(...)The odd-order Butterworth crossover networks have a constant
interdriver phase difference of 90 ° independent of frequency
and thus are ideal for the (3,2) driver configuration when
smooth off-axis response is desired. As shown in Fig. 3 this
class of networks produces a polar response ripple of only
3 dB at Wc, which is substantially more uniform than that of
the Linkwitz-Riley or symmetric constant voltages crossovers.
Polar response variations through the crossover region
obtained with the (3,2) driver configuration are shown in
Figs. 5, 6 and 7, respectively for three popular crossover
networks; the first- and third-order Butterworth crossovers
and the fourth-order Linkwitz-Riley (LR4) network. The firstorder
Butterworth crossover, which is also a constant voltage
network, exhibits exceptionally smooth off-axis response through
the crossover region. The third-order Butterworth response is
also relatively smooth. The character of the off-axis response
obtained with the LR 4 filter, however, changes sharply through
the crossover region. In the octave below w c the LR4 crossover
displays an off-axis null in the 35°-40 ° region. Above wc the
polar response transitions to omnidirectional, but not as quickly
as with the Butterworth crossovers. Given the steeper slope
of the LR 4 crossover, the slower transition to omnidirectional
response is unexpected. It is, however, a direct consequence
of the (3,2) geometry. (...)