Unfortunately, there's no such thing as a "simple, plain, wire". Any
current you put into the wire will force an equal current into the
"ground" connection. If, for example, you just plug a wire into the
center conductor of your transmitter's output connector, a current will
flow out of the connector along the outside transmitter's chassis. This
current will equal the current into your wire. So the radio, along with
the path to the Earth, becomes the other half of a very asymmetrical
dipole. You can't avoid this, except by making the return current flow
where you want, for example into the other half of a regular symmetrical
dipole.

So to simply answer your question, if the wire is very close to a
quarter wavelength and connected as I've said, the resistance can be
anything from 10 or a few tens of ohms (if it's close to the chassis) to
a thousand or more ohms (if the path to the Earth is particular
lengths). The reactance can easily be plus or minus a few hundred ohms.

That's why you don't find a simple formula. If you did find one, it
would be wrong and useless.

Roy Lewallen, W7EL

wrote:
I searched all over the Internet and many books but just could not find
a formula or rough number of a wire antenna's impedance (not dipole or
anything else, just a simple, plain wire). I need this number to match
my small transmitter's final stage output, about 10mW, at 450MHz. The
final stage's transistor has fT of 6GHz, and is not unconditionally
stable at 450MHz. So I need to match it using Smith Chart. I know those
portion of work. But I just don't know the wire's impedance's range,
say, is it in the 50-80 ohms or in the 500-600 ohms range or even
1000-2000 ohms? Right now I do not guess this number right, and my
transmitter seems always oscillating at a wrong frequency. So take an
example, if I use a wire antenna, say, 22 AWG, spools of solid, and the
length=wavelength/4, what is its approximate impedance? Thanks.