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dipole

Antennas are new to me so the questions I ask may not be entirely sensible. But here goes anyway:

My understanding is that a dipole antenna is in the shape of a T where the length of each horizontal branch is equal to a quarter wavelength. So, for 2.4 GHz, each horizontal branch would be about 1.2 inches long. But I've seen articles and spec sheets that call the stock "rubber duck" antennas that come with many routers and client radios dipoles. They don't seem to be in the shape of a T at all. Rather they just seem to be a length of wire. What gives?

Would it be possible to build my own T-shaped dipole by soldering a couple of 1.2 inch pieces of wire on to the end of a coax cable? Well, it would be possible, but would it work ok and why or why not? :) Would I get more signal if I made the dipole a full wavelength long or longer? How about many wavelengths like a couple of wires running all the way across a room?

I know this borders on "turn your electrical wiring into a giant antenna" but, as a novice, I can't help thinking that I can "grab" a larger signal by putting up a bigger antenna.

Thanks, Bruce