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In-Phase Crossover Network Design

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We consider crossover networks whose low- and high-pass outputs sum to unity magnitude, i.e., all-pass crossovers. 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. We show 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 (i.e., roll-off) parameters against phase response (i.e., 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 authors' delay-derived crossover configuration.

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