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

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.  

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:

• Q is Sallen-Key Q Factor (R&C) 
• R₁ is a resistance
• R₂ is a resistance
• C₁ is a capacitance
• C₂ is a capacitance

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:

• 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)