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

 

[arthorios]

I don't understand your first point. That would be true if you increase only the DC gain (with a fixed GBW). If you are talking about an OTA, increasing its current consumption, i.e., increasing its Gm, would lead to an increase in both DC gain and GBW. If that's not the case, it should be related to the topology being used.

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.

That would be the straightforward way to increase your GBW. You probably have a <x% accuracy specification, so it wouldn't hurt to have a gain higher than needed if that means meeting the GBW.

 

[Junus2012]

That would be the straightforward way to increase your GBW. You probably have a <x% accuracy specification, so it wouldn't hurt to have a gain higher than needed if that means meeting the GBW.

Increasing the gain I usually hear it from people trying to increase the DC accuracy, but increasing the gain for the sake of increasing the GBW is the thing which I am not able to digest.

Take it this way, I want to increase the speed, it is not logical to increase it by increasing the gain

 

[d123]

Hi,

Your threads are always interesting, and I get to learn a fair bit from what I see of your work.

OTA or TIA, or what? Is it a 741-style amplifier (joke) or an R2RIO? No schematic makes parsing what could be suggested really hard.

Whilst still having a lot to grasp about OAs, I associate disappointing -3dB with optimistic GBW, and slew rate with rise/fall times.

Clearly, your current gain is convenient to your design goals and I can appreciate unwillingness to fiddle with it after getting it right.

What about a feed-forward capacitor to speed it up, then? Joke?

 

[Junus2012]

Hello d123

Thank you for appreciating my threads

Actually here I am discussing in general for any type of voltage feedback amplifier weather it is OTA or buffered opamp but for sure not TIA.

Hence here the prionciple of GBW, f -3dB, speed, etc.. are applied similarly regardless the circuit topology,
Just for your curiosity I do love working with folded cascode buffered op-amp

I have tried the negative compensation capacitor, may it is the same what you call it feed-forward compensation but it only increase the unity gain frequency and didn't change the f -3 dB or the GBW value. As a result my response was not perfect single pole LPF, hence get worse settling time or peaking effect on the output.

Here is the negative compensation I used:

Evaluation of compensation techniques for CMOS operational amplifier design

This paper presents and compares two CMOS (complementary metal oxide semiconductor) operational amplifier (op-amp) designs. Each op-amp is based on a two-stage rail-to-rail output where the first stage is a differential input with folded cascode and the second stage forms a class-AB amplifier...

ieeexplore.ieee.org

The settling time in my opinion is the target of speed. The settling time should be less when we have larger f-3 dB, and this is the original problem of my thread because datasheet of opamps define the speed by GBW, not by f -dB. The latter one can be increased by gain and have then nothing to do with speed.

 

[crutschow]

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.

-3dB at what frequency?
The advantage of the GBW spec is that you can determine the -3dB point for any closed-loop gain.

 

[arthorios]

Increasing the gain I usually hear it from people trying to increase the DC accuracy, but increasing the gain for the sake of increasing the GBW is the thing which I am not able to digest.

Take it this way, I want to increase the speed, it is not logical to increase it by increasing the gain

You want to meet certain DC gain and GBW specifications, larger or equal than, less or equal than, etc. So why bother if your gain is higher?

The logic here is that you know GBW and DC gain of an OTA are linked. If you don't like having a higher gain when increasing the GBW, reduce the output impedance of your output stage, which is only logical if you have a compelling reason to do. Also, the -3dB point of an OTA would only be important if you are using it in an open-loop configuration. GBW is what you need to define closed-loop BW.

 

[Junus2012]

Dear friends,

I am not sure if my statement was clear or not, so I will represent it numerically.

Suppose I want a closed loop gain of 10 (20 db), so for the error requirement I need loop gain = 40 dB for the signal frequency up to 100 kHz.

Therefore a DC gain of 60 dB should work as minimum, but I need to extend the amplifier bandwidth so I save the loop gain requirement.

The problem I face is when I increase the gain, the f -3dB drops, or when I increase the f -3dB th DC gain drops, resulting by this way a constant GBW that I am not able to improve.

--- Updated Nov 10, 2022 ---

-3dB at what frequency?
The advantage of the GBW spec is that you can determine the -3dB point for any closed-loop gain.

I usually measure it from the open loop AC test, the first -3 dB drop from the DC gain

 

[crutschow]

Redefining how the bandwidth of an op amp is measured won't help you solve you problem of how to increase the gain-bandwidth of that op amp.

 

[Junus2012]

Ok friends let me this time graphically explain my problem,

you see the two graphs in the image below, both have the same GBW, but they have different open loop gain and different f -3 dB (with respect to DC gain), which one of them shall be considered faster response, assume that my op-amp is unity gain connected.

 

[FvM]

They different open loop DC gain and respectively Aol and Aol corner frequency has effectively no effect on dynamic behavior of Acl=1 amplifier. Just a small effect on DC gain accuracy in closed loop.

By the way, I think the question title as well as many statements in this thread are misunderstandable because the term "-3dB frequency" is usually not applied to Aol corner frequency, only to Acl.

--- Updated Nov 11, 2022 ---

There may be effects on large signal behaviour.

 

[Junus2012]

They different open loop DC gain and respectively Aol and Aol corner frequency has effectively no effect on dynamic behavior of Acl=1 amplifier. Just a small effect on DC gain accuracy in closed loop.

By the way, I think the question title as well as many statements in this thread are misunderstandable because the term "-3dB frequency" is usually not applied to Aol corner frequency, only to Acl.

--- Updated Nov 11, 2022 ---

There may be effects on large signal behaviour.

Dear FvM, thank you for your reply, I was waiting to see you in this post

How they have no effect on the dynamic performance?, the settling time and the full power bandwidth are direct proportional to the amplifier bandwidth,

but as you said, may be the correct thing is the closed loop amplifier benadwidth (f -3 dB), not of the Aol.

They different open loop DC gain and respectively Aol and Aol corner frequency has effectively no effect on dynamic behavior of Acl=1 amplifier. Just a small effect on DC gain accuracy in closed loop.

By the way, I think the question title as well as many statements in this thread are misunderstandable because the term "-3dB frequency" is usually not applied to Aol corner frequency, only to Acl.

--- Updated Nov 11, 2022 ---

There may be effects on large signal behaviour.

That I can understand from you, but what about the unity gain frequency which is measured at 0 dB,

Suppose you have unity gain buffer, how you will measure the opamp bandwidth? if at -3 dB, then you will cross the unity gain region at you might count a peak if my phase margin is not big

 

[sutapanaki]

Junus2012, you should be clear what you are talking about and how you look at things. Since you have a feedback amplifier, then you will have to deal with the loop gain. UGBW is something related to the loop gain and the DC value of the loop gain will also define the accuracy of your closed loop gain to some extend. The UGBW of the loop gain is defined by the DC gain and the -3dB frequency of that loop gain. The gain-bandwidth trade off in voltage amplifiers says that if you increase the DC gain, you inevitably decrease the -3dB frequency of the loop. It is just because if you increase the DC gain by reducing for example the tail current of the amplifier, it will result in higher node resistances, hence lower dominant pole or -3dB frequency. Or, if you increase L of the transistors to get more gain, that higher L will result again in higher node resistances with the same effect. Ultimately, the UGBW of the loop (assuming the non-dominant pole is high enough beyond the UGBW frequency) is Gm/C, where C is either your load capacitance in a load compensated amplifier, or the Miller capacitance in a Miller compensated 2 stage amplifier. All this is for the loop gain. Its UGBW defines the -3dB BW of the closed loop amplifier and how fast is you closed loop amp depends on that -3dB frequency, because tau=1/F_3db. In other words, the UGBW defines the speed. And you can increase it by either burning more current to get higher Gm, or reduce the C. But reducing C will most probably increase the noise. The -3dB frequency of the loop has little effect as long as you keep the loop stable.

 

[Junus2012]

Thank you friends for your help,

toward improving my GBW to get faster settling response, I increase the current (or reduce the Cc as possible for stability) but the gain reduce so GBW still the same.
shall I boost the gain as well? thaugh I still have high gain of 90 dB, and my circuit configuration is unity gain buffer, I mean I don't need higher AOL gain unless if it is the only way to increase the GBW.

 

[sutapanaki]

Maybe you can plot or draw something to show what you are doing and what you are getting.

 

[Junus2012]

Maybe you can plot or draw something to show what you are doing and what you are getting.

Thank you Suta for your reply,
Please my post #10 which describe exactly the problem I have. To repeat it again, I am not upset of the drop in the open loop gain, still it is above my accuracy requirement since I am using it for buffer connection. But this drop is what makes the GBW constant, I want to increase the GBW

 

[KlausST]

Hi,

Please my post #10 which describe exactly the problem I have.

do the two graphs of post#10 into one diagram. Maybe then you will see that there is no difference at high frequencies.

Klaus

 

[sutapanaki]

Thank you Suta for your reply,
Please my post #10 which describe exactly the problem I have. To repeat it again, I am not upset of the drop in the open loop gain, still it is above my accuracy requirement since I am using it for buffer connection. But this drop is what makes the GBW constant, I want to increase the GBW

I assume the plots on #10 are for the loop gain.
Are you saying that if you decrease the Cc without changing the bias current you don't get higher frequency where the frequency response crosses 0dB?

 

[Junus2012]

I assume the plots on #10 are for the loop gain.
Are you saying that if you decrease the Cc without changing the bias current you don't get higher frequency where the frequency response crosses 0dB?

No actually I missed explained it, I mean to say other way than reducing Cc, because I reached the limit of stability I can not decrease it further.

 

[sutapanaki]

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