High Pass Filter Design Equations
The Sallen- Key filter is a very popular active filter which can be used to create 2nd order filter stages that can be cascaded together to form larger order filters. The op-amp provides buffering between filter stages, so that each stage can be designed independently of the others. These circuits are suitable for filters which have complex conjugate poles.
When implementing a particular transfer function, a designer will typically find all of the poles, and group them into real poles and complex conjugate pairs. Each of the complex conjugate pole pares are then implemented with a Sallen-Key filter, and the circuits are cascaded together to form the complete filter.
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The transfer function for a low pass unity gain Sallen-Key filter is:
The derivation for this can be found at:
We can transform any low pass active filter to a high pass filter with the following substitutions:
Thus, the transfer function for a unity gain high pass Sallen-Key filter is:
From which we can derive:
If we set C1=C2=C, then
Solving for R1 and R2:
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