Low-Voltage Bandgap References

[circuitking]

Hi all,

How do we choose R1 value in the below figure. It is from Razavi's Design of Analog CMOS Integrated Circuits Second Edition

The discussion in chapter 12 on bandgap references doesn't include resistor's temperature behavior. How do we consider them in the design?
Thanks

 

[arthorios]

The core of this circuit is a temperature-compensated current reference. As you already know, you want to combine a PTAT current (dVbe/R1) with a CTAT current (Vbe/R2). Your PTAT voltage is mainly determined by the "n" ratio. For the chosen n, calculate (or simulate) what should be the ratio of R1/R2 to make the equivalent current (flowing through M3,4) flat across temperature. Now pick R1 and R2 based on the equivalent current you want. Keep in mind that the current at which you bias your BJTs also has an influence on your Vbe non-linearity across temp, and so will affect Vref's TC.

Ideally, and assuming all resistors in the circuit are of the same type, their TCs are canceled to first-order since Vref is defined by the ratio of R4/R1 and R4/R2.

 

[circuitking]

For the chosen n, calculate (or simulate) what should be the ratio of R1/R2 to make the equivalent current (flowing through M3,4) flat across temperature.

How do we find the ratio from simulation?. It is possible only if we give the exact values to R1 and R2 right

--- Updated Dec 1, 2021 ---

Ideally, and assuming all resistors in the circuit are of the same type, their TCs are canceled to first-order since Vref is defined by the ratio of R4/R1 and R4/R2.

It seems like the resistors have a temperature behavior that's why my Iref is also varying with temperature. I verified it by keep ideal resistors from analogLib. What ideas are there to cancel the resistor temperature dependency?

 

[dick_freebird]

You can get near zero TC out of metallic thin film resistors,
NiCr at 100-200 ohms/sq and SiCr 1K-2K/sq are typical
ranges. Tend not to be available outside of bipolar and
maybe "linear CMOS" technologies although I have seen
some TFRs up in the metal stack (some other composition
and the foundry indicated they "didn't really do much
of that", existed in only a few mixed signal subflows of
a too-many-subflows process family.

But a super low TC isn't necessarily what you want
for a temperature compensating scheme like the
classical bandgap. You'd prefer a strong but linear TC
(silicon doped regions have the former, but bad
second order TC (nonlinear), adding significantly to
VBG curvature).

Resistor models will have at least 1st and 2nd order
TC params and you can quickly find the range on
tempco and compV resistors using looped params.
Just plot 'em and pick 'em.