Bandgap voltage reference
Based on lecture of Paul Brokaw in 1989
Why voltage reference?
1)
2) Reference in LDO feedback
3) Analog multiplier
4) And more…
Zener vs. Bandgap
•
•
•
•
predictable reverse voltage.
fairly constant over temperature.
very constant over time.
very low noise.
• relatively high variances in initial voltage.
• lack flexibility: require high supply voltages,
and offer relatively few output voltages.
• Easy to implement on silicon.
• Accurate initial voltage and low temperature
drift.
• More flexibility, lower supply voltages needed.
BJT
𝐼𝐶 = 𝐼𝑆 (𝑒 𝑉𝐵𝐸/𝑉𝑇 −1) ≈ 𝐼𝑆 𝑒 𝑉𝐵𝐸/𝑉𝑇
𝑘𝑇
𝑉𝑇 =
≈ 26𝑚𝑉 @ 𝑇 = 300𝐾
𝑞
𝐼𝑆 = 𝐼0 exp(−𝑉𝐺0 /𝑉𝑇 )
I0 – process and geometry depended current. Also depends on temperature.
VG0 – bandgap voltage: about 1.25V in silicon
Current mirror
The two transistors are identical: is1 = is2
Current mirror
4:1 mirror operates all transistors at the same
current density
Current mirror
Voltage driven current source
VBE is controlled by V1 source, it’s not ~0.7V as in the current mirror.
For small values of V1 where currents are relatively small, the voltage across R1 will be
small and will hardly interfere with Vbe of Q1, so the collector currents will stay very nearly
in the ratio eight to one. At 450mV the eight to one ratio is only
starting to be reduced by the difference in the two Vbes resulting from ~15 nA in R1.
Voltage driven current source
While the current in Q2 can rise exponentially with V1, the rise of current in Q1 will be
asymptotic to a linear slope defined by R1.
This means that as V1 rises, the ratio of collector currents falls until it is below one. In the
figure this happens as V1 crosses ~720mV in a room temperature simulation.
In order to more accurately set and maintain this crossover voltage an opamp may be used
to adjust Vbe2 to the value that makes the collector currents equal.
Using a feedback loop
While the feedback makes the two collector currents equal it does not answer the question
of what value the currents actually have. However, it should be apparent that the common
value for the currents is closely approximated by the current in R1, which itself is
determined by the difference between Q1 Vbe and Q2 Vbe.
∆VBE
𝑉𝐵𝐸1
𝑒 𝑉𝑇
𝐼𝐶1 𝐴1 𝐼𝑆
𝐴1 𝑉𝐵𝐸1𝑉−𝑉𝐵𝐸2
𝑇
≈
=
𝑒
𝑉
𝐵𝐸2
𝐼𝐶2
𝐴2
𝑉
𝐴2 𝐼𝑆 𝑒 𝑇
∆𝑉𝐵𝐸 = 𝑉𝐵𝐸1 − 𝑉𝐵𝐸2
𝑘𝑇
𝐼𝐶1 𝐴2
=
𝑙𝑛
∙
𝑞
𝐼𝐶2 𝐴1
𝑘𝑇
𝐴2
=
𝑙𝑛
𝑞
𝐴1
This is the voltage across R1!
Called also PTAT: proportional to
absolute temperature
VBE vs. Temperature
Called also CTAT: complementary
to absolute temperature
PTAT and CTAT
Implementation
Different output voltages
There is an error due to
base currents in R5, with
no corresponding
current in R6. Can often
be neglected, if R5 and
R6 are small enough.
Another error is due to
the VBE curvature vs.
temperature.
CTAT curvature