Jon,
"I have to admit to some concern that you "don't suffer fools gladly" when I say what a complete 'fool' I am when it comes to speaker engineering"
Fear not, I'm not at all averse to inquisitive minds and genuine interest. In fact, I welcome constructive debate and discussion. The fools I refer to tend to have an opposite raison d'etre.
"The design of the crossover that you've been going into above - how does that influence the way the crossover actually gets built in practice? Ie. does it affect materials used, the way they are wired together, etc. Also, what is meant by a first-order or second-order crossover, or fourth-order?"
By way of example, a second order crossover has an attenuation rate of 12dB per octave beyond its cutoff frequency, 3rd order is 18dB per octave, 4th order is 24dB per octave, and so on. The point of confusion for most people is that it is the final acoustic crossover that matters. All loudspeaker drivers are passband devices, which means they will naturally roll off at their frequency extremes. So, if a driver is used up to the limits of its flat frequency response, then the effect of its natural roll off combined with any electrical filters in place will yield the actual acoustic attenuation slope.
There are many different slope shapes that, in symmetrical pairs, yield a different phase, acoustic, and power response. I have a preference for Linkwitz-Riley crossovers because they sum flat and if properly implemented maintain phase integrity of the crossover.
To achieve the acoustic transfer target, I have to first measure the native (acoustic and electrical) response of each individual driver in situ on the cabinet, and then use CAD software to model the filter components needed to achieve my design. I also strive to use as few components as possible to preserve the integrity of the musical signal and yet meet my design targets. As a result, the PFM-Special uses a single inductor on the woofer (in concert with natural roll-off) to yield a 2nd order transfer at 500Hz, just two inductors, a single capacitor, and two resistors in the midrange filter to realise a second order LR cross at 500Hz and 3kHz, and a single series capacitor with a resonance trap (resistor, capacitor and inductor in series across the driver) to achieve a second-order LR transfer at 3kHz.
When I'm happy with the result, I will publish the filter circuit here so everyone can see how it all hangs together.
James