Active Filter Step Response

Dear friends,

This is the step response of the designed 4th order Sallen-key LPF,



As you see I have ringing, however, the op-amp used before connecting it in filter has phase margin of 70 Deg,

If you would like to suggest me increasing the compensation capacitor, then I already did and has no effect. Therefore, I am not sure if it is due to the op-properties or it is normal properties of the filter.

By the way, the peaking was less with only 2nd order and became worse when I move to 6th order

Thank you

Dear Junus,

For a closed-loop system you should check the phase margin of the loop-gain, not the opamp alone.

If you have too much peaking in the filter AC response, this is also indicating that you don't have enough phase margin (in the loop).

Regards.

Junus2012 said:

This is the step response of the designed 4th order Sallen-key LPF

Click to expand...

Meaningless. Which filter prototype? Some filters have overshoot by design.

If this thread is also about a Butterworth filter as your previous one https://www.edaboard.com/threads/measuring-the-cutoff-frequency-with-q-1.395450/, it just shows that the realized transfer function is slightly different from Butterworth prototype. So we are back to the previous discussion. It's a problem of the whole filter transfer function, not particularly OP open loop gain.

For your info, an ideal 4th order Butterworth filter has about 10% overshoot, your filter has 15 %.



If you don't want overshoot, you should select a different filter prototype, e.g. Bessel.

You should not be bothered by this type of ringing, or you should, depending on the application, but you should understand that ringing is natural for these kind of filters. It is not related to the PM of the opamps but is related to the structure of the filter itself and the fact that different biquads work with some obvious amount of Q, hence there is ringing. This type of ringing is related to the phase response of the whole filter and also to the group delay. If you don't want the ringing, you should use a linear phase filters, for which the phase changes linearly with frequency. For example Chebishev and elliptic filters have good magnitude response with regard to steepness but bad phase response with respect to linearity and one should expect them to ring a lot. Butterworth is also not great when it comes to phase response but is better compared to Chebishev and elliptic. Probably best of all in terms of phase is Bessel filter but it is not steep for the same order. That's why people usually choose Butterworth as a compromise, because it's relatively steep, it has maximally flat magnitude response and not a lot of ringing i.e. not very non-linear phase response.

Some principles... I hope it helps

Dear friends,

Thank you very much for your help, yes it is Butterworth what I have shown you, your explanation was really helpful.

FvM said:

For your info, an ideal 4th order Butterworth filter has about 10% overshoot, your filter has 15 %.

Click to expand...

If you provide me with the source material it will be helpful to cite it

Thank you once again

Simulation comparing Bessel and Butterworth type.
Found in the Circuits menu of Falstad's animated simulator. Free to download and use at:

falstad.com/circuit

Junus2012 said:

If you provide me with the source material it will be helpful to cite it

Click to expand...

This is elementary analysis. Take filter transfer function, calculate it step response in Laplace domain and go to time domain by calculating inverse Laplace transform.
If you don't know how to do it by hand, you can use any math tool, like Mathematica, Maple or Maxima.

A Bessel Filter still has a slight overshoot to a step input.
For no step input overshoot, you would use a Gaussian Filter.