Active Filter Gain (MFB)

Formula

Description

The multiple feedback (MFB) topology is a second-order active filter that provides inverted output. Its passband gain is set by the ratio of feedback to input resistor, identical to a simple inverting amplifier. The MFB topology uses five components (two resistors and three capacitors, or three resistors and two capacitors) to implement a complete second-order filter section with independent control of gain, cutoff frequency, and Q factor. It has lower sensitivity to op-amp gain-bandwidth limitations compared to Sallen-Key at high Q values.

Variables

• Gain — Passband voltage gain (negative, indicating inversion)
• Rf — Feedback resistor (Ω)
• Ri — Input resistor (Ω)

Practical Notes

MFB advantages: lower component sensitivity at high Q, better high-frequency stopband rejection, gain and frequency can be independently tuned. Disadvantages: inverting output, higher component count than Sallen-Key, requires matched component values for proper response shape. MFB is preferred for bandpass filters where Q > 5.