A Curvature Compensated CMOS Bandgap Voltage Reference
for High Precision Applications
Jianghua Chen*, Xuewen Ni, and Bangxian Mo
Institute of Microelectronics, Peking University, Beijing 100871, P. R. China
* Email: chenjianghua@ime.pku.edu.cn
Abstract
This paper describes a high precision high order
curvature compensated bandgap voltage reference in a
0.5-μm 2P3M n-well mixed signal CMOS technology.
This newly proposed bandgap voltage reference utilizes a
Buck’s voltage transfer cell and a temperature
independent current, to provide a high order
compensation of the V
BE
. Cascode structures are also
introduced in this bandgap voltage reference to improve
the power supply rejection ratio (PSRR). This circuit
achieves 5.6 ppm/
ć of temperature coefficient with
temperature ranging from -20 to 100
ć at 5V power
supply. The variation in the output voltage of the
bandgap voltage reference is 0.4mV when V
DD
varies
from 4V to 6V.
Index Terms
— CMOS, analog integrated circuits,
bandgap reference, low temperature coefficient, high
order curvature compensation.
1. Introduction
Precision bandgap references (BGRs) are always in great
needs in integrated analog, digital or mixed signal
building blocks such as A/D converters, filters, DRAMs
and flash memory controlling circuits for their high
accuracy and temperature independence. There exists,
however, a limit to improve the temperature coefficient
(TC) of a first-order temperature compensated BGR[1]
which exhibits TC limit typically between 20 and 100
ppm/
ć[2][3], due to the non-linearity in the base-emitter
voltage of the BJTs used in BGRs. To overcome this
drawback, many high order temperature compensation
techniques have been developed, such as quadratic
temperature compensation by Song et al.[4][5],
exponential temperature compensation by Lee et al. [6],
piecewise linear curvature correction by Rincon-Mora et
al.[7], and temperature dependent resistor ratio with high
resistive poly resistor and a diffusion resistor by Leung et
al.[8][9]. With these techniques, the temperature stability
of the BGRs has been increased significantly. However,
the above BGR structures require precision matching of
current mirrors or a pre-regulated supply voltage to
implement the advanced mathematical functions with
high accuracy, as current mismatch will introduce an
error voltage at the reference output. On the other hand,
high resistive poly resistor cannot be fabricated under
conventional standard CMOS processes.
A high order curvature compensated bandgap voltage
reference based on a temperature independent current
and a Buck’s transfer cell [10][11] is presented in this
paper. The proposed BGR utilizes a conventional BGR, a
temperature independent current and an inverse function
voltage transfer cell first proposed by A. E. Buck et al. to
implement a very low TC bandgap reference. This circuit
structure can effectively reduce the temperature drift of
the bandgap voltage reference. Cascode current mirrors
can help improve the high PSRR. The novel proposed
BGR has a stable reference output V
ref
of 1.196V and TC
of 5.6 ppm/
ć over a temperature range of -20 to 100ć
under supply voltage 5V.
This paper starts with a brief introduction to
conventional bandgap reference in Section 2. An analysis
on the temperature dependence of the emitter-base
voltage is given in Section 3. The proposed high
precision high order curvature compensated CMOS
bandgap voltage reference is introduced in Section 4.
Simulation results and conclusion are presented in
Sections 5 and 6, respectively.
2. Conventional Bandgap Voltage Reference
The conventional BGR is a weighted sum of a negative
TC voltage V
BE
which is the forward-bias voltage across
a p-n junction, and a positive TC voltage V
T
which is the
thermal voltage kT/q, proportional to absolute
temperature (PTAT), shown in Fig. 1, where M is the
adjusted weighted factor. The output voltage reference
should be insensitive to temperature changes and stable
over the range of supply voltage change in the first-order
compensation.
Fig. 1 Conventional BGR overview
1-4244-1132-7/07/$25.00 © 2007 IEEE
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Fig.2 A typical implementation of conventional BGR
Fig. 3 Buck’s voltage transfer cell.
A typical implementation of the conventional bandgap
voltage reference in CMOS technology is shown in Fig.
2 [12]. A current which is proportional to the absolute
temperature (PTAT) is generated and the voltage drop
across the resistance R2 formed, and then added onto the
base-emitter voltage of Q2. Thus, the output of V
ref
is
2
2
1
ln
ref EB
RkT
VV
Rq
§·
¨¸
©¹
n
(1)
where k is the Boltzmann’s constant, q is electronic
charge, and T is the absolute temperature in degrees
Kelvin (K). The second item is proportional to the PTAT,
which is used to compensate for the negative TC of V
EB2
.
The factor n is the emitter area ratio of transistors Q1 and
Q0.
3. V
EB
Temperature Dependence
The main goal of the first-order compensated BGR is to
cancel the negative temperature dependence of the
emitter base voltage V
EB
(pnp) by adding a PTAT voltage,
which is a fully linear function of T. The relationship
between V
EB
and T, however, is a nonlinear behavior, and
V
EB
is a complex function of T containing many higher
order items. Therefore, even in the optimally
compensated case, the output reference voltage V
ref
has
some temperature drift terms. Since this drawback is
inherent, it is impossible to increase the temperature
stability of the first order compensated BGR above a
certain limit.
The temperature characteristic of V
EB
is studied
extensively and its analytical form can be expressed by
the following [1][9][13][16].
ln
EB G o EB o G o
o
o
T
VVT VTVT
T
kT T
m
qT
K
§·
ªº
¨¸
¬¼
©¹
§·
§·
¨¸
¨¸
©¹
©¹
(2)
where V
G
is the bandgap voltage of silicon extrapolated
at 0 K, k is the Boltzmann’s constant, Ș is a temperature
constant depending on the technology, m is the order of
the temperature dependence of the collector current, q is
the charge of an electron, and T
o
is the reference
temperature.
From (2), there is a TlnT term, which is the high order
nonlinear temperature dependence factor of V
EB
. First
order temperature compensation involves the
cancellation of the T term while high order temperature
compensation involves the cancellation of high order T
terms. In this paper, we will cancel the second order term
of V
EB
by adding a voltage, which is proportional to the
square of the absolute temperature (PTAT
2
).
4. Proposed Precision Curvature compensated CMOS
BGR
4.1 Buck’s Voltage Transfer Cell
The principle in Buck’s voltage transfer cell is shown in
Fig.3. The parameter A is the ratio of the size of the
differential pairs M3-M4 and M2-M1, and the parameter
G is the current-mirror gain from M9 to M10 as well as
the ratio of the tail currents of the two differential pairs.
The required gain, i.e. the weighted factor M, is obtained
by using ratio transistors and the inverse function
technique—transconductance and transresistance [14].
The differential pair M3-M4 acts as a transconductance.
The resulting current is multiplied by G using current
mirror M9-M10 and is delivered to another differential
pair M2-M1, which functions as a transresistance due to
the negative feedback around M1.
The main idea in the inverse function technique is to
apply a pair of functions—transconductance g
mc
and
transresistance g
mr
to ǻV
BE
= (V
BE2
-V
BE1
) so that g
mr
[g
mc
ǻV
BE
] = MǻV
BE
. g
mc
(possibly nonlinear) maps ǻV
BE
to
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Fig. 4 The proposed complete schematic of the high order curvature compensated BGR
some current i, and then g
mr
cancels the nonlinearity in i
and provides the required gain M. The inverse function
technique operates with any smooth nonlinearity
[10][11][15].
The MOSFET transistors operate in the saturation region,
and the channel length modulation effect of the
transistors is neglected here because of their long
channel lengths used in this circuit. From Fig.3, we have
the following equations.
22
34
1
2
T p OX GS t GS t
W
IC AVVABVV
L
P
§·
ªº
¨¸
¬
©¹
¼
(3)
2
21
1
2
TpOX GSt GSt
W
GI C V V B V V
L
P
§·
ª
¨¸
¬
©¹
2
º
¼
1
(4)
(5)
4
GI I
Combining equations(3), (4) and (5) gives
2
,
GS t GS t
VVAGVV
3
(6)
1
.
GS t GS t
VV AGVV
4
(7)
Equation
(7) minus equation (6) results in
12 4GS GS GS GS
VV AGVV
3
(8)
DOVR
(9)
43 21GS GS EB EB EB
VVVV V '
Therefore, the output voltage reference is
2ref EB EB
VV AGV '
(10)
4.2 Implementation of High Order BGR
The proposed complete circuit which is mainly
composed of three parts is shown in Fig. 4.
Part I of the BGR generates a voltage V
2
as following
2
22
1
ln
EB
R
kT
VV n
Rq
§·
¨¸
©¹
(11)
Part II of the BGR produces a temperature independent
current injected into Q3. Q0 has the same emitter area as
Q3, and the current of Q0 is proportional to T. According
to equation (2), V
EB0
-V
EB3
can be expressed as following
13 0 3
ln
EB EB
o
kT T
VV V V
qT
§·
§·
¨¸
¨¸
©¹
©¹
(12)
Part III of the BGR is the Buck’s voltage transfer cell
given in subsection 4.1. Combining equations (8), (11)
and (12) yields
213
2
2
1
ln ln
ref
EB
o
VV AGVV
R
kT kT T
VnAG
R
qq
§
§· §·
¨¸
¨¸ ¨¸
©¹ ©¹
©¹
T
·
(13)
V
EB2
can thus be compensated by both first order (linear)
and second order (nonlinear) items in this proposed BGR.
A precision curvature compensated BGR can be achieved
by trimming the ratio of resistors R1 and R2, and
parameters A and G..
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4.3 V
DD
Variation Effect on Bandgap Reference
The bandgap reference is required to be stable over the
change of the power supply voltage. Therefore, the less
the effect of power supply V
DD
on the bandgap reference
is, the better the performance of the bandgap reference is.
We use cascode current mirror structures, which is
supply voltage independent to a certain extent and may
greatly reduce the variation of the power supply V
DD
, to
bias the bipolar transistors in order to improve the PSRR
in this proposed BGR circuit.
5. Simulation Results
The temperature behavior of the proposed BGR output is
shown in Fig. 5. The output voltage V
ref
of the proposed
BGR is 1.196f0.0004V with temperature ranging from
-20 to 100
ć and supply voltage 5V. Its temperature
coefficient is 5.6 ppm/
ć. Fig. 6 shows that the reference
voltage variation of the proposed BGR is 1.196 f
0.0004V when the power supply varies from 4 to 6V.
Fig. 5 Output reference V
ref
vs. temperature.
Fig. 6 Output reference V
ref
vs. power supply V
DD
.
6. Conclusion
A high precision high order curvature compensated
CMOS bandgap voltage reference has been proposed.
The temperature compensation is achieved by a Buck’s
voltage transfer cell and a temperature independent
current which introduces a voltage proportional to TlnT,
giving a high order compensation of V
BE
. The TC of this
proposed circuit is only 5.6 ppm/
ć with temperature
ranging from -20 to 100
ć at power supply 5V in a
0.5-μm 2P3M n-well mixed signal CMOS technology.
The variation of the BGR output is only 0.4mV when
V
DD
varies from 4V to 6V because it can be immune
from the supply voltage variation by the cascoded
current mirror. The proposed BGR is well suited for
many mixed signal systems which require high precision.
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