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388 IEEEJOURNAL OF SOLID STATECIRCUITS VOL.SC 9 NO. 6 DECEMBER 97

Simple Three Terminal IC Bandgap ReferenceA. PAUL BROKAW MEMBER IEEE

A?r sfracfA n ew con fig ur a tion for r ea liza t ion of a st a biliz edb a nd ga p v ol t a ge i s d es cr ib ed Th e n ew t w o t r a n si st or ci rcu it u sescollect or cu rr en t s en sin g t o elim in a te er ror s d ue t o ba s e cu rr en t .B eca u se t h e s ta biliz ed v olt a g e a ppea r s a t a h ig h im ped a nce poi ntt h e a p pl ica t ion t o ci rcu it s w i t h h ig he r ou t pu t v ol t a ge is s im pl ifi ed .I ncor por a tion of t he n ew t w o t ra ns is tor cell in a t hr ee t er min al2.5 V m on ol it h ic r ef er en ce i s d es cr ib ed . Th e com pl et e ci rcu it isou t li ne d in f un ct ion a l d et a i l t og et h er w i t h a n a ly t ica l m et h od s u se di n t h e d es ig n . Th e a n a l y t ica l r es u lt s i ncl ud e s en s it i vi t y coe ff ici en t sg a in a n d f re qu en cy r es pon se p a ra m et er s a n d b ia s in g f or op ti mu mt e m pe r a t u r e p er f or m a n ce . Th e p er f or m a n ce of t h e m on ol it h ic ci rcu it w h i ch i ncl ud es t e m pe r a t u r e coe ff ici en t s of 5 p pm / C o ve r t h emili tary temperature ran ge is repor ted .

I . I N TR OD U C TI ON

TH E RE QU IRE ME NT for a st a ble r eference volta ge is a lmost universa l in elect ron ic design. Thet em pera ture compensa tecl a va la nche brea kdow n

diode fills ma ny of t he needs but ca n not be used w it hlow volt a ge supplies a nd oft en suffers from long t ermst abilit y problems. U se of a t ra nsist or base em it t er d iod et empera t ure compensa t ed t o t he ba ndga p volt a ge ofsilicon is a t echniq ue w hich overcomes some of t hea va la nche cliode limit a t ions. B a ndga p circuit s ca n beopera t ed from low volt a ge sources a nd depen d ma inlyupon subsur fa ce effect s w hich t end t o be more st a blet ha n t he surfa ce brea kdow ns gen era lly obt a ined w it ha va la nch e d iod es.

The convent iona l t hree t ra nsist or ba ndga p cell w orksw ell for very low volt a ge t w o t ermina l or synt het icZener cliocle req uirement s. The t lmee t ra nsist or cell isless flexible in t hree t ermina l a pplica tions a nd in circuit s w here t he desired out put is not a n int egra l mult ipleof t he ba ndga p volt a ge.

The t w o tra nsist or cell present ed here is simplerm or e flexible in t hr ee t erm ina l a pplica tions a nd elimina tes sources of error inheren t in t he t hree t ra nsist orcell. Th e two-transistor cell offers separate control overoutput voltage and temperature coefficient in a circuitusing only a single control loop.

The new bandgap circuit has been used as the basisof a monolithic three-terminal reference circuit sup-plying stable 2.5 V output and operating down to4-V input.

11 CONVENTIONAL CIRCUITConventional bandgap circuits are based on the con-

cept illustrated in Fig. 1. The transistors QI and Qz areM a nu scr ip t r ece iv ed M a y 6 1974; r ev is ed J u l y 25 1974. Th isp ~ pe r w a s p re se nt ed a t t h e I n te rn a t ion a l S ol id S t a t e C ir cu it s C onference Philadelphia Pa . February 1974.Th e a ut hor is w it h t he S em icon du ct or D ivis ion An alog D evices Inc. Wilmington Mass.

v

f Q~

Fig. 1. C on v en t i on a l b a n dg a p ci r cu it .

operated at different current densities to produce tem-perature proportional voltages across R~ and Rz Athird transistor Q3 is used to sense the output voltagethrough Rz As a result Q8 drives the output to a volt-age which is the sum of its ~7~E and the tcmperature-dependent voltage across Rz When the output voltageis set to approximate the banclgap voltage of siliconthe voltage across Rz will compensate the temperaturecoefficient of VBE and the output voltage will be tem-perature invariant [1]. To minimize the output voltagetemperature coefficient the collector current of Qa mustbe made proportional to temperature as are the cur-rents in QI and Qz. This large temperature-clependentcurrent at the point where the stabilized voltage ap-pears makes it inconvenient to produce an output greaterthan the bandgap voltage. Higher voltages can be gen-erated by stacking several junctions to produce ineffect several circuits like Fig. 1 in series [2].The theory used to predict the temperature behavior

of circuits like Fig. 1 neglects the effect of base currentflowing in RI and R The va ria bilit y in t his current duet o processing a nd t empera ture effect s on hrn gives r iset o a n out put volt a ge error a nd dr ift . This effect is pa rt icula rly severe w h en t h e curren t in Q2 is ma de muchsma ller t ha n curren t s in Q1 a nd Q8 t o produce t he req uired current densit y differen ce. U se of S uper B et a processing t o reduce t his problem result s in low volt aget ra nsist ors n ot suit able for a t hree t erm ina l reference.An a ddit iona l t empera ture st abilit y problem a rises outof t he nonlinea rit y a nd nonuniformit y of t he t emperat ur e ch ar act er ist ics of d iffu sed r es ist or s. Th e n on lin ea rit yca nnot ea sily be com pensa t ecl a ncl t he nonuniform it yca nnot be a ccommoda ted in t he design.

Th e idea lized circuit show n in Fig. 2 minimizes t hedifficult ies of obt aining out put s a bove t he ba ndga p volta ge r ed uces t he pr oblem of hj E variability to one of ~match and can be implemented with thin-film resistorson the monolithic chip to virtually eliminate nonlinear


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BROKAW : THREEJTERMINAL IC BANDGAP REFERENCE 9

Fig.

v+T TR R

1b

OUT

q kO+ m-[)

.

2 I d ea l iz ed ci rcu it i ll us t ra t i ng t w o t r a n si st or b a n dg a p cel l

v+

CID4 OUT .

Q2 ~ vGo+ m-l ~

R[v-

temperature coefficients of resistance TCR as an error Eliminate error due to base currentIn R4 by aettlne:factor. The circuit uses two transistors and collector- R7.R4Rscurrent sensing to establish the bandgap voltage. The R3= Ri R4+R5voltage appears at active transistor as opposed todiode-connected bases, so that it is a straight forward Fig. 3. Simplified circuit for developing higher output voltages.and simple matter to obtain overall output voltagesabove the bandgap voltage. Assuming that the resistor ratio and current density ratioare invariant, this voltage varies directly with T, the

III. BASIS OF THE NEW CONFIGURATION absolute temperature. This is the voltage which is usedA enerating the andgap Voltage to compensate the negative temperature coefficient ofT,

In the circuit of Fig. 2 the emitter area of Qz is madelarger than that of QI by a ratio of 8-to-1 in t,he ex-ample given . When the voltage at their common baseis small, so that the voltage drop across R2 i s small, thelarger area of Qz causes it to conduct more of the totalcurrent available through RI The resulting imbalance incollector voltages drives the op amp so as to raise thebase voltage. Alternatively, if the base voltage is high,forcing a large current through R the voltage developedacross Rz will limit the current through Qz so that it willbe less than the current in Q1. The sense of the collectorvoltage imbalance will now be reversed, causing the opamp to reduce the base voltage. Between these two ex-treme conditions is a base voltage at which the twocollector currents match, toward which the op amp drivesfrom any other condition. Assuming equal ti or common-base current transfer ratio for QI and Qz, this will occurwhen the emitter current densities are in the ratio 8-to-1,the emitter area ratio.

When this difference in current density has been pro-duced by the op amp, there will be a difference in V~~between QI and Qz, which will appear across Rg Thisdifference will be given by the expression

1Since the current in QI is equal to the current in Qz, thecurrent in RI i s twice that in R2 and the voltage acrossRI is given by

2

v BEThe voltage at the base of QI is the sum of the V~~ of

QI and the temperature-dependent voltage across RThis is analogous to the output voltage of the conven-tional bandgap circuit and can be set, hy adjustment ofR 1/ R 2 to a temperature stable value, as described in theAppendix.B I n cr ea si n g t h e S ta bi l i zed O ut pu t V ol t age

Assuming that the amplifier of Fig. 2 has sufficientgain, it will balance the collector currents of QI and Qzdespite an additional voltage drop added between its out-put and the common-base connection, This additionaldrop will not affect the base voltage which results in col-lector current balance. If the voltage is introduced bymeans of a resistive voltage clivider, the op amp outputvoltage will be proportional to the common-base voltage.

The circuit of Fig. 3 uses an active load to sense thecollector current of QI and Q2 more directly. The func-tion of the op amp is replaced by Q,,, Q,,, and Q Ihep n p transistors form a simple current mirror whichtakes the difference of the collector currents of QI andQ2. This difference current drives the base of Q, whichsupplies the circuit output voltage. This voltage is di-vided by Rd and R5 and applied to the base of Q1. Thesense of the signal to Q, drives QI and Qz to minimizethe collector current difference. By designing the circuitto stabilize the base voltage at the bandgap voltage theoutput will be stabilized at a higher voltage. Since theoutput voltage depends upon RA and R5 it can be set toany convenient value and need not be an integral nlul-tiple of the bandgap voltage.


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BROKAW : THREE TERMINAL IC BANDGAP REFERENCE 391

i2 LQ2 A ~ 1c,R2 ERIFig. 5. Tra nsconduct a nce a nd frequency compensa tion model,

V. FREQUENCYCOMPENSATIONThe amplifier in this circuit operates in a closed loop

to regulate the output voltage. A composite junction-MOS capacitor Cl is used to control the open-loop cross-over frequency and stabilize the closed-loop response.The analytical basis for this compensation is illustratedby Fig. 5. When the two-transistor bandgap cell is op-erated into a current mirror an output current is pro-duced whenever the common-base voltage departs fromthe nominal voltage determined by the current densityratio and by RI and R2. The change in this current as afunction of the departure of base voltage from its nom-inal value has the dimensions of transconductance andcan be used as such in design. The following incrementalapproximation gives a simple result which is more thanadequate for most design procedures.

Incremental changes in the base voltage of Q1 giverise to changes in collector current which can be approxi-mated by the ratio of the voltage change to R., the incre-mental emitter resistance. This same voltage incrementalso drives R2 and the incremental impedance of Qz. Ifthe transistors are operating at equal currents, the twoRe terms will be equal, making the total effective resist-ance in the Q2 branch higher. This will result in a lowerincremental current in Q2. Equating the incremental basevoltage changes gives

Ai., Ret = Ai., (R,, + R,). 5)Substituting for Re and for Rz in terms of the voltageacross it and current through it converts 5) tokT _ Ai L cT / r T l n~ ) 6) qi e, q ., qi , J ,A second approximation made is that the total incre-mental current is due to the voltage change across RIresulting from a voltage change AE at the common bases.That is

Ai., + Ai,, = ,1

7)

which neglects R. as compared with the value of RI .After eliminating common factors and assuming i ,, = i ,,,the combination of 6) and 7) can be manipulated toform

,l Ai., 1

In (J , / J , )AE ) 2 + in (J ,/ J 3 (8)

The difference in the Ql, Qz collector currents is the out-put current iO and is approximately given by the differ-ence of the emitter current increments. Taking 8) to thelimit at iO= Oyields

d 1

in (J 1 / J ,)dE ,0= , = )2 + in (J ,/ J ,) (9)

With a current density ratio of 8:1, the term in J1/J2 isapproximately 2, so that the transconductance of theentire circuit is approximately 1/ 2R1).

A capacitive load on the current output of the circuitin Fig. 5 will give a 6 dB/octave rolloff of voltage trans-fer ratio. The frequency at which the capacitive re-actance equals the transconductance will be the unity-gain frequency of the simple circuit. This is given by theexpression for F. in the figure. In the circuit of Fig. 4,the loop attenuation due to R4 and R5 reduces the overallunity-gain frequency by the ratio of the bandgap voltageto 2.5 V, which is approximately two.

The transconductance can also be used to estimatea low frequency {gain. In the simple circuit of Fig. 3,the gain is expressed as the ratio of the voltage at thebase of Q, to a small-signal input applied to the baseof Q1 at balance. Using a value of 3 k~ for RI and esti-mating the output impedance of Qll at about 300 k~gives a gain of about 50. In the monolithic circuit, theeffective open-loop gain is increased several orders ofmagnitude by the bootstrap connection to the currentmirror.

VI. MONOLITHIC CIRCUIT PERFORMANCEThe circuit of Fig. 4 is shown in Fig. 6 as it appears

in monolithic form. Several diffusion lots have been madeand measurements of these units indicate the typicalproperties given by the following table.

Typi ca l R ef er en ce C ir cu it P a r amet er s55 to + 125 C

Out pu t v ol ta g e 2.5 V + 2 percen tM in im um i npu t v olt a ge 4VLoa d regula tion, O t o 10 m A 3 mVS upply reject ion , 4.5 t o 7 V 0.25 mVS upply reject ion , 7 t o 30 V 0.25 mVS ta n db y cu rr en t 1 mAOut pu t v ol ta g e t empe ra t u re 5 to 60 ppm/ C

coe ff ici en t 7Vmri Vmin

7 = vnomi.a , AT

The observed variation in temperature coefficients


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392

Fig. 6. I llust ra t ion of 37 x 62 mil monolit hic die show ing thinfilm r esist ors a nd ba la nced t herm al la yout .

arises mainly from variability in absolute voltage at thebase of QI and variation in the coefficient m (see Ap-pendix). Unite showing a very constant temperature co-efficient generally show a good correlation between ab-solute output voltage and drift.

Several units showing large but constant temperaturecoefficients have been adjusted to very small final tem-perature coefficients. This has been done by measuringthe temperature coefficient calculating the ideal zerotemperature coefficient voltage correction and laser-trim-ming RI or R2 as required. Other units which are closerto the nominal output voltage exhibit very stable tem-perature characteristics initially. In extremely low-driftunits, the performance of the basic cell appears to bemasked by other drifts arising in the remainder of thecircuit. These residual drifts are on the order of 2 to 4ppm/C over a temperature range of 55 to -I-125C.

Some diffusion lots have shown a greater curvaturein the temperature characteristic. These units exhibit theroughly parabolic temperature characteristic, which isimplied by (14) of the Appendix. They show good tem-perature performance around a peak which occurs at atemperature related to initial output voltage. At tem-perature extremes the temperature coefficient may in-crease to 60 ppm/ C or morej if the peak is not cen-tered in the 55 to +125C range.

The elapsed time since obtaining the first completedunits has not been sufficient to accumulate long-term driftresults. Accelerated life tests have been made at hightemperatures to uncover any gross drift problems. Thetemperature stability and monitoring equipment have notbeen adequate to determine the ultimate stability of thedevice. Examination of data taken over the course of1000 hours at + 125 C does not reveal any trends orsystematic drifts at the 100 ppm level, which approxi-mates the repeatability of the measurements.

IEEEJOURNAL OF SOLID-STATECIRCUITSDECEMBER9APPmwm

THEORETICALTEMPERATUREBEHAVIORA. Opt i mum Cel l V ol tage

The optimum voltage at the base of QI is approxi-mately the bandgap voltage. A general analysis of thtwo-transistor bandgap cell yields a more-exact resuland some insight into the residual temperature drift in aoptimally adjusted circuit.

As a matter of convenience, the circuit descriptionhas involved the assumption that the required currentdensity ratio is established by the use of emitter areratio alone. The circuit can also be based on differentcollector currents and equal areas or a combination ounequal areas and currents.The equation describing the voltage across R can b

generalized by including- a parameter P, which is thratio of emitter currents 26,i@,, as follows:

lAn expression given by Brugler [3] has been modifiedby the addition of a current-dependent term to give th

where VOOis the

mlcT~ ln +~ln - (11.bandgap voltage of silicon and VB~O

the value of 1~~1 at a reference temperature TO.Since the voRages across both RI and Rz are propor-

tional to temperature, it follows that the current and thcurrent density in Q1 are also proportional to temperature.Therefore, the current density ratio in the last term o(11) can be equated to a temperature ratio as J/JO =T / T O. This relation can be used to reduce the sum oVI and V~,l to the form

E = v..+ ; V,,. VaO)+(ml)~ln~o+(Pl+l) ~ln (122 2

This represents the stable voltage established at the basof QI in the circuit of Fig. 1. Differentiating this resulttwice with respect to temperature yields

+(m1)~ln~1 (13and


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BROKAW : THREE TERMINAL IC BANDGAP REFERENCE

d2E-. dT _(~ 1) . 14Equating the first derivative to zero results in the equa-tion

15The left side of 15 is the value of E t T = T O.Thismeans that, in principle, if the base voltage of Q1 is setto VgO+ (VZ 1 l cT O / qt temperature T O,the tempera-ture coefficient of the output voltage will be zero. As-suming values of m greater than one in 14 implies,however, a nonzero temperature coefficient at tempera-tures other than T o. Experimental data indicate thatvalues of m as low as 1.2 have been achieved.

Examination of 13 and 15 shows that departuresfrom the optimum output voltage will result in an ap-proximately constant temperature coefficient. The mag-nitude of this coefficient will be the absolute error voltagedivided by the absolute temperature. For example, a 3percent absolute voltage error at 300 K will result in a3 percent/300 K = 100 ppm/C temperature coefficient.B . E fl ect s of R esi st or T em per at ur e C oej ici en ts

Both the common and differential temperature co-efficients of resistance of RI and R2 enter into the overalloutput voltage stability. The differential TCR may betreated by assuming that the total change in resistorratio is due to change in RI , Since the remainder of thecircuit forces a predetermined current in RI , its tempera

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