Topic No. 3

Linkwitz-Riley Crossovers
by
John L. Murphy
Physicist/Audio Engineer

2nd Order Linkwitz Crossover

This 12 dB per octave crossover is designed to solve the problem of centering the main lobe of the forward radiation pattern of a two-way speaker system. . This crossover is unusual in that each filter is down 6 dB at crossover and that the two drivers are actually "in phase" at all frequencies when the drivers are wired in opposite polarity. That is, even though the filters have their own characteristic phase responses the phase difference between the two output signals is the same at all frequencies. As a result, each filter section has the same group delay. This crossover is recommended over the 2nd order Butterworth type due to its accurate summed frequency response and forward pointing main lobe. Inverted polarity is required for one of the drivers.

4th Order Linkwitz Crossover

This complex 24 dB per octave crossover is designed to solve the problem of centering the main lobe of the forward radiation pattern of a two-way speaker system. This crossover is unusual in that each filter is down 6 dB at crossover and that the two drivers are actually "in phase" at all frequencies. That is, even though the filters have their own characteristic phase responses the phase difference between the two output signals is the same at all frequencies. As a result, each filter section has the same group delay. This crossover is recommended over the 4th order Butterworth due to its superior summed frequency response and lobing characteristics. Both drivers are wired with similar polarity.

In general, Linkwitz-Riley crossovers can be constructed in all even orders, that is 2nd, 4th, 6th, 8th order and so on. This filter family is also referred to as a "Butterworth Squared" crossover because it is equivalent to two Butterworth sections in series. That is, two identical 1st order Butterworth filters in series make a 2nd order Linkwitz filter. Two 2nd order Butterworth filters make a 4th order Linkwitz filter, and so on. The individual Butterworth filters are down 3 dB at crossover, where the Linkwitz filters are down 6 dB at crossover.

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For more detail on the Linkwitz (aka Linkwitz-Riley) crossovers see:

Linkwitz, Seigfried H, "Active Crossover Networks for Noncoincident Drivers",
J. Audio Eng. Soc., Vol.24, No. 1, pp. 2-8 (Jan/Feb 1976)

Linkwitz, Seigfried H, "Passive Crossover Networks for Noncoincident Drivers",
J. Audio Eng. Soc., Vol.26, No. 3, pp. 149-150 (Mar 1978)