REFERENCE CIRCUITS

A reference circuit is an independent voltage or current source which has a high degree of precision and stability.

• Output voltage/current should be independent of power supply.• Output voltage/current should be independent of temperature.• Output voltage/current should be independent of processing variations.

I-V curves of ideal references

Concept of Sensitivity

),,( 321 xxxfy

3

12

11

1

xxf

xxf

xxf

y

3

33

12

22

11

11

1 xx

yx

xf

xx

yx

xf

xx

yx

xf

yy

3

3

2

2

1

1321 xx

Sxx

Sxx

Syy y

xyx

yx

yxiS

Let

Then:

is called the sensitivity of y with respect to xi

Total percentage change in y = Sensitivity w.r.t. x1 * percentage

change in x1 + Sensitivity w.r.t. x2 * percentage

change in x2 + ……

Goal: Design reference circuits so that the reference’s sensitivities w.r.t.

various variations are minimized.

Types of commonly used references

• Voltage dividers - passive and active.

• MOS diode reference.

• PN junction diode reference.

• Gate-source threshold reference circuit.

• Base-emitter reference circuit.

• Thermo voltage reference circuit

• Bandgap reference circuit

Typical variations affecting the references

• Power supply variation (main concern here)

• Load variation (ro=∞ for I-ref, ro=0 for V-ref)

• Temperature variation (main concern also)

• Processes variation (good process and layout)

• Interferences and noise (not considered here)

yTST

1Ty

y 1

For temperature variation, typically use fractional temperature coefficient:

TCF = =

Voltage references

Passive Divider Limited accuracy, ~6-bit, or 2%

Large static powerfor small ro

Large area

Power sensitivity =1

Temp coeff depends on material

Active Dividers

These can be used as “start up” circuits.

S REF

CC

V

V )/ln(1

sCC RIV

S REF

CC

V

V

PN Junction Voltage References

=

If VCC = 10V, R = 10 k, and IS = 10-15A, then = 0.0362.

TV

VREF

REF 1

TRR

qVkT

qVk

TVVV

REFREFREF

GOREF

3

)/

exp(3

qkT

VVKT

R

VV GOREFREFCC

For a diode:

Taking ∂/∂T and using: VCC − VREF + kT/q ≈ VCC − VREF:

=

where VGO = 1.205 V is the bandgap voltage of

silicon.If VREF = VBE = 0.6V, TCF of R = 1500 ppm,

then TCF of VREF = -3500 ppm/oC

TCF≈

HW: Calculate S REF

CC

V

V

Calculate TCF

MOS equivalent of VBE reference:

S REF

DD

V

V

S REF

DD

V

V

The sensitivity w.r.t. VDD:

If VDD = 10V, W/L = 10, R = 100k,and using

parameters from Table3.1-2,then VREF = 1.97V and

This is not nearly as good as the VBE reference.

= 0.29

o = KT-1.5 ; VT = VT0 - T or VT(T) = VT(To) - (T-To)

For temperature coefficient

T

V

RTR

R

R

VVT

V

R

VV

L

WC

R

VV

T

T

V

RTR

R

R

VV

T

V

T

VVV

L

WCVV

L

WC

T

R

VVVV

L

WC

REFREFDD

REFREFDDoxREFDD

REFREFDD

TREFTREF

oxTREF

ox

REFDDTREF

ox

1

)(2

25.1

1

)(2

22

22

2

)(2

11

15.121

1

REFDD

REFDD

REF

REF

REFF

VVR

TR

RTRVV

V

T

V

VTC

Solving for ∂VREF/∂T and computer TC:

The book has one example of using this.

VGS based Current referenceMOS version: use VGS to generate a current and then use negative feed back stabilize i in MOS

Current mirror

Startup

VGS

Why the start up circuit?There are two possible operating points:The desired one and

The one that gives I1 = I2 = 0.

At power up, I1 = I2 = 0 without the start up.

RB bias M6 to be on, which turns M2 and M1 on.

Considering the -effect, (1) is more like:

Then:

Differentiating wrt VDD and assuming constant VDS1 and VGS4 gives the sensitivity of IOUT wrt VDD.

HW: Verify the following sensitivity expression:

HW: Show that approximately:

VEB based current reference

VEB=VR

Startup

A cascoded version to increase ro and reduce sensitivity:

VEB reference

Requires start up

Not shown here

Come up with a start up circuit for the circuit on the previous slide, using only active resisters without RB. Note that you need to make sure

that at the desired operating point, the connection from the start up circuit should be turned off.

HW:

Analyze the sensitivity of the output I with respect to VDD and temperature.

A thermal voltage based current reference

I1 = I2, J1 = KJ2,

but J = Jsexp(VEB/Vt)

J1/J2 = K =

exp((VEB1─ VEB2)/Vt)

VEB1─ VEB2 = Vt ln(K)

I = (VEB1─ VEB2)/R

= Vt ln(K)/R Vt = kT/q

A band gap voltage reference Vout = VEB3 + I*L*R =

VEB3 + (kT/q)*Lln(K)

Vout/T = VEB3/T +

(k/q)*Lln(K)At room temperature,

VEB3/T = ─2.2 mV/oC,

k/q = +0.085 mV/oC.Hence, choosing

appropriate L and K can makeVout/T=0

When this happens, Vout

= 1.26 V

General principle of bandgap reference

Generate a negatively PTAT (Proportional To Absolute Temperature) and a positively PTAT voltages and sum them appropriately.

PositiveTemperatureCoefficient

(PTC)

K

NegativeTemperatureCoefficient

(NTC)

XOUT

XP

XN

A Common way of bandgap reference

VBE is negatively PTAT at roughly -2.2 mV/°C at room temperature

Vt (Vt = kT/q) is PTAT that has a temperature coefficient of +0.085 mV/°C at room temperature.

Multiply Vt by a constant K and sum it with the VBE to get

VREF = VBE + KVt

If K is right, temperature coefficient can be zero.

In general, use VBE + VPTAT

How to get Bipolar in CMOS?

A conventional CMOS bandgap reference for a n-well process

VOS represents input offset voltage of the amplifier.Transistors Q1 and Q2 are assumed to have emitter-base areas of AE1 and AE2, respectively.

If VOS is zero, then the voltage across R1 is given as

Bandgap reference still varies a little with temp

Converting a bandgap voltage reference to a current reference

VDD

VREF

R1

R2

R3 R4

Q1 Q2

TR

R

A

A

q

kVVV

E

EBEBEBE

4

3

2

112 ln

111

1

1

1 1 EECIII

222

2

2

2 1 EECIII

BEBEREF

VRR

RR

VV

4

3

2

1

2

1

21

Vref=I3*R3=

)]ln(1

))ln(1

([1

0

1

2

013 T

TkT

qR

mT

T

VV

A

A

q

k

RR

VR o

o

GBEGo

Curvature corrected bandgap circuit

Vref

R3= R4

Q2 Q1

R2

R1

)(2

22

2

122

12

11212

2

122

4431

BEBEBE

RBERBEREF

BEBER

RRRR

VVR

RV

RIVVVV

R

VVI

IIII

:factIn

constbut const,2

:Problem

2

1

T

VV

R

R

TBE

BE

VBE

T

Vref

T

R4= R5

D2 D1

R1

R2

Solution:

Vref

IPTAT↓

R3

IPTAT2

Vref

T

VPTAT

VPTAT2

VBE

? get toHow 2

2

1

1

1

12

32

324

2

ln1

22

PTAT

E

E

BEBEPTAT

PTATPTATBEref

I

A

A

q

kT

R

R

VVI

RIRRR

IVV

Ex:

1. Suppose you have an IPTAT2 source characterized by

IPTAT2 = T2, derive the conditions so that both first

order and second order partial derivative of Vref with respect to T are canceled at a given temperature T0.

2. Suggest a circuit schematic that can be used to generated IPTAT

2 current. You can use some of the circuit elements that we talked about earlier together with current mirrors/amplifiers to construct your circuit. Explain how your circuit work. If you found something in the literature, you can use/modify it but you should state so, give credit, and explain how the circuit works.