Consider traditional two-way speaker system comprising a woofer and a tweeter. We're going to build a crossover for these drivers. Assume the measurement has been done and the crossover point of 2.5kHz was chosen. There are two choices here for an educational purpose: 12dB/octave with reversing polarity of the tweeter and 24dB/octave without reversing polarity. Goal for these two choices is to imply ASSUMING two drivers are perfectly "in-phase" with each other--any phase issues will not be taken into account. As a result the frequency response of the speaker system will also be assumed FLAT. The only difference presented on the amplitude curve are the slope rates of all drivers between 12dB/octave and 24dB/octave. The most important part is it's obvious that the 12dB/octave will create larger overlapping area and vice versa for the 24dB/octave. Despite flat frequency response curve and theoretically correct phase behavior, which way do you prefer between having large overlap (12dB/octave) or less overlap (24dB/octave)? And please give some supporting reasons.
Cr. for picture: RANE Corporation
Cr. for picture: RANE Corporation
I don't have a preference, and think it pretty much depends on the drivers used, and the intended use of the speaker. Power handling for the tweeter is a factor. Woofer breakup is a factor. Big peaks, or dips in the driver responses would be a factor. Sometimes a flaw in one driver forces a steeper x-over on both. With all that said, my current speakers have shallow roll-offs, and I think they are the best I've made. The drivers are smooth, and I could have used steep filters if I wanted. In fact, I tried many x-overs before settling on the final one.
Traditionally, the woofer and a tweeter are purpose built for their respective bandwidths.
The assumption the drivers are perfectly "in-phase" with each other requires they have flat frequency response at least an octave outside the crossover point, the woofer having flat response to 5kHz, tweeter 1.25kHz.
Four times the displacement (excursion) is required for each halving of frequency to maintain the same level.
Using your assumptions, a 12dB/octave crossover still allows a 6dB excursion "buffer", traditionally enough to keep tweeter excursion relatively low.
That said, further reduction of tweeter excursion will reduce it's intermodulation distortion (IMD), which improves sound quality as excursion limits are approached or exceeded at high peak levels.
The reduction in IMD using a 24dB/octave crossover may offset the additional crossover component cost for high level use, or allow the use of smaller tweeters with less excursion that tend to have lower mass, better transient response, and wider dispersion.
The wider overlap of the 12dB/octave crossover increases the frequency range of the off axis peaks and dips due to driver center to center spacing, another drawback tending to favor 24dB/octave crossovers if a wide vertical listening angle is required or desired.
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