Linkwitz Filters

An analysis by Siegfried Linkwitz in the January 1976 issue of the Journal of the Audio Engineering Society shows that conventional cross-over filters have a negative effect on the radiation pattern of a multi-way loudspeaker system as regards both directivity and amplitude. On the basis of his research, Linkwitz proposed a new type of network that gives a uniform radiation pattern and constant amplitude. This filter, which is essentially a Butterworth-de- rived type, was first described by Riley and is, therefore, some- times referred to as a Linkwitz- Riley network. For simplicity"s sake, the follow- ing discussion is based on a two-way loudspeaker system. For optimum results, Linkwitz suggested that the filter must meet three requirements: • there must be no phase shift between the outputs of the loudspeakers at the relevant cross-over frequency to pre- vent an upward or downward displacement of the radi- ation pattern; • the signal attenuation at each filter output must be...