RAZAVI AND WOOLEY: DESIGN TECHNIQUES FOR HIGH-SPEED, HIGH-RESOLUTION COMPARATORS
1917
vi,
(b)
Fig.
1.
Comparator offset cancellation techniques: (a) input offset storage,
and
(b)
output offset storage.
Since the value of the input coupling capacitors with
10s
is governed by charge injection,
kT/C
noise, and at-
tenuation considerations, the input capacitance of this to-
pology is usually higher than that of the
00s
configura-
tion. During offset cancellation, the input capacitance of
the
10s
circuit is equal to the offset storage capacitor,
while in the comparison mode it is approximately the sum
of the input capacitance of the preamplifier and the para-
sitic capacitances of the offset storage capacitor. These
parasitic capacitances are typically as large as
0.1
to
0.2
pF for input storage capacitors in the range of
0.5
to
1
pF, whereas the preamplifier input capacitance can be
maintained below
30
fF.
For this reason
00s
is generally
preferable in flash stages, where many comparators are
connected in parallel.
Of
course, the dc coupling at the
input of an
00s
comparator limits the common-mode
range. Also, in applications where a large differential ref-
erence voltage must be stored in the comparator
[2],
the
preamplifier of the
00s
topology must be designed for a
low gain
so
that it does not saturate at its output.
While
10s
is accomplished by means of a closed feed-
back loop, which forces the preamplifier into its active
region,
00s
is normally an open-loop operation that re-
quires tight control of the amplifier gain. Therefore,
00s
is typically implemented using a single-stage amplifier
with a gain of less than
10
to ensure operation in the active
region under extreme variations in device matching and
supply voltage.
In conventional CMOS comparator designs, the pream-
plifier is typically followed by a standard dynamic CMOS
latch. As shown in the following subsection, this latch has
a potentially large input offset and therefore requires the
use of a high-gain preamplifier in order to achieve a low
offset. Consequently, in high-resolution applications a
single stage of
00s
cannot be used, while a single-stage
high-gain preamplifier with
10s
suffers from a long delay.
The above considerations have led to the use of multi-
stage calibration techniques in high-resolution applica-
T
Fig.
2.
Multistage offset cancellation
tions. Fig.
2
illustrates a typical multistage comparator
topology that, in effect, utilizes both
10s
and
00s
when
it is clocked sequentially
[2],
[3].
The overall gain of the
circuit is chosen
so
that an input of
0.5
LSB
overcomes
the offset of the latch
(50
to
100
mV), and the number of
stages is then selected to provide the smallest delay
[2].
In the configuration of Fig.
2
a large latch offset
is
ac-
commodated through the use of multiple preamplifier
stages, each with offset cancellation. Alternatively, the
offset of the latch can be reduced
so
as to relax the gain
required of the preamplifier. This can be accomplished
through the use of either devices with inherently low
off-
sets or offset cancellation in the latch.
B.
Design Constraints
in
a Dynamic CMOS htch
In order to synchronize the operation of a comparator
with other parts of a system, as well as provide the gain
needed to generate logic levels at the output, a regenera-
tive amplifier is normally used as the final comparator
stage. Fig.
3
shows a dynamic CMOS latch similar to that
used in
[4]
to amplify small differences to CMOS levels.
In this circuit, when
9
is low,
M5
is off,
SI
and
S2
are
on, and the latch senses the inputs
Vjnl
and
Vjn2.
When
9
goes high,
S1
and
S2
turn off to isolate nodes
X
and
Y
from input terminals and
M5
turns on to initiate regen-
eration.
In order to simplify calculations and estimate a lower
bound for the offset of the latch in Fig.
3,
only the mis-
matches between
M
1
and
M2
and between
S
1
and
S2
are
considered here. In practice, other errors such
as
mis-
matches between
M3
and
M4
further increase the offset.
Considering only the
M1,
M2
and
S1,
S2
mismatches,
the input offset
of
the latch can be expressed as
(3)
where
AV,,
and
V,,
are the standard deviation and mean
of the threshold voltage,
AW/W
and
U/L
are relative
dimension mismatches,
VGs
-
VTH
represents the initial
gate-source overdrive,
AQ
is the charge injection mis-
match between
S
1
and
S2,
and
CD
is
the total capacitance
at
X
or
Y
(assumed equal on both sides). For optimistic
values of
AVTH
=
5
mV,
AW/W
=
AL/L
=
0.05,
VGs
-
VTH
=
1
V,
AQ
=
0.5
fC, and
CD
=
100
fF,
the latch
offset voltage is approximately
60
mV, with its major
component arising from the second term in
(3).
This term
can be reduced by increasing
W
and
L
and/or decreasing
VGs
-
VTH,
i.e., decreasing the initial drain current of
M
1
and
M2.
However, these remedies can degrade the speed
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