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Linkwitz-Riley: A specific type of filtering scheme commonly used in electronic crossover networks. The 4th-order (24 dB/octave slopes) Linkwitz-Riley (LR-4) design has become nearly a de facto standard among professionals in the sound reinforcement community. Consisting of cascaded 2nd-order Butterworth (another filter design) low-pass filters, the LR-4 represents a vast improvement over the previous 3rd-order (18 dB/octave) standard. Named after S. Linkwitz, a Hewlett-Packard engineer, who first described the problems and solution in his paper "Active Crossover Networks for Non-coincident Drivers," J. Audio Eng. Soc., vol. 24, Jan/Feb 1976, pp. 2-8. In this paper, he credited his co-worker Russ Riley for the idea that cascaded Butterworth filters met all his crossover requirements. Their effort became known as the Linkwitz-Riley alignment. Linkwitz showed a significant weakness of the Butterworth design was the behavior of the combined acoustic lobe along the vertical axis, which results when both drivers operate together reproducing the crossover frequency band. In the Butterworth case it exhibits severe peaking and is not on-axis (it tilts toward the lagging driver). Linkwitz showed that this results from the Butterworth outputs not being in-phase. Riley demonstrated an elegant solution by cascading two 2nd-order (any even-ordered pair works) Butterworth filters, which produced outputs that were always in-phase and summed to a constant-voltage response. Thus was created a better crossover.

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