Chapter 11-Bandgap References

Vout = R2 I PTAT + VBE 3 = VBE 3 + R2 VT ln n R1
Case study (1)
The circuit producing PTAT current reference, with two series base-emitter voltages in each branch so as to reduce the effect of MOSFET mismatch:
PTAT current (2)
A real implementation of PTAT current reference:
I PTAT = (VT ln n) / R1
PTAT current (3)
Using PTAT current to create a bandgap voltage reference:
VT = kT q − Eg kT
IC IS
I S = bT 4+ m exp
∂VBE VBE − (4 + m)VT − E g / q = ∂T T
The TC of VBE itself also depends on the temperature; When T=300oK, VBE≈750 mV, ∂VBE/ ∂T≈-1.5 mV/oK ;
R2 ) R3
Bandgap References (6)
Use this structure can reduce the effect of offset:
Increase this term to reduce the effect of VOS
Vout = 2VBE 2 + [2VT ln(mn) − VOS ](1 + R2 ) R3
Bandgap References (5)
Sometimes due to asymmetries, there exists input offset for op amp, it will affect the reference output:
Vout = VBE 2 + (VT ln n − VOS )(1 +
PTAT current (1)
PTAT current can be obtained by following structure: If VX=VY, then:
I out = I D1 = I D 2 = (VT ln n) / R1
VX
VY
Generating a PTAT current reference
If keep lnn(1+R2/R3)=17.2, then Vout exhibits zero temperature coefficient!
Bandgap References (4)
Sometimes use pnp as banndgap for compatible with CMOS technology:
PTAT References (3)
Add transistors to adjust coefficient:
∆VBE = VBE1 − VBE 2 = VT ln nI 0 I − VT ln 0 I S1 mI S 2
= VT ln(mn)
Bandgap References (1)
If VO1=VO2:
I out = KI REF
Iout independent on VDD but Iout is not uniquely defined.
Supply independent biasing (3)
A resistor is added at source of NMOS. PMOS mirror
If we can make lnn=17.2, then:
∂VT / ∂T ln n ≈ +1.5 mV / o K = −∂VBE 2 / ∂T
And:
∂VO1 / ∂T = ∂VO 2 / ∂T = 0
Zero temperature coefficient reference!
Bandgap References (2)
PTAT References (2)
Positive-TC voltage: the difference between two base-emitter voltages:
∆VBE = VBE1 − VBE 2 = VT ln nI 0 I − VT ln 0 I S1 IS2
= VT ln n = kT ln n q
A zero TC floating voltage is produced by following structure:
I R 6 = VBE 4 / R6
I R 5 = I D 2 = I R1 = [(VBE 2 + VBE 4 ) − (VBE1 + VBE 3 )] / R1 = 2VT ln n / R1
2 1 1 2 ⋅ 2 (1 − ) µ n Cox (W / L) P R S K
Supply independent biasing (5)
A diode connected transistor is added to the circuit to solve “start-up” problem.
VGS 1 = VGS 2 + I D 2 RS I out = I REF
2 I out + VБайду номын сангаасH 1 = µ n Cox (W / L) N
2 I out + VTH 2 + I out RS µ nCox K (W / L) N
I out =
2 1 1 2 ⋅ 2 (1 − ) µ n Cox (W / L) N R S K
Supply independent biasing (1)
Simple current mirror.
∆I out =
∆VDD (W / L) 2 ⋅ R1 + 1 / g m1 (W / L)1
Iout dependent on VDD.
Supply independent biasing (2)
Case study (4)
To improve the supply rejection, a local supply (局部电源） is used and a regulation circuit (稳压电路）is added:
PTAT References (1)
Negative-Temperature Coefficient (TC) voltage: the baseemitter voltage of bipolar transistor:
I C = I S exp(VBE / VT ) ⇒ VBE = VT ln
If M5 is not added, Iout = 0 satisfy the current mirror conditon, in this case, all transistor will be in off state, this problem is called “start-up” problem. When M5 is added, this will not happen again.
General Consideration
An accurate circuit design needs an accurate voltage or current reference. The best references should be: independent on supply; independent on temperature In practice, there are several kinds of references exist: 1. Supply-independent biasing; 2. Proportional to absolute temperature (PTAT) reference; 3. Constant-Gm behavior reference; 4. Temperature independent reference. Other parameters affecting references may be: output impedance, output noise and power dissipation.
VT ln n = −[VBE 2 − (4 + m)VT − E g / q]
Therefore:
VREF = (4 + m)VT + E g / q
As T→0:
VREF → E g / q
Here comes the term “bandgap”
Bandgap References (3)
How to keep VO1=VO2 in reality? Why not use Op Amp? If VX≈VY then:
VBE1 = RI + VBE 2 ⇒ RI = VBE1 − VBE 2 = VT ln(n) ⇒ VO1 = VO 2 = VBE 2 + RI = VBE 2 + VT ln n
At room temperature:
∂VBE 2 / ∂T ≈ −1.5 mV / o K ∂VT / ∂T ≈ +0.087 mV / o K
Case study (2)
Using low-voltage cascode to reduce the power-supply dependence; “self-biased” is introduced to produce Vb1 and Vb2 by itself: