A Subthreshold MOSFET Bandgap Reference with Ultra-Low Power
Supply Voltage
Yilei Li*, Yu Wang, Na Yan, Xi Tan and Hao Min
State Key Lab of ASIC & System, Fudan University, Shanghai 200433, China
* Email:liyilui@gmail.com
Abstract
A novel bandgap reference(BGR) with ultra low supply
voltage is presented. The proposed bandgap reference
uses subthreshold MOSFETs to provide temperature
compensation. Analysis and comparison between
proposed bandgap and conventional current-mode
bandgap are made, and it is shown that when working
with low supply voltage, the proposed bandgap is less
sensitive to mismatch and power supply noise. The
bandgap reference is implemented in SMIC O.13f.1lll RF
technology, and simulation results show that it can
provide the output voltage of 429 mV with a supply
voltage as low as 0.6 V.
1. Introduction
Bandgap references (BGR) are necessary blocks for
many applications, such as wireless communication
system and analog-digital converters. They provide
standard voltage/ current reference insensitive to process,
power supply voltage and temperature variations.
Traditional bandgap reference is based on temperature
characteristic of bipolar transistors (BJT), and its output
voltage is about 1.2 V. Thus, for advanced technology
with nominal supply voltage lower than 1.2 V, traditional
bandgap reference can no longer function. In [1],
current-mode bandgap was proposed to enable bandgaps
to work under low supply voltage. The current-mode
bandgap is shown in Fig. 1. Current-mode bandgap uses
addition of current instead of voltage, thus can work
under lower supply voltage. However, the output voltage
of current-mode bandgap is just the voltage drop of
temperature-compensated current on output resistor, so it
is more sensitive to power rail noise and output resistor
mismatch than traditional bandgap. In [2], the proposed
bandgap eliminates the use of opamp to work under
sub-lV power supply. However, it still uses BJT to
achieve temperature compensation, and thus the forward
voltage drop of BJT limits the lower bound of supply
voltage, which can be as high as 700 mV.
In this paper, a bandgap based on subthreshold
MOSFET is presented. It uses the temperature
characteristics of subthreshold MOSFET to achieve
temperature compensation, and can work under very low
supply voltage.
This paper is organized as follows. In Section 2, basic
principle of temperature compensation is explained.
After that, we analyze our circuit and compare it with
conventional current-mode bandgap in Section 3.
Implementation and simulation results are presented in
Section 4. Finally, the conclusion is given in Section 5.
2. Proposed Temperature Compensation
2.
The schematic of proposed bandgap is shown in Fig.
The gate-source voltage of subthreshold MOSFET
can be expressed as [3]:
W
VgS = �h + n VT(In C-In + (r-2)In T)
(1)
L
where n and y are constants related to process of
MOSFET, and C is related to the current of MOSFET in
subthreshold. The value of the fIrst-order derivative of(1)
is negative [4]; or we can say, Vgs of MOSFET in
subthreshold region has negative temperature coefficient.
Since for MOSFETs in the same process, n and y are
basically the same (ignore the mismatch effect), so we
can express the Vgs difference (ilVgs) between two
subthreshold MOSFETs with the same current but
different width-to-Iength ratios as:
W
( )2
L
ilVg = Vgs\ -Vg = n VT In ----w(2)
S2
S
(
)\
L
Apparently, if (W/L)2>(W/L)J, then ilVgs has positive
temperature coefficient.
In Fig. 2, the operational transconductance amplifIer
(OTA) provides large feedback loop gain to ensure that
node a and b have the same voltage. Capacitor Co is
inserted to perform compensation to ensure stability.
Transistors M4 and M5 has the same size the gate-source
voltage to ensure that Ml and M2 have the same drain
current. Since input impedance of OTA is very large, the
current flowing through M2 equals to the current flowing
through Rl, and it is just the Vgs difference of Ml and
M2 divided by Rl:
W
( )2
ilVg
S n VT
(3)
In L
I2 =
=
Rl
Rl
(
: )\
On the other hand, M6 mirrors fz. Thus, the output
voltage of bandgap can be expressed as:
978-1-61284-193-9/11/$26.00 ©2011 IEEE
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Vout
Vout
Fig.1 Traditional Current-Mode Bandgap
Fig.2 Proposed Ultra-Low Voltage Bandgap
W
n VTR2 (L)2
Vout=VgS3 + I3R2 = Vgs3 + --- In ---wRI
( )
(4)
_
L
l
Indeed, h changes with temperature, so C also
changes with temperature; however, consider (I), since
inC only varies a little throughout the temperature
change, thus we can ignore the effect of changing current
to the gate-source voltage of M3. Consequently, the
gate-source voltage of M3 still has the negative
temperature coefficient, while the voltage drop on R2
has the positive temperature coefficient. So, the output
voltage will have zero temperature coefficient if the
following expression is satisfied:
RI
=
R2
-
n k In
-_·
q
W
(L)2
L
I
3.2 Power Supply Noise Rejection
Suppose the proposed bandgap has the same loop gain
as the conventional current-mode bandgap, and there
exists noise in power supply generating noise output
current M. For conventional current-mode bandgap, the
ratio of output voltage variance and nominal output
voltage can be expressed as:
Av"ut = M
Vout
lout
--
1
-·-
( W)
mV lower than conventional current-mode bandgap. In
addition, with the progress of technology, the threshold
voltage of MOSFET decreases, so the voltage drop of
subthreshold MOSFET can be even lower with advanced
technology. On the other hand, the forward voltage drop
of BJT does not scale significantly with technology.
Thus, the proposed bandgap has more potential to work
with ultra low supply voltage in advanced technology.
aVgS3
aT
(5)
3. Analysis, Comparison and Design
3. 1 Lower Bound of Supply Voltage
For conventional current-mode bandgap in Fig. I,
since usually the forward voltage drop on BJT is about
700 mV, and suppose the saturate voltage of MOSFETs
M4, M5 and M6 is 100 mV, then the lower bound of
supply voltage is about 800 mV. Actually, the main
factor determining the lower bound of supply voltage of
conventional current-mode bandgap is the relatively
large forward voltage drop on BJT. By using special BJT
such as Schottky diode can reduce the forward voltage
drop, but it is complicated to implement such device in
standard CMOS process.
In proposed bandgap, the voltage drop in mainly on
drain-source voltage of MOSFET current mirror and
gate-source voltage of subthreshold MOSFET. The
drain-source voltage of MOSFET in saturation region
can be as low as about 100 mV, and the gate-source
voltage of subthreshold MOSFET is around 300�400 mV,
thus the lower bound of proposed bandgap can be 200
(6)
-
For proposed bandgap, since the variance of gate-source
voltage of M3 generated by M is very small and can be
ignored, the ratio of output voltage variance and nominal
output voltage can be expressed as:
Av"ut
v"ut
�
M · R2
M
lout' R2 + Vgs3
lout + Vgs3 / R2
(7)
Apparently, the value of(7) is smaller than(6). Since the
gate-source voltage of subthreshold MOSFET is less
sensitive to current than the voltage drop on resistor, we
can conclude that with the same amount of current noise
generated by power supply noise, the change of output
voltage of proposed bandgap is less than that of
conventional current-mode bandgap; or, we can say that
proposed bandgap structure has better power supply
rejection (PSR) than conventional current-mode
bandgap.
3.3 Sensitivity to Mismatch and Process Variation
The mismatch in proposed bandgap can be mainly
divided into two parts. First is the mismatch of threshold
voltage of MOSFETs. If the threshold voltage of
subthreshold MOSFETs MI and M2 has a mismatch of
AVth, then the difference of gate-source voltage of Ml
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and MI can be expressed as:
W
)2
T
Ll VgS = M'th + n VT In
---w( )
T\
(
(8)
And it may lead to error in temperature compensation
since LlVth has negative temperature coefficient [5]. To
reduce this kind of mismatch, MOSFETs with large sizes
should be selected, and care must be taken in layout
design.
Another source of mismatch is resistor mismatch. For
conventional current-mode bandgap, suppose there exists
mismatch for R4 and its value becomes R4+LlR, then the
ratio of output voltage variance to nominal output
voltage can be expressed as:
Vout
(9)
R4
For proposed bandgap, the ratio can be expressed as:
Ll Vout
v;,ut
lout • LlR
lout· R2 + VgS3
LlR
R2 + Vgs3 / lout
(10)
Since the output voltage of traditional current-mode
bandgap is proportional to output resistor R4, it is
sensitive to the mismatch of R4; on the other hand, the
output voltage of proposed bandgap is the sum of
voltage drop on R2 and the gate-source voltage of M3.
The voltage drop on R2 is just a small part of output
voltage, and the gate-source voltage of M3 is basically
independent from resistor mismatch, so the output
voltage of proposed bandgap is less sensitive to resistor
mismatch than conventional current-mode bandgap.
Finally, the output voltage of proposed bandgap will
change with different process comers since the threshold
voltage of MOSFET is different, but this effect in
proposed bandgap is not more significant than that in
traditional current-mode bandgap, since the forward
voltage drop of BJT also varies in different comers, and
this varies the output current and thus the output voltage.
3.4 OTA with Subthreshold Input Pair
One challenge in designing the proposed bandgap is
OTA. The main reason is that the gate-source voltage of
subthreshold MOSFET is around 300 mV, and this
voltage is in the mid-point of V DD to ground for low
supply voltage of 600 mV. Thus, the input-pair of OTA
works in subthreshold region whether we use NMOS or
PMOS as input transistor. In actual design, since NMOS
has lower threshold voltage than PMOS, we choose
NMOS as input transistor. In order to make the status of
input pair close to moderate inversion region, we choose
NMOS with long channel length (8 �), since the
threshold voltage of MOSFET decreases with longer
channel length due to halo doping [6].To reduce power
consumption, we chose a simple OTA structure (Fig. 3).
Since the supply voltage is very low, cascode is not
available. The loop gain, and thus power supply rejection
Fig.3 OTA with Subthreshold Input Pair
can be improved by using multi-stage OTA, but at the
cost of higher power consumption and design complexity.
The bias of OTA is done by subshreshold MOSFET
voltage divider, which consumes very little power.
4. Implementation and Simulation
The circuit is implemented in SMIC 0.13 � RF
technology. The output voltage is 430 mV.
The output voltage versus power supply voltage is
shown in Fig. 4. The bandgap can work with V DD
higher than 0.6 V, which is a very low value as a power
supply voltage.
The curve of output voltage versus temperature under
0.6 V V DD is shown in Fig. 5. As we can see from Fig. 3,
as the temperature change from -20 DC to 80 DC, the
maximum output voltage variance is about 1.1 mV, and
the temperature coefficient is 25.6 ppm/DC.
The PSR simulation result under V DD of 0.6 V and
1.2 V is shown in Fig. 6. With 0.6 V power supply
voltage, since the OTA works in subthreshold region, the
loop gain of feedback loop is limited, and thus the PSR
at low frequency is about -31 dB. With 1.2 V V DD,
however, the OTA no longer works in subthreshold
region, so the low frequency PSR increases to -65 dB.
Considering the fact that the OTA is single stage and no
cascode transistor is used, this PSR is considerable,
which verifies our discussion in Section 3.2. At higher
frequency (> 1 MHz), the high-frequency component is
filtered out by RC low-pass network.
A comparison with other low voltage BGRs from
other references is in Table 1. Compared with other
state-of-art works, the proposed bandgap has the lowest
power supply voltage and comparable performances.
5. Conclusion
A bandgap reference with ultra-low supply voltage is
presented. By using the characteristics of subthreshold
MOSFET, it can work under supply voltage as low as 0.6
V, with a temperature coefficient of 25.6 ppm/DC.
Compared with traditional current-mode bandgap for
low voltage application, the proposed bandgap is less
sensitive to resistor mismatch and power supply noise.
Finally, the proposed bandgap has the potential to work
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0.4
�0 3
'5
>
°
0.2
0.1
0.2
0.4
0.6
0.8
1
VDD(V)
1.2
1.4
1.6
1.8
2
Fig. 4 Output Voltage vs. VDD
under even lower supply voltage with progress of
technology.
Acknowledgments
The project is supported by Important National Science
and
Technology
Specific
Projects
of
China
No.2009ZX01031-003-002, National High Technology
Research and Development Program of China
No.2009AA01l605 and Important National Science &
Technology
Specific
Projects
of
China,
2010ZX03001-004.
Systems, 2009.
[5] G. Giustolisi, G. Palumbo, M. Criscione, and F. Cutri,
"A low-voltagelow-power voltage reference based on
subthreshold MOSFETs, " IEEE J. Solid-State
Circuits, vol. 38, no. 1, pp. 151-154, Jan. 2003
[6] K. M. Cao, W. Liu, X. Jin, K. Vasanth, K. Green, J.
Krick, T. Vrotsos and C. Hu, "Modeling of pocket
implanted MOSFETs for anomalous analog
behavior, " in IEDM Tech. Dig., 1999, pp. 171-174.
[7] Po-Hsuan Huang, Hongchin Lin and Yen-Tai Lin,
"A Simple Subthreshold CMOS Voltage Reference
Circuit With Channel- Length Modulation
Compensation, " IEEE Trans.Circuits Syst.II, vol. 53,
No. 9, Sep. 2006, pp. 882-885
0.431,---�--�----,
�
., 0.4306
F
� 0.4304
'5
%0.4302
o
0.43
1:able
I . Per tIormance Companson between Banlgaps
d
This
work
[2]
[4]
[7]
Technology
0.13 �
CMOS
0.18 flm
CMOS
0.18 flm
CMOS
0.18 �
CMOS
V DD(V )
0.6
0.85
0.7
0.85
0.42 S.�'=-i ----=-----02f=- ----c0=----,6f=80
4
0----='
O
0
0
Temperature ('C)
Fig.5 OUtput Voltage vs. Temperature
-20
Temperature
Range(0C)
-20�80
0�100
0�130
-30
-20�120
in -40
�
Temperature
Coefficient
(ppm/0C)
25.6
9
19
190
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oc
� -50
-60
-7�OO
10
'
10
4
10
·
Frequency (Hz)
10
'
Fig.3 PSR vs. Frequency
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