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Temp. Indep. Biasing (7/14/00)^ ECE 4430 - Analog Integrated Circuits and Systems^
^ P.E. Allen, 2000
4.5 (A4.3) - TEMPERATURE INDEPENDENT BIASING (BANDGAP)INTRODUCTIONObjective The objective of this presentation is:1.) Introduce the concept of a bandgap reference2.) Show circuits that implement the bandgap reference3.) Show how to improve the performance of the bandgap reference Outline • Introduction• Development of the bandgap circuit• Bandgap reference circuits• Improved bandgap reference circuits• Summary
Temp. Indep. Biasing (7/14/00)^ ECE 4430 - Analog Integrated Circuits and Systems^
^ P.E. Allen, 2000
Temperature Stable References •^ The previous reference circuits failed to provide small values of temperature coefficient although sufficientpower supply independence was achieved.•^ This section introduces the bandgap voltage concept combined with power supply independence to create a verystable voltage reference in regard to both temperature and power supply variations.Bandgap Voltage Reference PrincipleThe principle of the bandgap voltage reference is to balance the negative temperature coefficient of a pnjunction with the positive temperature coefficient of the thermal voltage,
V =^ kT/q. t^
Concept:^ VDD
VBE^ -2mV/°C I 1^ T V =^ V^ +^ KV^ REF^ BE^ t +^ Σ V^ VtBE -^ +0.085mV/°C KVt^ T kTV = (^) t Kq^ Fig. 4.6-
Result: References with^ TC ’s approaching 10 ppm/°C. F
Temp. Indep. Biasing (7/14/00)^ ECE 4430 - Analog Integrated Circuits and Systems^
^ P.E. Allen, 2000
Derivation of the Temperature Coefficient of the Base-Emitter Voltage - Continued 2.) Combine the above relationships into one:q DnV- VBE^ GO^3 J^ =DTexp= ATC^ NWVAB^ t^
V- VBE^ GOγ expVt
where,^ γ^ = 33.) The value of J^ at a reference temperature of T = TC^
is 0 qγ J = ATexp (V- V)C0 0 BE GOkT 0
while the value of J^ at a general temperature, T, isC^ qγ^ J^ = ATexp^ (V- V)C^ BE^ GOkT 4.) The ratio of J^ /J^ can be expressed as,C^ C0^ J^ T^ γ^ C=^ exp^ J^ TC0^0
V- VV- VqBE G0BE0 G0- k T T 0
orJ^ CTqln^ =^ γ^ ln+ J^ TkT^ C0^0
T V- V- (V- V)BE GO BE0 GOT 0
where Vis the value of Vat T = TBE0^ BE^ 0. 5.) Solving for V^ from the above results gives,BE^ TTγkTV(T) = V^ 1 - + V+^ BEGOBE0TTq^0 0
TJ^ kT^0 Cln+ lnT^ q J^ C0
Temp. Indep. Biasing (7/14/00)^
Page 5
ECE 4430 - Analog Integrated Circuits and Systems^
^ P.E. Allen, 2000
Derivation of the Temperature Coefficient of the Base-Emitter Voltage - Continued α^ 6.) Next, assume J^ ∝ Τ^ and find^ ∂V/∂T.C^ BE VVVVTγkTBEGOGOBE0=^ 1- - + +^ TTTq^ T^ T^0 0 0
ln(TT(γkT/q)kT0/T)^0 · + ln+ Tq^ T T^
ln(J /J )J^ kC C0C+ lnq J^ Τ C0
7.) Assume that T = Twhich means J^ = J^. Since,^0 C^ C
∂V/∂T = 0,GOVVVln(Tln(J^ /J^ )γkTkTBEGOBE00/T)C^ C0|= - + + · + T=T 0 TTq q^ TT Τ 0 0
8.) Note that,ln(T(T-T0/T)T0/T)T^0 -1= = = and^2 TTT^ T^ T^ T^00
ln(J^ /J^ J^ (J^ /J^ J^ J^ C^ C0)C0C^ C0)C0αC =^ = =J^ J^ TJ^ Τ^ T^ CC^ C0^
α T
Therefore,VVVBEGOBE0γkαk|= - + -^ +^ T=T^0 TTq^ q^ T^0
VV- VBEBE0^ GOk|or = + (α^ -^ γ)T=T^0 TqT^0
Typical values of^ α^ and^ γ^ are 1 and 3.2. Therefore, if V
= 0.6V, then at room temperature:BE0 VBE0.6-1.2050.0260.6-1.205-0.1092|= + (1-3.2)= = -1.826mV/°CT=T 0 300 300 300 T
Derivation of the Temperature Coefficient of the Thermal Voltage (
kT/q )
1.) Consider two identical pn junctions having different current densities,
Temp. Indep. Biasing (7/14/00)^ ECE 4430 - Analog Integrated Circuits and Systems^
^ P.E. Allen, 2000
Derivation of the Gain, K, for the Bandgap Voltage Reference 1.) In order to achieve a zero temperature coefficient at T = T
0, the following equation must be satisfied:
V(∆V)BEBE|0 = + K"^ T=T^0 T^ Τ where K" is a constant that satisfies the equation. 2.) Therefore, we getVJ^ V- V(α^ -^ γ)Vt0C1BE0^ GO0 = K"^ ln+ + TJ^ T^0 C2^0
t0 T 0
J^ C13.) Define K = K" ln, thereforeJ^ C2^ VV- V(α^ -^ γ)Vt0BE0^ GOt00 = K+ + TTT 0 0 0 V- V- VGO^ BE0^ t04.) Solving for K gives^ K =
(α-γ) Vt
Assuming that J^ = A/A= 10 and VC1/JC2^ BE0E1E^
= 0.6V gives, 1.205 - 0.6 + (2.2)(0.026)K = = 25.4690.
5.) The output voltage of the bandgap voltage reference is found as,V|= V+ KV= V+ VREF^ BE0^ t0^ BE0^ GOT=T^0
- V+ (γ-α)Vor^ V= V+ (γ-α BE0^ t0^ REF^ GO^
)Vt
For the previous values, V= 1.205 + 0.026(2.2) = 1.262V.REF^
Temp. Indep. Biasing (7/14/00)^ ECE 4430 - Analog Integrated Circuits and Systems^
^ P.E. Allen, 2000
Variation of the Bandgap Reference Voltage with respect to Temperature^ The previous derivation is only valid at a given temperature, T
- As the temperature changes away from T0,
the value of^ ∂V/∂T is no longer zero.REFIllustration: -60^ -40^ -20^0
V^ (V)REF ∂V^ 1.290^ REF= 0T= 400°KT^ ∂^0 1.280V^ 1.270^ ∂REF= 0T= 300°KT∂^0 1.260V1.250 ∂REF= 0T= 200°K^0 T∂1.240T°C^20 40 60 80 100 120 Fig. 4.6-
Bandgap Curvature Correction will be necessary for low ppm/C bandgap references.
Temp. Indep. Biasing (7/14/00)^ ECE 4430 - Analog Integrated Circuits and Systems^
^ P.E. Allen, 2000
A CMOS Bandgap Reference using PNP Lateral BJTs Bootstrapped Voltage Reference using PNP Laterals-
V^ DD+R^2 R 3 V^ Q1^ Q2M3REF^ I REFI^ R^24 IR^11 - M2M1 VFig. 4.6-5SS V- VVI I VI^ VABE1 BE2t 12 ts2tE2I = = ln- ln= ln= ln 2 RRI I RI^ RA 2 2 s1 s2 2 s1^2 E1
if I^ = I^ which is forced by the current mirror consisting of M1 and M2.^1 2 ∴^ V= V+ I^ = V+^ REF^ BE1^ 1R^1 BE1^
RA 1 E2lnV= V+ KVt^ BE1^ tRA 2 E1
While an op amp could be used to make I= I^ it suffers from offset and noise and leads to deterioration of the^1 2 bandgap temperature performance.Vis with respect to Vand therefore is susceptible to changes on VREF^ DD^
.DD
Temp. Indep. Biasing (7/14/00)^ ECE 4430 - Analog Integrated Circuits and Systems^
^ P.E. Allen, 2000
A CMOS Bandgap Reference using Substrate PNP BJTs^ Operation:
The cascode mirror (M5-M8) keeps the currents in Q1, Q2,and Q3 identical. Thus,V= I^ BE1^ 2R + VBE2or Vt I^ = ln^ n( )^2 R^ Therefore,V= V+ I^ + kV·ln(n)REF^ BE3^ 2(kR) = VBE3^ t^ Use k and n to design the desired value of K (n is an integer greaterkRR than 1).n 1 VSS
M8M7 M9 M6M5 M10 M4M3 + M1 M2 VREF Q2^ Q3Q1 n - Fig. 4.6-
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^ P.E. Allen, 2000
Weak Inversion Bandgap Voltage Reference - Continued^ The reference voltage can be expressed as,V= R^ + VREF^ 2I^6 BE5However,WWV6L^3 6L^3 tI^ = I^ = ln^6 R1^ LLR6W^3 6W^31
W1W4L2L 3 .L1L4W2W 3
Substituting Iand the previously derived expression for V^6
(T) in Vgives,BEREF^
WRWW6L^321 4L2L^3 V= Vln+ VREF t^ GOLRL6W^31 1L4W2W^3
TTT^0 1 - + V+ 3VlnBE0 t TTT 0 0
To achieve^ ∂V/∂T = 0 at T = TREF0, we getVRWWkREF^2 6L^3 1W4L2L^3 =^ lnq^ RLLT^ ^1 6W^3 1L4W2W^3
VV3kGOBE0- + + TTq^0
Therefore,RWq2W6L^3 1W4L2L^3 ln=^ (VGORLkT1L6W^3 1L4W2W^3 0
Under the above constraint, Vhas an approximate zero value of temperature coefficient at T = TREF^
and has a 0
value ofT3kT^0 V= V+^ 1 + ln= V+ REF^ GO^ GO^ q^ T^
3kTq
Practical values of^ ∂V/∂T for the weak inversion bandgap are less than 100 ppm/°C.REF
Temp. Indep. Biasing (7/14/00)^ ECE 4430 - Analog Integrated Circuits and Systems^
^ P.E. Allen, 2000
IMPROVEMENT OF THE BANDGAP REFERENCE CIRCUIT Curvature Correction Techniques: • Squared PTAT Correction:^ VBE^ V^ PTAT V^ V^ VRef =BE +PTAT +
Voltage^2^ V^ PTAT^2 V^ PTAT TemperatureFig. 4.6-
Temperature coefficient^ ≈^ 1-20 ppm/°C• V loop BE^ M. Gunaway,^ et. al. , “A Curvature-Corrected Low-Voltage Bandgap Reference,”
IEEE Journal of Solid-
State Circuits , vol. 28, no. 6, pp. 667-670, June 1993.• ß compensationI. Lee^ et. al. , “Exponential Curvature-Compensated BiCMOS Bandgap References,”
IEEE Journal of
Solid-State Circuits , vol. 29, no. 11, pp. 1396-1403, Nov. 1994.• Nonlinear cancellationG.M. Meijer^ et. al. , “A New Curvature-Corrected Bandgap Reference,”
IEEE Journal of Solid-State
Circuits , vol. 17, no. 6, pp. 1139-1143, December 1982.
Temp. Indep. Biasing (7/14/00)^ ECE 4430 - Analog Integrated Circuits and Systems^
^ P.E. Allen, 2000
ß^ Compensation Curvature Correction Technique Circuit:^ Operation:^ V =^ VREF^
BT BTVin +^ AT^ +^ R^ ♠^ V +^^ AT^ +^ RBE BE^^ (1+ ß )^ ß^ where I=AT I=BT A and B are constant T = temperatureThe temperature dependence of^ ß^ is VREFBTR -1/ T^ -1/ T ß ( T ) ∝ e ⇒^ ß ( T ) =^ Ce 1 +ß 1/ T BTe Fig. 4.6-11 ∴ V = V ( T ) +^ AT^ +^ REF BEC Not good for small values of^ V. in V ≥ V + V =^ V +^ V = 1.4V in REF sat.^ GO^ sat.^
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Page 17 ECE 4430 - Analog Integrated Circuits and Systems^
^ P.E. Allen, 2000
Nonlinear Cancellation Curvature Correction Technique Objective: Eliminate nonlinear term from the base-emitter.Result: 0.5 ppm/°C from -25°C to 85°C.Operation: From above,^ V =^ V + 4 V ( I^ ) - 3 V ( I^ ) REF^ PTAT^ BEPTATBEConstant^1 Note that,^ I^ ⇒^ I^ ∝Τ^ ⇒^ α^ = 1 PTAT^ c^^0 and^ I^ ⇒^ I^ ∝^ T^ ⇒^ α constant^ c^
Previously we found, T V ( T )^ ♠^ V -^ V - V ( T )^ -(^ γ^ -^ α) Vln BEGO^ [^ ] GOBE^0 t^ T^0
T T 0
so that T^ V ( I^ ) = V -^ V - V ( T )^ -(^ γ^ -1) VBEPTATGO^ [^ ] GO^ BE^0 T^0
Tln t T^0
and T^ V ( I^ ) = V -^ V - V ( T )^ -^ γ VBEConstantGO^ [^ ] GO^ BE^0 tT^0
Tln T^0
Combining the above relationships gives, T^ V ( T ) =^ V +^ V -^ [ V -^ V ( T )] - [ REFPTAT^ GO^ GO^ BE^0 T^0
T γ - 4] Vln t T^0
T If γ ≈ 4, then V ( T ) ♠ V + V^ 1 -^ + REFPTAT GOT^0
Q4 Q3 Q2 Q1 T V ( T ) BE 0 T 0
V^ CCIConstant I PTATVREF = VCCR^2 Q8Q7 IPTAT Q6 Q5 VBE V VREFBE^ RV^2 VPTATREFR 1 VRPTAT 1 ConventionalCurvature CorrectedBandgap ReferenceBandgap ReferenceFig. 4.6-
Temp. Indep. Biasing (7/14/00)^ ECE 4430 - Analog Integrated Circuits and Systems^
^ P.E. Allen, 2000
How do you get a Stable Reference Current from the Bandgap?^ Assume that a temperature stable reference voltage is available (i.e. bandgap reference) and use the zero TCNMOS current sink.The problem is that^ V may not be equal to the value of REF^
V that gives zero TC. GS^ VDD 1:1 Current Mirror R^ I^ I 1 I^ REFR 1 R^2 V REF +^ VGS 1:1 Current Mirror^ R^2 -^ Fig. 4.6-
VRREF^2 V = I R = R =^ VGS R 22 2 REF R^ R^1 1 dVR dVV^ dRR^ dRRGS 2 REFREF^2212 ∴ = +^ -^ =^ ^2 dT RdT^ R^ dT^ dT^ R^ R 111 ^1
dVdRdRREF^21 +^ -^ dT^ dT^ dT
If the temperature coefficients of^ R and^ R are equal^1
dRdR^12 =^ , then^ dT^ dT^ dVR dVGS 2 REF = and V is proportional to the temperature dependence of^ V. GS REFdT RdT 1
If the MOSFET is biased at the zero TC point, then the current should have the same dependence on temperatureas^ V. REF
Temp. Indep. Biasing (7/14/00)^ ECE 4430 - Analog Integrated Circuits and Systems^
^ P.E. Allen, 2000
Practical Aspects of Temperature-Independent and Supply-Independent Biasing A temperature-independent and supply-independent current source and its distribution:-^ +
V^ DD^ M7M8M9M5M6M10^ BandgapVoltage,^ R^4^ V^ BGR^3 M13M15M17M19M11M4M3 M1M2M14M16M18M20M12^ I^ PTAT^ RRI^^1 2 To SlaveTo Slave REF Bias Ckt.Bias Ckt.^ R^ ext Q2Q3Q1^ x n Fig. 4.6-
Constant current: VBG^ I^ =^ where^ V =^ V +^ I^ REF^ BG^ BE^3 PTATRext^
VTR = V + ln(n) · R 2 BE 3 2 R^1
