Which filter toplogy is this?

[matrixofdynamism]

Initially I thought that it is Sallen-Key but then I realized that it does not have any positive feedback using a resistor so it can't be sallen key. This filter is given in page 260 of Practical Electronics for Inventors.



The image is attached to this question.

 

[FvM]

This is of course Sallen Key topology. Don't know what you mean with "positive feedback using resistor"?

 

[LvW]

It is the classical unity-gain Sallen-Key topology.
A negative feedback loop sets the gain of the stage (in this case: unity) and the frequency-dependent RC part resembles the positive feedback topology.

 

[matrixofdynamism]

What I meant to say is that the Sallen-Key uses positive feedback via capacitor. Sorry for saying resistor. Most of what I have seen as labelled Sallen Key is slightly different from this filter given in the book. I have attached the Sallen Key from wikipedia.



There is a capacitor that connects the output to the noninverting input. That is precisely what I don't find in the circuit from the book.

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here is comparison of the transfer functions:

Maybe Sallen-Key


Certainly Sallen-Key

 

[FvM]

That is precisely what I don't find in the circuit from the book.

Both circuits are exactly the same, just drawn a bit different. Look sharp.

 

[KlausST]

Hi,

as far as I can see all three pictures show exactely the same circuit. (Also exactely the same as in post#1 the left picture)

--> Unity gain, two pole Sallen-Key low pass filter.

Klaus

 

[matrixofdynamism]

OK, I see, what confused me was how the feedback input was connected. Now it all makes sense.

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Finally, does it matter in what order the different stages of a multistage filter are connected? Each stage would be a 2 pole or 3 pole filter.

 

[LvW]

Finally, does it matter in what order the different stages of a multistage filter are connected? Each stage would be a 2 pole or 3 pole filter.

Because of dynamic range considerations, it is advantageous to place the stage with the largest Q at the end of the chain (sequence from small to larger Q factors).

 

[CataM]

Certainly Sallen-Key
View attachment 126909

The positive feedback's purpose is to create the filter, but would not that affect the stability ? Or can be used as a simple filter with no restrictions ?

 

[LvW]

The positive feedback's purpose is to create the filter, but would not that affect the stability ? Or can be used as a simple filter with no restrictions ?

Of course, a high-Q filter is more close to the stability limit than a low-Q design. However, this is the nature of the filter´s transfer function (and the corresponding pole location).
This applies to ALL filter topologies and, thus, constitutes no additional criterion for selecting one of the various filter topologies.

 

[FvM]

It depends. The filter with negative feedback factor of 1 is unconditionally stable because the positive feedback is always smaller than the negative. Sallen key filters with gain can become unstable with unsuitable RC values (not implementing a useful filter characteristic).

 

[LvW]

It depends. The filter with negative feedback factor of 1 is unconditionally stable because the positive feedback is always smaller than the negative. Sallen key filters with gain can become unstable with unsuitable RC values (not implementing a useful filter characteristic).

Perhaps I misunderstand something - do you speak of parts tolerances and sensitivities to these tolerances? In this case, I agree of course.
On the other hand, a second-order filter with a pole-Q of Qp=5.58 (second stage of a 4th-order Chebyshev filter, w=3 dB) has a stability margin which is smaller than in case of Qp=1.077 (first stage of this filter). And, of course, these values (and the corresponding stability properties) are independent on the filter topology.

 

[FvM]

No, I meaned to say that the circuit in post #9 is resilient against becoming unstable, even with arbitrary wrong RC values. But I agree with your general viewpoint that stability is a matter of pole locations and not of the filter circuit.

 

[Audioguru]

Without the positive feedback the two RC filters create a very gradual corner that begins far from the cutoff frequency and the calculated cutoff frequency is at -6dB instead of at -3dB. The positive feedback causes the response to be Butterworth that has a sharp cutoff frequency that is at -3dB but it causes a little damped ringing at the cutoff frequency.