Bob Pease and opamp-modelling

[Candide Voltaire]

I came across the following article by analog guru Bob Pease
concerning real opamp behaviour:
http://electronicdesign.com/Articles/Print.cfm?ArticleID=20565
Unfortunately the article is printed/edited badly, which makes it hard
to understand what Bob is trying to tell
e.g the first formula should be:
AV = AV_O × 1/(1 + s × tau_ol) or
AV = AV_O × 1/(1+ s/( 2piF_O))

for the second formula I guess p is equal to pi and the question mark
should be an integral sign
in the third formula he uses p first as the differential operator and
then as pi

I can't however figure out what he means with the fourth formula?
Can anyone here explain what Bob means (clarify the symbols he uses
there)

regards,
Candide Voltaire

 

[Darren Holdstock]

Taking the Panglossian view, this is the best of all possible worlds and all is right and proper. But being a bit more realistic, I think the "p" in the 4th eq'n is the "s" operator - there's a hint in the last paragraph, which is unreadable on the original page: RAP - "I like to use p = d/dt. The derivative operator. In linear systems, in the frequency domain, p = s = 2pj(f), but I won’t waste much time with that."

This printer-friendly version of the page is more readable (sorry, a copy-and-paste link as this forum won't let me do hyperlinks yet):

electronicdesign.com/Articles/Print.cfm?ArticleID=20565

 

[cassiope]

I came across the following article by analog guru Bob Pease
concerning real opamp behaviour:http://electronicdesign.com/Articles/Print.cfm?ArticleID=20565
Unfortunately the article is printed/edited badly, which makes it hard
to understand what Bob is trying to tell
e.g the first formula should be:
AV = AV_O × 1/(1 + s × tau_ol) or
AV = AV_O × 1/(1+ s/( 2piF_O))

for the second formula I guess p is equal to pi and the question mark
should be an integral sign
in the third formula he uses p first as the differential operator and
then as pi

I can't however figure out what he means with the fourth formula?
Can anyone here explain what Bob means (clarify the symbols he uses
there)

regards,
Candide Voltaire

I can't make out what he means from the rendering of the article -
makes no sense to me either.

There is a simple way around his dislike of using the -3dB point of
the Laplacian open-loop gain expression:

H= Ao
-----------------
1 + (s*Ao/wo)

where Ao is the dc open loop gain, and the new wo is the radian
frequency at which the gain goes to unity. While it is a tiny bit
ugly (Ao appearing twice), it can now be varied without altering wo.

-f

 

[Candide Voltaire]

I can't make out what he means from the rendering of the article -
makes no sense to me either.

There is a simple way around his dislike of using the -3dB point of
the Laplacian open-loop gain expression:

H= Ao
-----------------
1 + (s*Ao/wo)

where Ao is the dc open loop gain, and the new wo is the radian
frequency at which the gain goes to unity. While it is a tiny bit
ugly (Ao appearing twice), it can now be varied without altering wo.

-f

Thanks for answering but I think the expression you suggested should
be:
A0
H=-----------------
1+ s /w0

with A0 the DC-gain and w0 the openloop corner frequency (rad/
s)
of course Bob's equation (4) still remains a mystery

 

[Candide Voltaire]

As usual, Pease tries to make things too complicated.

maybe he does, but to be sure of that we first have to know what he
really meant with the fourth equation...
I guess we all know here the first order opamp model
but Bob seems to want to replace it with a more accurate model, I
really like to know what it is, I don't care if it is in the time
domain or in the f-domain as converting from one to the other is not
difficult.