How evaluate the gain bandwidth product

[houly]

Hello all,
I'm designing an active filter (low pass Bessel 4th order filter) with FilterPro from TI. This gives me a very high value for the GBW product of each stage of my filter, so I asked to TI how they calculate the value for each state and they answer me that they evaluate the GBW with this expression :

GBW=fn*Q*Acl*100

with
fn : natural frequency
Q : Q of the stage
Acl : Closed loop gain
the value of 100 is added to have a gain error of 1%

But they don't explain where does it come from how they can deduce this expression ... ? Does anyone could help me to better understand it ?

thanks for your help

 

[LvW]

Hello all,
I'm designing an active filter (low pass Bessel 4th order filter) with FilterPro from TI. This gives me a very high value for the GBW product of each stage of my filter, .........

Hi houly,

Because of your wording (This gives me ...value for the GBW) I am not quite sure if you got the real meaning of the GBW.

The GBW for each opamp circuit - and also for each filter stage - should be "as large as possible". This is because all formulas to calculate parts values are derived based on ideal opamps (GBW infinite). Thus, a finite GBW value will cause deviations from the desired filter response. As a consequence, if for example deviations in the order of 1% are acceptable a minimum GBW for the opamps is necessary.
However, an exact calculation of this GBW minimum is not possible because
(a) different filter topologies react in a different way, and
(b) the error caused by the finite GBW can be allocated to different parameters (pole Q or pole frequency or damping factor or ....).

For this reason, something like a "rule of thumb" can be formulated to assess the minimum required GBW (like the formula provided by TI).

 

[houly]

Hello LvW,
Thanks a lot for your reply. Sorry for my mistake, I wanted to say that Filter Pro gives me a very high value for each stages of my filter.

Thanks for your explanation, I understand better why I can't see this expression anywhere.

 

[FvM]

In practice, you often won't be able to fulfill the criterion of < 1% parameter error compared to an ideal OP. It's completely illusional for active filters in the higher MHz range and not necessarily reasonable even for audio filters. If the used OP has stable GBW over temperature and not much type variation, designing the filter for the real OP parameters can be an alternative.

 

[LvW]

...................
If the used OP has stable GBW over temperature and not much type variation, designing the filter for the real OP parameters can be an alternative.

Hi FvM,

I agree, there are some methods to take the limited opamp bandwidth (single pole model) into account during parts calculation - and I am interested to learn which method you have in mind.
Thank you.