Post on 08-Mar-2018
Willy Sansen 10-05 161
Bandgap and current reference circuits
Willy Sansen
KULeuven, ESAT-MICASLeuven, Belgium
willy.sansen@esat.kuleuven.be
Willy Sansen 10-05 162
Voltage regulator
+-
R1
R2
+
- Vref
VoutVDD
Vout = VrefR1 + R2
R2
Willy Sansen 10-05 163
Current regulator
+-
+
- Vref
Iout
R
+-
V1
Iout
Iout =V1 - V2
R
+-R
V2
Iout =Vref
R
Willy Sansen 10-05 164
Table of contents
PrinciplesBipolar bandgap referencesCMOS bandgap referencesBandgap references < 1 VCurrent referencesLDO Regulators
Ref.: B.Gilbert, G.Meijer, ACD , Kluwer 1995
Willy Sansen 10-05 165
Bipolar transistor equations
+
-VBE
IBIC = IS exp ( )
VBE
kT/q
or IC = CTη exp ( )VBE - Vg0
kT/q
with Vg0 = 1268 mV - η kTr/q
and Tr = 323 K
which gives VBE = Vg00 - λT + c(T) for IC ~ Tm
- 2 mV/oC
- 2 µV/oC
Willy Sansen 10-05 166
VBE versus Temperature
VBE = Vg00 - λT + c(T) for IC ~ TmVBE
Vg00 = Vg0 + (η-m) kTr/q
λ =Tr
Vg00 - VBE (Tr)
c(T) = (η-m) (T -Tr -T ln )qk
Tr
T
Tr Tφ
tg φ = λ
c(T)Vg00
Vg0
VBE
Vg0 = 1156 mVη= 4Tr = 300 K VBE(Tr) = 700 mV
Willy Sansen 10-05 167
The curvature c(T)
m = 1 IC ~ T gm constantm = 0 IC constant gm ~ T-1
m = - IC ~ VBE gm ~ T-x
VBE (V)
T (K)
IC ~ T
IC constant
IC ~ VBE
∆VBE = 0.7 mV∆T = 30o
m = 1
m = 0
∆VBE = 5 mV∆T = 50o
Willy Sansen 10-05 168
Bandgap reference Vref
VBE
Vg00
0 Tr T
VBE
is PTAT- 2 mV/oC
≈ 0.6 V
Vref ≈ 1.2 V
Vref = VBE + VC VC ~kTq
≈ 0.6 V
VC
Willy Sansen 10-05 169
PTAT voltage and current
R2
1 : r ∆VBE = ln r+
-
kTq
∆VBE
IC = IS exp ( )VBE
kT/q
IC IC
Q1 Q2
∆VBE = VBE1 - VBE2
VBE = lnkTq
ICIS
∆VBE = lnkTq
IS2IS1
IC = ln rkT
qR2
r is 10-1000 !!
Willy Sansen 10-05 1610
Bandgap reference circuit
+
-
Vref
+
-VC R1
R2
n : 1
1 : r
VBE
Vg00
0 Tr T
VBE
PTAT- 2 mV/oC
≈ 0.6 V
≈ 1.2 V
∆VBE = ln nr+
-
kTq IC2 = ln nr =
kTqR2
Vref = VBE + VC VC = n ln nrkTq
R1R2
∆VBE
Q4 Q3
Q2Q1 AR2
Willy Sansen 10-05 1611
Noise Bandgap reference - 1
+
-
Vref
+
-VC R1
R2
n : 1
1 : r +
-
VC = n ln nr = n A = nR1IC2 ≈ 0.6 VkTq
R1R2
∆VBE
IC2 = ln nr = kT
qR2
AR2
R1
R2
R1 >> 1/gm1 R1IC1 ≈ 0.5 V gm1R1 ≈ 20
R2 >> 1/gm2 R2IC2 ≈ 0.06 V gm2R2 ≈ 2.3
Noise sources : R1 R2gm3,4 negligible for large VGS -VT or RE !!
A = ln nr ≈ 0.12 V kTq
IC2
Q4 Q3
Q2Q1
Willy Sansen 10-05 1612
Noise Bandgap reference - 2
+
-
Vref
+
-VC R1
R2
n : 1
1 : r +
-
VC = n ln nr = n A = nR1IC2 ≈ 0.6 VkTq
R1R2
∆VBE
IC2 = ln nr = kT
qR2
AR2
R1
R2
A = ln nr ≈ 0.12 V kTq
dVRef2 = 4kT R1 df + R1
2n2 4kT/R2 df
= 4kT R1 df (1 + n2 )R1R2
n2 = R1n = R1R2
nR2
nR2
VCIC2
nVC
∆VBE= >> 1
IC2
Q4 Q3
Q2Q1
Willy Sansen 10-05 1613
Noise Bandgap reference - 3
+
-
Vref
+
-VC R1
R2
n : 1
1 : r +
-
∆VBE
dVRef2 = 4kT R1 n2 df
R1R2
IC2
n2 = = R1R2
(R1n)2
R2
1R2
VC2
IC22
VC2
IC2 ∆VBE=R1
VC ≈ 0.6 V :>> Large IC2 : small R’s>> Large r : large ∆VBE
Q4 Q3
Q2Q1
Willy Sansen 10-05 1614
Table of contents
PrinciplesBipolar bandgap referencesCMOS bandgap referencesBandgap references < 1 VCurrent referencesLDO Regulators
Ref.: B. Gilbert, G.Meijer, ACD , Kluwer 1995
Willy Sansen 10-05 1615
Bandgap reference with bipolar transistors
-
2Vref
+R1
R2
n: 1
1 : r
Insensitive to β and VE !
∆VBE = ln nrkTq IC = ln nr
kTqR2
Vref = 2VBE + VR3
VR3 = 2R3 ( + ) ln nrkTq
1R2
2R3
1R1
Ref.: G.Meijer, ACD , Kluwer 1995
Willy Sansen 10-05 1616
Start-up circuits required
IC
-
Vref
+R1
R2
1 : 1
1 : r
IC2
Q4 Q3
Q2Q1
IC1
VBE1
IC2
IC1
required operating point
unwanted operating point
R2
R1
qkT
Vref = VBE1 + ln r
Willy Sansen 10-05 1617
Start-up circuits
Cstart
D1 D2
r : 1Q2
Q1Q4
Q3
R3
R2
R1
r : 1Q1Q2
R2
R1R3
RSTART
D2
4x
Willy Sansen 10-05 1618
Bipolar Bandgap reference without opamp
R21 : r
IC
Q1 Q2
R1 R1
Q3
VOUT
Ref. Widlar, JSSC Feb.1971, 2-7
IC
VOUT = VBE1 + R1 IC
R2
R1
qkT
= VBE1 + ln r
Willy Sansen 10-05 1619
All NPN bipolar bandgap reference
Ref.: B.Gilbert, ACD , Kluwer 1995
Willy Sansen 10-05 1620
Bipolar Bandgap references with opamps
+-
Vref
1 : n
R
RPTAT
R
+
-
+-
Vref
1 : n
R
RPTAT
R
+
-Bad PSRR
Willy Sansen 10-05 1621
CMOS Bandgap ref.with opamp: error analysis 1
+-
Vref
1 : n
R
RPT
R
+
-
kTq
dICIC
IC = ln nkT
qRPT
Vref = VBE + A (VBE1 - VBE2)
dVBE = ( - )dISIS
kTq
1ln n
= ( - - )dRPTRPT
dISIS
dnn
= 26 mV (0.46 2% - 30 % - 20%) ≈ 13 mV (if n = 10)
is PTAT !
Q1 Q2 A =RPT
R
Willy Sansen 10-05 1622
CMOS Bandgap ref.with opamp: error analysis 2
Vref = VBE + A (VBE1 - VBE2)
d(VBE1 - VBE2) =
kTq
1ln n
= A ln n ( + ) dnn
= 600 mV (1 % + 0.46 2% ) ≈ 11 mV 24 mV or 2%
is PTAT !
VBE1 - VBE2 = ln nkTq
kTq
dnn
dAA
d[A(VBE1 - VBE2)] = +-
1 : n
R
RPT
R
+
-
Q1 Q2
Willy Sansen 10-05 1623
Bipolar Bandgap reference AD580
+-
Vref = VBE + VR1
1 : 8
R R
+
-R1
R2 R3
R4
VOUT = Vref
VIN
VR1
VR2
R3 + R4
R3
= VBE + 2 VR2R2
R1
= VBE + 2 ln 8R2
R1
qkT
≈ 1.205 V
+
+
-
-
Willy Sansen 10-05 1624
Curvature correction with ∆VBE
Ref. Widlar, Meijer, van Staveren
VBE(V)
m=1 PTAT currentratio η/(η-1) or 1/a2η = 3.5 a2 ≈ 0.714
m=0 constant currentstronger curvature
Vref ≈ 210 mV
Willy Sansen 10-05 1625
Curvature correction with ∆VBE
IB (const) ≈ 1.5 + 7 + 7 µA
+
-
Vref≈ 210 mV
I(PTAT) I (VBE)
I (const)
Q2Q1
7 µA7 µA
1.5 µA
Ref. Widlar JSSC Dec.78, 838-846
R1 R2
R4
R5
R3
Vref = VBE2 + R2 I (VBE)
- R1(I (const) + I (PTAT))
- VBE1
≈ VPTAT + AVBE2
Willy Sansen 10-05 1626
Curvature correction with PTAT2
Ref. Song JSSC Dec.83, 634-643, Degrauwe ISSCC Febr.85, 142-143
-
IPTAT
1 : 1
+ 1
R2
R1
IPTAT
IPTAT2
Vref = VBE3 + ln rkTq
R2R1
translinear circuit
r : 1 : 1IBQ1Q2
Q3
+ γT2
Willy Sansen 10-05 1627
Table of contents
PrinciplesBipolar bandgap referencesCMOS bandgap referencesBandgap references < 1 VCurrent referencesLDO Regulators
Ref.: B.Gilbert, G.Meijer, ACD , Kluwer 1995
Willy Sansen 10-05 1628
Polysilicon gate
Gate oxyde
N-well CMOS technology
Willy Sansen 10-05 1629
CMOS Bandgap reference with opamp
+-
Vrefn : 1
R
RPTAT
R
+
-
+-
Vref
n : 1
RPT
+
-
1:1
Willy Sansen 10-05 1630
Full CMOS bandgap reference circuit
Ref. MIETEC; Meijer, ACD, Kluwer 1995
2.7 ... 5.5 V
17 µA
1.2 ± 0.02 V10 µA max.
4000 ppm-50 oC
+150 oC
Startup
PDI
PDII
Willy Sansen 10-05 1631
Bandgap reference with high PSRR
Ref.Tham, JSSC, May 95, pp.586-590
1 : 1 : N
M : 1
1.2 V 1.2 V
2.4 V > 2.5 V
VBG = VBE2 + N ln [M (N+1)]R2R1
kTq
300 µA
1.236 V± 20 mV85 ppm/oC
Willy Sansen 10-05 1632
Floating CMOS bandgap reference
Ref.Ferro, JSSC, June 89, pp.690-697
2.48 V ± 24 mV21 ppm/oC
5 V 1.2 mA
Willy Sansen 10-05 1633
CMOS Bandgap without resistors
Ref.: Buck, JSSC Jan. 2002, 81-83
∆VD = VD2 - VD1
VOUT = VD2 + AG ∆VD
VOUT ≈ 1.12 V9 mV 0 …70 oC3.7 V; 0.4 mA
A = 1.5B = 4 G = 6AD1/AD2 = 8
Willy Sansen 10-05 1634
Single-junction CMOS Bandgap reference
+- Vout ~ ∆VBE
IB1
Sw2t1: opent2: opent3: closed Sw1
IB2
t1: closed : Vout = VBE1t2: opent3: openC1 C2 + ∆VBE21C2
C1+C2
Ref. Gilbert, ACD, Kluwer 1995
Willy Sansen 10-05 1635
MOST in weak inversion ?
+
-VGS
IB IDS = IDS0 exp ( )VGS
nkT/q
n = 1 + CD
- 2 mV/oC
- 20 µV/oC
Cox
CD (VCB)
Willy Sansen 10-05 1636
Table of contents
PrinciplesBipolar bandgap referencesCMOS bandgap referencesBandgap references < 1 VCurrent referencesLDO Regulators
Ref.: B. Gilbert, G.Meijer, ACD , Kluwer 1995
Willy Sansen 10-05 1637
Sub-1 V CMOS bandgap reference
Banba, .., JSSC May 99, 670-673
Vref = VBE +R4R2
R4R3
kTq
ln n
VBER3 R2
R4
518 mV± 15 mV
n = 100
Willy Sansen 10-05 1638
CMOS Bandgap with supply < 1 V
+-
Vref
R2 = R1
+
-R1
Ref.: Malcovati, JSSCJuly 01, 1076-1081
R0
1 : 11 : 1
R3IPTAT
+
-kT ln n
R0q
n1
Vref = VBE +R3R2
R3R0
kTq
ln n
0.536 V
1V92 µA
Willy Sansen 10-05 1639
1 V opamp (1.2 MHz 25 pF 35 µA)
Vout
Vin-Vin+
VB
Cc
Willy Sansen 10-05 1640
Start-up circuit
+-
Vref
+
-R2 = R1R1
R0
n1
1 : 11 : 1
VB
0.536 V
MS
Willy Sansen 10-05 1641
Curvature correction
+-
Vref
+
-
VB
R2 = R1R1
R0
n1
IPTATI(ct) I(ct)
1 : 11 : 1
R4
R5
∆VBE
0.8mV
0.3mV
0oC80oC
1V92 µA
Willy Sansen 10-05 1642
CMOS Bandgap with supply < 1 V
+-
Vref
R2a +
-
R1
Ref.: Leung, JSSCApril 2002, 526-530
1 : 11 : 1
R3
n1
Vref = VBER3R2
R3R1
kTq
ln n
0.603 V
1V18 µA
+
R2b
R2a
R2b
Willy Sansen 10-05 1643
Table of contents
PrinciplesBipolar bandgap referencesCMOS bandgap referencesBandgap references < 1 VCurrent referencesLDO Regulators
Ref.: B. Gilbert, G.Meijer, ACD , Kluwer 1995
Willy Sansen 10-05 1644
Voltage-current converter
+-
+
- Vref
Iout
Iout =Vref
R
RTemperature coefficient :depends onVrefR !
Willy Sansen 10-05 1645
Temperature coefficient of resistors
cm-3
Willy Sansen 10-05 1646
Voltage to current converter
Blauschild, ACD Kluwer 1995
Willy Sansen 10-05 1647
Current reference without resistors
M1+ -
a : 1
1 : b
V2
Iref = K’nW1
L1m = ab(1 - √m)2
V2 2 1
Ref. Op ‘t Eynde, JSSC June 88, pp. 821-824
K’n ~ T -1.5 V2 ~ T Iref ~ T -0.5Vcc > 3.5 V 2 µA0.774 ± 0.02 µA3 % 0o ... 80oC
V2 ≈ 0.32 V
IC
VBE1
IM1
IM2
required operatingpoint Iref
unwanted operating point
M2
VT2+V2VT1
Iref
Willy Sansen 10-05 1648
Current reference
Ref. Op ‘t Eynde, JSSC June 88, pp. 821-824Ref. Vittoz, JSSC June 79, pp. 573-577
Vo
Both in wi.
Vo = ln (1 + )q
nkT Sb
Sa
V2 ≈ 0.32 V Vcc > 3.5 V 2 µA0.774 ± 0.02 µA3 % 0o ... 80oC
Sb/Sa = 5Vo ≈ 64 mV
Willy Sansen 10-05 1649
SC Voltage-current converter
Ref. H.Klein, W. Engl, ESSCIRC 83, pp. 119-122
C1 = C2 = 3 pF fc = 270 kHz ±5 V 4 µA
Vref C1 = Iref Tc/2
Reff =
Iref =
12fcC1
Vref
Reff
Willy Sansen 10-05 1650
Table of contents
PrinciplesBipolar bandgap referencesCMOS bandgap referencesBandgap references < 1 VCurrent referencesLDO Regulators
Ref.: B. Gilbert, G.Meijer, ACD , Kluwer 1995
Willy Sansen 10-05 1651
Low drop-out regulator : principle
+-
R1
R2
+
- Vref
Vout = 2 VVin = 3.1 V
Vout = VrefR1 + R2
R2
+-
+
- Vref
Vout = 2 VVin = 2.2 V
R1
R2
2.9 V 1.3 V
VGS ≈ 0.9 V
Gain !
Willy Sansen 10-05 1652
Table of contents
PrinciplesBipolar bandgap referencesCMOS bandgap referencesBandgap references < 1 VCurrent referencesLDO Regulators
Ref.: B. Gilbert, G.Meijer, ACD , Kluwer 1995
Willy Sansen 10-05 1653
References
P. Brokaw, “A simple three-terminal IC bandgap reference” JSSC Dec.74, pp.388-393
M. Degrauwe, etal, “CMOS voltage references using lateral bipolar transistors”, JSSC Dec.85, pp.1151-1157
K. Kuijk, “A presicion reference voltage source” JSSC June 1973, pp.222-226G. Meijer etal “An integrated bandgap reference”, JSSC June ‘76, pp.403-406G. Meijer etal “A new curvature-corrected bandgap reference”
JSSC Dec.82, pp.1139-143G. Meijer, “Bandgap references”, ACD Kluwer, 1995B. Song, P.Gray, “A precision curvature-compensated CMOS bandgap
reference” JSSC Dec.83, pp.634-643A. van Staveren etal “An integratible second-order compensated
bandgap reference for 1 V supply”, ACD Kluwer 1995.R. Widlar, “New developments in IC Voltage Regulators”, JSSC Febr.71, pp. 2-7.R. Widlar, “Low-voltage techniques”, JSSC Dec.78, pp.838-846.