The Short Dipole Antenna
The short dipole antenna is the simplest of all antennas. It is simply an open-circuited wire, fed at its center as shown in Figure 1.
Figure 1. Short dipole antenna of length L.
The words "short" or "small" in antenna engineering always imply "relative to a wavelength". So the absolute size of the above dipole antenna does not matter, only the size of the wire relative to the wavelength of the frequency of operation. Typically, a dipole is short if its length is less than a tenth of a wavelength:
If the short dipole antenna is oriented along the z-axis with the center of the dipole at z=0, then the current distribution on a thin, short dipole is given by:
The current distribution is plotted in Figure 2. Note that this is the amplitude of the current distribution; it is oscillating in time sinusoidally at frequency f.
Figure 2. Current distribution along a short dipole antenna.
The fields radiated from the short dipole antenna in the far field are given by:
The above equations can be broken down and understood somewhat intuitively. First, note that in the far-field, only the and fields are nonzero. Further, these fields are orthogonal and in-phase. Further, the fields are perpendicular to the direction of propagation, which is always in the direction (away from the antenna). Also, the ratio of the E-field to the H-field is given by (the intrinsic impedance of free space).
This indicates that in the far-field region the fields are propagating like a plane-wave.
Second, the fields die off as 1/r, which indicates the power falls of as
Third, the fields are proportional to L, indicated a longer dipole will radiate more power. This is true as long as increasing the length does not cause the short dipole assumption to become invalid. Also, the fields are proportional to the current amplitude , which should make sense (more current, more power).
The exponential term:
describes the phase-variation of the wave versus distance. The parameter k is known as the wavenumber. Note also that the fields are oscillating in time at a frequency f in addition to the above spatial variation.
Finally, the spatial variation of the fields as a function of direction from the antenna are given by . For a vertical antenna oriented along the z-axis, the radiation will be maximum in the x-y plane. Theoretically, there is no radiation along the z-axis far from the antenna.
In the next section further properties of the short dipole will be discussed.
Directivity, Impedance and other Properties of the Short Dipole Antenna
The directivity of the center-fed 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 (physical or non-theoretical) antennas. Since the fields of the short dipole antenna are only a function of the polar angle, they have no azimuthal variation and hence this antenna is characterized as omnidirectional. The Half-Power Beamwidth is 90 degrees.
The polarization of this antenna is linear. When evaluated in the x-y plane, this antenna would be described as vertically polarized, because the E-field would be vertically oriented (along the z-axis).
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 finite-conductivity of the antenna is given by:
(Want to see where this comes from? See the Loss resistance derivation)
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 (milli-Ohms), 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 dipole antennas 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.
In the next section, we'll look at general dipole antennas.
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