Help needed in making a stable opamp with big load

[saro_k_82]

Re: Opamp with big LOAD

I hope you'll agree with me that if I measure the total gain as V2(s)/Vin(s) this should be the real gain of the amplifier, right? Let's call this simply GAIN. There are two stages in this amplifier. As is shown in my original file I attached in the beginning, I call the voltage at the output of the 1st stage V1(s). I define A1(s)=V1(s)/Vin(s). Then, I define A2(s)=V2(s)/V1(s). V2(s), of course, is the voltage at the output of the 2nd stage, which is also the output voltage of the whole amplifier. Then finally I define GAIN_TOT=A1(s)*A2(s). According to what you say, GAIN is not equal to GAIN_TOT - did I understand right? Because if I do it this way the two stages appear decoupled. I don't agree with this and it is because when I look from the output of the 1st stage into the the second stage I see Z12(s) which includes also CM. A quick simulation, yet another attachment shows GAIN and GAIN_TOT for CM=0, 1p, 10p, 100p, 1n. As you see, those two gains are completely identical, overlapping perfectly. So, they are the same.

Please refer to the attached figure. The beta in this case is sCM/GM1 has to be around both the stages. The amplifier can be modeled this way without any error. You have made corrections to A1(s) and tried to isolate by computing Z12., and get a picture with two separate blocks in cascade., which allows you to write Atot(s)=A1m(s)*A2m(s) (A1m and A2m are modified transfer functions) (which is not so useful from control theory as CM impacts both the transfer functions) which can have very different poles and zeros than A1(s) and A2(s). I only doubt the way the isolation is done.
So A1m and A2m dont necessarily yield their own stage poles.
I did read your pdf file 10 days back I guess., I'll now take a serious look and find out the flaws if any.
Just a quick question.,

If you look at the plot of A1(s) there are two poles and a zero. The first pole I call P1, the second pole I call P2. P1 is also the dominant pole of the whole amplifier and P2 happens to be it's non-dominant pole - of course after a certain value of CM, which is in the table. P2s is just the pole of the second stage.

I agree that all this happens when you try to isolate in to two separate blocks., but do you really see three poles for some values?., there are only three caps of which only two can have independent voltages.., so there can only be two poles in any case., so this is an obvious error.

Just to point out again., the A1(s) (and Z12(s)) plot is heavily influenced by what happens in the second stage., the graph of A1(s) is what both of us acknowledge., what matters is what drives the pole of A1(s)., which is not easy to obtain from ac plots. My claim is that the first pole in A1(s) plot is the output pole and yours is that it is the first stage pole. I hope we agree on everything else.
I mentioned that the Atot(s) plot in your previous post does not match the values in the pole table., I was able to see higher CM separating the poles further in the graph.

Thanks,
Saro

 

[sutapanaki]

Re: Opamp with big LOAD

Please refer to the attached figure. The beta in this case is sCM/GM1 has to be around both the stages. The amplifier can be modeled this way without any error. You have made corrections to A1(s) and tried to isolate by computing Z12., and get a picture with two separate blocks in cascade., which allows you to write Atot(s)=A1m(s)*A2m(s) (A1m and A2m are modified transfer functions) (which is not so useful from control theory as CM impacts both the transfer functions) which can have very different poles and zeros than A1(s) and A2(s). I only doubt the way the isolation is done.
So A1m and A2m dont necessarily yield their own stage poles.
I did read your pdf file 10 days back I guess., I'll now take a serious look and find out the flaws if any.

I don't quite understand how you came up with this block diagram. The model I used, I think, adheres more closely to the physical structure of the amplifier. I think my A1(s) reflects the loading coming from the second stage. Because of this my A1(s) is different than just the isolated gain of the 1st stage if it were only loaded by its own C1. Yes, for sure the poles of A1(s) and A2(s) are different than the poles of just the first stage and the second stage taken separately. The reason is that CM couples them together. But you'll agree, I hope, that the simulations show Atot=A1(s)*A2(s) (the way I define them) and A(s)=V2(s)/Vin(s) match.
As a side note, I'm aware that the analysis I offered is graphical and as such it is to an extend approximate. I don't argue that if you do complete analytical derivation you can get exact poles and zeroes. However, I prefer the graphical one since to me it gives more insight, less complicated expressions and as such is more convenient for design purposes.

Just a quick question.,

I agree that all this happens when you try to isolate in to two separate blocks., but do you really see three poles for some values?., there are only three caps of which only two can have independent voltages.., so there can only be two poles in any case., so this is an obvious error.

But of course there are 2 poles in Atot(s). As I said before P2s - the pole of A2(s) is not in the total gain - it just signifies the beginning in the roll-off of A2(s) but Atot(s) continues to roll-off with -20db/dec (and Z12(s) flattens)
I think our discussion is fueled by the fact that you look at the TF of the amplifier as a whole while I'm trying to show the individual contributors to it as physical entities.

 

[sutapanaki]

Re: Opamp with big LOAD

Hi Saro,
I already know that you like pz analysis, so I did it for CM=1f, 10f, 100f, 1p, 10p, 100p, 1n. The table from before with the addition of the pz results I attach as a ppt file. All poles ending with _pz are from the pz analysis - red and blue in color.
The calculated results from my previous table are in black.
I realized I need to correct the results from my previous table for small values of CM. The corrected results are in green. The formulas I used to calculate the poles assume that the Miller effect has already moved P1 (the first pole of stage 1) below the pole of A2(s) - P2s. This happens after CM=1p - up to that value P1>P2s. That means that Z12(s) flattens before P1 and for these small values P1 is not really determined by the Miller effect. So now, the first stage is loaded by Ro1||R12 and this resistance together with C1 produces P2 of A1(s) and ultimately of the total gain. However, as CM increases, the value of R12, as we discussed before, decreases and the "DC gain" of the 1st stage changes (decreases) - from gm1*Ro1 before P2s, to gm1*(Ro1||R12) after P2s and before P2. So, in effect there is a lower pole and then a zero in A1(s) - in other words the shape of A1(s) starts to look like the one from my plots - both in the pdf file and in the simulations. Because the DC gain gets to its new value at P2s - the pole of A2(s), this is in effect the frequency of the zero in A1(s). In the corrected results, which are suitable for hand calculations I somewhat freely assumed that for very small CM this pole and zero happen at approximately the frequency of P2s - this is confirmed by the pz results as seen for P1_pz and P2s_pz. For CM=1p, Ro1||R12≈0.5*Ro1 and I can no longer assume that the pole and the zero are at the same frequency. The zero is still at the frequency of P2s, but the pole happens at about 2 times lower frequency, for about 2 times higher DC gain - the usual gain-bandwidth trade-off.
For CM=10p, 100p, 1n the first pole of A1(s) becomes dominant and lower than P2s and everything I said before holds and the formulas for P1, P2 and P2s are correct. This is obvious from the table as the hand-calculated results and the pz analysis results match quite well. It is also obvious that P1 and P2 - the first and second pole in A1(s) are the first and second pole of the total gain. P2s - the pole of A2(s) does not appear in the total gain. So you can be happy, the total gain has only two poles - and of course the RHP zero which we don't care about here.

 

[saro_k_82]

Re: Opamp with big LOAD

Hi Sutapanaki,
I dont contest the graphs of A1(s) and Z12(s). All I wanted to see was the two poles moving toward each other and crossing each other in the real axis. Your statements say that, but both your ATOT(s) ac plots and pz results dont show that. In the table, I only see one pole moving from 795Hz to 1Hz and other from 40KHz to 310KHz for CM 1f to 1n (just looking at the pz results). Am I missing something?
I hope you used the same values that I had provided a few posts back. The initial pole locations and the final pole locations of both of us match exactly (from CM=0 to CM=1n) but there are considerable errors in between., but nevertheless direction of pole movement is just the same again going against your argument.
Your analysis is a bit too much for me., I was able to follow but with lot of scepticism about that being applied to our case. I want to tread the safe path for any analysis I doubt and develop intuition based on that result. To apply an already developed intuition to a new problem, one has to be absolutely sure about what he is doing. In this case you may be, but I'm not.
Analysis treating the entire block as one amplifier cannot give wrong results, while trying to simplify it as two simple blocks can. I just want you to take some pain and convince yourself by working the full expression and possibly educate me the missing link in your analysis.

Thanks,
Saro

 

[sutapanaki]

Re: Opamp with big LOAD

Hi Sutapanaki,
I dont contest the graphs of A1(s) and Z12(s). All I wanted to see was the two poles moving toward each other and crossing each other in the real axis.

Of course you can not contest the results - simulation is what we trust at the end. However, I thought that we were arguing about this:

Hi Sutapanaki,
If I understand your post correctly. You dont agree with my claims that the output pole moves further in with miller compensation where it is intially dominant. You are trying to say that with Cc=0, the output pole dominates and with Cc=1f, suddenly the poles swap places. Something to think about.

That is, you did not agree that the dominant pole was determined by P1 - the pole of the 1st stage and not by the pole of A2(s) - P2s. And I insist that it is the pole P1 at the output of the 1st stage that determines the dominant pole of the total TF and I show it in the pz analysis. If you are not convinced by this, then I don't really know what else I can do. I also said this:

I agree that both poles of the total gain move to lower frequencies as you increase CM. I was wrong by stating initially that they'll move in opposite directions. Needed to do the analysis, that I posted in my previous post to see it.

According to me we were talking after that about where were the poles that define the two poles of the total TF and also how important for this is Z12 and how it influences the movement of the pole at the output of the 1st stage and ultimately the dominant pole of the whole amplifier.

Your statements say that, but both your ATOT(s) ac plots and pz results dont show that. In the table, I only see one pole moving from 795Hz to 1Hz and other from 40KHz to 310KHz for CM 1f to 1n (just looking at the pz results). Am I missing something?

Yes, I think you are missing the point. That's why I put all the info in the table and tried to give explanation to show that it is P1 that appears as the dominant pole.

I hope you used the same values that I had provided a few posts back. The initial pole locations and the final pole locations of both of us match exactly (from CM=0 to CM=1n) but there are considerable errors in between., but nevertheless direction of pole movement is just the same again going against your argument.

Yes, I used the values that you provided in your second case - for CL=1n. I leave it up to you to figure out where the errors come from. For me what I did is correct because it matches the calculations with the simulation.

Your analysis is a bit too much for me., I was able to follow but with lot of scepticism about that being applied to our case. I want to tread the safe path for any analysis I doubt and develop intuition based on that result. To apply an already developed intuition to a new problem, one has to be absolutely sure about what he is doing. In this case you may be, but I'm not.

May be if you try without skepticism it may work better. From my side I don't believe in developing intuition based on lengthy formulas of 2nd or 3rd order. Being able to see the physical contributors to a result to me is more valuable. It may be done through a bit of approximations but as long as it helps in design and in quickly converging to a result, it is ok.

Analysis treating the entire block as one amplifier cannot give wrong results, while trying to simplify it as two simple blocks can. I just want you to take some pain and convince yourself by working the full expression and possibly educate me the missing link in your analysis.

As Einstein once said, simple is good, but not too simple. In other words, if you know what you're doing, there is nothing wrong in splitting the analysis. I think I already took enough pain in preparing all the things I posted.

 

[saro_k_82]

Re: Opamp with big LOAD

That is, you did not agree that the dominant pole was determined by P1 - the pole of the 1st stage and not by the pole of A2(s) - P2s. And I insist that it is the pole P1 at the output of the 1st stage that determines the dominant pole of the total TF and I show it in the pz analysis. If you are not convinced by this, then I don't really know what else I can do.

I still dont agree . Your pz report is very similar to mine., but you still say that first stage pole becomes dominant. The poles which were initially at 800Hz and 40KHz moved to 1Hz and 315KHz in their own paths apart from each other. I dont see them getting closer for CM=1pF and then moving apart. You are quoting the last two columns in your table as the poles of the total TF from the simulation right?
Looking at ATOT(s), the poles get well separated with increase in CM from your plots. My point was these two most conspicuous results are not consistent with your statements.

According to me we were talking after that about where were the poles that define the two poles of the total TF and also how important for this is Z12 and how it influences the movement of the pole at the output of the 1st stage and ultimately the dominant pole of the whole amplifier.

Not exactly. For me the first stage, second stage, Z12 are all artificially created. I just want to see the movement of the two poles of the total TF with CM.

Yes, I think you are missing the point. That's why I put all the info in the table and tried to give explanation to show that it is P1 that appears as the dominant pole.

Well if I consider the last two columns (pz sim results of the total TF), it is the other way round. By interchanging P1_pz and P2_pz in the table, poles dont swap for 1f.

May be if you try without skepticism it may work better. From my side I don't believe in developing intuition based on lengthy formulas of 2nd or 3rd order. Being able to see the physical contributors to a result to me is more valuable. It may be done through a bit of approximations but as long as it helps in design and in quickly converging to a result, it is ok.

It is hard to shed that., because I have seen it applied and seen it work in silicon. The only thing I'm not confident about is your analysis.
Intuitions work differently with everyone. I'm not comfortable with yours, and you are not seemingly comfortable to my intuition that illustrates the concept easily.
Believe me., all it took was less than 10 minutes and a sheet of paper to do the complete analysis.

Thanks,
Saro

 

[sutapanaki]

Re: Opamp with big LOAD

That is, you did not agree that the dominant pole was determined by P1 - the pole of the 1st stage and not by the pole of A2(s) - P2s. And I insist that it is the pole P1 at the output of the 1st stage that determines the dominant pole of the total TF and I show it in the pz analysis. If you are not convinced by this, then I don't really know what else I can do.

I still dont agree . Your pz report is very similar to mine., but you still say that first stage pole becomes dominant. The poles which were initially at 800Hz and 40KHz moved to 1Hz and 315KHz in their own paths apart from each other. I dont see them getting closer for CM=1pF and then moving apart. You are quoting the last two columns in your table as the poles of the total TF from the simulation right?
Looking at ATOT(s), the poles get well separated with increase in CM from your plots. My point was these two most conspicuous results are not consistent with your statements.

Actually, I'm quoting no the last 2 columns in the table, but the last 5 columns. That's why first I show the pz results for P1, P2 and P2s and then the two poles of Atot, just to show that they really match with P1 and P2. If you like I can summarize all the things we went through from my point of view in a file. But you'll have to read it then

Not exactly. For me the first stage, second stage, Z12 are all artificially created. I just want to see the movement of the two poles of the total TF with CM.

Can't agree here. When one designs an amplifier he/she designs the first stage, the second stage (or vice-versa) and then looks at the response. If there are 2 stages, why not use them. Z12 is just result of the architecture.

It is hard to shed that., because I have seen it applied and seen it work in silicon. The only thing I'm not confident about is your analysis.
Intuitions work differently with everyone. I'm not comfortable with yours, and you are not seemingly comfortable to my intuition that illustrates the concept easily.

I did see it too - many times. About intuition, of course, I agree. I also tend to agree that it probably takes 10-15 minutes to write it down on paper. But this is for 2 stage Miller amplifier, well know thing, with many things written about it. But what about something more involved - say Ahuja type of compensation, or Nested Miller, or whatever else. One has to wait for 1-2 pages of equations? Not my way. Break it down in parts, analyze with approximations and design. Sounds better to me.

 

[ranier]

Re: Opamp with big LOAD

I read your discussion well and will analyze your opinions more.

one more question is how i can make low output resistance rail to rail amp.

1. Voltage follower for output buffer is good output stage. but it have voltage headroom due to stacked mos.

2. common source with negative shunt feedback is also diffcult to use for rail to rail output stage.

Thank you.

 

[sutapanaki]

Re: Opamp with big LOAD

You have to use some kind of a common-source amplifier if you want rail to rail output. Look at Philip Allen's book CMOS analog circuit design - there is a chapter on buffered opamps there.

 

[leebluer]

It seems negative shunt feedback is used in Allen's book (buffered OPs). Could I think the method is to push P2(output pole) higher to A1*Gm/CL, and then make loop stable, especially for larger CL?

I met the similar problem, use the structure as below, while loads with 0.1uF Cl.

Any other choice? Thanks