2nd order low pass filter

[gehan_s]

Hi all,

I was going through these two ways of implementing a second order low pass filter. One is a Sallen - Key configuration while the other is just two low pass filters connected in series. I simulated the AC analysis of both of them and got the same response. What are the advantages and disadvantages of the two?

Thanks in advance !!!!!!!!!!!!!!

 

[MikeMl]

Not the same response at all. Compare A to B which are your versions. Now compare those to proper Sallen-Key Butterworth (C) and Chebyshev 1% ripple (D) responses. Note the sharper knee. The secret is computing the proper values of the resistors and capacitors to get the Butterworth and Chebyshev responses.

 

[MrAl]

Hi,

You can get some wicked responses from some of those filters by including a gain in the output op amp stage. Basically some of the damping can be canceled for some unusually wild responses.

 

[MikeMl]

Hi,

You can get some wicked responses from some of those filters by including a gain in the output op amp stage. Basically some of the damping can be canceled for some unusually wild responses.

By fooling with the two Rs and two Cs in the Sallen-Key configuration, you can get any response you want, including over damped, critically damped, under damped, and even an oscillator.

 

[MrAl]

Hi Mike,


You mean you can get a 1/(A*s^2+1) type response without a gain? Not that we might actually use that as is, but I'll take another look at this. It seems to me that there would be an 's' term in the denominator no matter what choice of R's and C's we had.

LATER:
It seems that with the gain G at the output we can get other interesting responses. Maybe not as practical but worth looking into. For example, with a gain G=1 we are limited to whatever we can get with the R's and C's (that's the way it stands in the drawings), which means the response will be limited. However, with a gain G of:
G=(C4*R3)/(C3*R4)+C4/C3+1

we can actually get an infinite response. This of course is not practical as is, but may mean other interesting responses could be had. With both R's equal and both C's equal we can get an infinite response with a gain of G=3.

We could investigate this further.

 

[WTP Pepper]

Cascading two 2nd order LPF of say -3dB at 1KHz will NOT give you the same response as designing a proper stage 4th order LPF with the same specs.

 

[MrAl]

Hi there WTP Pepper,

What is your point here, are you saying that you can get a steeper response with a true 4th order rather than two 2nd order cascaded filters?
What do you see as the main advantage?

 

[WTP Pepper]

I was saying that if you design a -3dB filter at say 1KHz, then cascading two of them identically will resort in a weird non -3dB filter @ 1KHz. There exists proper tables for four pole filters that can offer -3dB @ 1KHz with a proper steeper roll off.
IIRC the -3dB point of two cascaded filters is the geometric mean of the two which is far from optimised as if the whole 4 pole filter had been designed using tables of tChebychev or Butterworths from the start. I can dig out some LTSpice models I did a few years ago to show the point and principle. The rest is from 25 years ago in designing filters without simulators, but using sums from first principles. Happy Days!

 

[MrAl]

Hi,

Oh ok, sounds interesting. If you feel like posting more we can take a look.