Correction circuit for beta mismatch between thermometer...

Details Correction circuit for beta mismatch between thermometer... Correction circuit for beta mismatch between thermometer...

2001-06-22

2003-06-24

Williams, Howard L. (Department: 2819)

Coded data generation or conversion

Analog to or from digital conversion

Digital to analog conversion

C341S118000, C341S135000

Reexamination Certificate

active

06583744

ABSTRACT:

BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates generally to data converters, and more particularly to a system and method for correcting the beta mismatch between thermometer encoded and R-2R ladder segments of a current steering digital-to-analog converter (DAC).
2. Description of the Prior Art
The technique of segmentation has been used, among other reasons, to reduce both the area and power consumption of digital-to-analog converters (DACs). Each segment generally uses either a binary-to-thermometer encoder or a binary-to-binary encoder. For an N-bit current steering DAC, there is a desire to combine an M-bit thermometer encoded segment with an L-bit binary encoded segment. In this notation, the M-bit segment represents the most significant bits (MSBs), and the L-bit segment represents the least significant bits of the N-bit DAC, where N=M+L.
FIG. 1
illustrates a block diagram of an N-bit current steering DAC
100
.
The M-bit thermometer encoded segment
102
of the DAC
100
as shown in
FIG. 1
consists of 2
M
−1 equal current sources
104
. These current sources
104
are individually switched to either the true or complement output as determined by the thermometer encoding of the M most significant bits. Also shown in
FIG. 1
is a binary encoded L-bit segment
106
of the DAC
100
as an R-2R ladder. The R-2R ladder outputs a binary weighted current to the true or complement output as determined by the L least significant bits of the N-bit input.
The foregoing DAC
100
has a boundary condition between the MSB and the LSB segments that must be satisfied for the DAC
100
output to remain linear. This boundary condition necessitates that the total output current of the R-2R ladder must be one least significant bit less than the output current of a single current source in the MSB segment. This condition is met to first order by using a replica MSB current source
108
to supply the total current to the R-2R ladder where it is noted that the R-2R circuit already functions to subtract the equivalent of an LSB current from the total current supplied. The replica MSB current source
108
is labeled I
REP
in FIG.
1
.
According to one embodiment, the foregoing boundary condition requiring the DAC
100
to remain linear across the two segments
102
,
106
is only met to first order because the NPN devices used throughout have a current gain, &bgr;
F
, that is dependent on the collector current density. This will cause the total base current of the R-2R ladder to not equal that of the cascode of an MSB unit current source and result in a nonlinearity. This concept can be better understood by taking a closer look at the M-bit thermometer encoded segment
102
MSB current source
104
and the binary encoded L-bit segment
106
R-2R ladder designs.
One embodiment of a current source
200
that can be used in the MSB segment
102
is shown in FIG.
2
. The current source
200
consists of a bipolar junction transistor (BJT)
202
designated as Q
1
, a degeneration resistor
204
, designated as R
E
, a cascode device
206
, designated as Q
c
, and a differential output switch
208
, consisting of transistors
210
and
212
, designated as Q
SW
—
MSB
and Q{overscore (
SW
—
MSB
)} respectively.
One embodiment of the LSB segment circuit
106
which includes the R-2R ladder
300
is shown in FIG.
3
. The LSB segment circuit
106
consists of a BJT
302
, designated as Q
1r
, and degeneration resistor
304
, designated as R
Er
, where the subscript r denotes the devices to be replicas to those in the MSB current source
200
described herein before with reference to FIG.
2
. The R-2R ladder
300
consists of L binary weighted currents that are established with a binary weighted number of BJT devices
306
(Q
bi
). Here, the notation b represents the significance of the current from 1 to L, and i represents the NPN device within that current from 1 to 2
b−1
. For example, the LSB device
308
has a b=1 and NPN devices indexed from 1 to 2
0
=1. The most significant current weight in the R-2R ladder
300
has a b=L and NPN devices indexed from i=1 to i=2
L−1
. Also shown in
FIG. 3
is an output switch for each binary weighted current. These output switches
310
are identical to those of the MSB segment
200
described in FIG.
2
.
It can be seen from
FIG. 3
that the R-2R ladder
300
in the LSB segment
106
is substituted for a single cascode device of an MSB unit current source. Further, the LSB segment
106
has L output switches
310
(differential pairs) and one dump device
320
(Q
d
), compared with the MSB unit current source that has just one output switch. The boundary condition, discussed herein before, requires the total output current of the LSB segment
106
to be one LSB less than that supplied to the output by an MSB unit. This boundary condition requires that the total base current of the R-2R ladder
300
NPN devices
306
, &Sgr;I
B
(Q
bi
), L output switches
310
, I
B
(Q
SW
—
LSB
), and dump device
320
, I
B
(Q
d
), should be equal to the total base current of the MSB unit cascode
206
, I
B
(Q
c
), and the output switch
208
, I
B
(Q
SW
—
MSB
). This boundary condition is described by equation (1) below as:
∑
 
b
=
1
L
⁢
 
⁢
(
∑
i
=
1
2
b
-
1
⁢
 
⁢
I
B
⁡
(
Q
bi
)
+
I
B
⁡
(
Q
SW_LSB
)
)
+
I
B
⁡
(
Q
d
)
=
I
B
⁡
(
Q
c
)
+
I
B
⁡
(
Q
SW_MSB
)
(
1
)
The boundary condition of equation (1) however is not satisfied since the NPN current gain, &bgr;
F
, has a dependence on collector current density. A typical plot of current gain as a function of collector current is illustrated in FIG.
4
. The collector current density of an MSB unit current source which uses a minimum feature size cascode device
206
is in the range of 400 &mgr;A/&mgr;m
2
. This same current density will be present in the MSB
20
unit output switch
208
as well.
With continued reference to
FIG. 4
, it can be seen that the current gain, &bgr;
F
, at a 400 &mgr;A/&mgr;m
2
current density is approximately 87 A/A. The collector current density for an L=4 bit R-2R ladder is approximately 27 &mgr;A/m
2
or a factor of 16 less.
FIG. 4
shows that this lower current density corresponds to a current gain of 92 A/A or an increase of 6%. This 6% difference in current gain, &bgr;
F
, will cause the total base current in the R-2R ladder to be 6% less than the cascode device
206
of an MSB unit since I
C
=&bgr;
F
I
B
. A 6% error at the boundary of an L=4 bit segment will translate into a differential nonlinearity with a magnitude approximately equal to one LSB (i.e. 2
4
*0.06=0.96) and repeats every 16 codes.
Adding to the differences between the R-2R ladder and the cascode device
206
are the different current densities associated with the output switches
208
,
310
. Since the MSB unit current source
200
uses an output switch NPN of size equal to the cascode device
206
, the current density will be the same 400 &mgr;A/&mgr;m
2
. The effective current density of the output switches
310
in the LSB segment
106
however, will be (400 &mgr;A/&mgr;m
2
)/L. For an LSB segment of L=4, the current density will be 100 &mgr;A/&mgr;m
2
and the current gain will be 90. This is a smaller error of 3%; however, this will correspond to a differential nonlinearity having a magnitude of 0.5 LSB.
The above described effective base current mismatches between an MSB unit and the LSB segment
106
are additive and will result in a differential nonlinearity of approximately 1.5 LSBs that repeat every 2
L
codes in the DAC
100
transfer function. This error is present even with a perfect R-2R ladder and no mismatch between a MSB unit and replica current source. Further, the magnitude of this error increases with L.
In view of the foregoing, there is a need for a system and method for eliminating the differential nonlinearities caused by beta mismatches between thermometer encoded and R-2R ladder segments of a current steering digital-to-

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