hello,
η and α are the how mobility and intrinsic concentration (ni) depends on the temp. Normally η is 4. Please refer some device physics book.

Thanks,
Raj.

lhlbluesky_lhl wrote on Dec 9^th, 2011, 7:34am:

The equation has nothing to do with MOS.

Jerry - those terms determine the amount of curvature and some of the slope so they matter a lot in Bandgap references.

I tried to find my notes on this and realized I haven't done the derivation in more than 10 years! I believe the last part of the equation should be -(η-α)*VT*(ln(T/T0)+1) however.

At the risk of making you regret asking, α comes from the temp co of the current biasing the bipolar. If the current is PTAT α=1, but it also depends on resistor temp co. η is XTI in the old bipolar models and is sort of used as a curve fitter rather than a physical constant. Its physical value depended a bit on process and is closer to 3 than 4. Grey/Meyer 2nd edition lists it at 4-n on page 291. It comes from the temperature dependance of IS (saturation current).

For modeling, XTI's value (aka η) largely determined by the temp cos used for the silicon Bandgap voltage (TCEG1 and TCEG2 if memory serves). Some modelers set these to zero which requires a larger XTI cloer to 4 to get the proper curvature, others give them values resulting in XTI being closer to 3. To make things even more confusing the models for Vbe vary across simulators.

I'm willing to bet if you goggle "Rincon Mora bandgap reference" you will find an explanation with derivation online.

rg

thanks all.

Good memories actually - if you do it with a pair of PN junctions, and different currents a large number of the process dependent varaibles fall out of the equations.

Introduced in the Pentium a while back, no longer have fans at full blast all the time.