In-Phase Crossover Network Design

Crossover networks whose low- and high-pass outputs sum to unity magnitude, that is, all-pass crossovers, are considered. Of these, the only known designs which have identical phase responses for both low- and high-pass sections, and thus provide optimal polar behavior, are the Linkwitz-Riley squared-Butterworth alignments. This is a most desirable property as the main lobe of the loudspeaker system's output then shows no tilt through the crossover region. It is shown that the Linkwitz-Riley alignments are particular cases of a whole class of all-pass crossovers satisfying this condition. The designer has at his disposal the denominator polynomial of the all-pass transfer function to which the complete crossover network is equivalent. To this extent he has the freedom to trade off frequency response (that is, rolloff) parameters against phase response (that is, group delay) parameters without compromising polar behavior. The Linkwitz-Riley alignments are the frequency-symmetrical cases. These new crossovers, being subtractively derived, represent a variation on the author's delay-derived crossover configuration.