IEEE Solid-State Circuits Magazine - Summer 2015 - 39

VIN

16
VA

20
VB

1-b
Encoder

14

FF

24
VC

1-b
Encoder

DC

DB

DA
10

1-b
Encoder

18
14

FF
FF

28
VD

1-b
Encoder

DD
22
18
14

FF
FF
FF

32
VE

1-b
Encoder

DE
26
22
18
14

FF
FF
FF
FF

36
VF

1-b
Encoder

DF
30
26
22
18
14

FF
FF
FF
FF
FF

40
VG

1-b
Encoder

DG
34
30
26
22
18
14

FF
FF
FF
FF

44
VH

1-b
Encoder

DH
38
34
30
26

FF

FF
FF
FF
FF
FF

22
FF

FF
18
14

FF

DI
42
38
34
30
26
22
18
14

FF
FF
FF
FF
FF
FF
FF
FF

48
VI

1-b
Encoder
DJ

46
42
38
34
30
26
22
18
14

FF
FF
FF
FF
FF
FF

Digital Output Data

12
1-b
Encoder

FF
FF
FF

Figure 1: A patent showing a 1-bit/stage pipelined ADC.

details can be found elsewhere in
this issue [6].

Quantization by Binary Search
Analog-to-digital conversion comprises two fundamental functions,
namely, sampling and quantization.
The latter can be viewed as an operation wherein an "analog estimate" is
identified and the digital equivalent
of this estimate is created. In a flash
ADC, for example, the reference ladder generates the analog estimates,
and the comparators identify one as
the closest lower value, producing
its digital value at the output.
In their basic form, both pipelined and SAR ADCs use binary
search to compute analog estimates
that successively converge toward
the input voltage. Suppose, as shown
in Figure 3(a), that an ADC having an
input range of 0 to VREF senses an
input Vin . Binary search begins by
nominating VREF /2 as the best analog
estimate. Next, since Vin 2 VREF /2,
the search identifies 3VREF /4 as a
better approximation, etc. That is,
in each cycle the ADC compares Vin

with the most recent analog estimate
and directs the search according to
the polarity of their difference. We
call this difference the "residue"
and denote it by Vin - aVREF, where
a = 1/2, 3/4, 5/8 etc., in the above
example. The goal of binary search
is to reduce the residue to less than 1
least significant bit (LSB). Figure 3(b)
illustrates how the decision result in
one cycle leads to comparison with
the proper analog estimate in the
next cycle.

Pipelined ADCs
Basic Operation
To arrive at the basic pipelined architecture, we first note that the binary
search begins with a residue of
Vin - VREF /2, which has the same polarity as 2 (Vin - VREF /2) = 2Vin - VREF .
We can thus form 2Vin - VREF as the
residue and benefit from the 2 #
amplification that it provides before
going to the next binary search cycle.
This method is attractive if the function f (Vin, VREF) = 2Vin - VREF can be
realized efficiently and compactly.

Shown in Figure 4 [8] is a popular
implementation known as the "multiplying DAC" (MDAC) stage. In the sampling (acquisition) mode, C 1 and C 2
(= C 1) track Vin while node X is kept
at zero by the unity-gain amplifier. In
the amplification mode, C 1 is "flipped"
around the operational amplifier (opamp), and the left plate of C 2 jumps
to VREF . The output voltage thus settles to 2Vin - VREF if the op-amp gain
is high and the mismatch between C 1
and C 2 small.
We now ponder operation in the
next cycle. If the residue, 2Vin - VREF,
is subjected to a subsequent MDAC
stage, we have a new residue equal to
f (2Vin -VREF, VREF) =2 (2Vin -VREF) -VREF
= 4V in - 3VREF, whose polarity allows
comparison of Vin with 3VREF /4. But,
according to Figure 3(b), this comparison is meaningful only if Vin 2 VREF /2;
in the case of Vin 1 VREF /2, we must
compare with Vin /4. This observation points to the need for a residue equal to 4Vin - VREF if Vin 1 VREF .
However, this value cannot be obtained recursively from the function
f (Vin, VREF) = 2Vin - VREF .

IEEE SOLID-STATE CIRCUITS MAGAZINE

su m m E r 2 0 15

39



Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Summer 2015

IEEE Solid-State Circuits Magazine - Summer 2015 - Cover1
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IEEE Solid-State Circuits Magazine - Summer 2015 - 1
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