Will have better matchingBut: only approximate common centroid

no plican be more compact

HW: suggest a better layout for ratio of 4.

G G G G G GG G G GS S S S S S

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 (want ro=∞ for I-ref, ro=0 for V-ref)

• Temperature variation (main concern also)

• Processes variation (use good process and layout)

• Interferences and noise (not considered here)

yTST

1Ty

y 1

For temperature variation, typically use fractional temperature coefficient:

TCF =

rather than sensitivity

=

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≈

)exp(

/),exp(

3

t

GOs

tt

s

V

VKTI

qkTVV

vIi

HW: Calculate S REF

CC

V

V

Calculate TCF

MOS equivalent of VBE reference:

22

1)(21

)(2

RR

VV

RVV

R

VVVVV

TDDTREF

REFDDTGSREF

GSREF VR

RRV

2

21

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

)(1

1

TREFREF

DD

VVRV

V

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.

)(1

1

1

1

1

4

3

4

1

2

DSDDP

GSP

DSP

DSP

VV

V

V

V

I

I

1

111

2141

2)(1

))(1()1(

IVVV

RIVVVRI

TDSDDP

DSDDPGSP

HW: Verify the following sensitivity expression:

HW: Find approximately the temperature coefficient of Iout

1114

1

11

2/)(1)1(

2

IVVVR

IV

I

V

DSDDPGSP

TP

out

DD

Current mirror

Startup

VGS

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 make

Vout/T=0

When this happens, Vout

= 1.26 V