Hi all,

For a switched-cap. filter the required bandwidth can be calculated from the settling constraints.
It is straight-forward and often appears in literature.
But how is the amplifier bandwidth determined in a continuous-time filter?  I have never seen
people doing calculations, but only simulation. How do I calculated the required amplifier bandwidth
for a continuous-time filter (from a set of specifications)?

Regards

Hi Berti,

I agree with HCWWong, that the required BW depends on the structuire chosen as well as on the pole parameters (Q resp. pole frequency). However, of course it depends also on the allowed deviation from the nominal response.
More than that, you should not forget the influence of the slew rate, because it makes no sense to look only at the small signal BW.
In addition. the topologies as mentioned by HCWWong (Tow-Thomas resp. Akerberg-Mossberg) are multiple opamp-structures and, therefore, are economical only if their specific advantages (lowpass, highpass and bandpass simultaneously, all of second order) are to be used.
According to my experience and in agreement with nearly all recommendations in filter books, the "best" second order structure from the viewpoint of economical use of the small signal BW is the GIC-based topology. The influence of the limited opamp BW on the filter response will be reduced if both opamps are matched (dual amp chip). The situation is even more complicated since there are other active candidates than opamps, each with their own structure (OTAs, CFAs and Current Conveyors).
In general, your question touches a very important and - at the same time - a very difficult question:
What is the "best" filter topology for a certain application ?
I am involved in filter design since 25 years (and I have written two books in german on filters), but up to now I did not come to a final conclusion. The answer resp. the choice of a specific topology depends on several items (accuracy requirements, filter characteristics, filter order, frequency range, pole data, application conditions and economical as well as operational aspects like power requirements).
But, in any case, I am sure that circuit simulation gives much more information than a simple formula because it can take into account more important opamp nonidealities like input/output impedance, slew rate, load influence, parasitic signal pathes (i. e. through the passive network directly to the opamp output; very important for Sallen-Key-structures).
Sorry, too much came into my mind.......
Regards
Lutz vW

Hi Vivek,
I agree, of course, with you that cascade design is more sensitive to tolerances, but easier to design.
(This is another proof of my opinion, that everything in analog design is always a compromize between several conflicting requirements resp. conditions)
More than that, also dynamic range considerations are more critical in cascaded structures.

But let me come back to the original question of this topic:
There is a textbook from M. Herpy and J.C. Berka (in german: Aktive RC-Filter) including a table with formulas for opamp BW recommendations to be applied for various filter topologies of second order*. I am not sure if it is available in english.

* Sallen-Key, Deliyannis, Scultety, Boctor, elliptical, double-T, Fliege (GIC), KHN, Fleischer-Tow, Berka-Herpy.

Regards
L.

Thanks everybody for the explanations.

In general I was more interested in continuous time loop filters for ΔΣ modulators.
I found that the transfer function is not so important but that distortion and phase-shift
dictate the required amplifier bandwidth.

But anyway, the discussion above was interesting.

Regards

buddypoor wrote on May 17^th, 2008, 7:59am:


Hi,

Looks like you are assuming some value for some performance parameter implicitly, because of these numbers 20 and 100 in your equations.
Perhaps you should add a note telling what goes into making up those 2 numbers.

Regards
Vivek