Since I have several runs of 75 ohm hardline feeding my antennas, I assume my antenna analyzer readings will be inaccurate. Is this true?
No. The impedance will still be correct. The SWR reading relative to 50 ohms will be correct for
what your rig sees, but as W5DXP says, it won't tell you the actual SWR on the 75 ohm coax.
You can calculate that, however, (and the impedance at the antenna) using VK1OD's transmission
line calculator at http://www.vk1od.net/calc/tl/tllc.php
If so, would resonance still be the x=0 point.
That doesn't matter whether you are using 50 ohm or 75 ohm coax. The antenna itself most
likely will NOT
be resonant when you measure X=0 on the analyzer at the rig end
of the cable, unless the SWR is exactly 1 : 1.
You can easily observe this behavior using VK1OD's calculator: give it an impedance
(Mismatch = "Zload") of 25 ohms for a vertical or 75 ohms for a dipole. That will be
resonant if you don't also specify a "j" term (reactance) to the impedance. Now look
at the impedance at the rig end of the feedline for various lengths of coax - you can
choose many different types from his list, including 75 ohm types. For most coax
lengths the result impedance will not have X = 0 at the rig even though we started
with a resonant antenna. Even a couple of feet will throw it off significantly on the
higher bands. And the sign of X will vary with length too, so you can't use that to
tell whether the antenna is too long or too short without factoring in the length and
velocity factor of the line (as his calculator will do if you choose a mismatch type
of "Zin" and give it the measured impedance at the shack end of the coax.
Would the transceiver swr reading also be inaccurate?
Yes. The transceiver SWR reading will tell you the SWR relative to 50 ohms that the transmitter
sees, which is what it cares about. It doesn't tell you the SWR on the 75 ohm feedline.
I am trying to trim a homebrew vertical by using the analyzer.
Are you expecting a low SWR at the rig, or are you planning to use a tuner anyway?
That makes a difference because the SWR seen by the rig will depend on the length of the
75 ohm coax. If you tune it for resonance and the antenna is, say, 25 ohms (which might
be typical of a ground mounted quarter wave) then the SWR on the 75 ohm coax will be
3 : 1. At the rig the impedance might be 25 ohms or 225 ohms, or something in between
with some reactance. If you can adjust the impedance of the vertical to 75 ohms then
the SWR at the rig will be 1.5 : 1 regardless of coax length. If you tune the vertical for
50 ohms then the SWR at the rig might be 1 : 1, or it might be over 2 : 1.
So it all depends on the design of the antenna (whether it can be matched to 50 or
75 ohms) and the length of the feedline. In some cases you can get a perfect 50 ohm
load for the rig when the antenna is NOT resonant at the other end of the feedline.