Hi,

Back again with some interesting results of the biquads that we have been discussing on the previous posts.

I have downloaded the Filter Solutions software trial and produced 4 3rd order active Butterworth LPFs. I have to admit that Filter Solution is great and can save a lot of time in the process of filter configuration research. I then simulated the ferquency response and noise of the filters and it seems that theh Sallen-Key filter has the best noise performance even over the LeapFrog filter (any idea why, ssahl??). I then wanted to see the sensitivity of the different configurations to component variations and the opamp GBW, so I set all the component values to vary +/-3 std and also the opamps GBW was varied by +/- 3std (using MC simulation). as you can see also here (in the attached plot) the Sallen-Key configuration has least sensitivity.

It seems that these results does not support the laepfrog configuration as havin gthe best noise and sensitivity performance.

Hi ssahl,

I agree about the peak at the band edge but still, an integration of the noise on the entire frequency range ends up with the SK a little better than leapfrog. My design criterion was maximum capacitor value of no more than 4.5pF (for area considerations) and the resistors value were set accordingly.

I still think that the leapfrog and MFB advantages are not evident in this simulation and it might got to do with the fact that it is a relatively low order filter (3rd order Butterworth), maybe if I repeat this simulation for a 5th order filter the results will be different. I think it worth the effort.

Anyway, thanks for the tips regarding the current consumption and maximum voltage peaks at the opamps, I will take that into consideration

Hi rfmagic,

in your evaluation of the filter software simulation results you shouldn't forget that all simulations assume ideal opamp properties - as far as input and output impedances are concerned.
Because of this, you did not detect the following disadvantage of the S+K topology:
Above a certain frequency the attenuation will again decrease (the filter transfer curve is rising).
This effect is due to the feedback capacitor:
For higher frequencies there is a remarkable and rising portion of the input signal that reaches the opamp output DIRECTLY (not via the internal amplifier chain). This portion creates at the finite opamp output a signal voltage that increases with frequency. You can observe this effect via circuit simulation based on real amplifier macro models.
Example: opamp type LM741, second order lowpass with Qp=1 and 3-dB frequency 50 kHz. As a result, the attenuation will be not better than -35 dB (at app. 400 kHz) and then will decrease again.  

Regarding Monte Carlo simulation: May be you didn't get the right picture because - in some cases - tolerance variations can cancel or reduce each other. The worst case for S+K topology is variation of one of the gain fixing resistors alone! Try it - it's really bad!
(Obviously, this is not the case for unity gain design - however, this alternative has other disadvantages).

rfmagic, for clarification I enclose a pdf-picture with a comparison of some different approaches.
Regarding your question: For a unity gain S+K topology you will have a relatively large component spread for resistors as well as capacitors (in the order of 10 or something similar). In some cases (IC technology) this is not wanted.

Yes, you are right. The peaking of No. 3 is a consequence of the additional phase shift - introduced by the non-ideal opamp which in this case (negative feedback topology) gas a rather large gain of app (-20).
Because of the relatively high pole frequency (app. 50 kHz) and this gain requirement, the non-idealities have a remarkable influence and cause a pole Q enhancement.
This is a disadvantage of this structure (for high pole frequencies). The advantage is a much better (lower) sensitivity to parts tolerances.
This is a general rule: negative feedback topologies always have smaller sensitivities to tolerances - if compared with positive feedback structures.
However, they are more sensible to opamp non-idealities.
Another general rule: Each circuit alternative is a compromize between several - mostly conflicting - requirements.
Regards