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Sallen-Key Unity Gain Low Pass Filter - Transfer Function (R&C)

$H(s) = (1/(sqrt( R_1 R_2 C_1 C_2 )))^2 / ( "s" ^2 + 2 alpha "s" + (1/(sqrt( R_1 R_2 C_1 C_2 )))^2)$

$(R_1)"Resistance 1"$

$(R_2)"Resistance 2"$

$(C_1)"Capacitance 1"$

$(C_2)"Capacitance 2"$

$(alpha)"Attenuation"$

$(s)"Complex Angular Frequency"$

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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.

The angular frequency term in this equation is derived from the Resistances and Capacitances ( $R_1, R_2, C_1, C_2$ ) shown in the diagram.

/attachments/344ed8e3-3d39-11e3-83ad-bc764e049c3d/SallenKeyUnityGainLowPassFilterTransferFunctionRC-illustration.png

Sallen-Key Calculators: