I agree that in the coax side, there is no real 0V because the current has a
standing wave. But the transceiver has a DC power supply (normally 12V) that
is controlled or modulated. One side of the power supply is regarded as 0V
and connected to 0V rail of circuits. The modulated side is the RF live that
is connected to the centre contact of transceiver output connector.

In theory, while transceiver is transmitting, if I touched the outer of the
output connector, I would not expect to get a shock or RF burn. If I touched
the centre contact of output connector, then I would expect to get a shock
or RF burn. Admittedly, I could touch the outer and find that I am close
enough to the centre contact for RF to capacitively couple into me. In real
life, I would never touch the output connector while the rig is
transmitting.

Does RF live and ground not exist on the output connector of the
transceiver?

"Live" and "ground" aren't absolute, universal things. These terms
exist only in relation to a specific reference point, which you must
choose.

Yes, it's true that the outer rim of the coaxial connector is usually
tied to the chassis of the transceiver, and that this chassis is also
tied to your DC ground. So, the potential voltage between the
connector and your body is usually low and it's not all that likely to
shock you.

However, this doesn't mean that this same thing is true at the other
end of the coaxial cable (i.e. up at the antenna)! Although the far
end of the coax braid is at (or very close to) DC ground, it's far
enough away in RF terms (that is, in terms of wavelengths) that its
voltage is going to be very different much of the time.

Consider also the case in which your transceiver isn't "grounded" at
all... it's sitting on a wooden table, powered by a battery, and the
coax cable runs directly from it to the antenna. There's no "third
wire" in the power cord, or other grounding wire connecting the
transceiver to a water pipe or electric outlet or a grounding rod or
anything like that. Let's further assume that your antenna is a
vertical, with radials, elevated up on an insulated mast.

Now, when you transmit - what's the voltage present at the base of
each radial? If it's "0V", then why, and with respect to what?

--
Dave Platt AE6EO
Hosting the Jade Warrior home page: http://www.radagast.org/jade-warrior
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