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Antenna impedance and radiation resistance
What the feed line sees at the feed point.
What the feed line sees at the feed point.
Feed-point impedance is the voltage-to-current ratio at the spot where the feed line meets the antenna. It is a complex quantity, R + jX: the resistance R is the part that takes power, and the reactance X is energy sloshing back and forth. Matching this to the feed line is what keeps SWR low.
The resistance at the feed point has two parts. Loss resistance is real: wire, ground and coil losses that turn into heat. Radiation resistance is a stand-in. No physical resistor exists, but power really does leave the antenna as a wave, and from the transmitter's side that looks exactly like power being used up in a resistance. The power radiated is I² × R(rad).
RememberRadiation resistance is how the transmitter "sees" the power that leaves as radio waves.
A short antenna has a very low radiation resistance, a few ohms or less, so its wire and ground losses can matter as much as the radiation. That is why efficiency falls as antennas shrink; see Bandwidth and efficiency.
On a resonant wire the current and voltage are not the same everywhere. Voltage is highest at the ends and current at the centre, and impedance is voltage divided by current, so it is low at the centre and very high toward the ends. Feeding a half-wave wire in the middle gives a few tens of ohms; feeding it at one end gives thousands. See End-fed half-wave antennas and Off-center-fed dipoles for antennas that exploit this.
A wire too short for the frequency looks like a capacitor in series with its resistance (negative X); one too long looks like an inductor (positive X). At the resonant frequency the two cancel and X is zero. This is why trimming length moves the SWR minimum; see The half-wave dipole.
It does not depend on the length of the feed line or on any tuner at the radio, and it does not change with power. A tuner can make the radio see 50 Ω, but it does not change the antenna. See Antenna tuners.
Measure feed-point impedance with an antenna analyzer at the feed point rather than guess. If it is not near the feed line's characteristic impedance, match it where the problem is: adjust height or length, or add a matching section or transformer.