EE 435

Lecture 44

References

Consider Voltage References

VBIASVREF

Voltage

Reference

Circuit

VDD

VREF

M2

M1

21

12

21

120

1

1

LW

LW

LW

LWVV

V

TDD

REF

VDD,VT reference

Observation – Variables with units Volts needed to build any voltage reference

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Voltage References

VBIASVREF

Voltage

Reference

Circuit

Observation – Variables with units Volts needed to build any voltage reference

What variables available in a process have units volts?

VDD, VT, VBE (diode) ,VZ,VBE,Vt ???

What variables which have units volts satisfy the desired properties of a

voltage reference?

How can a circuit be designed that “expresses” the desired variables?

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Voltage References

Consider the Diode

ID

VD

t

D

V

V

SD AeJI

t

G0

V

-V

m

SXS eTJJ~

pn junction characteristics highly temperature dependent through both

the exponent and JS

VG0 is nearly independent of process and temperature

V.VG 20610

q

kTVt

K

Vx.

K

V

x.

x.

q

koo

5

19

23

106148106021

10381

termed the bandgap voltage

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Voltage References

VBIASVREF

Voltage

Reference

Circuit

Observation – Variables with units Volts needed to build any voltage reference

What variables available in a process have units volts?

VDD, VT, VBE (diode) ,VZ,VBE,Vt ,VG0 ???

What variables which have units volts satisfy the desired properties of a

voltage reference? VG0 and ??

How can a circuit be designed that “expresses” the desired variables?

VG0 is deeply embedded in a device model with horrible temperature effects !

Good diodes are not widely available in most MOS processes !

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Standard Approach to Building

Voltage References

Negative

Temperature

Coefficient

(NTC)

K

Positive

Temperature

Coefficient

(PTC)

XOUT

XN

XP

Pick K so that at some temperature T0,

0T

KXX

0TT

PN

PNOUT KXXX

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Standard Approach to Building

Voltage References

Negative Temperature

Coefficient

V

T

Positive Temperature

Coefficient

T0

V

TT0

XN+KXP

0TT

PN

T

KXX

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Q1

VBE1

Bandgap Voltage References

Consider two BJTs (or diodes)

Q2

VBE2

TI

Iln

q

kΔVVV

C1

C2BEBE1BE2

C1

C2BE1BE2

I

Iln

q

k

T

VV

25.8mVx3008.6x10VV 5

BE1BE2

At room temperature

CV/868.6x10

T

VV o5

K300TT

BE1BE2

o0

μ

If ln(IC2/IC1)=1

The temperature coefficient of the PTAT voltage is rather small

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t

BE

t

G0

V

(T)V

V

-V

m

SXC eeTI(T)I

~

Q1

VBE1

Bandgap Voltage References

Consider two BJTs (or diodes)

Q2

VBE2

mlnTAJVVIlnVV ESXtG0CtBE ~

ln

t

G0BEBE

V

VVm-

q

k

T

V

If IC is independent of temperature, it follows that

C2.1mV/25mV

1.20.652.38.6x10

T

V o5

K300TT

BE

o0

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VBE and ΔVBE with constant IC

0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200 250 300 350 400

Temperature

Vo

lts

ΔVBE

VBE

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First Bandgap Reference (and still widely used!)

VDD

VREF

R1

R2

R3 R

4

Q1

Q2

P.Brokaw, “A Simple Three-Terminal IC Bandgap Reference”, IEEE

Journal of Solid State Circuits, Vol. 9, pp. 388-393, Dec. 1974.

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First Bandgap Reference (and still widely used!)

VDD

VREF

R1

R2

R3 R4

Q1Q2

VBE2

BE

2

1 ΔVR

R

Current ratios is R4/R3

Current not highly dependent upon T

BE2BE1

2

1BE2REF VV

R

RVV

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Thanks to Damek for the following assessment !

Most Published Analysis of Bandgap Circuits

0 2REF G0 BE0 G0

0 1

T JT kT kTV =V + V -V + m-1 ln +K ln

T q T q J

where K is the gain of the PTAT signal

Negative

Temperature

Coefficient

(NTC)

K

Positive

Temperature

Coefficient

(PTC)

XOUT

XN

XP

First Bandgap Reference (and still widely used!)

2121 BEBEEVVRI

1212

RIIVVEEBEREF

3

OSC2DDC1

R

VVVI

4

C2DDC2

R

VVI

E11C1 IαI

E22C2 IαI β1

βα

V DD

V REF

R 1

R 2

R 3 R 4

Q 1 Q 2

31

1OS

4

3

2

1

2

1BE1BE2BE2REF

Rα

RV

R

R

α

α1

R

RVVVV

31

OS

3

4E2E1

R

V

R

RII

1

2

First Bandgap Reference (and still widely used!)

E11C1 IαI

E22C2 IαI

V DD

V REF

R 1

R 2

R 3 R 4

Q 1 Q 2

4

3

2

1

2

1BE1BE2BE2REF

R

R

α

α1

R

RVVVV

3

4E2E1

R

RII

1

2

mlnTAlnVVlnIVV SXE1tG0C1tBE1 J~

mlnTAlnVVlnIVV SXE2tG0C2tBE2 J~

TR

R

A

Aln

q

kΔVVV

4

3

E2

E1BEBE1BE2

First Bandgap Reference (and still widely used!)

V DD

V REF

R 1

R 2

R 3 R 4

Q 1 Q 2

4

3

2

1

2

1BE1BE2BE2REF

R

R

α

α1

R

RVVVV

mlnTAlnVVlnIVV SXE1tG0C1tBE1 J~

mlnTAlnVVlnIVV SXE2tG0C2tBE2 J~

TR

R

A

Aln

q

kΔVVV

4

3

E2

E1BEBE1BE2

4

3

E2

E1

4

3

SXE22

1ttG0BE2

R

R

A

Aln

R

R

JAR

α

q

klnV lnTVm1VV ~

From the expression for VBE2 and some routine but tedious

manipulations it follows that

First Bandgap Reference (and still widely used!)

V DD

V REF

R 1

R 2

R 3 R 4

Q 1 Q 2

4

3

2

1

2

1BE1BE2BE2REF

R

R

α

α1

R

RVVVV

TR

R

A

Aln

q

kΔVVV

4

3

E2

E1BEBE1BE2

4

3

E2

E1

4

3

SXE22

1ttG0BE2

R

R

A

Aln

R

R

JAR

α

q

klnV lnTVm1VV ~

TR

R

α

α1

R

R

R

R

A

Aln

q

kmlnTIlnVV

R

R

A

Aln

q

kT

R

R

R

αlnVV

4

3

2

1

2

1

4

3

E2

E1SX2tG0

4

3

E2

E1

4

3

2

1tREF

~

It thus follows that:

First Bandgap Reference (and still widely used!)

V DD

V REF

R 1

R 2

R 3 R 4

Q 1 Q 2

4

3

2

1

2

1BE1BE2BE2REF

R

R

α

α1

R

RVVVV

TR

R

α

α1

R

R

R

R

A

Aln

q

kmlnTIlnVV

R

R

A

Aln

q

kT

R

R

R

αlnVV

4

3

2

1

2

1

4

3

E2

E1SX2tG0

4

3

E2

E1

4

3

2

1tREF

~

TlnTcTbaV 111REF

GO1 Va

2SK2

E2

E1

1

3

1

4

3

E2

E1

4

3

24

13

2

11

RI

A

A

R

Rln

αR

R

q

kln

A

A

R

Rln

αR

αR1

R

R

q

kb ~

m1q

kc1

First Bandgap Reference (and still widely used!)

V DD

V REF

R 1

R 2

R 3 R 4

Q 1 Q 2

TlnTcTbaV 111REF

GO1 Va

2SK2

E2

E1

1

3

1

4

3

E2

E1

4

3

24

13

2

11

RI

A

A

R

Rln

αR

R

q

kln

A

A

R

Rln

αR

αR1

R

R

q

kb ~

m1q

kc1

0lnT1cbdT

dV11

REF

1

1

c

b1

INF eT

INF11 lnT1cb

INF11REF TcaV

1mq

kTVV INF

G0REF

First Bandgap Reference (and still widely used!)

V DD

V REF

R 1

R 2

R 3 R 4

Q 1 Q 2

TlnTcTbaV 111REF

1mq

kTVV INF

G0REF

Bandgap Voltage Source

1.237000

1.237500

1.238000

1.238500

1.239000

1.239500

1.240000

200 250 300 350 400

Temperature in C

VR

EF

VGO 1.206

TO 300

VBEO2 0.65

m-1 1.3

k/q 8.61E-05

Temperature Coefficient

T

V

VNOM

T1 T2

VMin

VMax

12

MINMAX

TT

VVTC

610)12NOM

MINMAXppm

T(TV

VVTC

TC of Bandgap Reference (+/- ppm/C)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 50 100 150 200 250

Temperature Range

TC

Bamba Bandgap Reference

D1D2

R1 R2

M1 M2M3

R4VREF

θ

VDD

VD1

R0

VD2

I1 I2

ID1 ID2

I3

[7] H. Banba, H. Shiga, A. Umezawa, T. Miyaba, T. Tanzawa, A. Atsumi,

and K. Sakkui, IEEE Journal of Solid-State Circuits, Vol. 34, pp. 670-674, May

1999.

Bamba Bandgap Reference

D1D2

R1 R2

M1 M2M3

R4VREF

θ

VDD

VD1

R0

VD2

I1 I2

ID1 ID2

I3BE1

R1

1

VI =

R

R2 R1I =I

BE R0

0

VI

R

2I

2 R0 R2I =I +I

3 2I =KI

4REF 3V =θI R

Substituting, we obtain

BE BEREF 4

1 0

V ΔVV =θKR +

R R

4 1REF BE BE

1 0

R RV =θK V + ΔV

R R

K is the ratio of I3 to I2

REF 11 11 11V a b T c TlnT

Kujik Bandgap Reference

D1D2

VREF

R0

VD2

I1 I2

ID1 ID2VD1

R1 R2

VX

[12] K. Kuijk, “A Precision Reference Voltage Source”,

IEEE Journal of Solid State Circuits, Vol. 8, pp. 222-226, June

1973.

Kujik Bandgap Reference

D1D2

VREF

R0

VD2

I1 I2

ID1 ID2VD1

R1 R2

VX

BE R0

0

VI

R

2 R0I =I

REF 2 2 BE1V =I R +V

2REF BE BE1

0

RV = V +V

R

solving, we obtain

REF 22 22 22V a b T c TlnT

End of Lecture 44