What is the difference between antenna input impedance and its radiation resistance? I got to know that the input impedance of the halfwave dipole antenna is given as:
$Z_{in}$=1/$I_m$* sin($\beta$(H-|Z|))
where $I_m$ is the maximum current on the antenna( when excited with a 1 volt supply),
H is the half-length of the antenna,
Z is the position on the antenna and $\beta$ is wave number.
Apart from the input impedance there is another parameter called as radiation resistance calculated by dividing the $I_m^2$ from the power radiated by the antenna.
Now my doubts are:

*

*Are both the radiation resistance and the input impedance one and the same?

*If I take a full wave dipole ($\beta*H$=$\pi$) then at Z=0 ( input terminal) the input impedance value becomes infinite which is similar to open circuit condition so does that mean there wouldn't be any radiation by the antenna?

*If I consider the current distribution of the antenna for the full wave dipole (as given in the figure, the current standing wave value becomes zero at the input end of the antenna how can there be a distribution of the current on the antenna if the input current is zero?


I seem to have confused myself a lot. kindly clarify me on this doubt.Thank you in advance.
 A: (1) According to your definition, they are the same if the feed point is at a current maximum. Otherwise, they are different.
(2) I'm unclear on the precise definitions of your symbols. Beware that antenna theory is transcendentally messy: all simple formulae are approximations, and will mislead you if you take them too seriously.
(3) In your standing wave diagram, you're assuming that the traveling wave reflected back toward the feedpoint has the same amplitude as the outgoing wave. But it loses energy to radiation on its round trip, which means that you don't have a pure standing wave. The current at the feedpoint isn't zero.
A: The radiation resistance of an idealized antenna is the nonreactive (real) component of the load impedance of an antenna. The real component "looks" like a purely ohmic resistance to the power flowing into the antenna, which means no power is reflected off the antenna and sent backwards up the feedline when the the load is purely real.
This occurs when the antenna is being driven at resonance, because then the capacitive component of the antenna's complex impedance is cancelled by the inductive component, leaving the purely real impedance component as the only electrical load seen by the source transmitter.
