Dipole antenna

In radio and telecommunications a dipole antenna or doublet
is one of the two simplest and most widely used types of antenna; the other is the monopole. The dipole is any one of a class of antennas producing a radiation pattern approximating that of an elementary electric dipole with a radiating structure supporting a line current so energized that the current has only one node at each far end. A dipole antenna commonly consists of two identical conductive elements
such as metal wires or rods. The driving current from the transmitter is applied, or for receiving antennas the output signal to the receiver is taken, between the two halves of the antenna. Each side of the feedline to the transmitter or receiver is connected to one of the conductors. This contrasts with a monopole antenna, which consists of a single rod or conductor with one side of the feedline connected to it, and the other side connected to some type of ground. A common example of a dipole is the rabbit ears television antenna found on broadcast television sets. All dipoles are electrically equivalent to two monopoles mounted end-to-end and fed with opposite phases, with the ground plane between them made virtual by the opposing monopole.
The dipole is the simplest type of antenna from a theoretical point of view. Most commonly it consists of two conductors of equal length oriented end-to-end with the feedline connected between them.
Dipoles are frequently used as resonant antennas. If the feedpoint of such an antenna is shorted, then it will be able to resonate at a particular frequency, just like a guitar string that is plucked. Using the antenna at around that frequency is advantageous in terms of feedpoint impedance, so its length is determined by the intended wavelength of operation. The most commonly used is the center-fed half-wave dipole which is just under a half-wavelength long. The radiation pattern of the half-wave dipole is maximum perpendicular to the conductor, falling to zero in the axial direction, thus implementing an omnidirectional antenna if installed vertically, or a weakly directional antenna if horizontal.
Although they may be used as standalone low-gain antennas, dipoles are also employed as driven elements in more complex antenna designs such as the Yagi antenna and driven arrays. Dipole antennas are used to feed more elaborate directional antennas such as a horn antenna, parabolic reflector, or corner reflector. Engineers analyze vertical antennas on the basis of dipole antennas of which they are one half.

History

German physicist Heinrich Hertz first demonstrated the existence of radio waves in 1887 using what we now know as a dipole antenna. On the other hand, Guglielmo Marconi empirically found that he could just ground the transmitter dispensing with one half of the antenna, thus realizing the vertical or monopole antenna.
For the low frequencies Marconi employed to achieve long-distance communications, this form was more practical; when radio moved to higher frequencies it was advantageous for these much smaller antennas to be entirely atop a tower thus requiring a dipole antenna or one of its variations.
In the early days of radio, the thus-named Marconi antenna and the doublet were seen as distinct inventions. Now, however, the monopole antenna is understood as a special case of a dipole which has a virtual element underground.

Dipole variations

Short dipole

A short dipole is a dipole formed by two conductors with a total length substantially less than a half wavelength Short dipoles are sometimes used in applications where a full half-wave dipole would be too large. They can be analyzed easily using the results obtained [|below] for the Hertzian dipole, a fictitious entity. Being shorter than a resonant antenna its feedpoint impedance includes a large capacitive reactance requiring a loading coil or other matching network in order to be practical, especially as a transmitting antenna.
To find the far-field electric and magnetic fields generated by a short dipole we use the result shown below for the Hertzian dipole at a distance from the current and at an angle to the direction of the current, as being:
where the radiator consists of a current of over a short length and in electronics replaces the customary mathematical symbol for the square root of. is the angular frequency and is the wavenumber is the impedance of free space which is the ratio of a free space plane wave's electric to magnetic field strength.
The feedpoint is usually at the center of the dipole as shown in the diagram. The current along dipole arms are approximately described as proportional to where is the distance to the nearest end of the arm. In the case of a short dipole, that is essentially a linear drop from at the feedpoint to zero at the end. Therefore, this is comparable to a Hertzian dipole with an effective current _h equal to the average current over the conductor, so With that substitution, the above equations closely approximate the fields generated by a short dipole fed by current
From the fields calculated above, one can find the radiated flux at any point as the magnitude of the real part of the Poynting vector, ', which is given by Because ' and are at right angles and in phase, there is no imaginary part and the cross product is equal to the phase factors cancel out, leaving:
We have now expressed the flux in terms of the feedpoint current and the ratio of the short dipole's length to the wavelength of radiation. The radiation pattern given by is seen to be similar to and only slightly less directional than that of the half-wave dipole.
Using the above expression for the radiation in the far field for a given feedpoint current, we can integrate over all solid angle to obtain the total radiated power.
From that, it is possible to infer the radiation resistance, equal to the resistive part of the feedpoint impedance, neglecting a component due to ohmic losses. By setting to the power supplied at the feedpoint we find:
Again, these approximations become quite accurate for Setting despite its use not quite being valid for so large a fraction of the wavelength, the formula would predict a radiation resistance of 49 Ω, instead of the actual value of 73 Ω produced by a half-wave dipole, when more correct quarter-wave sinusoidal currents are used.

Dipole antennas of various lengths

The fundamental resonance of a thin linear conductor occurs at a frequency whose free-space wavelength is twice the wire's length; i.e. where the conductor is wavelength long. Dipole antennas are frequently used at around that frequency and thus termed half-wave dipole antennas. This important case is dealt with in the next section.
Thin linear conductors of length are in fact resonant at any integer multiple of a half-wavelength:
where is an integer, is the wavelength, and is the reduced speed of radio waves in the radiating conductor. For a center-fed dipole, however, there is a great dissimilarity between being odd or being even. Dipoles which are an odd number of half-wavelengths in length have reasonably low driving point impedances. However ones which are an even number of half-wavelengths in length, that is, an integer number of wavelengths in length, have a high driving point impedance.
For instance, a full-wave dipole antenna can be made with two half-wavelength conductors placed end to end for a total length of approximately This results in an additional gain over a half-wave dipole of about 2 dB. Full wave dipoles can be used in short wave broadcasting only by making the effective diameter very large and feeding from a high impedance balanced line. Cage dipoles are often used to get the large diameter.
A -wave dipole antenna has a much lower but not purely resistive feedpoint impedance, which requires a matching network to the impedance of the transmission line. Its gain is about 3 dB greater than a half-wave dipole, the highest gain of any dipole of any similar length.
Other reasonable lengths of dipole do not offer advantages and are seldom used. However the overtone resonances of a half-wave dipole antenna at odd multiples of its fundamental frequency are sometimes exploited. For instance, amateur radio antennas designed as half-wave dipoles at 7 MHz can also be used as -wave dipoles at 21 MHz; likewise VHF television antennas resonant at the low VHF television band are also resonant at the high VHF television band.

Half-wave dipole

A half-wave dipole antenna consists of two quarter-wavelength conductors placed end to end for a total length of approximately The current distribution is that of a standing wave, approximately sinusoidal along the length of the dipole, with a node at each end and an antinode at the center :
where and runs from to.
In the far field, this produces a radiation pattern whose electric field is given by
The directional factor is very nearly the same as applying to the short dipole, resulting in a very similar radiation pattern as noted above.
A numerical integration of the radiated power over all solid angle, as we did for the short dipole, obtains a value for the total power radiated by the dipole with a current having a peak value of as in the form specified above. Dividing by supplies the flux at a large distance, averaged over all directions. Dividing the flux in the direction at that large distance by the average flux, we find the directive gain to be 1.64 . This can also be directly computed using the cosine integral:
We can now also find the radiation resistance as we did for the short dipole by solving:
to obtain:
Using the induced EMF method, the real part of the driving point impedance can also be written in terms of the cosine integral, obtaining the same result:
If a half-wave dipole is driven at a point other the center, then the feed point resistance will be higher. The radiation resistance is usually expressed relative to the maximum current present along an antenna element, which for the half-wave dipole is also the current at the feedpoint. However, if the dipole is fed at a different point at a distance from a current maximum, then the current there is not but only
In order to supply the same power, the voltage at the feedpoint has to be similarly increased by the factor
Consequently, the resistive part of the feedpoint impedance is increased by the factor
This equation can also be used for dipole antennas of any length, provided that has been computed relative to the current maximum, which is not generally the same as the feedpoint current for dipoles longer than half-wave. Note that this equation breaks down when feeding an antenna near a current node, where approaches zero. The driving point impedance does indeed rise greatly, but is nevertheless limited due to higher order components of the elements' not-quite-exactly-sinusoidal current, which have been ignored above in the model for the current distribution.