# Sallen-key filter

1. Jun 2, 2012

### likephysics

Trying to understand how sallen key LPF works. But I can't figure out why there is a feedback path from op amp output to input thru a capacitor. Is it a bootstrap cap. What exactly is bootstrap?

2. Jun 2, 2012

3. Jun 2, 2012

### Staff: Mentor

The Sallen and Key configuration is not for creating an amplifier. It's a particular arrangement to realize the second order system which performs the general filter function. Without that capacitor, the block would not have the desired transfer function. As frequency goes up, there is more feedback through the capacitor, thereby reducing the gain with increasing frequency: a filter characteristic.

4. Jun 2, 2012

### likephysics

Instead of connecting Z4 to ground, it's connected to opamp output. How would one come up with this idea?

5. Jun 2, 2012

### yungman

I find these kind of filter is quite complicate to be explained in simple terms. You notice the cap feedback from output to the junction that eventually driving the +ve input. It is some sort of positive feedback. Obvious it work with the RC low pass section to prevent the possible oscillation due to positive feedback. It is a balance dance of values. I had tried to adjust the amount of feedback from the output of the opamp and easily get into oscillation if just a little too much feedback.

Bottom line, it is not going to be apparent, and that's the reason a lot of people ( ME!!!) just use the circuit and concentrate on adjust the "d" of the circuit to get the right characteristics. If you really insist on understanding everything, go through the math step by step and see what happen.

6. Jun 2, 2012

### rbj

i corrected "Z4" to "Z3" as indicated in http://en.wikipedia.org/wiki/Sallen–Key_topology#Generic_Sallen.E2.80.93Key_topology

Z3 was connected to ground like Z4, there would be no "positive feedback" (is that what you mean by "bootstrapping"?). without positive feedback, if the circuit were to be used as a LPF (and Z3 and Z4 were capacitors), you could not get a high enough Q to have any resonance.

i way to understand the circuit is to solve it. represent the non-inverting op-amp circuit as an ideal voltage-controlled voltage source. apply KCL to the node that Z1, Z2, and Z3 are connected to. apply a voltage-divider on the node with Z2 and Z4 and the + terminal of the op-amp (which becomes the reference voltage for the voltage-controlled voltage sour). two equations, two unknowns and you can see how the transfer function comes out.

if you want, do it again, but with Z3 connected to ground and see what you get (not any different than a passive circuit and it will have a limit to the Q.

7. Jun 2, 2012

### yungman

What do you mean by "i corrected Z4 to Z3"?

8. Jun 3, 2012

### rbj

Z4 is connected to ground and it is not connected to the op-amp output. but the question makes perfect sense if "Z4" is changed to "Z3".

but i still don't know what like means by "bootstrap". i am presuming it means positive feedback.

sorry folks, but i didn't proofread this. some sentences were not complete. it's too late to edit it, so i am quoting it with corrections:

Last edited: Jun 3, 2012