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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!)