The laws of physics make perfection an impossibility. We can approach perfection by degrees, but the very nature of the planet we live on and the universe it’s floating around in force us to make constantly make compromises. Nowhere is this more true than in the audio world.
Crossovers are necessary to ensure that frequencies are sent to the driver best suited to them. Think of a crossover as a frequency gate – a woofer doesn’t reproduce mids and highs very well, so a low-pass filter stops those frequencies from going to the woofer. This is the job of a crossover, except it doesn’t operate as a gate because of the time shift, slope and phase delay introduced by the crossover network itself.
A perfect crossover is a driver that reproduces all frequencies equally well; by that definition because of the laws of physics, there can be no such thing as a perfect crossover. The next best solution is multiple speakers producing sound from the same point with no time shift between the drivers. As soon as we place drivers in different locations, we introduce a time shift – physics again.
Active crossover networks, in particular the Linkwitz-Riley 4th order active, and DSP-based crossovers eliminate a lot of the constraints Mother Nature places on audio filtering, but they are also far more complicated than we can cover in a short Blog article. In fact, crossovers in general are a bit too deep for just a quick Internet read so we’ll stick with just the basics.
Crossovers are generally specified by order number. The order number is derived from the amount of filters used in the circuit. A first order crossover has a single filter consisting of one inductor and one capacitor. A first order crossover introduces a minimal amount of time shift to the signal, but it also only rolls off the frequency by -6dB per octave. This means there is a lot of mixing of frequencies near the crossover point between the drivers the filter is operating with.
A second order crossover uses a double filter, and a third order uses a triple filter and so on. A second order crossover produces a -12dB roll-off, a third produces a -18dB roll-off. The slope (roll-off) increases by -6dB with each increase in order. A -12dB frequency roll-off is pretty good in terms of frequency mixing between drivers, but it introduces more time shift.
Everything is a compromise.
Loudspeaker designers also use the cabinet design and placement of the drivers to assist or compensate for the crossovers. A first order crossover, because of its gradual -6dB slope, introduces a lot of mix between low and mid frequency drivers (for example), so a cabinet designer may place the midrange slightly behind the low frequency driver to compensate for the phase shift between the frequencies. You can see that this will all become very sloppy and/or complicated if not done properly.
In short, the crossover and the cabinet must be designed to work with each other in a complementary fashion. With a driver array like the Uni-Q in the design, things like time-shift are mitigated, allowing our engineers more freedom with our crossover designs.
There is no “best” crossover. The type of crossover used in a loudspeaker depends on a lot of factors: cabinet design, driver array, etc. The quality of the components in a passive crossover, and the overall design standard are also critical for proper performance.
The Maximally Flat Magnitude Filter (commonly referred to as the Butterworth Filter which is much easier and more fun to say), solved the problem of uniform response in a filter network. First described in the early 1930s by British mathematician Stephen Butterworth, this type of filter rejects the unwanted frequencies but also produces as close to a flat response among the pass-band frequencies as we’ve been able to (feasibly) achieve so far. The Butterworth requires a higher order because of its relatively shallow roll-off, but benefits from a mostly linear phase within the passband.
The Chebyshev Filter, named after 19th Century Russian mathematician Pafnuty Chebyshev, has a much steeper roll-off than a Butterworth but the trade-off is a non-liner response in the passband.
Everything is a compromise. And the best compromise so far is the Butterworth in the passive realm, and the Linkwitz-Riley in the active realm – this type of filter is extremely complicated and expensive to implement in passive systems, but it the de facto standard in active filters, especially in the pro-audio world.
So, there’s over seven hundred words on crossovers and we barely discussed anything about how they do what they do. The biggest take-away from this should be that a first order crossover is not necessarily better than a third order (and vice-versa) so you shouldn’t judge a loudspeaker’s performance on just crossover order alone – there are a ton of other factors at play.