A Novel Bandgap Reference for Minimizing Current-MirrorMismatch

Li Sizhen1*, Zou Xuecheng1, Yu Kai1

, Zhang Hao1, LIN Shuangxe

1Department of Electronic Science & Technology, Huazhong University of Science & Technology, Wuhan 430074, P. R.China

2 School of Electric and Information Engineering, Wuhan Institute ofTechnology, Wuhan 430073, China*Email:lisizhen@gmail.com

r---........--ovref

input current of the operational amplifier employed andmismatch between RI and R2, there exits mirrormismatch between IC(QNl) and I C(QN2).

R2

(b)

Rl

(a)

Figure 1. (a) Conventional bandgap reference, (b)

Small-signal variation model of the conventional

bandgap core.

xQN2

.}----t--=---~

R3

Abstract

A novel bandgap reference for mInImIzIngcurrent-mirror mismatch is presented. In the proposedcircuit, the small-signal current variations in the twocurrent paths are self-compensated while in theconventional bandgap core they are multiplied. As aresult, error caused by current-mirror mismatch has beenmuch reduced in the proposed circuit. Moreover, thevoltage variations caused by temperature and supplyvoltage changes which make the small-signal current inthe bandgap core vary can also be minimized. Based onthe 0.6um BiCMOS process technology, the error causedby current-mirror mismatch has been reduced by about50 times in the proposed bandgap core and the completecircuit achieves a low temperature coefficient of 2.3ppm/°C and a high power supply rejection ratio (PSRR)of 72db without any PSRR boosting technique. Ontypical working conditions, the proposed circuitconsumes only a supply current of3.6uA.

1. Introduction

Fig. 1b illustrates the variation model of theconventional bandgap core described in Fig. 1a. Themirror mismatch between IC(QNl) and I C(QN2) producessmall-signal variations of IC(QNl) (iC(QNl)) and I C(QN2)

(iC(QN2)) from their nominal values generated whensupposing the currents are well matched. The change incurrent results in the total variation of the referencevoltage (Vrej) which can be represented by vrefCompared to the traditional method using equations, thesmall signal method will provide more convenience foranalysis.

Assuming there is a ~M current-mirror mismatch

between IC(QNl) and I C(QN2J,

I C (QN2) =(l + 8M )IC(QNl)· (2)

the erroneous PTAT current can be represented by IpTAT xand iC(QNl) is expressed as -

iC(QNl) = I PTAT _x - I pTAT

An ideal Bandgap reference (BGR) should be immuneto process, supply voltage, temperature, load and noise.In the aforementioned items, process variations have thebiggest impact on the absolute value of the referencevoltage. Among various error sources caused by processvariations, current-mirror mismatch has been discussedand defined as the leading one [1]. Thus, a bandgapreference with high immunity to current-mirrormismatch is desired.

Fig. la shows a widely used BGR with a populartopology---the Brokaw cell.

The bandgap voltage generated can be expressed as

V,q =VBEIQN2) + 2VT ( ~~ ) In C

2kT (R2)=VBElQN21 +--;;- m In C, (1 )

where C is the emitter ratio of QNlover QN2, q is theelectron charge, k is the Boltzmann constant and T is theabsolute temperature.

Ideally, (1) is obtained under the condition that thecollector current through the transistor QNI(Ic(QNl)) andQN2(Ic (QN2)) are identical. However, due to offsetting the

VT In[C(l +8M )] VT In C ~= --~-8Rl Rl Rl u·

In Fig. lb, gml,2 is represented by

(3)

978-1-4244-2186-2/08/$25.00 ©2008 IEEE

core.

Figure 2. (a) Proposed bandgap reference, (b)

Small-signal variation model of the proposed bandgap

-(b)

R2

(a)

Figure 3. A more precise small-signal variation model of

the proposed bandgap core.

1l~3

X t-------+--+I

QNl

ex

2. Proposed bandgap reference

alc Ic inC (4)gml,2 =av =~=R1.

BE T

Using the variation model described in Fig. Ib, theoverall error in reference voltage can be shown as

1 R2vref =VToM(l +-) + VTOM-(2 + inC) (5)

inC RIIt's obvious that the variation of PTAT current through

QNI (iC(QN1) has propagated to (2+lnC) iC(QN1) which isthe total PTAT current variation and finally results inlarge error in reference voltage.

As the PTAT slope, R2/RllnC, should be kept constantas about 18, it can be derived that the effect of errorcaused by current-mirror mismatch can be reduced bydecreasing the resistor ratio (R2/RI) at the expense ofincrease in C.

Other common techniques for the error minimizationare the post-processing trimming techniques, such asresistor trimming [2]. Some techniques and designmethodologies are discussed in [3] and [4] based on thetraditional bandgap core. Although the errors have beenminimized using the techniques, the voltage referencecircuit would become more complex requiring addedauxiliary circuit or the area of the layout would becomelarger.

In this paper, a novel bandgap circuit is presentedwhich features simplicity through internal compensationfor current-mirror mismatch.

The basic idea is to have the small-signal collectorcurrent of QNl and QN2 described in Fig. la change inthe opposite way.

The improved bandgap reference is presented in Fig.

2a.The reference voltage is obtained at the top tenninal

of R4 and is given by the following equation:

2~lnCVref = VBE(QN2) +---(R2 +R4)

RI (6)2kTlnC

=~E(QN2) +---(R2 + R4)qRI

Where C is the emitter ratio of QNI over QN2, q is theelectron charge, k is the Boltzmann constant and T is theabsolute temperature.

Fig. 2b illustrates the variation model of the proposed

bandgap core described in Fig. 2a. Assuming there is a

JM current-mirror mismatch between IC(QN1) and I C(QN2):

/C(QN2) = (1 + 8M )/C(QNl) ' (7)

Using the same method given in introduction, iC(QN2) is

expressed as

iC(QN2) = I PTAT _x -IPTAT ::; ~l OM. (8)

In Fig. 2b, gml,2 is represented by

g _ ale _ Ie _ In C (9)1111,2 - av - V - RI .

BE T

AndiC(QNl) ~ (I-In C)iC(QN2). (10)

vrefcan be derived from Fig. 2b as

vref = VT 8M + ~8M (R2 + R4)(2 -In C). (11)InC RI

It's obvious that for the case that InC>1, thesmall-signal current of QNl and QN2 described in Fig.2a change in the opposite way which results in theminimization of the total PTAT current variation.

It can be derived from (11) that when1 1

-+-(R2+R4)(2-1nC) =0, (12)inC Rl

vrefequals to zero. Solving (12), it was obtained that

(14)

In C =2x + I ~ 2 (13)x

where x, (R2+R4)lnC/Rl is a process dependent constantwhich is about 18.

In practical design, it's common to choose C=8 orC=24 for increasing the matching of Bipolar transistor.Thus, we choose C=8 for meeting the requirementdescribed in (13).

In the above analysis, the base current of QNI whichis one part of the current passing through RI is neglected.However, in practical circuit, it's necessary to considerthe effect of the base current of QN1. This is due to thefact that the two terms in (11) are close to each other.Thus, a more precise variation model of the proposedbandgap core is presented in Fig. 3, considering theeffect of the base current of QNI.

We SupposeI

ib(QNI) = pI iC(QNI) ,

where p1 depends on the operating conditions of thetransistor, such as temperature and transistor collectorcurrent [5]. iC(QNl) can be derived from Fig. 3 as

I-InCiClQNll ~ ~iClQN21'

1+-pI

(15)and results in

I-InC . iC(QN2)vref = (1 +li1C)lC(QN2)(R2+ R4)+--.

1+- gm2

pI(16)

Substitute (8) and (9) into (16),

vref = (1- InC -I) Vr£> M (R2+ R4)+ Vr£> M •

1+ InC RI InCpI

(17)By comparing between (5) and (17), it is shown that

the dominant term VrJM(2+lnC)R2/Rl in (5) iseliminated. The maxim vref in (17) is about VrJM/lnC.Thus, the variation in Vrej generated by current-mirrormismatch has been much reduced in the proposedbandgap core.

It has been demonstrated that the circuit showsimproved immunity to current-mirror mismatch throughthe self-compensated current paths. Moreover, theproposed circuit applying the idea can achieve goodperformance under temperature and supply voltagevariations which also cause the small-signal currents inthe two current paths vary. The good performance willbe shown in the next section.

3. The circuit and simulation

In this work, the novel bandgap core is applied. Fig.4(a) shows the circuit diagram. Transistor QN1,QN2along with resistor Rl, R2, R3, R4 compose the bandgapcore. The simple amplifier is made up of MPI, MP2,QN3, QN4 and R5. Transistor QN5-8 and resistor R6form a PTAT current generator which generates aconstant start-up current for bandgap core.

Based on the consideration of minimizing errorsources, choosing devices with good matchingcharacteristics is of great importance in circuit design. Inthe above circuit, the current-mirror mismatch errorwould be a function of the resistor value of RI and R3,the input offset voltage and offset current of theoperational.

Figure 4. (a) Complete schematic circuit of the BGR,(b) Layout of the BGR

Moreover, errors due to resistor mismatch andtransistor mismatch can only be reduced through layouttechniques such as common centroid layout and dummydevices.Choosing polysilicon resistors can minimize theerrors generated by resistor tolerance. The layout of thisBGR is shown in Fig.4(b).

Simulation has been carried out using a 0.6 umBiCMOS technology with HSPICE. Simulated circuitcharacteristics are listed in Tab. 1. The results show thatthe proposed circuit generates an output referencevoltage with a power supply rejection of 72dB. This is arelative high PSRR due to the fact that the open loopgain of the amplifier in the BGR is only 62 db and thesupply voltage directly affects the output of the amplifier[7]. With the power supply 3.6V and temperature rangefrom -25°C to 100°C, the temperature coefficient of thereference voltage is 2.3ppm/°C. On typical workingconditions, the proposed circuit consumes only a supplycurrent of 3.7uA. Higher PSRR may be achieved usingsome PSRR boosting techniques at the expense of morepower consumption and larger area of the circuit.

Table 1. Simulated circuit characteristicsCircuit Parameter Simulated value

Vref(@T=25°C) 1.24V

Quiescent Current 3.6uA

Temperature coefficient 2.3 ppm/DC

PSRR at low frequency 72dB

Figure 6. Comparision of simulated current variations of

(a) conventional BGR, and (b) the proposed BGR.

A design of high intrinsic accuracy bandgap referencefor current-mirror mismatch is described. The essentialidea is to have the small-signal currents in the twocurrent paths of BGR change oppositely. Based on thevariation model analysis, the area ratio of the twotransistors in BGR is chosen to 8 such that the errorcaused by the current-mirror mismatch can be largelyreduced. Applying the proposed bandgap core, acomplete circuit is designed in the paper which featuressimplicity and high accuracy over temperature andpower supply voltage which has been verified by thesimulation results.

References

[1] Drennan, P.G., McAndrew, C.C, Understanding

MOSFET mismatch for analog design, IEEE Journal

of Solid-State Circuits, 38(3), p. 450-456 (2003).

[2] GABRIEL A. RINCON-MORA, Voltage

References, From Diodes to Precision High-Order

Bandgap Circuits, IEEE Press, Georgia, p. 108-116

(2002).

[3] Brito, lP.M., Klimach, H., Bampi, S., A design

methodology for matching improvement in bandgap

references, Quality Electronic Design. ISQED. The

8th International Symposium, p. 586 - 594 (2007).

[4] Strik, S., Bandgap voltage reference: errors and

techniques for their minimization, Baltic

Electronics Conference, p. 1 - 4 (2006).

[5] Paul R. Gray, Paul 1 Hurst, Stephen H. Lewis and

Robert G. Meyer, Analysis and Design of Analog

Integrated Circuits, Wiley Press, p. 23-26 (2001).

[6] Gupta, V., Rincon-Mora, G.A., Predicting and

designing for the impact of process variations and

mismatch on the trim range and yield of bandgap

references, Quality of Electronic Design, ISQED,

Sixth International Symposium, p. 503 - 508 (2005).

[7] Giustolisi, G., Palumbo, G, A detailed analysis of

power-supply noise attenuation in bandgap voltage

references, Circuits and Systems I: Fundamental

Theory and Applications, IEEE Transactions, 50(2),

p. 185 - 197 (2003).

(b)

20 40 60 80 100Temperalure("C)

._- ......-~ .v,~~ .

~ •••.• , .••••.: ......1· •

i ...l.t ......~.. • '. ••••••• .. J•..•.•...", ....".. . .

(b)(a)

(a)

-4~--'w--.....~.... _

20 40 60 80 100 :~o 0Temperature("C)

.~ 0

5.5

1.8

1.6

;;(1.:g"1.2

~(J 0.8

0.6

o.~.-et"""""'''''­o~~o 0

Fig. 5a shows that the variation model described inFig. 1b provides a simple and good approximation forerror analysis. In Fig. 5b, a relative error is observedbetween the simulation and analysis due to the fact thatiC(QNJ) and iC(QN2) are very close to each other, it isdifficult to predict the difference between them. Thesimulation results given in Fig. 5b show that under the0.6um BiCMOS technology used for simulation andunder the low collector current level, error caused bycurrent-mirror mismatch in the proposed BGR core isdominated by the second term in (17). Even in the case,the variation of the reference voltage has been largelyreduced by about 50 times in the proposed circuit atroom temperature and as the temperature rises, errorbecomes less due to the increasing value of pI.Simulation results in Fig. 6a and Fig. 6b demonstratethat in the proposed bandgap core, the current variationsin the two current paths are self-compensated while inthe conventional bandgap core, they are multiplied.

Figure 5. Comparision of simulated and analytical vref

of (a) conventional BGR, (b) the proposed BGR with the

model described in Fig. 3 for analysis.

The results show that the current-mirror mismatchcause the error in the output reference and the error inconventional BGR is up to 6.2 mV while that in theproposed is only 0.13mV at room temperature. Therelative accuracy is increased by about 50 times.

4. Conclusion