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Bandpass Filter Design
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Wimberleytech:

--- Quote from: Rigolon on April 30, 2018, 09:02:45 pm ---
--- Quote from: Wimberleytech on April 30, 2018, 08:42:57 pm ---The zero in the modified SK compensates for the roll off of the op amp.

--- End quote ---

I'm having trouble to understand this, the roll off shouldn't impact on the corner frequency right? If I want a better roll off I'll have to use a higher order filter, correct? For example, if I use two identical Sallen-key LPF I will have a 4th order filter (I know that it's better to not use identical filters) and have a better roll off than just 1 SK LPF.

But this resistor is actually impacting on my corner frequency, I just can't find the equation for the corner frequency. All equations that I find/calculate doesn't include that resistor.

--- End quote ---

If you put an opamp in unity-gain configuration and observe its frequency response, you will see that it approximates a first-order response with a corner frequency at the unity-gain-bandwidth frequency (e.g., 1 MHz for a 741).  So, an opamp is a FILTER!!

So if you build a filter around an opamp, the frequency response of the amp itself comes into play.  That is what the zero is compensating for in the TI article. 
MarkF:
Jumping in the middle of this conversation...

Here is a passive LC Filter Design option that I've used:   https://www-users.cs.york.ac.uk/~fisher/lcfilter/
Wimberleytech:

--- Quote from: MarkF on May 01, 2018, 01:44:53 am ---Jumping in the middle of this conversation...

Here is a passive LC Filter Design option that I've used:   https://www-users.cs.york.ac.uk/~fisher/lcfilter/

--- End quote ---

Yes indeed!  And how appropriate that you should post.

One you have an RLC prototype, you can replace inductors and capacitors with active RC integrators using the LEAPFROG technique.

RLC ladder filters are the least sensitive to component tolerance.

LEAPFROG is not efficient in terms of active components (one opamp for every pole or zero).  It is also difficult to troubleshoot when not working right.

https://en.wikipedia.org/wiki/Leapfrog_filter
Benta:

--- Quote from: Rigolon on April 27, 2018, 05:02:26 pm ---So a true 4th order filter is a filter with same cutoff frequency but different poles (i.e. different capacitors and resistors combination for each stage)?

--- End quote ---

Just to give you a flavour of how to work with the filter poles: the poles are always in the left side of the complex plane (except Cauer filters).
For a Butterworth response, it's especially simple: all poles are equally spaced on a circle with centre at 0,0.
For a second-order response they're at 135 and 225 degrees.
For a third-order they're at 120, 180 and 240 degrees.
For a fourth order they're at 112.5, 157.5, 202.5 and 247.5 degrees.
And so on.
IIRC, the Bessel and Chebychev poles are placed on an ellipse. Tables will help here.


Cheers.
Wimberleytech:

--- Quote from: Benta on May 01, 2018, 04:42:11 pm ---
--- Quote from: Rigolon on April 27, 2018, 05:02:26 pm ---So a true 4th order filter is a filter with same cutoff frequency but different poles (i.e. different capacitors and resistors combination for each stage)?

--- End quote ---

Just to give you a flavour of how to work with the filter poles: the poles are always in the left side of the complex plane (except Cauer filters).
For a Butterworth response, it's especially simple: all poles are equally spaced on a circle with centre at 0,0.
For a second-order response they're at 135 and 225 degrees.
For a third-order they're at 120, 180 and 240 degrees.
For a fourth order they're at 112.5, 157.5, 202.5 and 247.5 degrees.
And so on.
IIRC, the Bessel and Chebychev poles are placed on an ellipse. Tables will help here.


Cheers.

--- End quote ---

Very nice explanation.  I don't think you meant to imply that Cauer (aka eliptic) filters can have poles on the imaginary axis.  There are zeros on the imaginary axis in Cauer filters (and Chebyshev Type II), but not poles.
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