Hilbert transformer's phase in .AC simulation I don't understand this: the HT works as it should but in an .AC simulation, the phase shows up like this (wrapped):



Why doesn't it look like a constant -90deg phase, like in a differentiator?





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The thing that also confuses me is that a regular low-pass FIR has the same phase, so does that mean the FIR also adds constant -90deg? Obviously not, and I can't see the explanation. Can someone please shed some light?
You have a linear phase because you probably implemented a causal filter. This just means that you have the desired phase shift of $-\pi/2$ plus a constant delay. The additional delay, which corresponds to a linear phase term, usually causes no problems. It is necessary to make the filter causal and therefore implementable.

The difference between an FIR lowpass filter and a Hilbert transformer is the phase value at frequency zero: it should be zero for a lowpass filter, and $-\pi/2$ for a Hilbert transformer.