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Sensitivity of High Order Loudspeaker Crossover Networks with All Pass Response

The sensitivity of high-order filter networks to component matching-tolerances increases with filter order. For an audio loudspeaker's crossover network that is designed to sum to an all pass network, we demonstrate that the sensitivity to component matching tolerances may be dwarfed by sensitivities to other effects. We examine second- to eighth-order Linkwitz-Riley crossovers. The analysis also subsumes networks with transmission zeros and optimized networks where the effects of frequency-response errors introduced by the driver's respective transfer functions are minimized. We remark on crossover networks that are least sensitive to the combined effects of component tolerances, path-delay effects, the interaction of filter sections in speakers that divide the incoming signal into three or more sub-bands, and driver transfer functions.

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