I will use some words that I have read on the forums and in books that I don’t necessarily understand. Hopefully, where I am wrong someone will jump in an correct me and we will learn together.
The MAIN thing that matters when we are talking about slopes is the acoustic slopes. If we are having fun with math and assuming ideal drives, then the acoustic order matches the electrical order of the filter. With real frequency responses and impedance curves they hardly ever match.
(I was typing some stuff here and checking with Gemini PRO and am pretty sure I was wrong. Here is a little of what I thought, followed by what AI is telling me.)
ME: (not totally correct) With different acoustic centers (and other stuff??) we may get close to a good frequency response but poor phase alignment. Adding reactive components (inductors, capacitors but not resistors) shifts phase 90 degrees and can give better phase alignment. Reversing polarity shifts phase 180 degrees. So depending on the electrical order, you may or may not need to reverse polarity. According to AI it REALLY IS ALL ABOUT THE ACOUSTIC SLOPES.
AI: (maybe correct, maybe totally full of sh!t)
Phase integration between drivers at the crossover point is dictated entirely by the final acoustic transfer function, not the electrical order of the filter components used to achieve it.
An acoustic Linkwitz-Riley 2nd order (LR2) crossover inherently dictates a 180-degree phase difference between the high-pass and low-pass sections at the crossover frequency. If your combined system (the driver’s natural mechanical roll-off plus the electrical network) perfectly traces an LR2 acoustic target, the sound waves from the tweeter and woofer will arrive completely out of phase.
If both drivers are wired with the same polarity in a true LR2 acoustic setup, they will destructively interfere, creating a deep null at the crossover point. Therefore, one of the drivers—typically the tweeter—must have its polarity inverted so that the signals sum perfectly flat (+6 dB at the crossover point for Linkwitz-Riley alignments).
The electrical order is simply the tool used to shape the driver’s natural response to fit that acoustic target. The scenario depends on what that extra capacitor actually does to the final output:
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Hitting an LR2 Acoustic Target with a 3rd Order Electrical Filter: If you use a 3rd order electrical network to achieve an LR2 acoustic slope, it usually means you are aggressively compensating for the tweeter’s natural rising response, an impedance peak, or proximity to its fundamental resonance (F_s). Because the final acoustic output is still strictly LR2, the 180-degree phase difference remains.
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Changing the Target to a 3rd Order Acoustic Slope: If adding that capacitor actually steepens the final acoustic slope to a 3rd order alignment (such as a 3rd-order Butterworth), the acoustic phase difference between the drivers shifts to 90 degrees. In a true 3rd-order acoustic crossover, the drivers will sum flat on-axis regardless of whether the tweeter is wired in normal or reversed polarity. The choice of polarity in this case simply dictates whether the main vertical radiation lobe tilts upward or downward.
Because an acoustic LR2 slope fundamentally requires a 180-degree phase flip to sum correctly, you still need to reverse the tweeter’s polarity to avoid a null, even if the electrical network driving it is third order.
