Multiple Feedback Active Low-Pass Filter

Schematic


Calculator

 f   Hz 
 Q   
|h|   
 R1    Ω
 R2    Ω
 R3    Ω
 C1    F
 C2    F
mflpf — (c) 2024 Takayuki HOSODA

Transfer function

T(s) &=& -\frac{R_2}{R_1} \frac{\displaystyle\frac{1}{C_1 C_2 R_2 R_3} }{ \displaystyle s^2 + sC_1 \left(\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \right) + \frac{1}{C_1 C_2 R_2 R_3}}\\ h &=&- \frac{R_2}{R_1}\\ \omega_0 &=& \frac{1}{ \sqrt{C_1 C_2 R_2 R_3}}\qquad | \quad \omega_0 = 2 \pi f\\ Q &=& \sqrt{ \frac{C_1}{C_2}} \frac{1}{\left(\displaystyle\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \right) \sqrt{R_2 R_3}}

Note

The ratio of C1 / C2 is minimized when 1 / R1 + 1 / R2 = 1 / R3.
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