theory on active filter

[franticET]

Hi i'm a new member.
I'm looking for the name and the theory-tutorial-book on this circuit

View attachment 68781

in order to obtain a bandpass filter 8-18 Khz
Thanks

 

[ronv]

Maybe this will get you started.

https://en.wikipedia.org/wiki/Sallen–Key_topology

 

[Winterstone]

Hi i'm a new member.
I'm looking for the name and the theory-tutorial-book on this circuit
in order to obtain a bandpass filter 8-18 Khz
Thanks

The topology as shown in your posting is based on the "Follow-the-leader (FLF)" principle.
As a special form, the FLF topology with identical band pass stages is called "primary resonator block (PRB)" technique.
It is a very efficient method to realize higher-order bandpass filters.
It is to be added that - if compared with the classical cascade approach - the FLF topology exhibits excellent properties as far as the sensitivity to component tolerances is concerned.

 

[Megamox]

Ron's article looks spot on. Here are some more tips that might help:

The core of your understanding should be a good knowledge of capacitor behaviour as a function of frequency.
1) At low frequencies a capacitor looks like an OPEN circuit. So for a low frequency analysis, replace capacitors by an open circuit then try to analyse how the remaining circuit will perform.
2) At High frequencies a capacitor looks like a SHORT circuit. In this case, replace a capacitor by a short circuit and then repeat your analysis to see how the circuit will now perform.

You should understand how this type of filter achieves gain.
1) Fundamentally the gain is caused by the op amp in negative feedback mode. This particular set up is called an Inverting Amplifier.
2) Gain is calculated by the ratio of 'the impedance in the feedback loop'/'impedance between the signal input and the negative terminal of the op amp'. This impedance between the signal and the op amp is also referred to as the input impedance of the filter.
3) The op amp will always try to maintain that both inputs are of the same value, which is why the feedback arrangement is used.
4) An ideal op amp has a very large input impedance so now current flows into its inputs.

Sallen-Key Low Pass Quick Analysis (referring to the diagrams in Rons post):
1) At low frequencies, the reactance (X) of the capacitors C1 and C2 are very large.
2) Vin therefore sees a Low pass passive filter made up of R2 and C1. At low frequencies, Vin is passed through this circuit to the op amp with hardly any degradation. So a rough approximation is to treat R2 and C1 like they're not there (As the signal is being passed right through them). Imagine R2 replaced with a short circuit and C1 replaced by an Open Circuit.
3) The low frequency gain is just X(C2)/R1 - as R1 is the remaining input impedance.
4) As the frequency of the input is made higher, you'll get to a point where X(C2) will equal R1 and this is a cut off frequency.
5) As X(C2) drops below the value of R1, the Gain of the filter falls too, as it's proportional to X(C2). See above equation.
6) At the same time, the reactance of C1 is getting smaller and smaller and so less of Vin is making it to the op amp.
7) So you've got a situation now where the gain is falling anyway, but now the signal that it's amplifying is also getting smaller.
8) The combined effect is the gain is getting smaller due to the falling reactance of C2, and at the same time the signal being amplified is also getting smaller due to falling reactance C1 so you get a much more pronounced roll off than either effect would have by itself. The reason for having this dual effect is to make a filter with a steep cut off response. This makes it more useful.
9) Conclusion: Low frequencies are passed through this circuit and amplified. Higher frequencies are degraded and attenuated. This is a low pass active filter.

There are many types of much simpler active filter, however the benefits of this arrangement is that at a higher frequency you have the combined efforts of the input circuit and feedback circuit working together to cut into the signal and attenuate it. In simpler filters, its usually just one of of either of these circuits doing that on its own. A more complete and sophisticated understanding is found through a mathematical analysis as in Ron's post but I hope this might give you a practical feel for what's happening and I apologise if for some reason, I have made this more complicated for you.

Try an analysis of how the High pass filter works.

Megamox

 

[Winterstone]

Maybe this will get you started.
https://en.wikipedia.org/wiki/Sallen–Key_topology

According to my experience, WIKIPEDIA can be recommended - as far as active filters/oscillators are concerned - only with some restrictions.
Examples:

"A Sallen–Key filter is a variation on a VCVS filter that uses a unity-gain amplifier"

That`s not correct. The original S&K topology is based on finite gain amplifiers - with unity-gain amplifiers as a special case.
More than that, there are also filters based on the S&K principle with negative gain stages.

"VCVS filters are relatively resilient to component tolerance"

That`s not correct. Exactly the opposite is true. S&K filters have a good (low) sensitivity to the finite gain-bandwidth product of the opamps used - however, a rather large senisitivity to component tolerances.
These properties are in contrast to the well-known multi-feedback topology (MFB), which is rather sensitive to opamp phase excursions but has good tolerance sensitivities.

Thus, for a start to become familiar with filter theory I rather would recommend one of the various textbooks available.