(The Linkwitz-Riley
filter has a crossover frequency where the output of each filter is 6dB down, and this
has the advantage of a zero rise in output at the crossover frequency.)
Second-order Linkwitz-Riley crossovers (LR2) have a 12 dB/octave (40 dB/decade) slope.
They can be realized by cascading two one-pole filters, or using a Sallen Key filter
topology with a Q value of 0.5.
There is a 180° phase difference between the lowpass and highpass output of the filter,
which can be corrected by
inverting one signal. In loudspeakers this is usually done by reversing the polarity of
one driver if the crossover is passive.

Bessel filter

( Maximally flat phase, Fastest settling time, Q:
0.5
to 0.7 (typ) )
A Bessel filter is a type of linear filter with a maximally flat group delay (maximally
linear phase response).
Bessel filters are often used in audio crossover systems. Analog Bessel filters are
characterized by almost constant
group delay across the entire passband, thus preserving the wave shape of filtered
signals in the passband.

Butterworth filter

( Maximally flat amplitude, Q: 0.707
)
The Butterworth filter is a type of signal processing filter designed to have as flat a
frequency response as
possible in the passband. It is also referred to as a maximally flat magnitude filter.

Chebyshev filters

( Fastest rolloff, Slight peaks / dips, Q: 0.8
to
1.2 (typ) )
Chebyshev filters are classified by the amount of ripple in the passband, for example a
1 dB Chebyshev low-pass
filter is one with a magnitude response ripple of 1 dB. Chebyshev filters are popular
because they offer steeper
roll-off rates than Butterworth filters for the same order, but for audio applications
the Chebyshev is virtually
never seen due to the superior magnitude and phase responses of the Butterworth class.