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In radio and telecommunications a dipole antenna or doublet^{[1]} is the simplest and most widely used class of antenna.^{[2]}^{[3]} It consists of two identical conductive elements^{[4]} such as metal wires or rods, which are usually bilaterally symmetrical.^{[3]}^{[5]}^{[6]} 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.^{[6]} A common example of a dipole is the "rabbit ears" television antenna found on broadcast television sets.
The most common form of dipole is two straight rods or wires oriented end to end on the same axis, with the feedline connected to the two adjacent ends. This is the simplest type of antenna from a theoretical point of view.^{[1]} Dipoles are resonant antennas, meaning that the elements serve as resonators, with standing waves of radio current flowing back and forth between their ends. So the length of the dipole elements is determined by the wavelength of the radio waves used.^{[3]} The most common form is the halfwave dipole, in which each of the two rod elements is approximately 1/4 wavelength long, so the whole antenna is a halfwavelength long.
Several different variations of the dipole are also used, such as the folded dipole, short dipole, cage dipole, bowtie, and batwing antenna. Dipoles may be used as standalone antennas themselves, but they are also employed as feed antennas (driven elements) in many more complex antenna types,^{[3]}^{[4]} such as the Yagi antenna, parabolic antenna, reflective array, turnstile antenna, log periodic antenna, and phased array. The dipole was the earliest type of antenna; it was invented by German physicist Heinrich Hertz around 1886 in his pioneering investigations of radio waves.
From a theoretical point of view, the dipole antenna is the simplest type of antenna. An elementary doublet or Hertzian dipole is a length of conductor δℓ that is small compared to the wavelength λ carrying an alternating current:
Here ω = 2πf is the angular frequency (and f the frequency), and i = √−1 is the imaginary unit, so that I is a phasor.
It is used in, for example, analytical calculation on more complex antenna geometries. Note that this dipole cannot be physically constructed because the current needs somewhere to come from and somewhere to go to. In reality, this small length of conductor will be just one of the multiple segments into which a real antenna is divided, in order to calculate its properties.
In the case of the elementary doublet it is possible to find exact, closedform expressions for its electric field, E, and its magnetic field, H. In spherical coordinates, they are^{[7]}
where r is the distance from the doublet to the point where the fields are evaluated, k = 2π/λ is the wavenumber, and Z = √μ/ε = 1/εc = μc is the wave impedance of the surrounding medium (usually air or vacuum).
The energy associated with the term of the near field flows alternately out of and back into the antenna. The exponent of e accounts for the phase dependence of the electric field on time and the distance from the dipole.
Often one is interested in the antenna's radiation pattern only in the far field, when r ≫ λ/2π. In this regime, only the 1/r term contributes,^{[7]} and hence
The far electric field, E_{θ}, of the electromagnetic wave is coplanar with the conductor and perpendicular with the line joining the dipole to the point where the field is evaluated. If the dipole were placed in the center of a sphere with the axis southnorth, the electric field would be parallel to geographic meridians and the magnetic field of the electromagnetic wave would be parallel to geographic parallels.
All antennas have a radiation resistance, which is the resistance the antenna presents to its circuit due to radiation. The radiation resistance of the elementary doublet in free space is
where Z_{0} is the impedance of free space. This is precisely four times the radiation resistance of the real short dipole with the linearly tapered current distribution.
The radiation resistance is typically a fraction of an ohm, making the elementary doublet an inefficient radiator.
The directivity of the elementary doublet—that is, the theoretical antenna gain assuming no ohmic losses—is 1.5, which corresponds to 1.76 dBi. The actual gain will be much less due to the ohmic losses (because of the very high currents) and the loss inherent in connecting a transmission line to the antenna, which is very hard to do efficiently because of the low radiation resistance.
The maximum effective aperture of the elementary doublet is
where G = 1.5 is the antenna gain.
A surprising result is that even though the elementary doublet is minute, its effective aperture is comparable to antennas many times its size. A real small antenna will have a smaller effective aperture because of its lower gain.
Dipoles that are much smaller than the wavelength of the signal are called Hertzian, short, or infinitesimal dipoles. These have a very low radiation resistance and a high capacitive reactance, making them inefficient antennas. Despite this inefficiency, they can be practical receiving antennas for long wavelengths.^{[8]} Dipoles whose length is half the wavelength of the signal are called halfwave dipoles, and are more efficient. In general radio engineering, the term dipole usually means a centerfed halfwave dipole.
A halfwave dipole is cut to length l for frequency f in hertz according to the formula
where λ_{d} is the wavelength on the dipole elements, λ_{0} is the freespace wavelength, c is the speed of light in free space (299,792,458 metres per second (983,571,060 ft/s)), and k is an adjustment factor. The adjustment factor compensates for propagation speed being somewhat less than the speed of light. The dipole elements will have distributed inductance and capacitance. The value of k is typically 0.95. For thin wires (radius = 0.000001 wavelengths), k is approximately 0.981; for thick wires (radius = 0.01 wavelengths), k drops to about 0.915.
The above formula is often shortened to the length in metres = 143/f_{MHz} or the length in feet = 468/f_{MHz}; f_{MHz} is the frequency in megahertz.^{[9]}
Dipoles have a radiation pattern, shaped like a toroid (doughnut) symmetrical about the axis of the dipole. The radiation is maximum at right angles to the dipole, dropping off to zero on the antenna's axis. The theoretical maximum gain of a Hertzian dipole is 10 log 1.5 or 1.76 dBi. The maximum theoretical gain of a halfwave bipole is 10 log 1.64 or 2.15 dBi.
A folded dipole has a central impedance of about 300 ohms. Therefore, the simplest way of feeding a folded dipole antenna is using a 300ohm ladder line.^{[10]} Ideally, a halfwave dipole should be fed with a balanced line matching the theoretical 73ohm impedance of the antenna. A folded dipole uses a 300ohm balanced feeder line. Many people^{[who?]} have had success in feeding a dipole directly with a coaxial cable feed rather than a ladder line.^{[citation needed]} However, coax is not symmetrical and thus not a balanced feeder. It is unbalanced because the outer shield is connected to earth potential at the other end. When a balanced antenna such as a dipole is fed with an unbalanced feeder, common mode currents can cause the coax line to radiate in addition to the antenna itself,^{[11]} and the radiation pattern may be asymmetrically distorted. This can be remedied with the use of a balun.
A dipole is a symmetrical antenna, as it is composed of two symmetrical ungrounded elements. Therefore, it works best when fed by a balanced transmission line, such as a ladder line, because in that case the symmetry (one aspect of the impedance complex, which is a complex number) matches and therefore the power transfer is extremal.
When a dipole with an unbalanced feedline such as coaxial cable is used for transmitting, the shield side of the cable, in addition to the antenna, radiates.^{[11]} This can induce radio frequency (RF) currents into other electronic equipment near the radiating feedline, causing RF interference. Furthermore, the antenna is not as efficient as it could be because it is radiating closer to the ground and its radiation pattern may be asymmetrically distorted. At higher frequencies, where the length of the dipole becomes significantly shorter than the diameter of the feeder cable, this becomes a more significant problem. To prevent this, dipoles fed by coaxial cables have a balun between the cable and the antenna, to convert the unbalanced signal provided by the coax to a balanced symmetrical signal for the antenna.
Several types of balun are commonly used to feed a dipole antenna: current baluns and coax baluns. Baluns can be made using ferrite toroid cores or even from the coax feedline itself.^{[12]} The choice of the toroid core is crucial. A rule of thumb is: the more power, the bigger the core.^{[13]}
A current balun consists of two windings that are closely coupled.^{[11]}^{[14]}
A coax balun is a costeffective method of eliminating feeder radiation, but is limited to a narrow set of operating frequencies.
One easy way to make a balun is to use a length of coaxial cable equal to half a wavelength. The inner core of the cable is linked at each end to one of the balanced connections for a feeder or dipole. One of these terminals should be connected to the inner core of the coaxial feeder. All three braids should be connected together. This then forms a 4:1 balun, which works correctly at only a narrow band of frequencies.
At VHF frequencies, a sleeve balun can also be built to remove feeder radiation.^{[15]}
Another narrowband design is to use a λ/4 length of metal pipe. The coaxial cable is placed inside the pipe; at one end the braid is wired to the pipe while at the other end no connection is made to the pipe. The balanced end of this balun is at the end where the pipe is wired to the braid. The λ/4 conductor acts as a transformer, converting the infinite impedance at the unconnected end into a zero impedance at the end connected to the braid. Hence any current entering the balun through the connection, which goes to the braid at the end with the connection to the pipe, will flow into the pipe. This balun design is impractical for low frequencies because of the long length of pipe that will be needed.
A short dipole is a physically feasible dipole formed by two conductors with a total length L very small compared with the wavelength λ. The two elements are fed at the center of the dipole. The current profile in each element, actually the tail end of a sinusoidal standing wave, is approximately a triangular distribution, declining linearly from a maximum at the center feed point to zero at the ends. At any instant the direction of the current is the same in both the dipole branches: to the right in both or to the left in both. The far field E_{θ} of the electromagnetic wave radiated by this dipole is
Field strength is maximal in the plane perpendicular to the dipole axis, declining monotonically to zero on the antenna's axis. The 3 dimensional radiation pattern (right) of a vertical dipole is torusshaped, with equal radiation in all horizontal directions.
Knowing the radiated electric field, we can compute the total emitted power and then compute the resistive part of the series impedance of this dipole due to the radiated field, known as the radiation resistance:
where is the impedance of free space. Using a common approximation of ohms, we get
Antenna gain, G, is the ratio of surface power radiated by the antenna to the surface power radiated by a hypothetical isotropic antenna:
The surface power carried by an electromagnetic wave is
while the surface power radiated by an isotropic antenna feed with the same power is
Combining these expressions with the farfield expression for E_{θ} for a short dipole gives
where dBi means decibels gain relative to an isotropic antenna.
Typically a dipole antenna is formed by two quarterwavelength conductors or elements placed back to back for a total length of L = λ/2. A standing wave on an element of length approximately λ/2 yields the greatest voltage differential, as one end of the element is at a node while the other is at an antinode of the wave. The larger the differential voltage, the greater the current between the elements.
The current distribution is assumed to be approximately sinusoidal along the length of the dipole, with a node at each end and an antinode in the center:^{[16]}
where k = 2π/λ and z runs from −L /2 to L /2.
In the far field, this produces a radiation pattern whose electric field is given by^{[16]}
where again Z = √μ/ε. The trigonometric factor cos[(π/2)cos θ]/sin θ is approximately equal to the factor sin θ appearing in the farfield radiation pattern for the elementary doublet, so the radiation pattern of a halfwave antenna is a slightly flattened torus.^{[16]}
This time it is not possible to compute analytically the total power emitted by the antenna (the last formula does not allow), though a simple numerical integration or series expansion leads to the more precise, actual value of the halfwave resistance:
This leads to the gain of a dipole antenna, :
The resistance, however, is not enough to characterize the dipole impedance, as there is also an imaginary part—it is better to measure the impedance.
In the image below, the real and imaginary parts of a dipole's input impedance are drawn for lengths going from to and with respect to diameter, accompanied by a chart comparing the gains of dipole antennas of other lengths, both as a number and in dBi:
Gain of dipole antennas  
length L in  Gain  Gain(dBi) 
0.1  1.50  1.76 
0.5  1.64  2.15 
This type of antenna is a special case where each wire is exactly one quarter of the wavelength, for a total of a half wavelength. The radiation resistance is about 73 ohms if wire diameter is ignored, making it easily matched to a coaxial transmission line. The directivity is a constant 1.64, or 2.15 dB. Actual gain will be slightly lower due to ohmic losses.
If the dipole is not driven at the center, then the feed point resistance will be higher. If the feed point is distance x from one end of a half wave (λ/2) dipole, the resistance will be described by the following equation.
If taken to the extreme then the feed point resistance of a λ/2 long rod is infinite, but it is possible to use a λ/2 pole as an aerial; the right way to drive it is to connect it to one terminal of a parallel LC resonant circuit. The other side of the circuit must be connected to the braid of a coaxial cable lead and the core of the coaxial cable can be connected partway up the coil from the RF ground side. An alternative means of feeding this system is to use a second coil that is magnetically coupled to the coil attached to the aerial.
The quarterwave monopole antenna is a singleelement antenna fed at one end, that behaves as a dipole antenna. It is formed by a conductor in length, fed in the lower end, which is near a conductive surface which works as a reflector (see effect of ground) and is an example of a Marconi antenna. The current in the reflected image has the same direction and phase as the current in the real antenna. The quarterwave conductor and its image together form a halfwave dipole that radiates only in the upper half of space.
In this upper side of space, the emitted field has the same amplitude of the field radiated by a halfwave dipole fed with the same current. Therefore, the total emitted power is half the emitted power of a halfwave dipole fed with the same current. As the current is the same, the radiation resistance (real part of series impedance) will be half of the series impedance of a halfwave dipole. As the reactive part is also divided by 2, the impedance of a quarterwave antenna is ohms. Since the fields above ground are the same as for the dipole, but only half the power is applied, the gain is twice (3 dB over) that of a halfwave dipole (), that is, 5.14 dBi.
The earth can be used as ground plane, but it is a poor conductor. The reflected antenna image is only clear at glancing angles (far from the antenna). At these glancing angles, electromagnetic fields and radiation patterns are the same as for a halfwave dipole.
Naturally, the impedance of the earth is far inferior to that of a good conductor ground plane. This can be improved (at cost) by laying a copper mesh.
When the ground is not available (such as in a vehicle) other metallic surfaces can serve as a ground plane (typically the vehicle's roof). Alternatively, radial wires placed at the base of the antenna can simulate a ground plane. For VHF bands, the radiating and ground plane elements can be constructed from rigid rods or tubes.
A folded dipole is a halfwave dipole with an additional wire connecting its two ends. If the additional wire has the same diameter and crosssection as the dipole, two nearly identical radiating currents are generated. The resulting farfield emission pattern is nearly identical to the one for the singlewire dipole described above, but at resonance its feedpoint impedance is four times the radiation resistance of a singlewire dipole. This is because for a fixed amount of power, the total radiating current is equal to twice the current in each wire and thus equal to twice the current at the feed point. Equating the average radiated power to the average power delivered at the feedpoint, we may write
It follows that
The folded dipole is therefore well matched to 300ohm balanced transmission lines. The T2FD antenna is a folded dipole.
Another common place one can see dipoles is as antennas for the FM band; these are folded dipoles. The tips of the antenna are folded back until they almost meet at the feedpoint, such that the antenna comprises one entire wavelength. This arrangement has a greater bandwidth than a standard halfwave dipole. If the conductor has a constant radius and crosssection, at resonance the input impedance is four times that of a halfwave dipole. Moreover, the folded dipole can be used for transforming the value of input impedance of the dipole over a broad range of stepup ratios by changing the thicknesses of the wire conductors for the fed and foldedsides.^{[17]}
There are numerous notable variations of dipole antennas:
The complex radiation impedance of a dipole antenna is the sum of the real resistance R_{dipole} and the imaginary reactance X_{dipole}. In practice numerical solutions are required to get useful results but several attempts to solve the problem analytically has been done.
Assuming sinusoidal current distribution, the Induced EMF method gives a rough estimate of reactance X and radiation resistance R for a dipole of length L and radius a operating at a frequency with wavenumber k in a medium with impedance Z:
where Ci and Si are the cosine and sine integral functions and γ is the Euler constant.^{[18]}
The Induced EMF method is inaccurate for dipoles longer than a half wavelength (kL>π) and verticals longer than quarter wavelength.^{[19]} Halléns integral solution and similar give more successful results.
Antenna gain is sometimes measured as decibels relative to a dipole, which means that the antenna in question is being compared to a dipole, and has a certain amount of gain relative to a dipole antenna tuned to the same operating frequency. In this case, one says the antenna has a gain of "x dBd" (see decibel). More often, gains are expressed relative to an isotropic radiator, which is an imaginary antenna that radiates equally in all directions. In this case one uses dBi instead of dBd (see decibel). As it is impossible to build an isotropic radiator, gain measurements expressed relative to a dipole are more practical when a reference dipole aerial is used for experimental measurements. 0 dBd is often considered equal to 2.15 dBi.
From Babinet's principle, a dipole antenna is complementary to a slot antenna consisting of a slot the same size and shape as a dipole cut from an infinite sheet of metal; both give the same radiation pattern.
The most common dipole antenna is the type used with televisions, often colloquially referred to as rabbit ears or bunny ears. While in most applications the dipole elements are arranged along the same line, rabbit ears are adjustable in length and angle, allowing for the user to adjust for nearby obstacles to gain better reception. Larger dipoles are sometimes hung in a V shape with the center near the radio equipment on the ground or the ends on the ground with the center supported. Shorter dipoles can be hung vertically. Some have extra elements to get better reception such as loops (especially for UHF transmissions), which can be turned around a vertical axis, or a dial, which modifies the electrical properties of the antenna at each dial position.
Horizontal wire dipole antennas are popular for use on the HF shortwave bands, both for transmitting and shortwave listening. They are usually constructed of two lengths of wire joined by a strain insulator in the center at which a ladder line or coaxial feedline is attached, with the ends supported by buildings, towers, or trees. These are simple to put up for temporary or field use. For transmitting antennas, it is essential that the ends of the antenna be attached to supports through strain insulators with a sufficiently high flashover voltage, since the antenna's high voltage antinodes occur there.
Dipoles are generally more efficient than whip antennas (quarterwave monopoles). The total radiated power and the radiation resistance are twice that of a quarterwave monopole. Thus, if a whip antenna were used with an infinite perfectly conducting ground plane, then it would be as efficient in halfspace as a dipole in free space an infinite distance from any conductive surfaces such as the earth's surface. However, in real life situations, if considering the antenna height, a monopole may have an advantage at certain radiating angles, especially at low heights.
Large constructed halfwavelength dipole towers include the Warsaw radio mast — the only halfwave dipole for longwave ever built.
Vertical dipoles can be stacked end to end to make collinear antenna arrays, to give a higher gain than a single dipole. The radiation pattern of the array is omnidirectional like a dipole, but the toroidalshaped pattern is "flattened" so more of the power is radiated in horizontal directions and less is radiated up into the sky and down toward the ground and wasted. Collinear arrays are a higher gain alternative to whip antennas for fixed base station antennas for mobile twoway radios, such as police, fire, or taxi dispatchers.
Elementary, short and halfwave dipoles:
