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likephysics
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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?
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.
A Sallen-Key filter is a type of active filter used in electronic circuits to filter out specific frequencies. It is commonly used as a low-pass filter, meaning it allows low frequencies to pass through while attenuating high frequencies.
A Sallen-Key filter uses an op-amp and a combination of resistors and capacitors to create a frequency-dependent voltage divider. The values of the components determine the cutoff frequency and attenuation of the filter. The op-amp amplifies the output signal, providing a high-pass or low-pass response depending on the configuration of the filter.
The bootstrap capacitor is used in a Sallen-Key filter to improve the stability and reduce distortion of the filter. It helps to isolate the input and output signals, resulting in a cleaner output signal with less distortion. It also helps to increase the gain bandwidth of the filter.
Sallen-Key filters have several advantages, including high input impedance, low output impedance, and a simple design that can be easily modified for different frequencies. They also have a relatively flat response and good attenuation of high frequencies.
Sallen-Key filters are commonly used in audio equipment, such as amplifiers and equalizers, to filter out unwanted frequencies and improve the quality of the sound. They are also used in communication systems, signal processing, and instrumentation circuits.