RobG wrote on Jun 16th, 2011, 5:06am:Vivek - If I remember the paper Bult claimed that as long as the auxillary amplifier had less bandwidth it didn't affect the response of the main amplifier. Then I think I heard him backtrack on that in a personal conversation. I've always gone more bandwidth since that is how it falls out - what do you think? Some famous professor I know is still saying less bandwidth.
Rob
Rob,
I would need to read that paper but I always thought that Bult mentioned the following criteria:
main amp BW < aux amp BW < main amp second pole
The first side of the inequality takes care of the doublet and the second one of the stability. Bult's notes (I had them from a course he gave at EPFL go into great detail on these fine points).
Anyway, I cannot imagine that you could get away with aux amp BW < main amp BW. Let's take a crude case for discussion.:
Adc, main (unboosted) = 60 dB = gm(1mS) x 1MOhm
Ro,main amp = 1MOhm
Timeconstant of main amp in loop = 1us
Timeconstant of aux amp = 10us (I am deliberately taking a wild case).
Gain of aux amp = 60 dB say
Now, at the start of a settling phase, the virtual grounds of the main amp would normally start to converge towards a precision level of 60 dB at the rate of 8.6 dB/1us, whereas the auxiliary amp virtual grounds start to settle at the rate of 8.6 dB/10 us.
At the end of about 7 us, the main amp inputs are precise to 60 dB, whereas the aux amp inputs are settled only to an accuracy of about 6 dB. If you recall the formula for gain boosting of the output impedance, your effective output impedance is now 1MOhm x 6 dB = 2MOhm. Your gain boosting factor is 6 dB, and not 60 dB!!
As for famous professors arguing the other way, the only thing I can say is that the Rout, boosted = Rout,unboosted x (1 + Aboost). So, if you cannot show me that Aboost has reached its maximum value, I cannot really understand why there ought to be any boosting. NOTE: If you are not considering transient response but steady state response, i.e. you are only applying a small signal, then you do see the boosting. I've had similar discussions with people from academia that sometime insist that the DC gain simulated from an AC analysis is all that matters, but all practising engineers, particularly those dealing with switched systems like ADCs etc. understand this difference between step and steady state response well. So no use having 120 dB DC gain if your settling time constants, both in the main and aux amp are not going to let you achieve the necessary accuracy in the amount of time you have available. I can rest my case on the excellent match between measurement, simulations and understanding of the different ADCs I've designed all based on this one concept, most of them using gain-boosted OTAs.
Vivek
N.B: Gain-boosting was already introduced in the late 70s (I don't recall by whom but it was a European paper in JSSC), but was limited to use in current mirrors for DC-type of applications. My guess is that most people did not appreciate the importance of the concepts laid out in Bult's paper or did not really understand the potential of gain boosting for building high accuracy circuits, despite a paper on settling behavior in the presence of doublets by Gray and his student (Kamath) in JSSC long ago (to be fair, that paper is full of equations but not very inspiring or intuitive, atleast to me).