How is Gain Bandwidth Product defined?

[14425324]

I am checking the definition of Gain Bandwidth Product in op amp design, but the definitions are different on different materials. Is there anybody can show me the correct definition? Thank you very much!

 

[LvW]

The gain-bandwidth-product (GBW) is the product GBW=Ao*fg .
(Ao=opamp open loop dc gain, fg=3-dB-frequency of the magnitude function).

In most cases the opamp is universal compensated and can be seen as a single pole model. In these cases, the GBW is approximately equal to the transit frequency fT where the gain has dropped to 0 dB.

 

[14425324]

The gain-bandwidth-product (GBW) is the product GBW=Ao*fg .
(Ao=opamp open loop dc gain, fg=3-dB-frequency of the magnitude function).

In most cases the opamp is universal compensated and can be seen as a single pole model. In these cases, the GBW is approximately equal to the transit frequency fT where the gain has dropped to 0 dB.

thank you very much.
but I saw some definition written as GBW = Gcl * fc
where Gcl is closed loop gain, fc is 3-dB-frequency.

Why?

 

[LvW]

Yes, that´s right. But only in case of universal compensation !
The answer is easy: In a single pole response the gain drops with 20 dB/dec. - which means: When the frequency increases by a factor of 10, then the magnitude gets smaller by a factor of 10. Thus, the corresponding product remains constant.

Comment: fc in your formula is the 3-dB-point of the closed loop gain !

 

[14425324]

Yes, that´s right. But only in case of universal compensation !
The answer is easy: In a single pole response the gain drops with 20 dB/dec. - which means: When the frequency increases by a factor of 10, then the magnitude gets smaller by a factor of 10. Thus, the corresponding product remains constant.

Comment: fc in your formula is the 3-dB-point of the closed loop gain !

Thanks!

Could you please explan me why in universal compensation we ues Ccl(closed loop gain) but in other condition we need to ues Gol(open loop gain)?
Is universal compensation a compensation approch, or just represent the singal pole op amp?

Thank you very much!

 

[LvW]

Could you please explan me why in universal compensation we ues Ccl(closed loop gain) but in other condition we need to ues Gol(open loop gain)?


The GBW is defined as mentioned before (Ao*fg).
In case of a universal compensated opamp this product equals (Acl*fg,cl) as explained before. That´s all one can say. That means, for a non-compensated opamp the GBW must be calculated as defined (Ao*fg) - and the other products which can be calculated (Acl*fg,cl) deviate from this product more or less.

Is universal compensation a compensation approch, or just represent the singal pole op amp?

It's the same. The aim of universal compensation is to create a single pole response in the active freqency range (where the gain is > 0 dB).

 

[cjron]

In the Perspective of a hardware circuit (with ampr APEX PA107DP)..how to find the GBP? should the feedbck resistance be removed? if so wen finding unity gain bandwith in open loop (open loop gain=1) the freq will be somewer in 100's of MHZ but the signal generatr is only upto 15MHZ??

Plz help me with my query...thank u!!

 

[LvW]

In the Perspective of a hardware circuit (with ampr APEX PA107DP)..how to find the GBP? should the feedbck resistance be removed? if so wen finding unity gain bandwith in open loop (open loop gain=1) the freq will be somewer in 100's of MHZ but the signal generatr is only upto 15MHZ??

Plz help me with my query...thank u!!

If you know that the opamp is unity-gain compensated (continuous gain drop with 20 dB/dec) you simply can extrapolate.
It's a basic geometric task when the slope and at least one point is known (watch the log scale n the BODE diagram).
If only partly compensated you must know the second pole frequency.

 

[cjron]

Thank u fr ur reply...but the roll off freq in my case is not 20db/decade exactly..and with the closed loop the unity gain is met at freq of 120KHz. Do I need to compensate my circuit and how?

Thank u!!

 

[LvW]

Thank u fr ur reply...but the roll off freq in my case is not 20db/decade exactly..and with the closed loop the unity gain is met at freq of 120KHz. Do I need to compensate my circuit and how?

Thank u!!

In posting #7 you mentioned a unity gain frequency "somewhere in the 100's of MHz".
And now? Please, clarify.

 

[cjron]

To be exact my feedback resistance(Rf) is 30K and my input resistance(R1) is 1.5K (which has a gain of 20) and the unity gain is met at 120KHz(for the closed loop case)..Now I need to find GBP and do I have to remove the Rf completely to find open loop gain??

I'm really confused with this plz help me out..thnk u

 

[jimito13]

Since your closed-loop gain-bandwidth product (GBP) deviates so much from the open-loop GBP of approximately 180MHz given in the opamp's APEX PA107DP datasheet,this means that the opamp is not universally compensated as LvW already said and has not a single-pole response (20dB/dec. roll-off asymptotically).

In order to find the open loop quantities (Low-Freq. Gain,GBW) you should remove the feedback resistanse Rf,the input resistanse R1 as well and deal with the opamp as a standalone cell.

 

[LvW]

Indeed, as mentioned already by jimito, the PA107 is stable for gains larger than approx. 20 dB only.
That means the implemented gain of 30 is within the region of instability.
Ciron, you mentioned a unity-gain frequency of 120 kHz. Question: Measured or simulated? AC or Tran simulation?

 

[cjron]

This is a measured value and i'm using a very little gain of 10 or 20 dB (which is Rf=15K,30K and Rin=1.5K)...will my circuit be stable if I increase the Rf eventuallly the gain ??

 

[LvW]

This is a measured value and i'm using a very little gain of 10 or 20 dB (which is Rf=15K,30K and Rin=1.5K)...will my circuit be stable if I increase the Rf eventuallly the gain ??

I only can repeat: According to the data sheet the amplifier is stable for gains>20 dB only (better with safety margin: 26...30 dB).
Question: Did you eventually confuse the 3-dB corner frequency with the unity gain frequency?

 

[cjron]

No I did not confuse with the 3-dB and unity gain frequency. the 3-dB frequency was -3dB from the maximum gain(19.70dB) and the unity gain is the frequency where the gain is 0dB...Many thanks for your posts anyways

 

[LvW]

In this case (unity gain at 120 kHz) , I assume a problem in your measurement set.
Did you already try to simulate the frequency response?
Regarding stability (oscillations): Any indication of that? Correct opamp quiescent (operating) point?

 

[cjron]

No i din't try simulating yet,but there is a sight of oscillations near the same freq

 

[LvW]

No i din't try simulating yet,but there is a sight of oscillations near the same freq

I only can repeat (for the 2nd time): According to the data sheet the amplifier is stable for gains>20 dB only (better with safety margin: 26...30 dB).
Thus, no surprise observing oscillations near 120 kHz.

 

[student_of_analog]

This is an informative thread.
So,

Gain (open loop) * 3 dB bandwidth (open loop) = Gain (closed loop) * 3 dB bandwdith (closed loop) for an compensated opamp (only 1 dominant pole before UGB).
Also if opamp is compensated, GBW = UGF

But if the opamp is not compensated, the the GBW (open loop) differs from GBW(closed loop) ???
and GBW differs from UGF ??

Am I understanding correctly ?