Capacitor phase shift

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nubble

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Preamble: Many year ago I studies acoustics at Varsity and recall that caps in a series circuit introduce 90 degree phase shift in the output.

Im doing a diy 2 way speaker and not using a passive  crossover but rather doing the crossover digitally in a minidsp.
It is suggested that one places a cap in series on the tweeter creating a HPF. the purpose of the cap is to protect the tweeter from dc/low frequency components coming from the minidsp at startup/shutdown/config change. this makes sense to me
the cutoff should be about an octave below where the minidsp crossover is to be. For example if the minidsp is crossing over at 1k, then the cap should have its cutoff be at about 500Hz and so have no effect on the final output 

when designing the digital crossover phase shift is considered also, but I think that the cap introduced a 90 degree phase shift as well.
Is this so? do I need to compensate for this in the digital crosssover so as to perfectly phase align the speaker pair?


thanks in advance
 
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