Approximate Relations of Impedance of Dipoles Independent of Their Arrangement

We derive the approximate relations of impedance Z of dipoles of approximately half a wavelength or shorter in length by introducing α as the ratio of the amplitude of the current that flows in a dipole when it is open-circuited to the port voltage. These relations are satisfied even when Z changes owing to the variations in the arrangement of the dipoles because α is almost independent of the other dipoles and is determined by the size of the dipole. We examine these relations by numerical calculation and measurement.