EE 505 CMOS and BiCMOS Data Conversion Circuitsclass.ece.iastate.edu/ee435/lectures/EE 435 Lect...

EE 435

Lecture 42

• References

• PLLs and VCOs

Desired Properties of References

VBIASVREF

Voltage

Reference

Circuit

• Accurate

• Temperature Stable

• Time Stable

• Insensitive to VBIAS

• Low Output Impedance (voltage reference)

• Floating

• Small Area

• Low Power Dissipation

• Process Tolerant

• Process Transportable.• •

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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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Voltage References

t

G0

V

-V

m

SXS eTJJ~

t

BE

t

G0

V

(T)V

V

-V

m

SXC eeTAJ(T)I

~

t

BE

V

V

SC AeJI

Bandgap Voltage Appears in

BJT Model Equation as well

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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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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

TI

Iln

q

kΔVVV

C1

C2BEBE1BE2

If the IC2/IC1 ratio is constant, the TC of ΔVBE is positive

ΔVBE is termed a PTAT voltage (Proportional to Absolute Temperature)

This relationship applies irrespective of how temperature dependent IC1 and IC2 may be

provided the ratio is constant !!

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Q1

VBE1



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

Q1

VBE1

Bandgap Voltage ReferencesConsider two BJTs (or diodes)

Q2

VBE2

C1

C2BE1BE2

I

Iln

q

k

T

VV

At room temperature

The temperature coefficient of the PTAT voltage is rather small even if large

collector current ratios are used

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 10 100 1000 10000 100000 1000000

Collector Current Ratio

PT

AT

De

riv

ati

ve

mV

/C

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t

BE

t

G0

V

(T)V

V

-V

m

SXC eeTI(T)I

~

Q1

VBE1



Q2

VBE2


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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Q1

VBE1



Q2

VBE2


C2.1mV/25mV

1.20.652.38.6x10

T

V o5

K300TT

BE

o0

If ln(IC2/IC1)=1

CV/868.6x10

T

VV o5

K300TT

BE1BE2

o0

μ

Magnitude of TC of PTAT source is much smaller than that of VBE source

PNOUT KXXX 0

T

KXX

0TT

PN

If K will be large

Q1

VBE1



Q2

VBE2


C2.1mV/25mV

1.20.652.38.6x10

T

V o5

K300TT

BE

o0


ln

ESXtCtG0BE AJ~

lnVmlnTIlnVVV

If IC is reasonably independent of temperature, VBE will still provide a negative TC

Rewriting VBE equation

Bandgap Reference Circuits

• Circuits that implement ΔVBE and VBE or ΔVD

and VD widely used to build bandgap

references

VD1VD2

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

VBE plot for 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

VBE

End Point

Fit Line

Comparison of VBE with constant

current and PTAT current

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 100 200 300 400 500 600

Temperature

Vo

lts

Constant

Current

PTAT

Current

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.

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


2121 BEBEEVVRI

1212

RIIVVEEBEREF

3

OSC2DDC1

R

VVVI

4

C2DDC2

R

VVI

E11C1 IαI

E22C2 IαI β1

βα

VDD

VREF

R1

R2

R3 R4

Q1Q2

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


E11C1 IαI

E22C2 IαI

VDD

VREF

R1

R2

R3 R4

Q1Q2

4

3

2

1

2

1BE1BE2BE2REF

R

R

α

α1

R

RVVVV

3

4E2E1

R

RII

1

2

mlnTAlnVVlnIVV SXE1tG0C1tBE1 J~


TR

R

A

Aln

q

kΔVVV

4

3

E2

E1BEBE1BE2


VDD

VREF

R1

R2

R3 R4

Q1Q2

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 ~

From the expression for VBE2 and some routine but tedious

manipulations it follows that


VDD

VREF

R1

R2

R3 R4

Q1Q2

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:


VDD

VREF

R1

R2

R3 R4

Q1Q2

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


VDD

VREF

R1

R2

R3 R4

Q1Q2

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


VDD

VREF

R1

R2

R3 R4

Q1Q2

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

lnREFV a bT cT T

Almost all of the published bandgap references have an output of the form:

End of Lecture 42

EE 505 CMOS and BiCMOS Data Conversion Circuitsclass.ece.iastate.edu/ee435/lectures/EE 435 Lect...

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Transcript of EE 505 CMOS and BiCMOS Data Conversion Circuitsclass.ece.iastate.edu/ee435/lectures/EE 435 Lect...