Sperner's lemma

File:Rabbit-ears dipole antenna with UHF loop 20090204.jpg

"Rabbit-ears" television antenna (the wire loop is a separate UHF loop antenna).

File:Dipole antenna m en.svg

Schematic of a (balanced) half-wave dipole antenna connected to an unbalanced coaxial cable.

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In radio and telecommunications a dipole antenna or doublet is the simplest and most widely used class of antenna. It consists of two identical conductive elements such as metal wires or rods, which are usually bilaterally symmetrical. 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.

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. 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. The most common form is the half-wave dipole, in which each of the two rod elements is approximately 1/4 wavelength long, so the whole antenna is a half-wavelength long.

Several different variations of the dipole are also used, such as the folded dipole, short dipole, cage dipole, bow-tie, 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, 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.

Elementary doublet

File:Elementary-doublet.jpg

Elementary doublet.

From a theoretical point of view, the dipole antenna is the simplest antenna type. An elementary doublet or Hertzian dipole is a small length of conductor δℓ (small compared to the wavelength λ) carrying an alternating current:

$I=I_0{e}^{i\omega t}.$

Here ω = 2πf is the angular frequency (and f the frequency), and i = Template:Sqrt 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 we must divide a real antenna, in order to calculate its properties.

In the case of the elementary doublet it is possible to find exact, closed-form expressions for its electric field, E, and its magnetic field, H. In spherical coordinates, they are

$E_r=\frac{Z{I}_0\delta \ell }{2\pi }(\frac{1}{r^2}-\frac{i}{k{r}^3})e^{i(\omega t-kr)}\cos (\theta )$

$E_{\theta }=i\frac{Z{I}_0\delta \ell }{4\pi }(\frac{k}{r}-\frac{i}{r^2}-\frac{1}{k{r}^3})e^{i(\omega t-kr)}\sin (\theta )$

$H_{\varphi }=i\frac{I_0\delta \ell }{4\pi }(\frac{k}{r}-\frac{i}{r^2})e^{i(\omega t-kr)}\sin (\theta )$

$E_{\varphi }=H_r=H_{\theta }=0,$

where r is the distance from the doublet to the point where the fields are evaluated, k = 2π/λ is the wavenumber, and Z = Template:Sqrt = 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, and hence

$E_{\theta }=i\frac{Z{I}_0\delta \ell k}{4\pi r}{e}^{i(\omega t-kr)}\sin (\theta )$

$H_{\varphi }=i\frac{I_0\delta \ell k}{4\pi r}{e}^{i(\omega t-kr)}\sin (\theta )$

$E_r=E_{\varphi }=H_r=H_{\theta }=0.$

The far electric field, E_θ, of the electromagnetic wave is co-planar 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 south-north, the electric field would be parallel to geographic meridians and the magnetic field of the electromagnetic wave would be parallel to geographic parallels.

Radiation resistance and aperture

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

$R_{\mathrm{r}\mathrm{a}\mathrm{d}}=\frac{2\pi }{3}{Z}_0{\left(\frac{\delta \ell }{\lambda }\right)}^2,$

where Z₀ 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

$A_{\mathrm{e}}=\frac{3{\lambda }^2}{8\pi }=\frac{G{\lambda }^2}{4\pi },$

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.

Dipole characteristics

Frequency versus length

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, so they are inefficient antennas; though inefficient, they can be practical antennas for long wavelengths. Dipoles whose length is half the wavelength of the signal are called half-wave dipoles, and are more efficient. In general radio engineering, the term dipole usually means a half-wave dipole (center-fed).

A half-wave dipole is cut to length l for frequency f in hertz according to the formula

$l=\frac{1}{2}{\lambda }_d=\frac{1}{2}k{\lambda }_0=\frac{1}{2}k\frac{c}{f}$

where λ_d is the wavelength on the dipole elements, λ₀ is the free-space wavelength, c is the speed of light in free space (Template:Convert), 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.

Radiation pattern and gain

File:Felder um Dipol.jpg

Electric fields (blue) and magnetic fields (red) radiated by a dipole antenna

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 λ/2-dipole is 10 log 1.64 or 2.15 dBi.

File:RadPatt-lin.png Radiation pattern of a half-wave dipole antenna. The scale is linear.

File:RadPatt-dB.png Gain of a half-wave dipole (same as left). The scale is in dBi (decibels over isotropic).

Feeding a Dipole Antenna

A folded dipole has a central impedance of about 300 ohms. Therefore the simplest way of feeding a folded dipole antenna is using a 300-ohm ladder line. Ideally, a half-wave (λ/2) dipole should be fed with a balanced line matching the theoretical 73-ohm impedance of the antenna. A folded dipole uses a 300-ohm balanced feeder line. Many people have had success in feeding a dipole directly with a coaxial cable feed rather than a ladder-linePotter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.. 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, and the radiation pattern may be asymmetrically distorted. This can be remedied with the use of a balun.

Feeding a Dipole with Baluns

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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. This is 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. This can induce 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 (and reception) pattern may be distorted asymmetrically. At higher frequencies, where the length of the dipole becomes significantly shorter than the diameter of the feeder coax, 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 baluns 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. The choice of the toroid core is crucial. A rule of thumb is: the more power the bigger the core.

Current balun

A current balun consists of two windings that are closely coupled.

Coax balun

A coax balun is a cost-effective method of eliminating feeder radiation, but is limited to a narrow set of operating frequencies.

• One easy way to make a balun is a (λ/2) length of coaxial cable. 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.

Sleeve balun

At VHF frequencies, a sleeve balun can also be built to remove feeder radiation.

• Another narrow band 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.

Dipole types

Short dipole

Diagram of a short dipole antenna.

Diagram of a short dipole antenna.

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

$E_{\theta }=\frac{-i{I}_0\sin \theta }{4{\epsilon }_{0}cr}\frac{L}{\lambda }{e}^{i(\omega t-kr)}.$

File:Elem-doubl-rad-pat.jpg

Radiation pattern of an elementary doublet, shown in profile.

File:Elem-doub-rad-pat-pers.jpg

Three-dimensional perspective of the radiation pattern of an elementary doublet.

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 torus-shaped, 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:

$R_{\text{series}}=\frac{\pi }{6}{Z}_0{\left(\frac{L}{\lambda }\right)}^2\text{ for }L\ll \lambda ,$

where $Z_0$ is the impedance of free space. Using a common approximation of $Z_0\approx 120\pi$ ohms, we get

$R_{\text{series}}\approx 20{\pi }^2{\left(\frac{L}{\lambda }\right)}^2\text{(in ohms)}.$

Antenna gain

Antenna gain, G, is the ratio of surface power radiated by the antenna to the surface power radiated by a hypothetical isotropic antenna:

$G=\frac{(P/S{)}_{\text{ant}}}{(P/S{)}_{\text{iso}}}.$

The surface power carried by an electromagnetic wave is

${\left(\frac{P}{S}\right)}_{\text{ant}}=\frac{1}{2}c{\epsilon }_0{E}_{\theta }^2\simeq \frac{E_{\theta }^2}{240\pi },$

while the surface power radiated by an isotropic antenna feed with the same power is

${\left(\frac{P}{S}\right)}_{\text{iso}}=\frac{\frac{1}{2}{R}_{\text{series}}{I}_0^2}{4\pi r^2}.$

Combining these expressions with the far-field expression for E_θ for a short dipole gives

$G=\frac{3}{2}=\mathrm{1.76}\mathrm{d}\mathrm{B}\mathrm{i},$

where dBi means decibels gain relative to an isotropic antenna.

Half-wave dipole<Half-wave antenna>...</Half-wave antenna>

File:Half – Wave Dipole.jpg

UHF–Half–Wave Dipole, 1.0–4 GHz

File:Dipole Antenna.svg

The instantaneous voltage distribution across a dipole antenna of total length λ/2.

Typically a dipole antenna is formed by two quarter-wavelength 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.

File:Lambdaover2-antenna.jpg

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:

$I(z)=I_0{e}^{i\omega t}\cos kz,$

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

$E_{\theta }=\frac{-iZ{I}_0}{2\pi r}\frac{\cos (\frac{\pi }{2}\cos \theta )}{\sin \theta }{e}^{i(\omega t-kr)},$

where again Z = Template:Sqrt. The trigonometric factor cos[(π/2)cos θ]/sin θ is approximately equal to the factor sin θ appearing in the far-field radiation pattern for the elementary doublet, so the radiation pattern of a half-wave antenna is a slightly flattened torus.

File:L-over2-rad-pat.svg

Cross-section of the far-field radiation pattern of the half-wave antenna (solid line) compared to the far-field radiation pattern of the elementary doublet (dashed line).

File:L-over2-rad-pat-per.jpg

Three-dimensional view of the far-field radiation pattern of the half-wave antenna.

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 half-wave resistance:

$\begin{array}{cc}{R}_{\frac{\lambda }{2}}& =\frac{Z_0}{2\pi }[\ln (2\pi \gamma )-\mathrm{Ci}(2\pi )]=\frac{Z_0}{4\pi }\mathrm{Cin}(2\pi )=29.9792458{\int }_0^{2\pi }\frac{1-\cos (\theta )}{\theta }d\theta ,\\ & \approx 73.0790102\Omega ;\end{array}$

This leads to the gain of a dipole antenna, $G_{\frac{\lambda }{2}}$:

$\begin{array}{cc}{G}_{\frac{\lambda }{2}}& =\frac{60^2}{30R_{\frac{\lambda }{2}}}=\frac{3600}{30R_{\frac{\lambda }{2}}}=\frac{120}{R_{\frac{\lambda }{2}}}=\frac{4}{\mathrm{Cin}(2\pi )}\approx 1.64\approx 2.15\mathrm{d}\mathrm{B}\mathrm{i}.\end{array}$

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 impedance are drawn for lengths going from $0.4\lambda$ to $0.6\lambda$, accompanied by a chart comparing the gains of dipole antennas of other lengths, both as a number and in dBi:

File:Dipole antenna impedance.svg

Dipole impedance

Gain of dipole antennas
length L in $\lambda$	Gain	Gain(dBi)
$\ll$ 0.1	1.50	1.76
0.5	1.64	2.15

Ideal half-wavelength dipole

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.

$R_r=\frac{75\Omega }{{\sin }^2(2\pi x/\lambda )}$

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 part-way 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.

Quarter-wave monopole

File:A6-3EN.jpg

The antenna and its image form a $\frac{\lambda }{2}$ dipole that radiates only upward.

The quarter-wave monopole antenna is a single-element antenna fed at one end, that behaves as a dipole antenna. It is formed by a conductor $\frac{\lambda }{4}$ 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 quarter-wave conductor and its image together form a half-wave 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 half-wave dipole fed with the same current. Therefore, the total emitted power is half the emitted power of a half-wave 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 half-wave dipole. As the reactive part is also divided by 2, the impedance of a quarter-wave antenna is $\frac{73+i43}{2}=36+i21$ ohms. Since the fields above ground are the same as for the dipole, but only half the power is applied, the gain is twice (3dB over) that of a half-wave dipole ($\frac{\lambda }{2}$), 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 half-wave 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 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.

Folded dipole

File:Folded dipole.jpg

Folded dipole antenna

A folded dipole is a half-wave dipole with an additional wire connecting its two ends. If the additional wire has the same diameter and cross-section as the dipole, two nearly identical radiating currents are generated. The resulting far-field emission pattern is nearly identical to the one for the single-wire dipole described above; however, at resonance its input (feedpoint) impedance $R_{fd}$ is four times the radiation resistance of a single-wire dipole. This is because for a fixed amount of power, the total radiating current $I_0$ 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

$\frac{1}{2}{R}_{\frac{\lambda }{2}}{I}_0^2=\frac{1}{2}{R}_{fd}{(I_0/2)}^2.$

It follows that

$R_{fd}=4R_{\frac{\lambda }{2}}\approx 292.32\Omega .$

The folded dipole is therefore well matched to 300-ohm 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 half-wave dipole. If the conductor has a constant radius and cross-section, at resonance the input impedance is four times that of a half-wave dipole. Moreover, the folded dipole can be used for transforming the value of input impedance of the dipole over a broad range of step-up ratios by changing the thicknesses of the wire conductors for the fed- and folded-sides.

File:AmateurRadioAntenna2.JPG

A self-made dipole antenna with mast

Other dipole antenna types

There is a variety of other important dipole antennas.

• The bow-tie antenna is a dipole with flaring, triangular shaped arms. The shape gives it a much wider bandwidth than an ordinary dipole. It is widely used in UHF television antennas.
• The G5RV Antenna is a dipole antenna with a symmetric feeder line, which also serves as a 1:1 impedance transformer allowing the transceiver to see the impedance of the antenna (it does not match the antenna to the 50-ohm transceiver. In fact the impedance will be somewhere around 90 ohms at the resonant frequency but significantly different at other frequencies).
• The Doublet Antenna is a dipole antenna with a resonant symmetric feeder line.
• The Sloper antenna is a slanted dipole antenna used for long-range communications or in limited space.
• The AS-2259 Antenna is an inverted-V dipole antenna used for NVIS communications.

General impedance formulas

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.

Induced EMF method

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:

$\begin{array}{cc}{R}_{\mathrm{d}\mathrm{i}\mathrm{p}\mathrm{o}\mathrm{l}\mathrm{e}}& =\frac{Z}{2\pi {\sin }^2(kL/2)}\{\gamma +\ln (kL)-\mathrm{Ci}(kL)+\frac{1}{2}\sin (kL)[\mathrm{Si}(2kL)-2\mathrm{Si}(kL)]\\ & +\frac{1}{2}\cos (kL)[\gamma +\ln (kL/2)+\mathrm{Ci}(2kL)-2\mathrm{Ci}(kL)]\}\end{array}$

$\begin{array}{cc}{X}_{\mathrm{d}\mathrm{i}\mathrm{p}\mathrm{o}\mathrm{l}\mathrm{e}}& =\frac{Z}{4\pi {\sin }^2(kL/2)}\{2\mathrm{Si}(kL)+\cos (kL)[2\mathrm{Si}(kL)-\mathrm{Si}(2kL)]\\ & -\sin (kL)[2\mathrm{Ci}(kL)-\mathrm{Ci}(2kL)-\mathrm{Ci}(2k{a}^2/L)]\},\end{array}$

where Ci and Si are the cosine and sine integral functions and γ is the Euler constant.

The Induced EMF method is inaccurate for dipoles longer than a half wavelength (kL>π) and verticals longer than quarter wavelength. Halléns integral solution and similar give more successful results.

Dipole as a reference standard

Antenna gain is sometimes measured as dB 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 aerial 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.

Common applications

Set-top TV antenna

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. 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 turnable around a vertical axis, or a dial, which modifies the electrical properties of the antenna at each dial position.

Shortwave antenna

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 versus whip antennas

Dipoles are generally more efficient than whip antennas (quarter-wave monopoles). The total radiated power and the radiation resistance are twice that of a quarter-wave monopole. Thus, if a whip antenna were used with an infinite perfectly conducting ground plane, then it would be as efficient in half-space 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.

Dipole towers

Large constructed half-wavelength dipole towers include the Warsaw radio mast — the only half-wave dipole for longwave ever built.

Collinear dipole arrays

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 toroidal-shaped 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 two-way radios, such as police, fire, or taxi dispatchers.

See also

• Electronic symbol
• Isotropic antenna
• Omnidirectional antenna
• Whip antenna
• Driven element
• Balun
• Coaxial antenna
• Amateur radio
• Shortwave listening
• T-aerial
• AM broadcasting
• FM broadcasting

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

Elementary, short and half-wave dipoles: Template:Refbegin

• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
• http://www.ece.rutgers.edu/~orfanidi/ewa/ Electromagnetic Waves and Antennas, Sophocles J. Orfanidis.
• Wire Antenna Resources for Ham Radio Wire Antenna Resources including off center fed dipole (OCFD), dipole calculators and construction sites
• http://stewks.ece.stevens-tech.edu/sktpersonal.dir/sktwireless/lin-ant.pdf
• http://www.nt.hs-bremen.de/peik/asc/asc_antenna_slides.pdf
• The Hertzian dipole
• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
• Reflections on Hertz and the Hertzian Dipole Jed Z. Buchwald, MIT and the Dibner Institute for the History of Science and Technology (link inactive February 2, 2007; archive accessed from Wayback, March 13, 2011)

External links

• Dipole Antenna Tutorial EM Talk
• Broadband Dipoles Antenna-Theory.com
• AC6V's Homebrew Antennas Links
• Your First HF Dipole - simple yet complete tutorial from eham.net