So, I don't even know what JHA is. Also I just noticed that this post was from two years ago, but I made an account to reply to this so I'm just gonna do it. EDIT: I also realized GoodbVibes is basically saying what I'm saying. I won't get upset if the mods take this down as I'm not adding any new information.
Since we want to not bother with petty semantics: crossovers are circuits. That's it. They're a couple of low/high/band-pass filters of varying order depending on the design. They are not "special" compared to any other filtering circuit. Like I said, I don't know what JHA is. It's not even fair to say I'm any kind of audiophile. I like good-sounding setups, but I'm nowhere near any "real" audiophile level.
In electrical engineering, circuits which feature ONLY PASSIVE components are called passive circuits. Circuits which feature ANY ACTIVE components -- namely transistors or diodes -- are called ACTIVE circuits. Suggesting that an active circuit features ONLY active components is ludicrous...an operational amplifier on its own is FULL of resistors which are PASSIVE components, paired in different configurations with a bunch of transistors.
Any crossover circuit which features any active components is an active crossover circuit. The ONLY way for something to be a passive crossover is for it to not have any active components. Crossovers on unpowered speakers, for example, are passive, otherwise you would need to feed external power to the speaker in order for it to function correctly.
While I'm on this topic, active does NOT imply digital. Not even a little bit. Yeah, you can have a digital setup, and since any kind of digital processing takes place on an IC full of transistors this means it would definitely be "active," but "active" on its own has NOTHING to do with analog or digital. Active filters are often analog circuits. Actually, filters and amplifiers, especially when you need them for very sensitive applications, are some of the main reasons why analog circuit design continues to be a highly active area of EE despite the huge amount of popularity in digital. Generally there are a lot fewer people doing analog, and those people tend to get paid a lot, because they're absolutely necessary and the topic can be quite difficult.