Tim, congratulations on wanting to learn the art of passive crossover design. I've never seen a good tutorial on this subject, but I would be happy to give you some pointers. You might know a lot of this, but it has taken me years to learn what I know. Others at ASR know much more than me but hopefully I can help.
The first thing you need to understand is that passive filters are expensive and take up space. As a result, we need to be judicious about what we choose to correct and what we do not. The crossover you created would be really large and difficult to even fit in the box.
If you look at crossovers of even fairly expensive speakers, you will notice they tend to be simple. It's rare to see a bunch of RLC notch filters in a commercial speaker, for example. A passive filter is an economical and convenient thing, but if done correctly, it can achieve very high quality.
Tips:
-First, correct the big things first and then move to smaller stuff. The most important component by far is the first inductor in the woofer circuit. I managed to get a decent LR4 response using one coil and one cap.
-See what the drivers want to do. Work with the existing roll-off of the drivers. Avoid their troubled zones rather than trying to correct them. Generally, a second order roll off is tricky but doable. Fourth order is generally quite easy. Jeff Bagby was the master at this in the DIY sphere. He has many designs where he got immaculate responses out of only a handful of components:
-Our CAD software shows us the response all the way to -50db. Irregularity at this low a level in the stop band of a driver will not impact the final response that much. It's okay for your response to deviate from your target line at this low level. Focus on getting the response correct in the 0 to -20 region.
-Don't over-correct. If you have a particularly egregious resonance, by all means address it, but these drivers are quite smooth and operating in their pistonic comfort zone. Not a lot of resonance or breakup mitigation is needed.
- If you have polar data like this, the phase window isn't that meaningful. It only shows phase in the design axis, and the only reason why getting your drivers to play in phase at the crossover frequency is important is that if they are very much out of phase on axis, they will be very much IN phase at some other point in space, indicating a peak off axis. You will see this in the sonogram chart.
- Imitate other people's crossover filters. As I mentioned, manufacturers' filters are cost constrained and typically do the bare minimum, so skilled DIYers are the place to look. See crossovers by Jeff Bagby, Troels Graveson, Speakerdesignworks and AudioExcite for good examples.
- The basic order for crossover components is, for a woofer, a series coil, then a parallel cap, then another coil and so on to get the slope you need. For a tweeter, it is the same but reversed - series cap, parallel coils. Then you can put notch filters if needed (and many designers use them only sparingly) The first component in that sequence is the most impactful. I like to add resistors to bring down tweeter level after all the main components. Experiment with using one series resistor or using a voltage divider like I did in my LR4 design. Midrange drivers are much trickier to design filters for since they have a lot of components which interact, and tend to be expensive as well, requiring big capacitors. Avoid designing a passive 3 way as a first project.
- If your woofer has a hump in the response and you want to bring down a large region, you can turn the first coil into a sort of notch. See my LR2 design - the first coil has a resistor and cap below it. This brings some notch-like behavior to what is the primary low pass coil.
- Passive crossovers should be elegant. It is very easy for a pair of passive crossovers to have so many components that they exceed the cost of a minidsp. If you get to that point, the passive crossover starts to make less sense. Don't be afraid to turn on 1/3 octave smoothing sometimes to see if the overall trend of your speaker is correct - small blips can obscure the big picture.
- Impedance is a complicated subject, but low impedance issues are caused by the fact that at any given frequency, the impedance is the result of the combination of your tweeter and woofer impedance. Maybe that's obvious, but let's break that down.
The purifi woofer has an impedance which dips down to 4 ohms between 200 and say 400 hz by itself. The impedance of the naked tweeter at 200hz is 6.2 ohms. To calculate the total impedance of the un-filtered drivers playing together, just add them like you would add resistors in parallel (hence the name parallel crossover):
1/R(Total) = 1/R1 + 1/R2 + 1/R3
If you do the math, you get around 2.4 ohms, which is very low and potentially problematic.
How do you rectify this? Well, the way we make things quieter is by adding resistance to them. If you look at the impedance of a single woofer with a coil on it, the coil adds resistance as frequency increases. This makes the woofer quieter as frequency goes up. The cap does the same thing in reverse for the tweeter.
If you want to keep your impedance above four ohms, you need to make sure your crossover filters are attenuating (adding resistance) sufficiently at the frequencies where the driver's impedance is naturally low. In the case of this woofer, you need to make sure the tweeter filter has a ton of resistance at 200hz, because the woofer is already at 4 ohms there. In your case, the reason you are down to 3.5 ohms is because at 200hz, your tweeter filter impedance is 28 ohms. You need to add some attenuation to the tweeter in that region. Simply using a more conventional crossover topology like the first two I show will probably get that done. Start by adding a coil in parallel after that first cap. Then worry about notches and bringing the overall level down. That first cap and coil will guarantee that after a certain point, the tweeter impedance is dropping like a rock as frequency goes down.
Other crossover tools show the impedance of your drivers separately and then the total, but VCAD doesn't do this for some reason. It can make rectification of impedance issues much easier.