Active filter stages having two (usually complex) poles and two (usually complex) zeroes can be very useful in applications such in active loudspeakers for correcting or extending the bass response of a woofer or for correcting for the roll-off of the tweeter in an active crossover circuit. A well-known circuit in this category is the Linkwitz transform: versatile, and the equations to calculate the component values are relatively simple. The disadvantage is that it needs four capacitors to realise two poles and two zeroes, although theoretically, only two capacitors are needed to make a two-pole, two-zero circuit. The capacitors typically have non-standard values, which means that in practice they may have to be constructed from series or parallel connections of capacitors. A State Variable filter can be made with only two capacitors with standard values, but the number of operational amplifiers in the circuit is relatively high. In this article, a modified Sallen and Key filter is proposed as a bass extending correction filter with two poles and two zeroes. It can be constructed with two capacitors with standard values. The active part is only a voltage follower. Tweeter response correction can be done with a filter based on an inverting second-order low-pass. One Annex explains how to find the poles of a speaker system and another Annex gives a crash course in Circuit Analysis.
Simple Loudspeaker Correction Filters