GBW and -3 dB relationship

[Junus2012]

Hello,

I am trying to increase the speed of my opamp by increasing the gain bandwidth product. As it is known, the common approachs of increasing the gain bandwidth product (GBW) leads to decrease the amplifier gain, for example when increasing the biasing current or use shorter channel length. Hence what happened that I still receive the same GBW, it became a constant because GBW = f (-3 dB)XDC gain, so the increment in f (-3 dB) will be compensated by the drop of the DC gain.

Since the DC gain I have in my circuit is enough for my closed loop gain accuracy, I don't want to enhance the gain further for the sake of having larger GBW. This led me to the fact that the opamp speed should be evaluated with respect to f (- 3 dB), not to the GBW. On the other hand all op-amp data sheet present the value of GBW as a measure of their AC speed.

Note: I am assuming the opamp have no slew rate limitation.

I would like to have your discussion on this regard
Thank you in advance

 

[Junus2012]

But before you reached the limit of stability you were reducing Cc and then did you get higher UGBW?

yes certainly it increase the UGBW strightforward, say I reached to 200 MHz, but I want 400 MHz,
I am no more able to decrease the Cc becasue the PM will become small

 

[sutapanaki]

That's a lot of increase. You will need 2x gm, which 4x the current. But increasing the UGBW by that much you will probably aproach the non-dominant poles and run into stability issues again. I am afraid your goal doesn't require just a simple tweak.

 

[Junus2012]

That's a lot of increase. You will need 2x gm, which 4x the current. But increasing the UGBW by that much you will probably aproach the non-dominant poles and run into stability issues again. I am afraid your goal doesn't require just a simple tweak.

Thanks Suta,

Absolutely you are right, and by the way increasing the the gm it means I am approaching the non dominant pole so I have tried it and the phase margin start to degrade. The thing that it make it worse is that I am designing class AB buffered folded opamp. this is causing me a lot of current to push the pole of the buffer stage so I can increase the gm further.

Right now my buffer output transistor is taking 5 mA !!, I don't want to go further increasing it because I will then need to increase the wire length during the layout which add more parasatics.

for your discussion you can refer to the simple circuit shown below

 

[sutapanaki]

I think this topology is not fit for a high frequency operation. First you have your cascode nodes which contribute non-dominant poles. Then you have the translinear loops to bias the output stage which are also not super fast. Usually people use just a simple 2 stage Miller OTA for high frequencies and they don't expect a lot of gain from the second stage, especially if it needs to drive resistive loads. Or a source follower output buffer which will not be rail to rail. But the trend is clear. The faster you want to go, the simpler the OTA is. Sometimes to get good DC loop gain people use gain boosting. As a rule of thumb, the highest frequency of operation is around Ft/80, to be conservative, Ft/100.

 

[Junus2012]

I think this topology is not fit for a high frequency operation. First you have your cascode nodes which contribute non-dominant poles. Then you have the translinear loops to bias the output stage which are also not super fast. Usually people use just a simple 2 stage Miller OTA for high frequencies and they don't expect a lot of gain from the second stage, especially if it needs to drive resistive loads. Or a source follower output buffer which will not be rail to rail. But the trend is clear. The faster you want to go, the simpler the OTA is. Sometimes to get good DC loop gain people use gain boosting. As a rule of thumb, the highest frequency of operation is around Ft/80, to be conservative, Ft/100.

Thank you Suta for your reply,

I found it interesting to discuss more on your comments,

I found some papers reporting GBW of 400 MHz using this folded buffer circuit,
if you use simple two stage opamp, you will get drop in the gain as you said when it drives resistive load, and if the gain is dropped it means the GBW will also drop, that what I ask several times

You also said "the highest frequency of operation is around Ft/80, to be conservative, Ft/100.", can you please refer me to a reference so I can use it in my report, and also how can I know the Ft of my technology or simulate it?

don't wary still I have other questions for you later

 

[sutapanaki]

Yes, if you use simple 2 stage ota the gain, or rather the loop gain will drop when driving resistive loads, but that dosn't mean the GBW of the loop will drop. The DC gain will drop but the dominant pole will increase, so very likely the GBW will stay roughly the same. Remember, GBW=gm1/Cc and doesn't depend on the resistor values, hence DC gain. What will change is your closed loop DC gain accuracy. For example, if you use your amplifier as a follower you won't get a gain exactly 1, but something smaller.
I can't really point to a reference about the Ft/80 rule. It's a rule of thumb. It may not be Ft/80, it may be Ft/70 or Ft/60, but around there.
You can simulate Ft for your technology. It is gm/Cgg. It will depend on L, but not so much on W. For example you can sweep Vgs and look what happens with the gm/Cgg while the device remains in saturation. Even better, you can plot gm/Cgg vs. gm/Id.

 

[Junus2012]

Yes, if you use simple 2 stage ota the gain, or rather the loop gain will drop when driving resistive loads, but that dosn't mean the GBW of the loop will drop.

Actually I am not talking about dropping or keeping it the same, I am talking about booting it up, otherwise the buffered folded Opamp should be better as at least it has higher DC accuracy,
In short by comparing the folded buffered opamp to your suggestion of using simple two stage opamp, I cant find advantagues with regard to the GBW

Thank you

 

[sutapanaki]

I don't understand what you mean by booting it up.

Actually I am not talking about dropping or keeping it the same, I am talking about booting it up, otherwise the buffered folded Opamp should be better as at least it has higher DC accuracy,
In short by comparing the folded buffered opamp to your suggestion of using simple two stage opamp, I cant find advantagues with regard to the GBW

Thank you

 

[Junus2012]

I don't understand what you mean by booting it up.

Mean achieving higher GBW,
So back to the main point, the GBW= gm/Cc, but this depends on the first non-dominant pole of the buffered second stage, here in particular talking about the buffered opamp.
You have suggested to use a simple two stage opamp rather than the buffered folded opamp I have shown before,

and my answer to your suggestion: two stage opamp has smaller DC gain when driving load, hence when we calculate the GBW, we mostly get worse result than folded buffered because GBW=DC gain X dominant pole freq

 

[sutapanaki]

The GBW depends on the gm of the 1st stage and the Cc. It doesn't depend on the DC gain because you have the gain and BW trade-off. If you increase DC gain, your dominant pole gets lower and vice versa - if you decrease your DC gain your dominant pole gets higher. The product of the two stays the same. The non-dominant pole is another issue. If your GBW gets closer to the non-dominant pole, then you get worse stability and the unity gain cross over frequency becomes smaller than the GBW. But in the case of a two stage OTA driving resistive loads the non-dominant pole will move towards higher frequencies because of the load and you will have room to increase the gm of the 1st stage to eventually get the GBW you need. Of course, all this within the limits of the technology. And yes, the DC loop gain will be lower with all accuracy consequences.

 

[Junus2012]

Dear Suta,
Thank you very much for your nice explanation, I am really learning from you and other friends a lot, I do appreciate your patience to answer me, I know for your level, some of my questions might look silly, but I am happy that I am learning from your practical experience.

I do agree on every word you stated in your last post, specially when you say that GBW depends on the gm/Cc, it is indeed fundamental definition.

But when you get your simulation (or even real measurement) result of the AC response, you are not going to calculate the GBW from gm/Cc, you will use DC gain X f-3dB (the dominant pole), right?, I know in case of ideal single pole response it will be equal to unity gain frequency, but my point is that the DC gain is in our way of calculation.

However, your last post may also gave the answer to this point, so by increasing the gm (to the limit of required stability), this pole will move up and we get a higher GBW which will be the same if we extract it from the AC response as DC gain X f-3dB

Thank you very much once again
Best Regards

 

[Junus2012]

Back to you Suta

You said that two stage opamp could have higher GBW performance because "non-dominant pole will move towards higher frequencies because of the load and you will have room to increase the gm of the 1st stage to eventually get the GBW you need."

I would comment here: when you have buffered OTA, either the simple two stage opamp or the folded class AB opap that I have shared, your first non dominant pole will be due to the driver stage itself, means the second stage.
In case of the buffered folded class AB circuit, it has equivalent transconductance of gmn+gmp, whilest in two stage opamp we have only gmn or gmp
so for first glance and by ignoring the other non-dominant poles, the folded class AB circuit can achieve higher GBW than two stage opamp for the same stability constraint

 

[sutapanaki]

I don't think so. If you are talking about the folded cascode you showed previously, it is still the ac current of the input diff pair that charges the compensation capacitors, so it is still gm/Cc. And I assume the non-dominant pole will be at the output of the class AB stage, plus other non-dominant pols from the cascodes etc. But you do have gmp+gmn of the output stage which may help with the non-dominant pole