the multiple-feedback filter

The multiple-feedback filter, MFB, is the other workhorse second-order section, the inverting cousin of the Sallen-Key. Where Sallen-Key uses the non-inverting input, MFB builds its filter around the op-amp's inverting input and virtual ground, with two feedback paths (hence the name) wrapping the components. It tends to be cleaner at high Q and a popular choice for band-pass sections.

The signal enters through resistors and capacitors into the inverting input, which the op-amp holds at a virtual ground. Because that node sits at a fixed near-zero voltage, the components see well-defined currents, and two separate feedback elements, typically a resistor and a capacitor from output back to the node, shape a second-order response. The output is inverted (it has a sign flip), the gain, cutoff, and Q are all set by the resistor and capacitor values, and there is no signal feed-through problem at high frequencies because everything funnels through the virtual ground.

MFB shines for band-pass filters and for high-Q sections where Sallen-Key gets fussy; it also gives better deep-stopband rejection because it has no direct input-to-output path. Its honest tradeoffs: it inverts the signal, it loads the source more (the input resistor is part of the gain), and it demands an op-amp with enough loop gain and bandwidth at the filter frequency, otherwise the op-amp's own roll-off corrupts the response. For very high Q you still move up to the state-variable topology, which controls Q, frequency, and gain almost independently.