IEEE Solid-States Circuits Magazine - Summer 2019 - 16

Andrew Yu,
Daniel Bankman,
Kevin Zheng, and
Boris Murmann

Understanding
Metastability
in SAR ADCs
Part II: Asynchronous

T

his article is the
second part of our
tutorial on metastability in successive
approximation register (SAR) analog-to-digital converters
(ADCs). Having covered the synchronous topology in Part I in the Spring
2019 issue of IEEE Solid-State Circuits
Magazine, we now invest ig ate its
asynchronous (or self-timed) counterpart. Even though the idea of successive approximation is rather old, it
Digital Object Identifier 10.1109/MSSC.2019.2922890
Date of publication: 27 August 2019

16

S U M M E R 2 0 19

was not until 2006 that the benefits
of asynchronous timing were unleashed through a seminal contribution by Chen et al. [1]. Since then, the
asynchronous variant has emerged
as a very popular option to achieve
higher speeds and tame metastability
issues more gracefully. The latter aspect is the focus of this article.
We begin by examining the differences that arise from asynchronous
timing and then enumerate their impact on the metastability rate and metastability error distribution. As in Part I,
we first consider the noiseless operation
and then look at the combined effects of

IEEE SOLID-STATE CIRCUITS MAGAZINE

thermal noise and metastability. Next, we apply the derived
models to an ADC-based serial link application and finish
with remarks about metastability detectors.
The material in this article
is most closely related to the
works of Cai et al. [2] and Waters et al. [3]. However, just as
in Part I, our distinguishing
features are our combined
treatment of noise and metastability and our framework
for computing the combined
error probability mass function (PMF).

From Synchronous to
Asynchronous
In the synchronous architecture, one clock period TCLK
is allocated to each bit cycle
of the successive approximation algorithm. This clock
period must be long enough
to accommodate both the
regeneration-independent delay in
the SAR loop TFIX [SAR logic, digitalto-analog converter (DAC) settling,
buffers, and so on] and the comparator regeneration time. If one clock
period cannot accommodate both of
these delays in any given bit cycle, a
metastability error occurs. The number of comparator time constants (x)
that fit into the time available for
regeneration per bit cycle is enough
information to fully characterize the
metastability behavior of the synchronous SAR ADC. We refer to this timing
parameter as N = ^TCLK - TFIXh /x. As
explained in Part I, assuming a uniform input signal distribution, the
probability of a metastability error is
Pmeta = 2 ^2B - 1h e -N , where B is the
number of bits.

1943-0582/19©2019IEEE



IEEE Solid-States Circuits Magazine - Summer 2019

Table of Contents for the Digital Edition of IEEE Solid-States Circuits Magazine - Summer 2019

Contents
IEEE Solid-States Circuits Magazine - Summer 2019 - Cover1
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