise shaping (2-MHz bandwidth

Open-Loop VCO ADC
Acting as Coarse Quantizer
With Full Input Swing
VCO1

Dout,coarse

Multibit
Readout
DAC
−
+ +

Vin

Open-Loop VCO ADC
Acting as Fine Quantizer
With Small Input Swing
VCO2

Multibit
Readout

+
Dout,Fine + + Dout

FIGURE 4: The input feedforward ADC architecture (also known as coarse/fine structure).
The first coarse quantizer makes a rough digital estimate such that the main fine quantizer
operates on only a very restricted input range. Both quantizers are VCO-based in this example structure [19].

Digital
Nonlinearity
Correction

Nonlinearity
Vin

f( )

Oversampling
VCO ADC With
Noise Shaping

Dout

f -1( )

Decimation

Ddec

FIGURE 5: The core principle of digital calibration for a VCO-based ADC.

x (t )

VCO

w (t )

Up-Down Counter 1
+
+
Counter
-
clk Discrete-Time
at fs Accumulator

DCO

Up-Down Counter 2 fs
+
+
Counter
-

Register

VCO Calibration

y [n]

clk Discrete-Time
at fs Accumulator

FIGURE 6: The block diagram of a VCO-based ADC with second-order quantization noise
shaping from [27]. Note that the first VCO is outside the feedback loop. DCO: digitally controlled oscillator.

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IEEE Solid-States Circuits Magazine - Summer 2020

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