IEEE Solid-States Circuits Magazine - Summer 2019 - 21
regenerated, resulting in zero code
error. By integrating the probability
mass of v ID in each range and incrementing the probability of the associated code error by this amount, we
can construct the ADC output code
error PMF (see "Computing the Noiseless Probability Mass Function").
Previously, we found that the
probability of any metastable event is
Pmeta = 2B +1 e - (BN -Teasy /x) . Teasy /x depends strictly on B, so Pmeta is deter-
mined entirely by a single design variable:
N. For the synchronous architecture,
we found that N determined both Pmeta
and the entire shape of the code error
distribution. For asynchronous architecture, this is not the case. The shape of
the ADC output code error PMF depends
on two design variables: N and TFIX /x,
the number of comparator time constants available for regeneration and the
number of comparator time constants
consumed by fixed delay. Note that, to-
gether, these two parameters specify the
number of comparator time constants
in the total normalized conversion time
Ts /x. To show why the asynchronous
code error PMF has a 2D design space instead of a 1D design space, we examine
two examples shown in Figure 5.
Let's begin with Figure 5(a), which
shows two design points sharing the
same value of N. Design 1 has zero
fixed delay, and design 2 has nonzero fixed delay. In design 2, the fixed
4
111
Time
3
110
000 X00 100
1X0
100
10X
2
101
101
vID
1
100
vID/VLSB
φs
φc
vod
0
011
-1
D
D2
Ttrack treg,1
D1
010
treg,2
TFIX
-2
treg,3
001
TFIX
-3
i=1
i=2
i=3
000
Metastable Bit
-4
(a)
D2
D1
Time
D0
Ts
(b)
000
-4
001
-3
010
-2
011
-1
100
0
vID/VLSB
(c)
101
1
110
2
111
3
4
FIGURE 4: (a) A timing diagram and timing bands for a particular input voltage near the bottom of code 101. Given the input voltage, each
regeneration time is determined. The timing bands illustrate how these regeneration times change and add together as a function of the
input voltage. The 3-b codes indicate ADC output during each particular timing band. (b) The timing bands are extended to cover the full-scale
range. Note that the ADC output code during each band changes across the full-scale range. (c) A 1D cross section of timing bands at the end
of the conversion time. This breaks the full-scale range down into segments, each corresponding to running out of time during a particular bit
cycle and incurring a particular code error. The probability mass of v ID inside each segment is used to increment the probability of the corresponding code error in the PMF.
IEEE SOLID-STATE CIRCUITS MAGAZINE
SU M M E R 2 0 19
21
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
IEEE Solid-States Circuits Magazine - Summer 2019 - Cover2
IEEE Solid-States Circuits Magazine - Summer 2019 - Contents
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IEEE Solid-States Circuits Magazine - Summer 2019 - Cover3
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