LETTER

A 1.8 V 0.918 ppm/°C CMOS bandgap voltage reference withcurvature-compensated

Gao Pan1a), Qing Hua2, and Bo Zhang1

Abstract A new precise current mode bandgap voltage reference withTlnT compensation of non-linear temperature is proposed. By using thevoltage difference of two transistors working in different current states, thenonlinear compensation term of TlnT is generated. At the same time, theoptimal high-precision reference voltage source is obtained by using themethod of piecewise compensation. This design with 0.18 µm CMOSprocess is achieved an ultra-low temperature coefficient (TC) of 0.918ppm/°C from −40 °C to 125 °C. The minimum required supply voltage is1.8V and the current consumption is 23 µA at 25 °C. And the lineregulation performance is 0.0055%/V at 25 °C with a supply voltagerange of 1.8V to 3.6V.Keywords: bandgap voltage reference, TlnT, temperature coefficientClassification: Integrated circuits

1. Introduction

Bandgap voltage reference is an important basic circuitmodule in analog and mixed single integrated circuits. It iswidely used in DC-DC, DAC, ADC, LDO, PLL and othercircuits [1, 2, 3, 4]. The performance of the Bandgapvoltage reference is an important indicator of the overallperformance. The deviation of the reference will verify thatthe linearity and accuracy of the chip will be affected tosome extent by the influence of other circuits. So, in orderto meet the urgent need of the system for high-precisionreference voltage source, the research of high-precisionbandgap voltage reference with curvature compensationis of great significance.

However, the temperature coefficient of the traditionalbandgap voltage reference, which mostly uses first-ordercompensation technique, is limited by the nonlinear com-ponent. To solve this problem, several high-order temper-ature compensation techniques have been developed. In thepapers [5, 6, 7, 8, 9, 10, 11], the new proposed realizationof a voltage reference uses a gate-source voltage of a MOStransistor working in sub threshold region, but its temper-ature coefficient will deviate greatly with the process.According to papers [12, 13, 14, 15], the resistances with

different temperature coefficients are used to generate volt-age for temperature correction. The disadvantage is that thestability of the process is poor. Two bandgap cores basedon parasitic PNP transistors and NPN transistors are usedin papers [16, 17], but it is incompatible with standardCMOS process. The piecewise compensation techniqueused in papers [18, 19, 20, 21, 22, 23, 24] eliminates thenon-linearity. The disadvantage is that the circuit is notonly complex in structure, but also has some influence onthe circuit due to the large current. The exponential curva-ture compensation method in papers [25, 26, 27] need touse the transistor current gain. Because the gain is afunction of temperature, the stability of the circuit becomesworse and the layout area is larger. In the paper [28], theCTAT current without thermal nonlinearity is used tocompensate a PTAT current to obtain the temperature-in-dependent bandgap reference voltage. Its disadvantages arethe large static current and the large layout with resistors.

In this paper, the nonlinear compensation term of TlnTis generated by using the voltage difference of two tran-sistors working in different current states. At the same time,the PTAT, CTAT and TlnT current is proportionally com-bined by the method of piecewise compensation to obtain ahigh accurate bandgap voltage reference with the optimaltemperature coefficient.

2. Proposed design

The working principle of bandgap voltage reference is touse negative temperature coefficient of triode’s VBE andpositive temperature coefficient of ΔVBE to get a zerotemperature coefficient output voltage by adding appropri-ate weights. However, due to the existence of non-lineartemperature coefficient in VBE, the first-order temperaturecompensation can not eliminate the influence of temper-ature very well. In this paper, a new type of non-lineartemperature with TlnT compensation circuit is proposed. Itsworking principle is shown in Fig. 1. The voltage differ-ence of TlnT temperature coefficient is obtained at bothends of resistor R1, showed in formula (1) as below.

VACðT Þ ¼ VAðT Þ � VCðT Þ ð1ÞThe emitter current of Q1 is the PTAT current. Accord-

ing to previous researches [29, 30], the A-point voltage isobtained as follow (2)

DOI: 10.1587/elex.16.20190616Received October 2, 2019Accepted November 1, 2019Publicized November 15, 2019Copyedited December 10, 2019

1State Key Laboratory of Electronic Thin films and IntegratedDevices, University of Electronic Science and Technology ofChina, Chengdu 610054, China2School of Physics Electronics, Shandong Normal University,Jinan 250014, Chinaa) pangao_2004@163.com

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Copyright © 2019 The Institute of Electronics, Information and Communication Engineers

VBE1ðT Þ ¼ VBG � ðVBG � VDQ1ðT0ÞÞ TT0

� ð� � 1Þ kTq

lnT

T0ð2Þ

VBG is the silicon bandgap voltage extrapolated to 0K,VDQ1ðT0Þ is the voltage of diode when the temperature ofQ1 transistor is T0, T is the temperature, T0 is the referencetemperature of 273K. And k is the Boltzmann constant,q is the electron charge. According to literature reports[29, 30], when emitter current is proportional to temper-ature (PTAT), α is equal to 1; when emitter current isimpendent of temperature, α is equal to 0.

According to Fig. 1, voltage of point A is the same aspoint B. So point A is a VBE voltage with PTAT current,and point C is a VBE voltage with temperature independ-ent current. Formula (3) can be obtained by subtracting thevoltage at point A to point C.

VACðT Þ ¼ ðVDQ2ðT0Þ � VDQ1ðT0ÞÞ TT0

� kT

qln

T

T0ð3Þ

VDQ1ðT0Þ is the voltage of diode when the temperature ofQ1 transistor is T0, VDQ2ðT0Þ is the voltage of diode whenthe temperature of Q2 transistor is T0. It can be seen fromformula (3) that the voltage difference of VAC includes afirst-order term which varies with temperature and a non-linear term whose temperature coefficient is TlnT. In this

paper, the nonlinear term of TlnT is used to eliminate thenon-linear term change of VBE in the first-order temper-ature compensation.

Fig. 2 is a schematic diagram of using PTAT currentand constant current to generate the current with temper-ature coefficient of TlnT.

The proposed bandgap voltage reference circuit isshown in Fig. 3. OP3 forces its input D and E pointvoltages to be equal, so that Q3, Q4, MP1, MP2, MP11,MP12, R1 and OP3 generate the PTAT current, as shown informula (4).

IPTAT ¼ kT

q

ln 8

R1ð4Þ

OP2 forces the input D and F point voltages to be equal.Because the temperature coefficients of F point are thesame as that of D point, and they are all negative temper-ature coefficients. Thus Q4, R2, OP2, MP3, MP13 gener-ates the CTAT current, as shown in formula (5).

ICTAT ¼VBG � ðVBG � VDQ4ðT0ÞÞ T

T0� ð� � 1ÞkT

qln

T

T0

R2ð5Þ

VDQ4ðT0Þ is the voltage of diode when the temperature ofQ4 transistor is T0.

In the core circuit of TlnT compensation current gen-eration, the emitter current of Q4 is PTAT current, and theemitter current of Q3 is constant current which generatedby PTAT and CTAT currents. If the voltage of point A isgreater than C, Q1, Q2, MP4, MP5, MP6, MP7, R3 andOP3 generate the TlnT current as below (6).

ITlnT ¼ðVDQ1ðT0Þ � VDQ2ðT0ÞÞ T

T0þ kT

qln

T

T0

R3ð6Þ

VDQ1ðT0Þ is the voltage of diode when the temperature ofQ1 transistor is T0, and VDQ2ðT0Þ is the voltage of diodewhen the temperature of Q2 transistor is T0.

If the voltage of point A is less than C, the TlnTcurrent is equal to 0 as shown in formula (7).

ITlnT ¼ 0 ð7ÞThe output reference voltage (VREF) in Fig. 3 can beexpressed as formula (8):

VREF ¼ IPTAT � R4 þ ICTAT � ðR4 þ R5Þþ ITlnT � R4 VA > VC

VREF ¼ IPTAT � R4 þ ICTAT � ðR4 þ R5Þ VA < VC

8><>:

ð8ÞAfter introducing formula (4) (5) (6) (7) into formula (8),the formula (9) can be obtained.

Formula (9) is sorted out, the first-order term and thenon-linear term related to temperature are removed, and theoutput reference voltage independent of temperature

Fig. 1. Principle of proposed design

Fig. 2. Schematic diagram of TlnT current

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VREF ¼ VBG

R2ðR4 þ R5Þ þ k ln 8

qR1R4 � VBG � VDQ4ðT0Þ

T0R2ðR4 þ R5Þ þ VDQ1ðT0Þ � VDQ2ðT0Þ

T0R3R4

� �T

þ k

qR3� R4 � ð� � 1Þk

qR2� ðR4 þ R5Þ

� �T ln

T

T0VA > VC

VREF ¼ VBG

R2ðR4 þ R5Þ þ k ln 8

qR1R4 � VBG � VDQ4ðT0Þ

T0R2ðR4 þ R5Þ

� �T

� ð� � 1ÞkqR2

ðR4 þ R5ÞT lnT

T0VA < VC

8>>>>>>>>>>>>><>>>>>>>>>>>>>:

ð9Þ

is obtained, as shown in formula (10).

VREF ¼ VBG

R2� ðR4 þ R5Þ ð10Þ

By setting the resistors of R1, R2, R3, R4, R5 and R6reasonably, the error caused by the non-linear term can beeliminated by using the TlnT current, and an ideal bandgapvoltage reference independent of temperature can beobtained.

3. Simulation results and discussion

The bandgap voltage reference circuit proposed in thispaper is designed with 0.18 µm CMOS process, and itssimulation results and performance are shown in thissection.

Fig. 4 is a comparison between the reference voltagereference (VREF) without TlnT compensation and thereference voltage with TlnT compensation. The averageVREF with TlnT compensation is 973.97mV, the peak topeak value is 147.521 µV, and the variation of temperaturecoefficient is 0.918 ppm/°C from −40 °C to 125 °C. Theaverage VREF without TlnT compensation is 972.796mV,and the peak value is 0.918 ppm/°C. The value is 3.307mV and the variation of temperature coefficient is 20.602ppm/°C from −40 °C to 125 °C. It can be seen that thebandgap voltage reference with TNT compensation struc-ture has excellent temperature coefficient.

Fig. 5 shows the variation of VREF with temperatureof different models under the condition of 1.8V supplyvoltage. The maximum value of VREF is 974.093mVunder FF model, and the minimum value of VREF is973.797mV under SS model. The temperature coefficientis 0.918 ppm/°C, 0.959 ppm/°C, 0.978 ppm/°C, 0.931ppm/°C, 1.045 ppm/°C for TT, FF, SS, SF, and FS model,respectively. The average temperature coefficient is 0.996ppm/°C.

Fig. 6 shows the simulated temperature dependence ofproposed bandgap voltage reference at TT corner over atemperature range from −40 °C to 125 °C with a supplyvoltage of 1.8V, 1.9V, 2.0V, 2.1V, 2.2V, 2.3V, 2.4V,2.5V, respectively. With a power supply of 1.8V, theproposed bandgap voltage reference has the minimumTC of 0.918 ppm/°C. The worst case of TC is 0.956ppm/°C with a supply voltage of 2.5V.

In Fig. 7, the VREF varies with the voltage at differenttemperatures, under the power supply voltage varying from1.8V to 3.6V. Over a supply voltage range of 1.8V to2.5V, the line regulation is 0.0066%/V, 0.0057%/V,0.0055%/V, and 0.0057%/V, respectively, at −40 °C,25 °C, 85 °C, and 125 °C.

Fig. 8 shows the VREF distribution obtained from 500Monte Carlo analyses, with an average of 973.925mV anda standard deviation of 1.31263mV. Fig. 9 is the distribu-tion of temperature coefficient obtained by 500 MonteCarlo analyses with an average of 1.75068mV. The layout

Fig. 3. Proposed circuit of the bandgap voltage reference

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of the design using a 0.18 µm standard CMOS process isshown in Fig. 10 and the active area is approximately0.024mm2 (102 �m � 238 �m).

Table I is a comparison of the performance of bandgapvoltage reference mentioned in different literatures. Ac-cording to the comparison, the proposed bandgap voltagereference has great advantages in TC, line regulation andlayout area.

4. Conclusion

A novel TlnT compensation method is used to eliminate thenonlinearity of the high precision bandgap voltage refer-

Fig. 6. Simulated temperature dependence with different voltages

Fig. 7. Simulated VREF versus supply voltage with differenttemperature

Fig. 8. Monte-Carlo simulation results of VREF

Fig. 9. Monte-Carlo simulation results of TC

Fig. 4. Comparison between VREF with TlnT compensation and VREFwithout TlnT compensation

Fig. 5. Simulated temperature dependence with different models

Fig. 10. Layout of the Proposed VBG

Table I. Comparison with existing designs in the literature.

[5] [12] [17] [18] [25] [28]ThisWork

Year 2013 2003 2015 2008 2019 2018 2019

Process (µm) 0.18 0.6 0.13 0.18 0.18 0.15 0.18

SupplyVoltage (V)

1.2 2 1.2 1.8 3.5 1.2 1.8

SupplyCurrent (µA)

36 23 120 2.5 108 51 23

VREF (mV) 767 1142 735 646.4 3110 569.8 973.97

Tem. Range(°C)

−40∼120

0∼100

−40∼120

−40∼125

−40∼130

−40∼120

−40∼125

TC (ppm/°C) 3.4 5.3 4.2 1.7 4.6 0.84 0.918

Line Reg.(%/V)

0.054 - - - - - - 0.31 0.023 0.0055

Active Area(mm2)

0.036 0.057 0.063 0.005 0.223 0.125 0.024

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ence designed in this paper. The design is based on 0.18µm CMOS process. The ultra-low temperature coefficientis achieved with 0.918 ppm/°C from −40 °C to 125°C. Itsminimum operating voltage is 1.8V, and its static currentconsumption is 23 µA at 25 °C. Under the condition thatthe power supply voltage changes from 1.8V to 3.6V, itsline regulation is only 0.0055%/V. The results show thatthe circuit is very suitable for high precision, low voltageand small area use.

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