OPA846: Relation between GBP as appears in the datasheet to the Gain/freq graph and general BW estimation

Hey Alex, Yes, I did this (among many) datasheets and that bandwidth extension at lower phase margins has always been a mystery - until recently. Briefly, 

1. The GBP idea you note only applies with a single pole Aol model (90deg phase margin). 

2. Minimum stable gain is a slippery concept. Probably should be minimum operating gain where each group targets some acceptable (and unstated) min phase margin.

3. The actual phase margin you get at that minimum gain will vary a lot from the data sheet as you use different R values and loads. 

4. The true GBP is the one pole projection to 0dB. I get that going to the Aol=40dB frequency and multiplying by 100X

5. Many datasheets (that I was not involved in) use the Aol = 0dB as the gain bandwidth product - most modern op amps have higher frequency poles (in the high speed parts, I use a 2nd order with some Q for that - and other things). If the higher frequency pole is real, then Aol = 0dB will often be lower then the projected GBP from 40dB. if they are complex like we often see in parts like the OPA846, it might extend out the Aol = 0dB. 

6. All that Aol = 0dB stuff is important for final modeling, but is not the GBP

7. I was able to solve for the Phase margin dependent bandwidth extension from the LG=0dB  frequency for a dominant plus one real higher frequency pole - going down in phase margin from 90deg where it a 1X multiplier, it rises quickly to about 1.6X by 65deg then goes asymptotic to 1.57 going down from there - this is the ratio of small signal F-3dB to Fxover. That is fig. 4 in this article giving some necessary background o stability analysis, 

https://www.planetanalog.com/author.asp?section_id=3404&doc_id=565056&

I could set up a LG sim for the OPA846, but lets' just try looking at the Aol curve at 20dB level, that is about 170Mhz I would say, then just using a 1.6X multiplier that would predict 272MHz.Not that close to 400Mhz, but this model is more involved than a simple real higher pole in the Aol. 

So essentially, the GBP model is pretty primitive and for anything with higher order poles in the Aol (or LG), the final result might be a little hard to predict by math - but a lot of what I was doing in the modeling was iterating on the Aol gain and phase until the closed loop sims matched bench pretty well. Can't always depend the models be that good. For instance, the OPA846 might not have a full open loop output impedance in the model - i think I was only doing R series L back then. More recent parts like the THS4551 are much more involved on the Zol. 

There is a later article on VFA LG stability analysis here, and the next one on CFA should post today or tomorrow. Starting on the FDA one soon. 

https://www.planetanalog.com/author.asp?section_id=3404&doc_id=565077&

And more accurately, the phase margin thing could be a single pole Aol model with another pole around the loop (like a C on the inverting node). So that plot of bandwidth extension is really loop gain phase margin where the system is two real poles.