4 - Pole filters not really four pole?

[metacohl]

I have been reading a lot lately about how a four pole filter cannot be achieved by cascading two identical two pole filter, as the would have the same poles... still two unique poles.

I have been looking at some filter schematics and it appears to me that each of the integrator blocks in the ota based filter are identical, have the same poles.

Maybe there is something im missing, maybe they are actually offset because of the control bias of the ota, at this point it doesn't make sense to me.

Thanks for any insight

[JovianPyx]

Hmm. I don't have an engineering degree, so I may be lost in the fog, but from various reading I've done, I've always thought that if integrators are used, each produces a pole and is counted as such even if it's position is identical to others within the same filter.

In fact, I've know others who've made 4 pole filters in the digital domain and in that case, the poles are often in identical positions, but the filter is still called a 4 pole filter. Such a filter will exhibit a steeper fall off than 1 or 2 poles. In at least one case, I was able to see the code and indeed the poles in that case were all identical. Moving the poles around results in different spectral shapes and affects the falloff at the end of the filter's band (I believe that non identical poles will result in falloff that is not optimal for the number of poles used).

I've also built up digital state variable filters which are called "2 pole" even though the poles are in identical positions.

[metacohl]

Ok, well I can't really speak about digital filters as I don't know much about the math behind that. From a more general perspective, the analog, mathmatically the slope of the filter is determined by the number of poles, so if you line up identical poles on the graph it is still only one zero crossing point.

I think what it comes down to is that the instability and variance in components actually generate unique poles even when the component values are identical.

*Once again, I know nothing about digital filters. I was just reading a little bit on FIR and IIR techniques and realized how little i know on the subject*