Antenna

An antenna is a transducer designed to transmit or receive radio waves which are a class of electromagnetic waves. In other words, antennas convert radio frequency electrical currents into electromagnetic waves and vice versa. Antennas are used in systems such as radio and television broadcasting, point-to-point radio communication, wireless LAN, radar, and space exploration. Antennas usually work in air or outer space, but can also be operated under water or even through soil and rock at certain frequencies for short distances.

Physically, an antenna is an arrangement of conductors that generate a radiating electromagnetic field in response to an applied alternating voltage and the associated alternating electric current, or can be placed in an electromagnetic field so that the field will induce an alternating current in the antenna and a voltage between its terminals. Some antenna devices (parabola, horn antenna) just adapt the free space to another type of antenna.

Thomas Edison used antennas by 1885. Edison patented his system in U.S. Patent 465,971 . Antennas were also used in 1888 by Heinrich Hertz (1857-1894) to prove the existence of electromagnetic waves predicted by the theory of James Clerk Maxwell. Hertz placed the emitter dipole in the focal point of a parabolic reflector. He published his work and installation drawings in Annalen der Physik und Chemie (vol. 36, 1889).

Terminology

The words antenna (plural: antennas) and "aerial" are used interchangeably; but usually a rigid metallic structure is termed an antenna and a wire format is called an aerial. The origin of the word antenna relative to wireless apparatus is attributed to Guglielmo Marconi. In 1895, while testing early radio apparatus in the Swiss Alps at Salvan, Switzerland in the Mont Blanc region, Marconi experimented with early wireless equipment. A 2.5 meter long pole, along which was carried a wire, was used as a radiating and receiving aerial element. In Italian a tent pole is known as l'antenna centrale, and the pole with a wire alongside it used as an aerial was simply called l'antenna. Until then wireless radiating transmitting and receiving elements were known simply as aerials or terminals. Marconi's use of the word antenna (Italian for pole) would become a popular term for what today is uniformly known as the antenna.

A Hertzian antenna is a set of terminals that does not require the presence of a ground for its operation (versus a Tesla antenna which is grounded). A loaded antenna is an active antenna having an elongated portion of appreciable electrical length and having additional inductance or capacitance directly in series or shunt with the elongated portion so as to modify the standing wave pattern existing along the portion or to change the effective electrical length of the portion. An antenna grounding structure is a structure for establishing a reference potential level for operating the active antenna. It can be any structure closely associated with (or acting as) the ground which is connected to the terminal of the signal receiver or source opposing the active antenna terminal, (i.e., the signal receiver or source is interposed between the active antenna and this structure).

The noun aerial is occasionally written with a diaresis mark - aërial - in recognition of the original spelling of the adjective aërial from which the noun is derived.

Overview

Antennas have practical uses for the transmission and reception of radio frequency signals (radio, TV, etc.), which can theoretically travel over great distances at the speed of light (in the transmission medium). These signals can also pass through nonconducting walls (although often there is a variable signal reduction depending on the type of wall, and natural rock can be very reflective to radio signals).

The vast majority of antennas are simple vertical rods a quarter of a wavelength long. Such antennas are simple in construction, usually inexpensive, and both radiate in and receive from all horizontal directions (omnidirectional). One limitation of this antenna is that it does not radiate or receive in the direction in which the rod points. This region is called the antenna blind cone or null.

There are two fundamental types of antennas, which, with reference to a specific three dimensional (usually horizontal or vertical) plane are:

either Omni-directional (radiates equally in all directions), such as a vertical rod or

Directional (radiates more in one direction than in the other).

All antennas radiate some energy in all directions in free space but careful construction results in substantial transmission of energy in a preferred direction and negligible energy radiated in other directions.

By adding additional conducting rods or coils (called elements) and varying their length, spacing, and orientation (or changing the direction of the antenna beam), an antenna with specific desired properties can be created, such as a Yagi-Uda Antenna (often abbreviated to "Yagi").

An antenna array is two or more antennas coupled to a common source or load to produce a specific directional radiation pattern. The spatial relationship between individual antennas contributes to the directivity of the antenna.

The term active element is intended to describe an element whose energy output is modified due to the presence of a source of energy in the element (other than the mere signal energy which passes through the circuit) or an element in which the energy output from a source of energy is controlled by the signal input.

An antenna lead-in is the medium, for example, a transmission line or feed line for conveying the signal energy from the signal source to the antenna. The antenna feed refers to the components between the antenna and an amplifier.

An antenna counterpoise is a structure of conductive material most closely associated with ground that may be insulated from or capacitively coupled to the natural ground. It aids in the function of the natural ground, particularly where variations (or limitations) of the characteristics of the natural ground interfere with its proper function. Such structures are usually connected to the terminal of a receiver or source opposite to the antenna terminal.

An antenna component is a portion of the antenna performing a distinct function and limited for use in an antenna, as for example, a reflector, director, or active antenna.

Parasitic elements are usually metallic conductive structures which reradiate into free space impinging electromagnetic radiation coming from or going to the active antenna.

An electromagnetic wave refractor is a structure which is shaped or positioned to delay or accelerate transmitted electromagnetic waves, passing through such structure, an amount which varies over the wave front. The refractor alters the direction of propagation of the waves emitted from the structure with respect to the waves impinging on the structure. It can alternatively bring the wave to a focus or alter the wave front in other ways, such as to convert a spherical wave front to a planar wave front (or vice versa). The velocity of the waves radiated have a component which is in the same direction (director) or in the opposite direction (reflector) that of the velocity of the impinging wave.

A director is usually a metallic conductive structure which reradiates into free space impinging electromagnetic radiation coming from or going to the active antenna, the velocity of the reradiated wave having a component in the direction of velocity of the impinging wave. The director modifies the radiation pattern of the active antenna and there is no significant potential relationship between the active antenna and this conductive structure.

A reflector is usually a metallic conductive structure (e.g., screen, rod or plate) which reradiates back into free space impinging electromagnetic radiation coming from or going to the active antenna. The velocity of the returned wave having a component in a direction opposite to the direction of velocity of the impinging wave. The reflector modifies the radiation of the active antenna. There is no significant potential relationship between the active antenna and this conductive structure.

An antenna coupling network is a passive network (which may be any combination of a resistive, inductive or capacitive circuit(s)) for transmitting the signal energy between the active antenna and a source (or receiver) of such signal energy.

Typically, antennas are designed to operate in a relatively narrow frequency range. The design criteria for receiving and transmitting antennas differ slightly, but generally an antenna can receive and transmit equally well. This property is called reciprocity.

Antenna parameters

There are several critical parameters that affect an antenna's performance and can be adjusted during the design process. These are resonant frequency, impedance, gain, aperture or radiation pattern, polarization, efficiency and bandwidth. Transmit antennas may also have a maximum power rating, and receive antennas differ in their noise rejection properties.

Resonant frequency

The "resonant frequency" and "electrical resonance" is related to the electrical length of the antenna. The electrical length is usually the physical length of the wire divided by its velocity factor (the ratio of the speed of wave propagation in the wire to c0, the speed of light in a vacuum). Typically an antenna is tuned for a specific frequency, and is effective for a range of frequencies usually centered on that resonant frequency. However, the other properties of the antenna (especially radiation pattern and impedance) change with frequency, so the antenna's resonant frequency may merely be close to the center frequency of these other more important properties.

Antennas can be made resonant on harmonic frequencies with lengths that are fractions of the target wavelength. Some antenna designs have multiple resonant frequencies, and some are relatively effective over a very broad range of frequencies. The most commonly known type of wide band aerial is the logarithmic or log periodic, but its gain is usually much lower than that of a specific or narrower band aerial.

Gain

Gain as a parameter measures the directionality of a given antenna. An antenna with a low gain emits radiation in all directions equally, whereas a high-gain antenna will preferentially radiate in particular directions. Specifically, the Gain, Directive gain or Power gain of an antenna is defined as the ratio of the intensity (power per unit surface) radiated by the antenna in a given direction at an arbitrary distance divided by the intensity radiated at the same distance by an hypothetical isotropic antenna:

We write "hypothetical" because a perfect isotropic antenna cannot exist in reality (the electric and magnetic field would not satisfy Maxwell's equations for electromagnetic fields). Gain is a dimensionless number (without units).

The gain of an antenna is a passive phenomenon - power is not added by the antenna, but simply redistributed to provide more radiated power in a certain direction than would be transmitted by an isotropic antenna. If an antenna has a greater than one gain in some directions, it must have a less than one gain in other directions since energy is conserved by the antenna. An antenna designer must take into account the application for the antenna when determining the gain. High-gain antennas have the advantage of longer range and better signal quality, but must be aimed carefully in a particular direction. Low-gain antennas have shorter range, but the orientation of the antenna is inconsequential. For example, a dish antenna on a spacecraft is a high-gain device (must be pointed at the planet to be effective), while a typical WiFi antenna in a laptop computer is low-gain (as long as the base station is within range, the antenna can be in an any orientation in space).

Bandwidth

The "bandwidth" of an antenna is the range of frequencies over which it is effective, usually centered around the resonant frequency. The bandwidth of an antenna may be increased by several techniques, including using thicker wires, replacing wires with cages to simulate a thicker wire, tapering antenna components (like in a feed horn), and combining multiple antennas into a single assembly and allowing the natural impedance to select the correct antenna. Small antennas are usually preferred for convenience, but there is a fundamental limit relating bandwidth, size and efficiency.

Impedance

As an electro-magnetic wave travels through the different parts of the antenna system (radio, feed line, antenna, free space) it may encounter differences in impedance (E/H, V/I, etc). At each interface, depending on the impedance match, some fraction of the wave's energy will reflect back to the source, forming a standing wave in the feed line. The ratio of maximum power to minimum power in the wave can be measured and is called the standing wave ratio (SWR). A SWR of 1:1 is ideal. A SWR of 1.5:1 is considered to be marginally acceptable in low power applications where power loss is more critical, although an SWR as high as 6:1 may still be usable with the right equipment. Minimizing impedance differences at each interface (impedance matching) will reduce SWR and maximize power transfer through each part of the antenna system.

Complex impedance of an antenna is related to the electrical length of the antenna at the wavelength in use. The impedance of an antenna can be matched to the feed line and radio by adjusting the impedance of the feed line, using the feed line as an impedance transformer. More commonly, the impedance is adjusted at the load (see below) with an antenna tuner, a balun, a matching transformer, matching networks composed of inductors and capacitors, or matching sections such as the gamma match.

Radiation pattern

The radiation pattern is a graphical depiction of the relative field strength transmitted from or received by the antenna. As antennas radiate in space often several curves are necessary to describe the antenna. If the radiation of the antenna is symmetrical about an axis (as is the case in dipole, helical and some parabolic antennas) a unique graph is sufficient.

Each antenna supplier/user has different standards as well as plotting formats. Each format has its own advantages and disadvangages. Radiation pattern of an antenna can be defined as the locus of all points where the emitted power per unit surface is the same. The radiated power per unit surface is proportional to the squared electrical field of the electromagnetic wave. The radiation pattern is the locus of points with the same electrical field. In this representation, the reference is usually the best angle of emission. It is also possible to depict the directive gain of the antenna as a function of the direction. Often the gain is given in decibels.

Polarization

The "polarization" of an antenna is the orientation of the electric field (E-plane) of the radio wave with respect to the Earth's surface and is determined by the physical structure of the antenna and by its orientation. It has nothing in common with antenna directionality terms: "horizontal", "vertical" and "circular". Thus, a simple straight wire antenna will have one polarization when mounted vertically, and a different polarization when mounted horizontally. "Electromagnetic wave polarization filters" are structures which can be employed to act directly on the electromagnetic wave to filter out wave energy of an undesired polarization and to pass wave energy of a desired polarization.

Reflections generally affect polarization. For radio waves the most important reflector is the ionosphere - signals which reflect from it will have their polarization changed unpredictably. For signals which are reflected by the ionosphere, polarization cannot be relied upon. For line-of-sight communications for which polarization can be relied upon, it can make a large difference in signal quality to have the transmitter and receiver using the same polarization; many tens of dB difference are commonly seen and this is more than enough to make the difference between reasonable communication and a broken link.

Polarization is largely predictable from antenna construction, but especially in directional antennas, the polarization of side lobes can be quite different from that of the main propagation lobe. For radio antennas, polarization corresponds to the orientation of the radiating element in an antenna. A vertical omnidirectional WiFi antenna will have vertical polarization (the most common type). An exception is a class of elongated waveguide antennas in which vertically placed antennas are horizontally polarized. Many commercial antennas are marked as to the polarization of their emitted signals.

Polarization is the sum of the E-plane orientations over time projected onto an imaginary plane perpendicular to the direction of motion of the radio wave. In the most general case, polarization is elliptical (the projection is oblong), meaning that the antenna varies over time in the polarization of the radio waves it is emitting. Two special cases are linear polarization (the ellipse collapses into a line) and circular polarization (in which the ellipse varies maximally). In linear polarization the antenna compels the electric field of the emitted radio wave to a particular orientation. Depending on the orientation of the antenna mounting, the usual linear cases are horizontal and vertical polarization. In circular polarization, the antenna continuously varies the electric field of the radio wave through all possible values of its orientation with regard to the Earth's surface. Circular polarizations, like elliptical ones, are classified as right-hand polarized or left-hand polarized using a "thumb in the direction of the propagation" rule. Optical researchers use the same rule of thumb, but pointing it in the direction of the emitter, not in the direction of propagation, and so are opposite to radio engineers' use.

In practice, regardless of confusing terminology, it is important that linearly polarized antennas be matched, lest the received signal strength be greatly reduced. So horizontal should be used with horizontal and vertical with vertical. Intermediate matchings will lose some signal strength, but not as much as a complete mismatch. Transmitters mounted on vehicles with large motional freedom commonly use circularly polarized antennas so that there will never be a complete mismatch with signals from other sources. In the case of radar, this is often reflections from rain drops.

Efficiency

"Efficiency" is the ratio of power actually radiated to the power put into the antenna terminals. A dummy load may have a SWR of 1:1 but an efficiency of 0, as it absorbs all power and radiates heat but not RF energy, showing that SWR alone is not an effective measure of an antenna's efficiency. Radiation in an antenna is caused by radiation resistance which can only be measured as part of total resistance including loss resistance. Loss resistance usually results in heat generation rather than radiation, and reduces efficiency. Mathematically, efficiency is calculated as radiation resistance divided by total resistance.

Overview of antenna parameters

Except for polarization, the SWR is the most easily measured of the parameters above. Impedance can be measured with specialized equipment, as it relates to the complex SWR. Measuring radiation pattern requires a sophisticated setup including significant clear space (enough to put the sensor into the antenna's far field, or an anechoic chamber designed for antenna measurements), careful study of experiment geometry, and specialized measurement equipment that rotates the antenna during the measurements.

Bandwidth depends on the overall effectiveness of the antenna, so all of these parameters must be understood to fully characterize the bandwidth capabilities of an antenna. However, in practice, bandwidth is typically determined by looking only at SWR, i.e., by finding the frequency range over which the SWR is less than a given value. Bandwidth over which an antenna exhibits a particular radiation pattern is also important, for in practical use the performance of an antenna at the extremes of an assigned frequency band is important.

Transmission and reception

All of these parameters are expressed in terms of a transmission antenna, but are identically applicable to a receiving antenna, due to reciprocity. Impedance, however, is not applied in an obvious way; for impedance, the impedance at the load (where the power is consumed) is most critical. For a transmitting antenna, this is the antenna itself. For a receiving antenna, this is at the (radio) receiver rather than at the antenna. Tuning is done by adjusting the length of an electrically long linear antenna to alter the electrical resonance of the antenna.

Antenna tuning is done by adjusting an inductance or capacitance combined with the active antenna (but distinct and separate from the active antenna). The inductance or capacitance provides the reactance which combines with the inherent reactance of the active antenna to establish a resonance in a circuit including the active antenna. The established resonance being at a frequency other than the natural electrical resonant frequency of the active antenna. Adjustment of the inductance or capacitance changes this resonance.

Antennas used for transmission have a maximum power rating, beyond which heating, arcing or sparking may occur in the components, which may cause them to be damaged or destroyed. Raising this maximum power rating usually requires larger and heavier components, which may require larger and heavier supporting structures. This is a concern only for transmitting antennas, as the power received by an antenna rarely exceeds the microwatt range.

Antennas designed specifically for reception might be optimized for noise rejection capabilities. An "antenna shield" is a conductive or low reluctance structure (such as a wire, plate or grid) which is adapted to be placed in the vicinity of an antenna to reduce, as by dissipation through a resistance or by conduction to ground, undesired electromagnetic radiation, or electric or magnetic fields, which are directed toward the active antenna from an external source or which emanate from the active antenna. Other methods to optimized for noise rejection can be done by selecting a narrow bandwidth so that noise from other frequencies is rejected, or selecting a specific radiation pattern to reject noise from a specific direction, or by selecting a polarization different from the noise polarization, or by selecting an antenna that favors either the electric or magnetic field.

For instance, an antenna to be used for reception of low frequencies (below about ten megahertz) will be subject to both man-made noise from motors and other machinery, and from natural sources such as lightning. Successfully rejecting these forms of noise is an important antenna feature. A small coil of wire with many turns is more able to reject such noise than a vertical antenna. However, the vertical will radiate much more effectively on transmit, where extraneous signals are not a concern.

Basic antenna models

There are many variations of antennas that have various configurations. These configurations contain space or medium which tends to confine the energy within specified boundaries along a predetermined path (known as "restricted space"), such as wave guides, hollow resonators, and conductive wires. B

Rooftop television antenna. It is actually three Yagi antennas in one. The longest elements are for the low band (channels 2-6) the medium-length elements are for the high band (channels 7-13) and the shortest elements are for the UHF band (channels 14-69)

The isotropic radiator is a purely theoretical antenna that radiates equally in all directions. It is considered to be a point in space with no dimensions and no mass. This antenna cannot physically exist, but is useful as a theoretical model for comparison with all other antennas. Most antennas' gains are measured with reference to an isotropic radiator, and are rated in dBi (decibels with respect to an isotropic radiator).

The dipole antenna is simply two wires pointed in opposite directions arranged either horizontally or vertically, with one end of each wire connected to the radio and the other end hanging free in space. Since this is the simplest practical antenna, it is also used as reference model for other antennas; gain with respect to a dipole is labeled as dBd. Generally, the dipole is considered to be omnidirectional in the plane perpendicular to the axis of the antenna, but it has deep nulls in the directions of the axis. Variations of the dipole include the folded dipole, the half wave antenna, the groundplane antenna, the whip, and the J-pole.

The Yagi-Uda antenna is a directional variation of the dipole with parasitic elements added with functionality similar to adding a reflector and lenses (directors) to focus a filament lightbulb.

Loop antennas (Magnetic loop) have a continuous conducting path leading from one conductor of a two-wire transmission line to the other conductor. "Symmetric" loop antennas have a plane of symmetry running along the feed and through the loop. "Planar" loop antennas lie in a single plane which also contains the conductors of the feed. "Three-dimensional" loop antennas have wire which runs in all of the x,y, and z directions. By definition they are not planar. They may, however, be symmetric about planes which contain the feed.

The (large) loop antenna is similar to a dipole, except that the ends of the dipole are connected to form a circle, triangle (delta loop antenna) or square. Typically a loop is a multiple of a half or full wavelength in circumference. A circular loop gets higher gain (about 10%) than the other forms of large loop antenna, as gain of this antenna is directly proportional to the area enclosed by the loop, but circles can be hard to support in a flexible wire, making squares and triangles much more popular. Large loop antennas are more immune to localized noise partly due to lack of a need for a groundplane. The large loop has its strongest signal in the plane of the loop, and nulls in the axis perpendicular to the plane of the loop.

The small loop antenna, also called the magnetic loop antenna is a loop of wire (in other words, both ends of the wire connect to the radio) less than a wavelength in circumference. Typically, the circumference is less than 1/10 for a receiving loop, and less than 1/4 for a transmitting loop. Unlike nearly all other antennas in this list, this antenna detects the magnetic component of the electromagnetic wave. As such, it is less sensitive to near field electric noise when properly shielded. The received voltage can be greatly increased by bringing the loop into resonance with a tuning capacitor. The small loop has a maximum output when the magnetic field is normal to the plane of the loop, and since this field is transverse to the direction of the wave, has a maximum in the plane of the loop. This is the same mechanism as the large loop.

The electrically short antenna is an open-end wire far less than 1/4 wavelength in length - in other words only one end of the antenna is connected to the radio, and the other end is hanging free in space. Unlike nearly all other antennas in this list, this antenna detects only the electric field of the wave instead of the electromagnetic field - think of the free end of the wire as measuring the voltage of that point in space, as opposed to measuring both the voltage and the magnetic field. Its receiving aperture cannot be changed by adding lumped components, but more efficient power transfer can be achieved by impedance matching with such circuits. Electrically short antennas are typically used where operating wavelength is large and space is limited, e.g. for mobile transceivers operating at long wavelengths.

The fractal antenna is a class where the structure is self similar, and includes log periodic antennas and fractal element antennas, which are used for smaller and wideband or multiband applications.

The parabolic antenna is a special antenna where a reflector dish is used to focus the signal from a directional antenna feeder. Antennas of this type are commonly found as Satellite television antennas, Wi-fi / WLAN, radio astronomy, radio-links, mobile phone backhaul and military tactical radio link -antennas. They are characterized by high directionality and gain but can only be used at UHF to microwave and higher frequencies due to dimensions getting too large at lower frequencies.

The microstrip antenna consists of a patch of metalization on a ground plane. These are low profile, light weight antennas, most suitable for aerospace and mobile applications. Because of their low power handling capability, these antennas can be used in low-power transmitting and receiving applications. Microstrip antennas are the most commonly used antennas in mobile communications, satellite links, W-LAN and so on because circuit functions can be directly integrated to the microstrip antenna to form compact transceivers and spatial power combiners.

The quad antenna is an array of square loops that vary in size. The quad is related to the loop in exactly the same way the yagi is related to the dipole. Typically, the quad needs fewer elements to get the same gain as a yagi. Variations of the quad include the delta loop antenna which uses a triangle instead of a square, requiring fewer supports for large wavelength antennas.

The random wire antenna is simply a very long (greater than one wavelength) wire with one end connected to the radio and the other in free space, arranged in any way most convenient for the space available. Folding will reduce effectiveness and make theoretical analysis extremely difficult. (The added length helps more than the folding typically hurts.) Typically, a random wire antenna will also require an antenna tuner, as it might have a random impedance that varies nonlinearly with frequency.

The Beverage antenna is a form of directional long-wire antenna which uses a resistive termination at one end and feed from the other.

The endfire helical antenna is a directional antenna suited for receiving signals that are either circular polarized or randomly polarized. These are usually used with satellites, and are frequently used for the driven element on a dish.

The broadside helical antenna is a variation of the dipole, which has been coiled up to decrease its physical size. A typical broadside helical will have lower gain than the equivalent full length dipole, but will be flexible and smaller. The stock antenna for most hand held radios ("rubber duck") is a broadside helical.

The Phased array antenna is a group of independently fed active elements in which the relative phases of the respective signals feeding the elements are varied in such a way that the effective radiation pattern of the array is reinforced in a desired direction and suppressed in undesired directions. In plain language, this is a directional antenna that can be aimed without moving any parts.

Synthetic aperture radar uses a series of observations separated in time and space to simulate a very large antenna. Interferometry allows the monitor to combine signals from several radio receivers or a single moving receiver.

A trailing wire antenna is used by submarines when submerged. These antennas are designed to pick up transmissions in the low frequency (LF) and very low frequency (VLF) ranges. Trailing wire antennas are also used in some aircraft, in the HF, LF and VLF ranges.

An evolved antenna refers to an antenna fully or substantially designed using a computer algorithm based on Darwinian evolution.

A dielectric resonator is a variation on the conventional antenna in which an insulator with a large dielectric constant is used to modify the electromagnetic field. It is claimed that the dielectric contains the antenna's near field and therefore prevents it from interfering with other nearby antennas or circuits, making it suitable for miniature equipment such as mobile phones.

A feed horn is an antenna system that handles the incoming waveform from the dish to the focal point. It usually comprises a series of rings with decreasing radius in order to drive the signal to the polarizer.

Antennas in reception

The gain in any given direction and the impedance at a given frequency are the same when the antenna is used in transmission or in reception.

The electric field of an electromagnetic wave induces a small voltage in each small segment in all electric conductors. The induced voltage depends on the electrical field and the conductor length. The voltage depends also on the relative orientation of the segment and the electrical field.

Each small voltage induces a current and these currents circulate through a small part of the antenna impedance. The result of all those currents and tensions is far from immediate. However, using the reciprocity theorem, it is possible to prove that the Thévenin equivalent circuit of a receiving antenna is:

• is the Thévenin equivalent circuit tension.
• is the Thévenin equivalent circuit impedance and is the same as the antenna impedance.
• is the series resistive part of the antenna impedance .
• is the directive gain of the antenna (the same as in emission) in the direction of arrival of electromagnetic waves.
• is the wavelength.
• is the electrical field of the incoming electromagnetic wave.
• is the angle of misalignment of the electrical field of the incoming wave with the antenna. For a dipole antenna, the maximum induced voltage is obtained when the electrical field is parallel to the dipole. If this is not the case and they are misaligned by an angle , the induced voltage will be multiplied by .
• is an universal constant called vacuum impedance.

The equivalent circuit and the formula at right are valid for any type of antenna. It can be as well a dipole antenna, a magnetic loop, a parabolic antenna, or an antenna array.

From this formula, it is easy to prove the following definitions:

Antenna effective length

• is the length which, multiplied by the electrical field of the received wave, give the voltage of the Thévenin equivalent antenna circuit.

Maximum available power

• is the maximum power that an antenna can extract from the incoming electromagnetic wave.

Cross section or effective capture surface

• is the surface which multiplied by the power per unit surface of the incoming wave, gives the maximum available power.

The maximum power that an antenna can extract from the electromagnetic field depends only on the gain of the antenna and the squared wavelength . It does not depend on the antenna dimensions.

Using the equivalent circuit, it can be shown that the maximum power is absorbed by the antenna when it is terminated with a load matched to the antenna input impedance. This also implies that under matched conditions, the amount of power re-radiated by the receiving antenna is equal to that absorbed.

Physical background

The measured electrical field was radiated seconds earlier.

The electrical field created by an electric charge is where the:

• speed of light in vacuum.
• permittivity of free space.
• distance from the observation point (the place where is evaluated) to the point where the charge was seconds before the time when the measure is done.
• unit vector directed from the observation point (the place where is evaluated) to the point where the charge was seconds before the time when the measure is done.

The "prime" in this formula appears because the electromagnetic signal travels at the speed of light. Signals are observed as coming from the point where they were emitted and not from the point where the emitter is at the time of observation. The stars that we see in the sky are no longer where we see them. We will see their current position years in the future; some of the stars that we see today no longer exist.

The first term in the formula is just the electrostatic field with retarded time.

The second term is as though nature were trying to allow for the fact that the effect is retarded (Feynman).

The third term is the only term that accounts for the far field of antennas.

The two first terms are proportional to . Only the third is proportional to .

Near the antenna, all the terms are important. However, if the distance is large enough, the first two terms become negligible and only the third remains:

Electrical field radiated by an element of current. The element of current, the electrical field vector and are on the same plane.

If the charge q is in sinusoidal motion with amplitude and pulsation the power radiated by the charge is watts.

Note that the radiated power is proportional to the fourth power of the frequency. It is far easier to radiate at high frequencies than at low frequencies. If the motion of charges is due to currents, it can be shown that the (small) electrical field radiated by a small length of a conductor carrying a time varying current is

The left side of this equation is the electrical field of the electromagnetic wave radiated by a small length of conductor. The index reminds that the field is perpendicular to the line to the source. The reminds that this is the field observed seconds after the evaluation on the current derivative. The angle is the angle between the direction of the current and the direction to the point where the field is measured.

The electrical field and the radiated power are maximal in the plane perpendicular to the current element. They are zero in the direction of the current.

The electric field of the electromagnetic wave radiated by an antenna formed by wires is the sum of all the electric fields radiated by all the small elements of current. This addition is complicated by the fact that the direction and phase of each of the electric fields are, in general, different.

Practical antennas

Although any circuit can radiate if driven with a signal of high enough frequency, most practical antennas are specially designed to radiate efficiently at a particular frequency. An example of an inefficient antenna is the simple Hertzian dipole antenna, which radiates over wide range of frequencies and is useful for its small size. A more efficient variation of this is the half-wave dipole, which radiates with high efficiency when the signal wavelength is twice the electrical length of the antenna.

One of the goals of antenna design is to minimize the reactance of the device so that it appears as a resistive load. An "antenna inherent reactance" includes not only the distributed reactance of the active antenna but also the natural reactance due to its location and surroundings (as for example, the capacity relation inherent in the position of the active antenna relative to ground). Reactance diverts energy into the reactive field, which causes unwanted currents that heat the antenna and associated wiring, thereby wasting energy without contributing to the radiated output. Reactance can be eliminated by operating the antenna at its resonant frequency, when its capacitive and inductive reactances are equal and opposite, resulting in a net zero reactive current. If this is not possible, compensating inductors or capacitors can instead be added to the antenna to cancel its reactance as far as the source is concerned.

Once the reactance has been eliminated, what remains is a pure resistance, which is the sum of two parts: the ohmic resistance of the conductors, and the radiation resistance. Power absorbed by the ohmic resistance becomes waste heat, and that absorbed by the radiation resistance becomes radiated electromagnetic energy. The greater the ratio of radiation resistance to ohmic resistance, the more efficient the antenna.

Effect of ground

At frequencies used in antennas, the ground behaves mainly as a dielectric. The conductivity of ground at these frequencies is negligible. When an electromagnetic wave arrives at the surface of an object, two waves are created: one enters the dielectric and the other is reflected. If the object is a conductor, the transmitted wave is negligible and the reflected wave has almost the same amplitude as the incident one. When the object is a dielectric, the fraction reflected depends (among others things) on the angle of incidence. When the angle of incidence is small (that is, the wave arrives almost perpendicularly) most of the energy traverses the surface and very little is reflected. When the angle of incidence is near 90° (grazing incidence) almost all the wave is reflected.

Most of the electromagnetic waves emitted by an antenna to the ground below the antenna at moderate (say < 60°) angles of incidence enter the earth and are absorbed (lost). But waves emitted to the ground at grazing angles, far from the antenna, are almost totally reflected. At grazing angles, the ground behaves as a mirror. Quality of reflection depends on the nature of the surface. When the irregularities of the surface are smaller than the wavelength reflection is good.

The wave reflected by earth can be considered as emitted by the image antenna.

This means that the receptor "sees" the real antenna and, under the ground, the image of the antenna reflected by the ground. If the ground has irregularities, the image will appear fuzzy.

If the receiver is placed at some height above the ground, waves reflected by ground will travel a little longer distance to arrive to the receiver than direct waves. The distance will be the same only if the receiver is close to ground.

In the drawing at right, we have drawn the angle far bigger than in reality. Distance between the antenna and its image is .

Situation is a bit more complex because the reflection of electromagnetic waves depends on the polarization of the incident wave. As the refractive index of the ground (average value ) is bigger than the refractive index of the air (), the direction of the component of the electric field parallel to the ground inverses at the reflection. This is equivalent to a phase shift of radians or 180°. The vertical component of the electric field reflects without changing direction. This sign inversion of the parallel component and the non-inversion of the perpendicular component would also happen if the ground were a good electrical conductor.

The vertical component of the current reflects without changing sign. The horizontal component reverses sign at reflection.

This means that a receiving antenna "sees" the image antenna with the current in the same direction if the antenna is vertical or with the current inverted if the antenna is horizontal.

Radiation patterns of antennas and their images reflected by the ground. At left the polarization is vertical and there is always a maximum for . If the polarization is horizontal as at right, there is always a zero for .

For emitting and receiving antenna situated near the ground (in a building or a mast) far from each other, distances traveled by direct and reflected rays are nearly the same. There is no induced phase shift. If the emission is polarized vertically the two fields (direct and reflected) add and there is maximum of received signal. If the emission is polarized horizontally the two signals subtracts and the received signal is minimum. This is depicted in the image at right. In the case of vertical polarization, there is always a maximum at earth level (left pattern). For horizontal polarization, there is always a minimum at earth level. Note that in these drawings the ground is considered as a perfect mirror, even for low angles of incidence. In these drawings the distance between the antenna and its image is just a few wavelengths. For greater distances, the number of lobes increases.

Note that the situation is different – and more complex – if reflections in the ionosphere occur. This happens over very long distances (thousands of kilometers). There is not a direct ray but several reflected rays that add with different phase shifts.

This is the reason why almost all public address radio emissions have vertical polarization. As public uses to be near ground, horizontal polarized emissions would be poorly received. Observe household and automobile radio receivers. They all have vertical antennas or horizontal ferrite antennas for vertical polarized emissions. In cases where the receiving antenna must work in any position, as in mobile phones, the emitter and receivers in base stations use circular polarized electromagnetic waves.

Classical (analog) television emissions are an exception. They are almost always horizontally polarized, because the presence of buildings makes it unlikely that a good emitter antenna image will appear. However, these same buildings reflect the electromagnetic waves and can create ghost images. Using horizontal polarization, reflections are attenuated because of the low reflection of electromagnetic waves whose magnetic field is parallel to the dielectric surface near the Brewster's angle. Vertically polarized analog television has been used in some rural areas. In digital terrestrial television reflections are less annoying because of the type of modulation.

Mutual impedance and interaction between antennas

Mutual impedance between parallel dipoles not staggered. Curves Re and Im are the resistive and reactive parts of the impedance.

Current circulating in any antenna induces currents in all others. One can postulate a mutual impedance between two antennas that has the same significance as the in ordinary coupled inductors. The mutual impedance between two antennas is defined as:

where the current flowing in antenna 1 and the voltage that would have to be applied to antenna 2 – with antenna 1 removed – to produce the current in the antenna 2 that was produced by antenna 1.

If some of the elements are not fed (there is a short circuit instead a feeder cable), as is the case in television antennas (Yagi-Uda antennas), the corresponding are zero. Those elements are called parasitic elements. Parasitic elements are unpowered elements that either reflect or absorb and reradiate RF energy.

In some geometrical settings, the mutual impedance between antennas can be zero. This is the case for crossed dipoles used in circular polarization antennas.

Computer external antennas for wireless connection

The most common external connectors for IEEE 802.11/WiFi antennas are reverse polarity SMA, MCX, and in laptops or other small form-factor devices, MMCX. Home-made antennas (colloquially referred to as cantennas) typically use N connectors.

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