The discussion revolves around understanding the Sallen-Key low-pass filter (LPF) configuration, specifically focusing on the role of feedback through a capacitor and the concept of bootstrapping. Participants explore the theoretical and practical aspects of the filter's design and operation.
Participants do not reach a consensus on the understanding of bootstrapping or the implications of feedback in the Sallen-Key filter. Multiple competing views and interpretations remain, particularly regarding the necessity and effects of positive feedback in the circuit.
Limitations include potential misunderstandings of terminology (e.g., "bootstrap") and the complexity of the mathematical analysis required to fully grasp the circuit's behavior. There are unresolved questions about the specific configurations of components and their impact on filter performance.
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.likephysics said: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?
yungman said:
likephysics said:I read the wiki before posting. Doesn't say much about bootstrapping.
Instead of connecting Z4 to ground, it's connected to opamp output. How would one come up with this idea?
yungman said:
likephysics said:I read the wiki before posting. Doesn't say much about bootstrapping.
Instead of connecting Z3 to ground, it's connected to opamp output. How would one come up with this idea?
rbj said: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.
likephysics said:Instead of connecting Z4 to ground, it's connected to opamp output. How would one come up with this idea?
yungman said:What do you mean by "i corrected Z4 to Z3"?
rbj said:if Z3 was connected to ground like Z4, there would be no "positive feedback" (is that what you mean by "bootstrapping"?). when this circuit is used as a LPF (and Z3 and Z4 were capacitors), you could not get a high enough Q to have any resonance, without positive feedback.
a way to understand the circuit is just 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, solve 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.