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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
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