!st order Butterworths exhibit 90 degrees instead of 45 degrees. This could be as I Haven't seen filter theory in 30 years and my memory is a bit rusty. But be careful about filter generalizations. This much I do remember..Butterworrth exhibit 90 degrees per order but this is not true for the other filter types I've mentioned.
It is 45 degrees per section so when you add high and low pass it is 90. In a first order filter, a Butterworth (constant power) and Linkwitz/Riley (constant voltage) are the same circuit! So the phase is the same which is: - 45 degrees advancement for the high pass and 45 degrees delay for the low pass for a total of 90 degrees. Phasing for Butterworth and LR are the same, this applies to third order also, where an L/R filter is not possible. However in the real world you just about never have a crossover with the same electrical slopes either side of the crossover point. The reason is that the seldom do you work with two drivers that have symmetrical roll off.
Basically if you have a symmetrical electrical crossover that sums to zero db (flat) then the phase shift between low and high pass filters will be 90 degrees per order and you can go to the bank with that.
