Originally Posted by ephilo
First, a simple warm-up question.
1. What does second
order roll-off mean?
The order and type of a filter specifies the shape of the filter's response.
All other things being equal, higher order suggests steeper slopes in the transition band. A filter of this kind has three bands - the pass band, the rejection band, and the transition band. The usual ideal is for the pass band to be flat, the rejection band to be very low, and the transition band to be narrow.
In speaker crossovers there is an additional system goal, which is for the merged frequency response of both speakers to sum to be smooth and flat both on-axis and off-axis. Non-flat pass band response and a non-ideal transition band can and have been used to achieve this goal.
What is missing from your sentence is the type of filter, such as Butterworth, elliptical, Bessel, Chebyshev, etc.
Suppose I would put the the roll-off at 80 Hz. I understood this would mean that the mains would not play frequencies below 80 Hz. So my next question is that, as the speaker manufacturers usually tell the frequency bandwidth the speaker is capable of (e.g. 48 Hz - 20kHz), what should the lower end of the speaker optimally be if the roll-off is at 80 Hz?
80 Hz or less.
Would it suffice to have 80 Hz or should the speaker in any case be capable of going down to, say, 50 Hz? If yes, why?
Good question. It is fair play to use a speaker down to its lower bandpass if it has good dynamic range and low distortion down to that frequency, which many modern speakers accomplish.
You see the speakers act like filters that add to the filters in the crossover. There are two simple condtions:
(1) The main speaker's lower bandpass is the same as that of the crossover and the two add together in reasonable way to produce a desirable filter characteristic that matches well with the subwoofer.
(2) The main speakers respond well down to a frequency that is significantly lower than the crossover frequency, and therefore this roll-off has little or nor effect on the crossover point. This is hard to achieve because the main speakers would need to go down an octave or more further than the crossover frequency, ideally several octaves (2 octaves below 80 Hz is 20 Hz)
The third case is messy, where the crossover and the speakers both roll off within the same octave and they interact. This is also the usual case. ;-( The good news is that the ear is less discerning at frequencies this low, and the room is probably contributing some issues of its own. This mess may be less significant than other messes that are going on at the same time.
It seems quite difficult to find ~$1,000-1,500 main speakers which have the lowest reported frequency above 40 Hz. So would I end up paying for the bass response in any case if I upgrade my mains at some point?
I don't know what you are talking about. I quickly pulled up this reviews of several high quality speakers inccluding some from Paradigm in that price range that went down to 40 Hz in a typical listening room setting. I also found some cheaper alternatives that at least looked good on paper such as the larger members of the Infiinty Primus Series.
I have also been wondering how does this "active crossover" really works. Does it just mean that the amp sends everything below, say, 80 Hz to the subwoofer and everything above to the other speakers?
r does the amp somehow dynamically decide what is sent to which speakers? If the process is somehow dynamic, I would think that there are differences between amps how they do this? If this is the case, how big are the differences between the amps (i.e. should I consider upgrading my amp at some point, too)?
Your imagination has run away with you. ;-) Crossovers are static, you set them and they stay that way, devices.
I've seen dynamic filters used to control the low end of speakers, which in this case would be your subwoofer. But if you think about matching between the mains and the subs, there is very little advantage to a dynamic filter here.