The Short Dipole Antenna (continued)
The directivity
of the centerfed short dipole antenna depends only on the
component of the fields. It can be calculated to be 1.5 (1.76 dB), which
is very low for realizable antennas. Since the fields are only a function of the polar
angle, they have no azimuthal variation and hence this antenna is characterized as omnidirectional.
The HalfPower Beamwidth is 90 degrees. The polarization of this antenna is linear. When evaluated in the xy plane, this antenna would be described as vertically polarized, because the Efield would be vertically oriented (along the zaxis). We now turn to the input impedance of the short dipole, which depends on the radius a of the dipole. Recall that the impedance Z is made up of three components, the radiation resistance, the loss resistance, and the reactive (imaginary) component which represents stored energy in the fields:
The radiation resistance can be calculated to be:
The resistance representing loss due to the finiteconductivity of the antenna is given by:
In the above equation represents the conductivity of the dipole (usually very high, if made of metal). The frequency f come into the above equation because of the skin effect. The reactance or imaginary part of the impedance of a dipole is roughly equal to:
As an example, assume that the radius is 0.001 and the length is 0.05 . Suppose further that this antenna is to operate at f=3 MHz, and that the metal is copper, so that the conductivity is 59,600,000 S/m. The radiation resistance is calculated to be 0.49 Ohms. The loss resistance is found to be 4.83 mOhms (milliOhms), which is approximatley negligible when compared to the radiation resistance. However, the reactance is 1695 Ohms, so that the input resistance is Z=0.49 + j1695. Hence, this antenna would be very difficult to have proper impedance matching. Even if the reactance could be properly cancelled out, very little power would be delivered from a 50 Ohm source to a 0.49 Ohm load. For short dipoles that are smaller fractions of a wavelength, the radiation resistance becomes smaller than the loss resistance, and consequently this antenna can be very inefficient. The bandwidth for short dipoles is difficult to define. The input impedance varies wildly with frequency because of the reactance component of the input impedance. Hence, these antennas are typically used in narrowband applications.
