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Bandgap Reference: Basics
Thanks for the help provided by M. Mobarak ,Faramarz Bahmani and Heng Zhang
ECEN 607 (ESS)
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Outline
IntroductionTemperature-independent referencePTAT generatorSupply insensitive current sourceDesign example
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IntroductionConditions to be satisfied for an IC in production:– Work even when Vcc changes (Supply variation):
• eg: Vcc: 2.7V 3.0V– Work even when temperature changes (Temperature variation):
• eg: T: -25C 0 25C 75C– Work even when physical properties change (Process variation):
• BJTs: β: ±30%• MOS: μ: ±10%, Vth: ±100mV• Resistors: R: ±20%• Capacitors: C: ±5%• Inductors: L: ±1%
All combinations of supply voltage (Vcc), temperature (T) and process (P) variations have to be considered in design. This is often referred to as PVT (process, voltage and temperature)
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Introduction: Case studySmall signal gain variation with PVT:
• Supply variation: low frequency gain almost insensitive to VCC variation (assuming Q in active region)
• Temperature variation: gm is changing (decreasing) with T (assuming ICQ independent of T) gain is dependent on temperature.– Solution: Make ICQ a function of T (increases with T) gain remains insensitive to T.
• Process variations: In BJTs, VT=KT/q is almost insensitive to process variation (assuming ICQinsensitive to process variations) gm remained intact. However, variations in resistor R results in gain variation.
Vcc
R R
Q1 Q2
biasI
+Vin −Vin
↑==
==
qKT
ICQT
CQm
min
out
VI
g
RgVV
Gain
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Introduction: Case studySmall signal gain variation with PVT:
• Supply variation: low frequency gain almost insensitive to VCC variation (assuming Q in active region)
• Temperature and Process variations: Holding R/Rs constant low frequency gain is held constant. can be easily accomplished by– using the same type of resistors for R & Rs– following the standard layout practices to
achieve good component matching
• Bad news: The gain has significantly reduced!
Vcc
biasI
R
Q1+Vin
R
Q1 +Vin
Rs Rs
RsR
VV
Gainin
out ≈=
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Temperature-Independent Reference
ref 1 21 2
V V V=c c 0T T T
∂ ∂ ∂+ =
∂ ∂ ∂
ref 1 1 2 2V c V c V= +
Reference voltages and/or currents with little dependence to temperature prove useful in many analog circuits.
Key idea: add two quantities with opposite temperature coefficient with proper weighting the resultant quantity exhibits zero temperature coefficient.
Eg: V1 and V2 have opposite temperature dependence, choose the coefficients c1 and c2 in such a way that:
Thus, the reference voltage Vref exhibits zero temperature coefficient.
1
1 22
V 0 : NTCTif c , c 0V 0 : PTCT
∂⎧ ⇒ ⎨∂⎪ >⎪ ∂⎩
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Bandgap Voltage ReferenceTarget: A fixed dc reference voltage that does not change with temperature.– Useful in circuits that require a stable reference voltage. E.g.
ADCThe characteristics of BJT have proven the most well-defined quantities providing positive and negative TCkT/q has a positive temperature coefficient– "PTAT" proportional to absolute temperature
VBE of a BJT decreases with temperature– "CTAT" complementary to absolute temperature
Can combine PTAT + CTAT to yield an approximately zero TC voltage reference
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Thermal behavior of BJT
Q
BEQV
CQI
CBE
S
IKTV ln( )q I
=
exp BEC ST
VI IV
⎛ ⎞= ⎜ ⎟
⎝ ⎠
Even though KT/q increases with temperature, VBE decreasesbecause IS itself strongly depends on temperature
• I0 is a device parameter, which also depends on temperature – We'll ignore this for now• VG0 is the bandgap voltage of silicon "extrapolated to 0° K"
Assuming both I0 and IC are constant over T:
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Extrapolated Bandgap
[Pierret, AdvancedSemiconductor
Fundamentals, p.85]
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PTAT GeneratorAmplifying the difference in VBE of two BJTs PTAT termDifferent VBE voltages can be obtained by:– Applying different ICQ– Using two BJT’s with different emitter areas but equal ICQ
Q2
ccV
CQ2I
BE2V
Q1
ccV
CQ1I
BE1V
0T
ΔV1II
if
)II
ln(q
KTV-VV
BE
CQ2
CQ1
CQ2
CQ1BE2BE1BE
>∂
∂⇒>
==ΔCQ CQ
BEQ1 BEQ2
I IKT KTV ln( ) , V ln( )q αA q αmA
= =
ln(m)q
KTV-VV BEQ2BEQ1BEQ ==Δ
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Bandgap Voltage Reference• Generate an inverse PTAT and a PTAT and sum them appropriately.
– VBE is inverse PTAT at roughly -2.2 mV/°C at room temperature– Vt = kT/q is PTAT that has a temperature coefficient of +0.085 mV/°C
at room temperature.• Multiply Vt by a constant M and summed with the VBE to get
VREF = VBE + MVt
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Bandgap Voltage Reference
Combining VBE and an appropriately scaled version of kT/qproduces a temperature independent voltage, equal to VG0
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PTAT Generator
tR1R1
1 1
2R2 2 R1 t
1
R2 2
1
VVI ln(m)R R
2RV 2R I V ln(m)R
V 2R K ln(m) 0 ; PTC!T R q
= =
= =
∂⇒ = >
∂
• How do we generate a voltage that is the difference of two VBE?
CQ CQBE1 BE2
I IKT KTV ln( ) , V ln( )q αA q αmA
= =
1 BE BE1 BE2KTV V -V ln(m)qR
V = Δ = =
IR1 IR1+
-VR1
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Bandgap Voltage Reference• More to come!
R2BE1BG VVV +=
(NTC)
0T
VBE1 <∂
∂
(PTC)
0T
VR2 >∂∂
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Supply Insensitive Current Source• How can we generate the bias currents ICQ?
– Conventional current mirror:• Current is essentially proportional to VDD• E.g. if VDD varies by X%, bias current will
roughly vary by the same amount. – Supply insensitive current source:
By using a sufficiently large device,we can make VOV
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Supply Insensitive Current SourceIn the above discussed bias generator circuits, the supply sensitivity is still fairly high, because IIN is essentially directly proportional to VDDIdea: Mirror output current back to input instead of using supply dependent input current!
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Start-up Circuit
There exists a stable operating point with all currents =0
(weak)
Can use a simple start-up circuit to solve this problem
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PTAT Current Generation
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Compatibility with CMOS Technology• In CMOS technologies, where the independent bipolar
transistors are not available, parasitic bipolar transistors are used.
• Realization of PTAT voltage from the difference of the source-gate voltages of two MOS transistors biased in weak inversion is also reported in the literature.
"parasitic" substrate PNP transistor available in any CMOS technology
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CMOS Bandgap Reference With Substrate PNP BJTs
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Design example
( ) 223
ln 1out BE TRV V V nR
⎛ ⎞= + +⎜ ⎟
⎝ ⎠
Specifications:Vsupply: 5V, 0.5um CMOS processVref : 1.2VTemperature dependence: < 60ppm/C
X Y 1 2 EQ2 EQ1
22 2 3
1
3 1 2
3 22 2 2 2
3 3
22
3
V V , R R , A A
1 ; ;
ln( )
ln( )
1 ln( )
Cout EB R R
C
R EB EB EB T
RR R T
out EB T
nJ V V V VJ n
V V V V V nV RV R I R V nR R
RV V V nR
= = =
⇒ = = + +
= − = Δ =
= = =
⎛ ⎞⇒ = + +⎜ ⎟
⎝ ⎠
A critical point: DC output of Op Amp should be > 700mV for start up
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Choice of n• Usually make n=integer2-1, e.g. n=8
Layout:
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Simulations Result
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A Low-Supply-Voltage CMOS Sub-Bandgap Reference
Ref: A. Becker-Gomez, T. L. Viswanathan, T.R. Viswanathan, "A Low-Supply-Voltage CMOS Sub-Bandgap Reference," IEEE Transactions on Circuits and Systems II: Express Briefs, vol.55, no.7, pp.609-613, July 2008
• Low supply voltage • No resistor or op-amp
is used, thus it is compatible with digital processes
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A Low-Supply-Voltage CMOS Sub-Bandgap Reference
( ) TT01C2
02C1TBE2BE1PTAT 4.6V100lnVII
IIlnVVVV ==⎟⎟
⎠
⎞⎜⎜⎝
⎛=−=
( )2i2
PTAT
iSG2SG1PTAT
/nA1
kVI
I/nkAI/kVVV
−=⇒
−=−=
PTATBE2i
iPTATBE2BG
iSG2SG6BE2BG
Vm/rV/nA1
/nAm/rVVV
I/nkAmI/rkVVVV
+≈−
−+=⇒
−=−=−
• r is the ratio between M6/M1• m is the ratio between M5/M1
• For Ai 1
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SummaryHow to Build a Bandgap.-
1. Generate two currents and dump into the transistors
2. Add a mechanism to force Vo1 = Vo2
3. Add a scale factor to generate zero TC output
4. Startup circuit, some tweaking
Done!!!
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ReferencesFirst bandgap voltage reference:R. J. Widlar, "New developments in IC voltage regulators," IEEE J. Solid-State Circuits, pp. 2-7, Feb. 1971.A classic implementation:A. P. Brokaw, "A simple three-terminal IC bandgapreference,“ IEEE J. Solid-State Circuits, pp. 388-393, Dec. 1974.Design of Analog Integrated Circuits, Behzad RazaviAnalysis and Design of Analog Integrated Circuits, P.R. Gray, P. Hurst