Second order (acoustic) high and low-pass responses are 180 degrees out-of phase.
You get deep notch if you don't invert one (in a perfect world you'd have no output).
Linkwitz Riley filters have Q=.5 with both outputs -6dB at their pole. Inverting one therefore causes the response to sum flat.
2nd order butterworth filters at the same frequency (Q=.707) so you get a 3dB peak when you invert one and combine. Spreading the cross-over frequencies is needed to avoid this.
Sloped baffles accomplish two things:
1. Time alignment of the drivers so the real phase relationship matches theoretical.
2. Having the highest output on-axis rather than off when you don't use a Linkwitz-Riley cross-over.
You get deep notch if you don't invert one (in a perfect world you'd have no output).
Linkwitz Riley filters have Q=.5 with both outputs -6dB at their pole. Inverting one therefore causes the response to sum flat.
2nd order butterworth filters at the same frequency (Q=.707) so you get a 3dB peak when you invert one and combine. Spreading the cross-over frequencies is needed to avoid this.
Sloped baffles accomplish two things:
1. Time alignment of the drivers so the real phase relationship matches theoretical.
2. Having the highest output on-axis rather than off when you don't use a Linkwitz-Riley cross-over.