Sallen-Key Unity Gain Low Pass Filter - Transfer Function (f0)

$H(s) = (2 pi f_0 )^2 / ( "s" ^2 + 2 alpha "s" + (2 pi f_0 )^2)$

$(alpha)"Attenuation"$

$(s)"Complex Angular Frequency"$

$(f_0)"Undampened Natural Frequency"$

Tags

This equation computes the transfer function H(s) for a unity gain low pass filter implementation of the Sallen-Key topology. This electronic filter is a special case of a second-order unity gain filter version of the voltage-controlled voltage-source (VCVS) topology.

In this equation the angular frequency $omega_0$ is replaced by a function of undamped natural frequency $f_0$ .

$omega_0$ = 2 $pi f_0$

/attachments/273072ea-3d41-11e3-83ad-bc764e049c3d/SallenKeyUnityGainLowPassFilterTransferFunctionf0-illustration.png

Sallen-Key Calculators:

Sallen-Key α filter
Sallen-Key Q Factor (ω₀ ,α)
Sallen-Key Q Factor (R&C)
Sallen-Key Unity Gain Low Pass Filter - Transfer Function
Sallen-Key Unity Gain Low Pass Filter - Transfer Function (f0)
Sallen-Key Unity Gain Low Pass Filter - Transfer Function (R&C)