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Sallen Key filter

A Sallen and Key filter is a type of active filter, particularly valued for its simplicity. The circuit produces a 2-pole (12dB/octave) lowpass or highpass response using two resistors, two capacitors and a unity-gain buffer amplifier. Higher-order filters can be obtained by cascading two or more stages.

All Sallen and Key filters have a gain of 1 in the passband. They are relatively resilient to component tolerance, although obtaining high Q factor may require extreme component values.

Contents

Low-pass configuration

An example of the low-pass configuration is shown below:


An operational amplifier is used as the buffer here, although an emitter follower is also effective. The cutoff frequency and Q factor are given by the following equations:

F_c = \frac{1}{2\pi\sqrt{R_1R_2C_1C_2}}

Q = \frac{\sqrt{R_1R_2C_1C_2}}{C_2(R_1+R_2)}

So, for example, the above circuit has an Fc of 15.9Khz and a Q of 0.5.

High-pass configuration

An example high-pass filter with an Fc of 72Hz and Q of 0.5 is shown below.


The relevant equations are:

F_c = \frac{1}{2\pi\sqrt{R_1R_2C_1C_2}}

(as before), and

Q = \frac{R_2C_x}{\sqrt{R_1R_2C_1C_2}}

where

C_x = \frac{C_1C_2}{C_1+C_2}


See Also

External link

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