Sallen-Key low-pass filter ($G(s)=K/[1+as+b{s}^2]$)

A second-order active low-pass architecture using a non-inverting amplifier and a resistor-capacitor network with output feedback into the network. For the convention with $R_1$ from source to A, $R_2$ from A to the non-inverting input, $C_2$ from that input to ground and $C_1$ from A to output, $a=C_1{R}_1(1-K)+C_2(R_1+R_2)$ and $b=R_1{R}_2{C}_1{C}_2$. The poles, not merely finite values of $G(i\omega )$, determine whether a settled sinusoidal response exists.^[ref]

For equal frequency-setting resistors $R$ and capacitors $C$, write $\tau =RC$. The denominator is $1+(3-K)s\tau +s^2{\tau }^2$. With positive $\tau$, asymptotic stability requires $K<3$; at $K=3$ the ideal poles are imaginary, and larger gain gives right-half-plane poles. In particular $K=5$ gives $(1-s\tau {)}^2$, a repeated unstable pole. A finite formal gain curve must not be confused with stable filter operation.