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Q Factor (R&C) - Sallen-Key Filter

`Q = sqrt( R_1 * R_2 * C_1 * C_2 ) / ( C_2 *( R_1 + R_2 ))`
`(R_1)"Resistance 1"`
`(R_2)"Resistance 2"`
`(C_1)"Capacitance 1"`
`(C_2)"Capacitance 2"`

The Sallen-Key Q Factor (R&C)  calculator computes the factor based on the resistances and capacitances. 

INSTRUCTIONS: Choose units and enter the following:

  • (R1) Resistance one
  • (R2) Resistance two
  • (C1) Capacitance one
  • (C2) Capacitance two

Sallen-Key Q Factor (R&C) : The calculator returns the factor.  
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The Math / Science

The Sallen-Key Q Factor (R&C) equation computes the Q factor of the 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 Sallen-Key Q Factor (R&C) formula is:

            `Q = sqrt( R_1*R_2*C_1*C_2 )/(C_2*(R_1+R_2)`

where:

The Q value is critical in determining the eventual shape of the waveform. For example, a second-order Butterworth filter, which has maximally flat passband frequency response, has a Q of 1/`sqrt(2)`.  This is compared to a series of two identical simple low-pass filters having a Q of 1/2.

Sallen-Key Calculators: