Willy Sansen 10-05 161

Bandgap and current reference circuits

Willy Sansen

KULeuven, ESAT-MICASLeuven, Belgium

willy.sansen@esat.kuleuven.be

Willy Sansen 10-05 162

Voltage regulator

+-

R1

R2

+

- Vref

VoutVDD

Vout = VrefR1 + R2

R2

Willy Sansen 10-05 163

Current regulator

+-

+

- Vref

Iout

R

+-

V1

Iout

Iout =V1 - V2

R

+-R

V2

Iout =Vref

R

Willy Sansen 10-05 164

Table of contents

PrinciplesBipolar bandgap referencesCMOS bandgap referencesBandgap references < 1 VCurrent referencesLDO Regulators

Ref.: B.Gilbert, G.Meijer, ACD , Kluwer 1995

Willy Sansen 10-05 165

Bipolar transistor equations

+

-VBE

IBIC = IS exp ( )

VBE

kT/q

or IC = CTη exp ( )VBE - Vg0

kT/q

with Vg0 = 1268 mV - η kTr/q

and Tr = 323 K

which gives VBE = Vg00 - λT + c(T) for IC ~ Tm

- 2 mV/oC

- 2 µV/oC

Willy Sansen 10-05 166

VBE versus Temperature

VBE = Vg00 - λT + c(T) for IC ~ TmVBE

Vg00 = Vg0 + (η-m) kTr/q

λ =Tr

Vg00 - VBE (Tr)

c(T) = (η-m) (T -Tr -T ln )qk

Tr

T

Tr Tφ

tg φ = λ

c(T)Vg00

Vg0

VBE

Vg0 = 1156 mVη= 4Tr = 300 K VBE(Tr) = 700 mV

Willy Sansen 10-05 167

The curvature c(T)

m = 1 IC ~ T gm constantm = 0 IC constant gm ~ T-1

m = - IC ~ VBE gm ~ T-x

VBE (V)

T (K)

IC ~ T

IC constant

IC ~ VBE

∆VBE = 0.7 mV∆T = 30o

m = 1

m = 0

∆VBE = 5 mV∆T = 50o

Willy Sansen 10-05 168

Bandgap reference Vref

VBE

Vg00

0 Tr T

VBE

is PTAT- 2 mV/oC

≈ 0.6 V

Vref ≈ 1.2 V

Vref = VBE + VC VC ~kTq

≈ 0.6 V

VC

Willy Sansen 10-05 169

PTAT voltage and current

R2

1 : r ∆VBE = ln r+

-

kTq

∆VBE

IC = IS exp ( )VBE

kT/q

IC IC

Q1 Q2

∆VBE = VBE1 - VBE2

VBE = lnkTq

ICIS

∆VBE = lnkTq

IS2IS1

IC = ln rkT

qR2

r is 10-1000 !!

Willy Sansen 10-05 1610

Bandgap reference circuit

+

-

Vref

+

-VC R1

R2

n : 1

1 : r

VBE

Vg00

0 Tr T

VBE

PTAT- 2 mV/oC

≈ 0.6 V

≈ 1.2 V

∆VBE = ln nr+

-

kTq IC2 = ln nr =

kTqR2

Vref = VBE + VC VC = n ln nrkTq

R1R2

∆VBE

Q4 Q3

Q2Q1 AR2

Willy Sansen 10-05 1611

Noise Bandgap reference - 1

+

-

Vref

+

-VC R1

R2

n : 1

1 : r +

-

VC = n ln nr = n A = nR1IC2 ≈ 0.6 VkTq

R1R2

∆VBE

IC2 = ln nr = kT

qR2

AR2

R1

R2

R1 >> 1/gm1 R1IC1 ≈ 0.5 V gm1R1 ≈ 20

R2 >> 1/gm2 R2IC2 ≈ 0.06 V gm2R2 ≈ 2.3

Noise sources : R1 R2gm3,4 negligible for large VGS -VT or RE !!

A = ln nr ≈ 0.12 V kTq

IC2

Q4 Q3

Q2Q1

Willy Sansen 10-05 1612

Noise Bandgap reference - 2

+

-

Vref

+

-VC R1

R2

n : 1

1 : r +

-

VC = n ln nr = n A = nR1IC2 ≈ 0.6 VkTq

R1R2

∆VBE

IC2 = ln nr = kT

qR2

AR2

R1

R2

A = ln nr ≈ 0.12 V kTq

dVRef2 = 4kT R1 df + R1

2n2 4kT/R2 df

= 4kT R1 df (1 + n2 )R1R2

n2 = R1n = R1R2

nR2

nR2

VCIC2

nVC

∆VBE= >> 1

IC2

Q4 Q3

Q2Q1

Willy Sansen 10-05 1613

Noise Bandgap reference - 3

+

-

Vref

+

-VC R1

R2

n : 1

1 : r +

-

∆VBE

dVRef2 = 4kT R1 n2 df

R1R2

IC2

n2 = = R1R2

(R1n)2

R2

1R2

VC2

IC22

VC2

IC2 ∆VBE=R1

VC ≈ 0.6 V :>> Large IC2 : small R’s>> Large r : large ∆VBE

Q4 Q3

Q2Q1

Willy Sansen 10-05 1614

Table of contents

PrinciplesBipolar bandgap referencesCMOS bandgap referencesBandgap references < 1 VCurrent referencesLDO Regulators

Ref.: B. Gilbert, G.Meijer, ACD , Kluwer 1995

Willy Sansen 10-05 1615

Bandgap reference with bipolar transistors

-

2Vref

+R1

R2

n: 1

1 : r

Insensitive to β and VE !

∆VBE = ln nrkTq IC = ln nr

kTqR2

Vref = 2VBE + VR3

VR3 = 2R3 ( + ) ln nrkTq

1R2

2R3

1R1

Ref.: G.Meijer, ACD , Kluwer 1995

Willy Sansen 10-05 1616

Start-up circuits required

IC

-

Vref

+R1

R2

1 : 1

1 : r

IC2

Q4 Q3

Q2Q1

IC1

VBE1

IC2

IC1

required operating point

unwanted operating point

R2

R1

qkT

Vref = VBE1 + ln r

Willy Sansen 10-05 1617

Start-up circuits

Cstart

D1 D2

r : 1Q2

Q1Q4

Q3

R3

R2

R1

r : 1Q1Q2

R2

R1R3

RSTART

D2

4x

Willy Sansen 10-05 1618

Bipolar Bandgap reference without opamp

R21 : r

IC

Q1 Q2

R1 R1

Q3

VOUT

Ref. Widlar, JSSC Feb.1971, 2-7

IC

VOUT = VBE1 + R1 IC

R2

R1

qkT

= VBE1 + ln r

Willy Sansen 10-05 1619

All NPN bipolar bandgap reference

Ref.: B.Gilbert, ACD , Kluwer 1995

Willy Sansen 10-05 1620

Bipolar Bandgap references with opamps

+-

Vref

1 : n

R

RPTAT

R

+

-

+-

Vref

1 : n

R

RPTAT

R

+

-Bad PSRR

Willy Sansen 10-05 1621

CMOS Bandgap ref.with opamp: error analysis 1

+-

Vref

1 : n

R

RPT

R

+

-

kTq

dICIC

IC = ln nkT

qRPT

Vref = VBE + A (VBE1 - VBE2)

dVBE = ( - )dISIS

kTq

1ln n

= ( - - )dRPTRPT

dISIS

dnn

= 26 mV (0.46 2% - 30 % - 20%) ≈ 13 mV (if n = 10)

is PTAT !

Q1 Q2 A =RPT

R

Willy Sansen 10-05 1622

CMOS Bandgap ref.with opamp: error analysis 2

Vref = VBE + A (VBE1 - VBE2)

d(VBE1 - VBE2) =

kTq

1ln n

= A ln n ( + ) dnn

= 600 mV (1 % + 0.46 2% ) ≈ 11 mV 24 mV or 2%

is PTAT !

VBE1 - VBE2 = ln nkTq

kTq

dnn

dAA

d[A(VBE1 - VBE2)] = +-

1 : n

R

RPT

R

+

-

Q1 Q2

Willy Sansen 10-05 1623

Bipolar Bandgap reference AD580

+-

Vref = VBE + VR1

1 : 8

R R

+

-R1

R2 R3

R4

VOUT = Vref

VIN

VR1

VR2

R3 + R4

R3

= VBE + 2 VR2R2

R1

= VBE + 2 ln 8R2

R1

qkT

≈ 1.205 V

+

+

-

-

Willy Sansen 10-05 1624

Curvature correction with ∆VBE

Ref. Widlar, Meijer, van Staveren

VBE(V)

m=1 PTAT currentratio η/(η-1) or 1/a2η = 3.5 a2 ≈ 0.714

m=0 constant currentstronger curvature

Vref ≈ 210 mV

Willy Sansen 10-05 1625

Curvature correction with ∆VBE

IB (const) ≈ 1.5 + 7 + 7 µA

+

-

Vref≈ 210 mV

I(PTAT) I (VBE)

I (const)

Q2Q1

7 µA7 µA

1.5 µA

Ref. Widlar JSSC Dec.78, 838-846

R1 R2

R4

R5

R3

Vref = VBE2 + R2 I (VBE)

- R1(I (const) + I (PTAT))

- VBE1

≈ VPTAT + AVBE2

Willy Sansen 10-05 1626

Curvature correction with PTAT2

Ref. Song JSSC Dec.83, 634-643, Degrauwe ISSCC Febr.85, 142-143

-

IPTAT

1 : 1

+ 1

R2

R1

IPTAT

IPTAT2

Vref = VBE3 + ln rkTq

R2R1

translinear circuit

r : 1 : 1IBQ1Q2

Q3

+ γT2

Willy Sansen 10-05 1627

Table of contents

PrinciplesBipolar bandgap referencesCMOS bandgap referencesBandgap references < 1 VCurrent referencesLDO Regulators

Ref.: B.Gilbert, G.Meijer, ACD , Kluwer 1995

Willy Sansen 10-05 1628

Polysilicon gate

Gate oxyde

N-well CMOS technology

Willy Sansen 10-05 1629

CMOS Bandgap reference with opamp

+-

Vrefn : 1

R

RPTAT

R

+

-

+-

Vref

n : 1

RPT

+

-

1:1

Willy Sansen 10-05 1630

Full CMOS bandgap reference circuit

Ref. MIETEC; Meijer, ACD, Kluwer 1995

2.7 ... 5.5 V

17 µA

1.2 ± 0.02 V10 µA max.

4000 ppm-50 oC

+150 oC

Startup

PDI

PDII

Willy Sansen 10-05 1631

Bandgap reference with high PSRR

Ref.Tham, JSSC, May 95, pp.586-590

1 : 1 : N

M : 1

1.2 V 1.2 V

2.4 V > 2.5 V

VBG = VBE2 + N ln [M (N+1)]R2R1

kTq

300 µA

1.236 V± 20 mV85 ppm/oC

Willy Sansen 10-05 1632

Floating CMOS bandgap reference

Ref.Ferro, JSSC, June 89, pp.690-697

2.48 V ± 24 mV21 ppm/oC

5 V 1.2 mA

Willy Sansen 10-05 1633

CMOS Bandgap without resistors

Ref.: Buck, JSSC Jan. 2002, 81-83

∆VD = VD2 - VD1

VOUT = VD2 + AG ∆VD

VOUT ≈ 1.12 V9 mV 0 …70 oC3.7 V; 0.4 mA

A = 1.5B = 4 G = 6AD1/AD2 = 8

Willy Sansen 10-05 1634

Single-junction CMOS Bandgap reference

+- Vout ~ ∆VBE

IB1

Sw2t1: opent2: opent3: closed Sw1

IB2

t1: closed : Vout = VBE1t2: opent3: openC1 C2 + ∆VBE21C2

C1+C2

Ref. Gilbert, ACD, Kluwer 1995

Willy Sansen 10-05 1635

MOST in weak inversion ?

+

-VGS

IB IDS = IDS0 exp ( )VGS

nkT/q

n = 1 + CD

- 2 mV/oC

- 20 µV/oC

Cox

CD (VCB)

Willy Sansen 10-05 1636

Table of contents

PrinciplesBipolar bandgap referencesCMOS bandgap referencesBandgap references < 1 VCurrent referencesLDO Regulators

Ref.: B. Gilbert, G.Meijer, ACD , Kluwer 1995

Willy Sansen 10-05 1637

Sub-1 V CMOS bandgap reference

Banba, .., JSSC May 99, 670-673

Vref = VBE +R4R2

R4R3

kTq

ln n

VBER3 R2

R4

518 mV± 15 mV

n = 100

Willy Sansen 10-05 1638

CMOS Bandgap with supply < 1 V

+-

Vref

R2 = R1

+

-R1

Ref.: Malcovati, JSSCJuly 01, 1076-1081

R0

1 : 11 : 1

R3IPTAT

+

-kT ln n

R0q

n1

Vref = VBE +R3R2

R3R0

kTq

ln n

0.536 V

1V92 µA

Willy Sansen 10-05 1639

1 V opamp (1.2 MHz 25 pF 35 µA)

Vout

Vin-Vin+

VB

Cc

Willy Sansen 10-05 1640

Start-up circuit

+-

Vref

+

-R2 = R1R1

R0

n1

1 : 11 : 1

VB

0.536 V

MS

Willy Sansen 10-05 1641

Curvature correction

+-

Vref

+

-

VB

R2 = R1R1

R0

n1

IPTATI(ct) I(ct)

1 : 11 : 1

R4

R5

∆VBE

0.8mV

0.3mV

0oC80oC

1V92 µA

Willy Sansen 10-05 1642

CMOS Bandgap with supply < 1 V

+-

Vref

R2a +

-

R1

Ref.: Leung, JSSCApril 2002, 526-530

1 : 11 : 1

R3

n1

Vref = VBER3R2

R3R1

kTq

ln n

0.603 V

1V18 µA

+

R2b

R2a

R2b

Willy Sansen 10-05 1643

Table of contents

PrinciplesBipolar bandgap referencesCMOS bandgap referencesBandgap references < 1 VCurrent referencesLDO Regulators

Ref.: B. Gilbert, G.Meijer, ACD , Kluwer 1995

Willy Sansen 10-05 1644

Voltage-current converter

+-

+

- Vref

Iout

Iout =Vref

R

RTemperature coefficient :depends onVrefR !

Willy Sansen 10-05 1645

Temperature coefficient of resistors

cm-3

Willy Sansen 10-05 1646

Voltage to current converter

Blauschild, ACD Kluwer 1995

Willy Sansen 10-05 1647

Current reference without resistors

M1+ -

a : 1

1 : b

V2

Iref = K’nW1

L1m = ab(1 - √m)2

V2 2 1

Ref. Op ‘t Eynde, JSSC June 88, pp. 821-824

K’n ~ T -1.5 V2 ~ T Iref ~ T -0.5Vcc > 3.5 V 2 µA0.774 ± 0.02 µA3 % 0o ... 80oC

V2 ≈ 0.32 V

IC

VBE1

IM1

IM2

required operatingpoint Iref

unwanted operating point

M2

VT2+V2VT1

Iref

Willy Sansen 10-05 1648

Current reference

Ref. Op ‘t Eynde, JSSC June 88, pp. 821-824Ref. Vittoz, JSSC June 79, pp. 573-577

Vo

Both in wi.

Vo = ln (1 + )q

nkT Sb

Sa

V2 ≈ 0.32 V Vcc > 3.5 V 2 µA0.774 ± 0.02 µA3 % 0o ... 80oC

Sb/Sa = 5Vo ≈ 64 mV

Willy Sansen 10-05 1649

SC Voltage-current converter

Ref. H.Klein, W. Engl, ESSCIRC 83, pp. 119-122

C1 = C2 = 3 pF fc = 270 kHz ±5 V 4 µA

Vref C1 = Iref Tc/2

Reff =

Iref =

12fcC1

Vref

Reff

Willy Sansen 10-05 1650

Table of contents

PrinciplesBipolar bandgap referencesCMOS bandgap referencesBandgap references < 1 VCurrent referencesLDO Regulators

Ref.: B. Gilbert, G.Meijer, ACD , Kluwer 1995

Willy Sansen 10-05 1651

Low drop-out regulator : principle

+-

R1

R2

+

- Vref

Vout = 2 VVin = 3.1 V

Vout = VrefR1 + R2

R2

+-

+

- Vref

Vout = 2 VVin = 2.2 V

R1

R2

2.9 V 1.3 V

VGS ≈ 0.9 V

Gain !

Willy Sansen 10-05 1652

Table of contents

PrinciplesBipolar bandgap referencesCMOS bandgap referencesBandgap references < 1 VCurrent referencesLDO Regulators

Ref.: B. Gilbert, G.Meijer, ACD , Kluwer 1995

Willy Sansen 10-05 1653

References

P. Brokaw, “A simple three-terminal IC bandgap reference” JSSC Dec.74, pp.388-393

M. Degrauwe, etal, “CMOS voltage references using lateral bipolar transistors”, JSSC Dec.85, pp.1151-1157

K. Kuijk, “A presicion reference voltage source” JSSC June 1973, pp.222-226G. Meijer etal “An integrated bandgap reference”, JSSC June ‘76, pp.403-406G. Meijer etal “A new curvature-corrected bandgap reference”

JSSC Dec.82, pp.1139-143G. Meijer, “Bandgap references”, ACD Kluwer, 1995B. Song, P.Gray, “A precision curvature-compensated CMOS bandgap

reference” JSSC Dec.83, pp.634-643A. van Staveren etal “An integratible second-order compensated

bandgap reference for 1 V supply”, ACD Kluwer 1995.R. Widlar, “New developments in IC Voltage Regulators”, JSSC Febr.71, pp. 2-7.R. Widlar, “Low-voltage techniques”, JSSC Dec.78, pp.838-846.