# Antenna gain

The antenna gain summarizes the directivity and the efficiency of an antenna . It is the ratio of those given in the main direction. recorded radiation power density compared with a lossless reference antenna with the same antenna feed power, which by definition has an antenna gain of 0  dB . A hypothetical isotropic radiator with the same radiation intensity in all directions or a dipole antenna is usually chosen as the reference antenna .

Parabolic antenna

## calculation

10 element yagi antenna with 1 - emitter, 2 - reflector, 3 - directors

Antennas with a high gain are always very sensitive to direction: In other directions than the main direction, the emission or reception is strongly suppressed. Such antennas can be used to reach transmitters or receivers that are further away. Typical directional antennas are the parabolic antenna , also known colloquially as the "satellite dish", and the Yagi-Uda antenna , such as is used for terrestrial television .

The antenna gain G is the product of the directivity factor D and the efficiency of the antenna: ${\ displaystyle \ eta}$

${\ displaystyle G = D \ cdot \ eta> 0}$

With

• Guideline factor ${\ displaystyle D \ geq 1}$
• Efficiency ${\ displaystyle \ eta \ leq 1.}$

Strictly speaking, a distinction must be made between sending and receiving:

${\ displaystyle G _ {\ mathrm {s}} = D \ cdot \ eta _ {\ mathrm {s}}}$
${\ displaystyle G _ {\ mathrm {e}} = D \ cdot \ eta _ {\ mathrm {e}},}$

since the efficiencies for sending and receiving are defined differently (see below).

Often, however, both efficiencies are set equal to 1 as a first approximation:

${\ displaystyle \ eta \ approx \ eta _ {\ mathrm {s}} \ approx \ eta _ {\ mathrm {e}} \ approx 1,}$

From which follows:

${\ displaystyle \ Rightarrow G \ approx G _ {\ mathrm {s}} \ approx G _ {\ mathrm {e}} \ approx D.}$

Losses of the feed line and of the contact up to the connector of the antenna are not included in the profit .

### Guideline factor

The directivity factor D of an antenna represents the ratio of the square of the maximum electric field strength  E max generated by it in the main beam direction  (or equivalent to the magnetic field strength  H max ) to the square of the field strength  E k of an assumed spherical radiator in the far field , with the same applied power and the same distance :

${\ displaystyle D = {\ frac {E _ {\ mathrm {max}} ^ {2}} {E _ {\ mathrm {k}} ^ {2}}} = {\ frac {H _ {\ mathrm {max}} ^ {2}} {H _ {\ mathrm {k}} ^ {2}}} = {\ frac {S _ {\ mathrm {max}}} {S _ {\ mathrm {k}}}}}$

S k is the radiation density of a spherical radiator at the same distance. It is equal to the square of the generating field strengths, since it is a far field.

### Antenna efficiency

The antenna efficiency η characterizes the electrical losses of the antenna, e.g. B. by ohmic line resistances in the antenna.

Since the current distribution in the antenna is different when transmitting than when receiving (which results from the fact that the near field of a receiving antenna differs from the near field of a transmitting antenna), a distinction must be made between transmitting and receiving in terms of efficiency:

• Send: ${\ displaystyle \ eta _ {\ mathrm {s}} = {\ frac {P _ {\ mathrm {s}}} {P _ {\ mathrm {s} 0}}}}$
• Receive: ${\ displaystyle \ eta _ {\ mathrm {e}} = {\ frac {P _ {\ mathrm {e} 0}} {P _ {\ mathrm {e}}}}}$
• P e0 : power delivered electrically to the consumer
• P e : electrical power taken from the electromagnetic radiation field ; this is determined from the antenna effective area , which is proportional to the gain and the square of the wavelength of the electromagnetic field.

• Since both the transmitting antenna can bundle their radiated power in the direction of the receiving antenna and the receiving antenna can be aligned with the transmitting antenna, the range of a radio link can be increased considerably.
• Alternatively, transmission power can be saved with the same range , since the desired spatial direction is illuminated with greater efficiency.
• By simultaneously reducing the opening angle, stations away from the desired direction are less disturbed.
• This means that a frequency can be used by several radio links as long as they are not in the same aisle .
• Since the power received depends on the correct alignment of the receiver antenna, the direction in which the transmitter is located can be determined, i.e. targeted. This is z. B. used for tracking down direction finders or for navigation with the help of non-directional radio beacons .

## unit

The antenna gain is usually given in the auxiliary unit of measurement decibel  (dB). Since dB is a relative ( logarithmic ) measure compared to a reference antenna, it is calculated based on the reference antenna:

${\ displaystyle {\ text {Profit in}} \ mathrm {dB} = {\ frac {g} {\ mathrm {dB}}} = 10 \ cdot \ log _ {10} \ left ({\ frac {P_ { \ text {Antenne}}} {P _ {\ text {Reference antenna}}}} \ right)}$

The reference antenna must be specified:

• If the antenna gain is given in relation to the isotropic radiator , the unit is written in dBi ( isotropic ).
• when specifying the value in relation to an antenna of the λ / 2 dipole type , one writes dBd ( dipole ).

The difference in antenna gain between isotropic radiators and λ / 2 dipole as reference radiators is about 2.15 dB with the following relationship:

${\ displaystyle {\ text {Profit in}} \ mathrm {dBi} \ approx {\ text {Profit in}} \ mathrm {dBd} +2 {,} 15 \ mathrm {dB}}$

If the calculation is not in dB, one speaks of the antenna gain factor  G:

${\ displaystyle G = {\ frac {P _ {\ text {antenna}}} {P _ {\ text {reference antenna}}}} = 10 ^ {\ frac {{\ text {profit}} [\ mathrm {dB}] } {10}}}$

## Antenna construction and profit

An antenna with increased gain inevitably leads to a reduction in its half-width , as the available energy is “focused” on a narrower area, ie it is only redistributed. The following approximation illustrates this relationship:

${\ displaystyle g = 10 \ cdot \ log {\ eta _ {\ mathrm {eff}} \ cdot {{4 \ pi} \ over \ theta \ cdot \ phi}} [\ mathrm {dBi}]}$; The efficiency η is usually between 0.6 and 0.8 and the angles are to be used in the wheel .

Another approximation provides a statement about the gain through the relationship between antenna size and wavelength. This z. B. with parabolic antennas, but not with Yagi antennas .

${\ displaystyle g = 10 \ cdot \ log \ left (\ eta _ {\ mathrm {eff}} \ cdot {\ frac {4 \ pi} {\ lambda ^ {2}}} \ cdot A _ {\ mathrm {eff }} \ right) = 10 \ cdot \ log \ left (\ eta _ {\ mathrm {eff}} \ cdot \ left (\ pi \ cdot {\ frac {d} {\ lambda}} \ right) ^ {2 } \ right)}$

The following table shows the antenna gain for some antennas:

Design Antenna gain
Isotropic radiator 0 dBi, −2.15 dBd
Hertzian dipole ideal: 1.76 dBi
λ / 2 dipole (half-wave dipole) ideal: 2.15 dBi, 0 dBd
Marconi antenna (λ / 4 dipole, quarter-wave dipole) ideal: 5.15 dBi, 3 dBd; real: 2.15 - 3.15 dBi, 0 - 1 dBd
Folding dipole approx. 3.7 dBi (wave impedance 240 Ω)
Moxon antenna approx. 9.7 dBi (characteristic impedance 50 Ω)
Bi-quad antenna 7.2 ... 10.2 dBi (without reflector)
10.2 - 12.2 dBi (with reflector) (wave impedance 60 Ω)
Patch antenna single patch in front of reflector up to approx. 10 dBi
Beverage - long wire antenna ( l = 5 ... 10 λ): approx. 7 - 9.5 dBi
Helical antenna 10-18 dBi
Yagi-Uda antenna approx. 15 - 20 dBd (depending on number of elements and length)
Logarithmic periodic dipole antenna approx. 6 - 10 dBd (depending on number of elements and length)
Parabolic antenna 20 dBi to well over 70 dBi
(depending on the ratio of the wavelength to the geometric dimension)

## Frequency management

The antenna gain is also used in the field of frequency management . The following wording is used in German-speaking countries in connection with frequency assignments for radio stations , interference investigations in the event of shared frequency uses and EMC analyzes of radio services .

Gain of an antenna ( english gain of an antenna ) is - in accordance with Article 1160 of the Radio Regulations of the International Telecommunication Union (ITU) - defined as:

Usually expressed in decibels , the ratio of the power required at the input of a lossless reference antenna to the power applied to the input of the given antenna; the ratio must be such that the two antennas in a given direction produce the same field strength or the same power flux density at the same distance . Unless otherwise stated, it is the main direction win. A certain polarization can be taken into account in the gain.

Depending on the choice of the reference antenna, a distinction is made between:

1. isotropic or absolute gain ( Gi ) when the reference antenna is an isotropic antenna in free space;
2. Gain related to a half-wave dipole ( Gd ) if the reference antenna is a half-wave dipole in free space and its equatorial plane contains the given direction;
3. Gain, relative to a short vertical antenna ( Gv ), if the reference antenna is a linear conductor which is substantially shorter than a quarter of the wavelength and is erected perpendicular to the surface of a perfectly conductive plane containing the given direction.

## literature

• Curt Rint : Handbook for high frequency and electrical technicians Volume 2. 13th edition. Hüthig and Pflaum Verlag, Heidelberg 1981, ISBN 3-7785-0699-4 .
• Hans Lobensommer: Handbook of modern radio technology. 1st edition. Franzis Verlag, Poing 1995, ISBN 3-7723-4262-0 .
• Ulrich Freyer: News transmission technology. Basics, components, processes and systems of telecommunications technology . 1st edition. Carl Hanser Verlag, Munich 2009, ISBN 978-3-446-41462-4 .
• Paul Lorrain, Dale R. Corson, François Lorrain: Electromagnetic fields and waves. Walter de Gruyter Verlag, Berlin 1995, ISBN 3-11-012232-4 .
• Klaus W. Kark: Antennas and radiation fields. Electromagnetic waves on lines - in free space and their radiation, Springer-Verlag, Berlin / Heidelberg 2016, ISBN 978-3-658-13965-0 .