Multifeedback Filter

Introduction¶

The multiple feedback (MFB) or multi-feedback filter is a widely used configuration that employs a modified inverting op-amp to realize a second-order filter. Its transfer function is more sensitive to the op-amp’s characteristics compared to the Sallen-Key design. Because it does not use positive feedback (as in the Sallen-Key filter), achieving high-Q and high-frequency filter sections with the same op-amp becomes more challenging.

Multiple Feedback Calculator

Multi-feedback filter low-pass filter¶

$$\cfrac{V_o}{V_i}=\cfrac{\cfrac{1}{R_1R_3C_2C_1}}{s^2+s\cfrac{1}{C_2}\left(\cfrac{1}{R_1}+\cfrac{1}{R_3}+\cfrac{1}{R_2}\right)+\cfrac{1}{R_3R_2C_2C_1}}$$

Multi-feedback filter high-pass filter¶

$$\cfrac{V_o}{V_i}=\cfrac{-s^2\cfrac{C_1}{C_2}}{s^2+s\cfrac{(C_1+C_3+C_2)}{C_3C_2CR_1}+\cfrac{1}{R_2R_1C_3C_2}}$$

Multi-feedback filter band-pass filter¶

$$\cfrac{V_o}{V_i}=\cfrac{-s\cfrac{1}{R_1C_2}}{s^2+s\cfrac{(C_1+C_2)}{C_1C_2CR_2}+\cfrac{1}{R_2C_1C_2}\left(\cfrac{1}{R_1}+\cfrac{1}{R_3}\right)}$$

Proporties of Multi-feedback filters¶

Stability advantage of multifeedback filters¶

Due to presence of feedback capacitors and absence of positive feedback, multifeedback filters are inherently more stable than Sallen-key filters. The feedback capacitors are C₁ in low-pass filter, C₂C₃/(C₂+C₃) in high-pass filter, C₂C₁/(C₂+C₁) in band-pass filter.

Distortion benefits of multifeedback filters¶

The distortion performance of Multifeedback filters are better than Sallen-Key filters because there is no large signal voltage swing at the input of the opamp in the former. This avoids common mode nonlinearity exertion. In custom designs, choosing a multifeedback filter architecture can relax the choice of opamp design because input swing is almost zero.

Hardware sensitivity¶

The multi-feedback filters are sensitive to opamp properties like finite gain-bandwidth product frequency, open-loop gain etc. However, the sensitivity towards the passive components like capacitor, resistors is less. Multifeedback filters are used widely used in applications where Q is less than 20.

In contrast, Sallen-Key filters have lesser sensitivity towards opamp's properties while higher sensitivity towards passives.