Hertzian dipole

A dipole antenna, developed by Heinrich Rudolph Hertz around 1886,[citation needed] is an antenna that can be made by a simple wire, with a center-fed driven element for transmitting or receiving radio frequency energy. These antennas are the simplest practical antennas from a theoretical point of view; the current amplitude on such an antenna decreases uniformly from maximum at the center to zero at the ends.

Hertzian (i.e. short or infinitesimal) dipole

The Hertzian dipole is a theoretical dipole antenna that consists of an infinitesimally small current source acting in free-space. Although a true Hertzian dipole cannot physically exist, very short dipole antennas can make for a reasonable approximation.

The length of this antenna is significantly smaller than the wavelength:

$ l < \frac{\lambda}{50} $

The radiation resistance is given by:

$ R_{r} = \frac{2 \pi}{3} Z_{0} \left( \frac{\ell}{\lambda}\right)^{2}. $

where $ Z_0 $ is the impedance of free space.

The radiation resistance is typically a fraction of an ohm, making the infinitesimal dipole an inefficient radiator. The directivity D, which is the theoretical gain of the antenna assuming no ohmic losses (not real-world), is a constant of 1.5, which corresponds to 1.76 dB. Actual gain will be much less due to the ohmic losses and the loss inherent in connecting a transmission line to the antenna, which is very hard to do efficiently considering the incredibly low radiation resistance. The maximum effective aperture is:

$ A_e = \frac{3 \lambda ^2 }{8 \pi} $

A surprising result is that even though the Hertzian dipole is minute, its effective aperture is comparable to antennas many times its size.


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