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Radiation resistance, \ R_\mathsf\ or \ R_\mathsf\ , is proportional to the part of an
antenna Antenna ( antennas or antennae) may refer to: Science and engineering * Antenna (radio), also known as an aerial, a transducer designed to transmit or receive electromagnetic (e.g., TV or radio) waves * Antennae Galaxies, the name of two collid ...
's feedpoint
electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels ...
that is caused by power loss from the emission of
radio wave Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 gigahertz (GHz) and below. At 300 GHz, the corresponding wavelength is 1 mm (short ...
s from the antenna. Radiation resistance is an ''effective'' resistance, due to the power carried away from the antenna as radio waves. Unlike conventional resistance or " Ohmic resistance", radiation resistance is ''not'' due to the opposition to current (
resistivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
) of the imperfect conducting materials the antenna is made of. The radiation resistance (\ R_\mathsf\ ) is conventionally defined as the value of loss resistance that ''would'' dissipate the same amount of power as heat, as is dissipated by the radio waves emitted from the antenna, when fed at a minimum-voltage / maximum-current point ("voltage node"). From
Joule's law Joule effect and Joule's law are any of several different physical effects discovered or characterized by English physicist James Prescott Joule. These physical effects are not the same, but all are frequently or occasionally referred to in the lite ...
, it is equal to the total power \ P_\mathsf\ radiated as radio waves by the antenna, divided by the square of the current \ I_\mathsf\ into the antenna terminals: \ R_\mathsf = P_\mathsf/I_\mathsf^2 ~. The feedpoint and radiation resistances are determined by the geometry of the antenna, the operating
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
, and the antenna location (particularly with respect to the ground). The relation between the feedpoint resistance (\ R_\mathsf\ ) and the radiation resistance (\ R_\mathsf\ ) depends on the position on the antenna at which the feedline is attached. The relation between feedpoint resistance and radiation resistance is particularly simple when the feedpoint is placed (as ususal) at the antenna's minimum ''possible'' voltage / maximum possible current point; in that case, the total feedpoint resistance \ R_\mathsf\ at the antenna's terminals is equal to the sum of the radiation resistance plus the loss resistance \ R_\mathsf\ due to "Ohmic" losses in the antenna and the nearby soil: \ R_\mathsf = R_\mathsf + R_\mathsf\ . When the antenna is fed at some other point, the formula requires a correction factor discussed below. In a receiving antenna the radiation resistance represents the
source resistance The output impedance of an electrical network is the measure of the opposition to current flow (impedance), both static ( resistance) and dynamic ( reactance), into the load network being connected that is ''internal'' to the electrical source. The ...
of the antenna, and the portion of the received radio power consumed by the radiation resistance represents radio waves re-radiated (scattered) by the antenna.


Cause

Electromagnetic wave In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
s are radiated by
electric charges Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respectiv ...
when they are accelerated. In a transmitting antenna radio waves are generated by time varying
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving pa ...
s, consisting of
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
s accelerating as they flow back and forth in the metal antenna, driven by the
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
due to the oscillating voltage applied to the antenna by the
radio transmitter In electronics and telecommunications, a radio transmitter or just transmitter is an electronic device which produces radio waves with an antenna. The transmitter itself generates a radio frequency alternating current, which is applied to the ...
. An electromagnetic wave carries
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
away from the electron which emitted it. The cause of radiation resistance is the
radiation reaction In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes: * ''electromagnetic radiation'', such as radio waves, microwaves, infrared, visi ...
, the recoil force on the electron when it emits a radio wave
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
, which reduces its
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
. This is called the
Abraham–Lorentz force In the physics of electromagnetism, the Abraham–Lorentz force (also Lorentz–Abraham force) is the recoil force on an accelerating charged particle caused by the particle emitting electromagnetic radiation by self-interaction. It is also called ...
. The recoil force is in a direction opposite to the
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
in the antenna accelerating the electron, reducing the average velocity of the electrons for a given driving voltage, so it acts as a resistance opposing the current.


Radiation resistance and loss resistance

The radiation resistance is only part of the feedpoint resistance at the antenna terminals. An antenna has other energy losses which appear as additional resistance at the antenna terminals; ohmic resistance of the metal antenna elements, ground losses from currents induced in the ground, and
dielectric loss Dielectric loss quantifies a dielectric material's inherent dissipation of electromagnetic energy (e.g. heat). It can be parameterized in terms of either the loss angle ''δ'' or the corresponding loss tangent tan ''δ''. Both refer to the ...
es in insulating materials. When the feedpoint is (as usual) at a voltage minimum and current maximum, the total feedpoint resistance \ R_\mathsf\ is equal to the sum of the radiation resistance \ R_\mathsf\ and loss resistance \ R_\mathsf\ :\ R_\mathsf = R_\mathsf + R_\mathsf\ The power P_\mathsf fed to the antenna is split proportionally between these two resistances. :\ P_\mathsf = I_\mathsf^2 (R_\mathsf + R_\mathsf)\ :\ P_\mathsf = P_\mathsf + P_\mathsf where :\ P_\mathsf = I_\mathsf^2 R_\mathsf \quad and \quad P_\mathsf = I_\mathsf^2 R_\mathsf\ The power \ P_\mathsf\ consumed by radiation resistance is converted to radio waves, the desired function of the antenna, while the power \ P_\mathsf\ consumed by loss resistance is converted to heat, representing a waste of transmitter power. So for minimum power loss it is desirable that the radiation resistance be much greater than the loss resistance. The ratio of the radiation resistance to the total feedpoint resistance is equal to the
efficiency Efficiency is the often measurable ability to avoid wasting materials, energy, efforts, money, and time in doing something or in producing a desired result. In a more general sense, it is the ability to do things well, successfully, and without ...
(\eta) of the antenna. :\ \eta = = \ To transfer maximum power to the antenna, the transmitter and feedline must be impedance matched to the antenna. This means the feedline must present to the antenna a resistance equal to the input resistance \ R_\mathsf\ and a reactance (capacitance or inductance) equal but opposite to the antenna's reactance. If these impedances are not matched, the antenna will reflect some of the power back toward the transmitter, so not all the power will be radiated. For "large" antennas, the radiation resistance is usually the main part of their input resistance, so it determines what impedance matching is necessary and what types of
transmission line In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmis ...
would match well to the antenna.


Effect of the feedpoint

When the feedpoint is placed at a location other than the minimum-voltage / maximum current point, or if a "flat" voltage minimum does not occur on the antenna, then the simple relation \ R_\mathsf = R_\mathsf + R_\mathsf\ no longer holds. In a
resonant Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscilla ...
antenna, the current and voltage form
standing wave In physics, a standing wave, also known as a stationary wave, is a wave that oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with respect ...
s along the length of the antenna element, so the magnitude of the current in the antenna varies sinusoidally along its length. The '' feedpoint'', the place where the
feed line In a radio antenna, the feed line (feedline), or feeder, is the cable or other transmission line that connects the antenna with the radio transmitter or receiver. In a transmitting antenna, it feeds the radio frequency (RF) current from the ...
from the transmitter is attached, can be located anywhere along the antenna element. Since feedpoint resistance depends on the input current, it varies with the feedpoint. It is lowest for feedpoints located at a point of maximum current (an
antinode A node is a point along a standing wave where the wave has minimum amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effect ...
), and highest for feedpoints located at a point of minimum current, a
node In general, a node is a localized swelling (a "knot") or a point of intersection (a vertex). Node may refer to: In mathematics *Vertex (graph theory), a vertex in a mathematical graph *Vertex (geometry), a point where two or more curves, lines, ...
, such as at the end of the element (theoretically, in an infinitesimally thin antenna element, radiation resistance is infinite at a node, but the finite thickness of actual antenna elements gives it a high but finite value, on the order of thousands of ohms). The choice of feedpoint is sometimes used as a convenient way to
impedance match In electronics, impedance matching is the practice of designing or adjusting the input impedance or output impedance of an electrical device for a desired value. Often, the desired value is selected to maximize power transfer or minimize sign ...
an antenna to its feed line, by attaching the feedline to the antenna at a point at which its input resistance happens to equal to the feed line impedance. In order to give a meaningful value for the antenna efficiency, the radiation resistance and loss resistance must be referred to the same point on the antenna, often the input terminals. Radiation resistance is by convention calculated with respect to the maximum ''possible'' current \ I_\mathsf\ on the antenna. When the antenna is fed at a point of maximum current, as in the common center-fed
half-wave dipole In radio and telecommunications a dipole antenna or doublet is the simplest and most widely used class of antenna. The dipole is any one of a class of antennas producing a radiation pattern approximating that of an elementary electric dipole wi ...
or base-fed quarter-wave monopole, that value \ R_\mathsf\ is mostly the radiation resistance. However, if the antenna is fed at some other point, the equivalent radiation resistance at that point \ R_\mathsf\ can easily be calculated from the ratio of antenna currents :\ P_\mathsf = I_\mathsf^2 R_\mathsf = I_\mathsf^2 R_\mathsf\ :\ R_\mathsf = \left( \right)^2 R_\mathsf \approx \left(\frac \right)^2 R_\mathsf\ where \ \theta_\mathsf\ and \ \theta_\mathsf\ are the
electrical length In electrical engineering, electrical length is a dimensionless parameter equal to the physical length of an electrical conductor such as a cable or wire, divided by the wavelength of alternating current at a given frequency traveling through th ...
s (as electrical degrees or radians) from the current node (usually measured from the tip of a linear antenna).


Receiving antennas

In a receiving antenna, the radiation resistance represents the
source resistance The output impedance of an electrical network is the measure of the opposition to current flow (impedance), both static ( resistance) and dynamic ( reactance), into the load network being connected that is ''internal'' to the electrical source. The ...
of the antenna as a ( Thevenin equivalent) source of power. Due to electromagnetic reciprocity, an antenna has the same radiation resistance when receiving radio waves as when transmitting. If the antenna is connected to an electrical load such as a
radio receiver In radio communications, a radio receiver, also known as a receiver, a wireless, or simply a radio, is an electronic device that receives radio waves and converts the information carried by them to a usable form. It is used with an antenna. Th ...
, the power received from radio waves striking the antenna is divided proportionally between the radiation resistance and loss resistance of the antenna and the load resistance. The power dissipated in the radiation resistance is due to radio waves reradiated (scattered) by the antenna. Maximum power is delivered to the receiver when it is impedance matched to the antenna. If the antenna is lossless, half the power absorbed by the antenna is delivered to the receiver, the other half is reradiated.


Radiation resistance of common antennas

In all of the formulas listed below, the radiation resistance is the so-called "free space" resistance, which the antenna would have if it were mounted several wavelengths distant from the ground (not including the distance to an elevated counterpoise, if any). Installed antennas will have higher or lower radiation resistances if they are mounted near the ground (less than 1 
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
) in addition to the loss resistance from the antenna's near electrical field that penetrates the soil. : The above figures assume the antennas are made of thin conductors and sufficiently far away from large metal structures, that the dipole antennas are sufficiently far above the ground, and the monopoles are mounted over a perfectly conducting
ground plane In electrical engineering, a ground plane is an electrically conductive surface, usually connected to electrical ground. The term has two different meanings in separate areas of electrical engineering. *In antenna theory, a ground plane is a ...
. The
half-wave dipole In radio and telecommunications a dipole antenna or doublet is the simplest and most widely used class of antenna. The dipole is any one of a class of antennas producing a radiation pattern approximating that of an elementary electric dipole wi ...
's radiation resistance of 73 ohms is near enough to the
characteristic impedance The characteristic impedance or surge impedance (usually written Z0) of a uniform transmission line is the ratio of the amplitudes of voltage and current of a single wave propagating along the line; that is, a wave travelling in one direction in ...
of common 50 Ohm and 75 Ohm
coaxial cable Coaxial cable, or coax (pronounced ) is a type of electrical cable consisting of an inner conductor surrounded by a concentric conducting shield, with the two separated by a dielectric ( insulating material); many coaxial cables also have a p ...
that it can usually be fed directly without need of an
impedance matching In electronics, impedance matching is the practice of designing or adjusting the input impedance or output impedance of an electrical device for a desired value. Often, the desired value is selected to maximize power transfer or minimize signal ...
network. This is one reason for the wide use of the half wave dipole as a
driven element {{Unreferenced, date=April 2016 In a multielement antenna array (such as a Yagi–Uda antenna), the driven element or active element is the element in the antenna (typically a metal rod) which is electrically connected to the receiver or transmi ...
in antennas.


Relationship of monopoles and dipoles

The radiation resistance of a monopole antenna created by replacing one side of a dipole antenna by a perpendicular ground plane is one-half of the resistance of the original dipole antenna. This is because the monopole radiates only into half the space, the space above the plane, so the radiation pattern is identical to half of the dipole pattern and therefore with the same input current it radiates only half the power. This is not obvious from the formulas in the table because the different lengths use the same symbol, \ell\,; the derived monopole antenna, however, is only half the length of the original dipole antenna. This can be shown by calculating the radiation resistance of a short dipole (length \ \ell_\mathsf\ ), which is twice the length of the corresponding monopole (\ \ell_\mathsf\ ): :R_\mathsf = 20\pi^2 \left( \frac \right)^2 = 20\pi^2 \left( \frac \right)^2 = 80\pi^2 \left( \frac \right)^2 \qquad (dipole length \ell_\mathsf = 2 \ell_\mathsf). Comparing this to the formula for the short monopole shows the dipole has double the radiation resistance of the monopole: :R_\mathsf = 40 \pi^2 \left(\frac\right)^2 \qquad \qquad \qquad \qquad (monopole of length \ell_\mathsf). This confirms the consistency of physically modelling a center-fed dipole as two monopoles, placed end-to-end, with adjacent feedpoints.


Calculation

Calculating the radiation resistance of an antenna directly from the reaction force on the electrons is very complicated, and presents conceptual difficulties in accounting for the self-force of the electron. Radiation resistance is instead calculated by computing the
far-field The near field and far field are regions of the electromagnetic (EM) field around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Non-radiative ''near-field'' behaviors dominate close to the ante ...
radiation pattern In the field of antenna design the term radiation pattern (or antenna pattern or far-field pattern) refers to the ''directional'' (angular) dependence of the strength of the radio waves from the antenna or other source.Constantine A. Balanis: “A ...
of the antenna, the power flux (
Poynting vector In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area per unit time) or '' power flow'' of an electromagnetic field. The SI unit of the Poynting vector is the watt ...
) at each angle, for a given antenna current. This is integrated over a sphere enclosing the antenna to give the total power P_\mathsf radiated by the antenna. Then the radiation resistance is calculated from the power by
conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means th ...
, as the resistance the antenna must present to the input current to absorb the radiated power from the transmitter, using
Joule's law Joule effect and Joule's law are any of several different physical effects discovered or characterized by English physicist James Prescott Joule. These physical effects are not the same, but all are frequently or occasionally referred to in the lite ...
R_\mathsf = P_\mathsf / I_\mathsf^2


Small antennas

Electrically short antennas, antennas with a length much less than a
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
, make poor transmitting antennas, as they cannot be fed efficiently due to their low radiation resistance. At frequencies below 1 MHz the size of ordinary
electrical circuit An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, ...
s and the lengths of wire used in them is so much smaller than the wavelength, that when considered as antennas they radiate an insignificant fraction of the power in them as radio waves. This explains why electrical circuits can be used with alternating current without losing energy as radio waves.


Low radiation resistance

As can be seen in the above table, for linear antennas shorter than their fundamental resonant length (shorter than for a dipole antenna, for a monopole) the radiation resistance decreases with the square of their length; for loop antennas the change is even more extreme, with sub-resonant loops (circumference less than for a continuous loop, or for a split loop) the radiation resistance decreases with the fourth power of the perimeter length. The loss resistance is in series with the radiation resistance, and as the length decreases the loss resistance only decreases in proportion to the first power of the length ( wire resistance) or remains constant (
contact resistance The term contact resistance refers to the contribution to the total resistance of a system which can be attributed to the contacting interfaces of electrical leads and connections as opposed to the intrinsic resistance. This effect is describe ...
), and hence makes up an ''increasing'' proportion of the feedpoint resistance. So with smaller antenna size, measured in wavelengths, loss to heat consumes a larger fraction of the transmitter power, causing the efficiency of the antenna to fall. For example, navies use radio waves of about 15–30 kHz in the
very low frequency Very low frequency or VLF is the ITU designation for radio frequencies (RF) in the range of 3–30  kHz, corresponding to wavelengths from 100 to 10 km, respectively. The band is also known as the myriameter band or myriameter wave a ...
(VLF) band to communicate with submerged submarines. A 15 kHz radio wave has a wavelength of 20 km. The powerful naval shore VLF transmitters which transmit to submarines use large monopole mast antennas which are limited by construction costs to heights of about Although these antennas are enormous compared to a human, at 15 kHz the antenna height is still only about 0.015 wavelength, so paradoxically, huge VLF antennas are electrically ''short''. From the table above, a monopole antenna has a radiation resistance of about 0.09 Ohm.


Essentially insurmountable loss resistance

It is extremely difficult to reduce the loss resistance of an antenna to this level. Since the ohmic resistance of the huge ground system and
loading coil A loading coil or load coil is an inductor that is inserted into an electronic circuit to increase its inductance. The term originated in the 19th century for inductors used to prevent signal distortion in long-distance telegraph transmission c ...
cannot be made lower than about 0.5 ohm, the efficiency of a simple vertical antenna is below 20%, so more than 80% of the transmitter power is lost in the ground resistance. To increase the radiation resistance, VLF transmitters use huge capacitively top-loaded antennas such as
umbrella antenna An umbrella antenna is a capacitively top-loaded wire monopole antenna, consisting in most cases of a mast fed at the ground end, to which a number of radial wires are connected at the top, sloping downwards. They are used as transmitting antennas ...
s and flattop antennas, in which an aerial network of horizontal wires is attached to the top of the vertical radiator to make a 'capacitor plate' to ground, to increase the current in the vertical radiator. However this can only increase the efficiency to 50–70% at most. Small receiving antennas, such as the ferrite
loopstick antenna A loop antenna is a radio antenna consisting of a loop or coil of wire, tubing, or other electrical conductor, that is usually fed by a balanced source or feeding a balanced load. Within this physical description there are two (possibly three) di ...
s used in AM radios, also have low radiation resistance, and thus produce very low output. However at frequencies below about 20 MHz this is not such a problem, since a weak signal from the antenna can simply be amplified in the receiver.


Definition of variables

:


See also

*
Antenna efficiency Antenna ''apertureillumination efficiency is a measure of the extent to which an antenna or array is uniformly excited or illuminated. It is typical for an antenna pertureor array to be intentionally under-illuminated or under-excited in order t ...
*
Impedance of free space The impedance of free space, , is a physical constant relating the magnitudes of the electric and magnetic fields of electromagnetic radiation travelling through free space. That is, , where is the electric field strength and is the magnetic fiel ...


Footnotes


References


Sources

* * * * * * * {{refend Antennas (radio)