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Sallen-Key Filter
One of the most popular op-amp filter circuits is the Sallen-Key circuit. The main reason for its popularity is that is uses only a single op-amp and 4 external components to achieve a 4-pole filter.
Low-Pass Circuit
The diagram below shows the low-pass version of the Sallen-Key.
The transfer function of this circuit is:
Where
Solving this equation for we get:
and:
High-Pass Circuit
The diagram below shows the high-pass version of the Sallen-Key.
The transfer function of this circuit is:
Solving this equation for we get:
and:
The same results as with the low-pass version. (Another reason why this is such a popular topology!)