1000/1000

Hot
Most Recent

Submitted Successfully!

To reward your contribution, here is a gift for you: A free trial for our video production service.

Thank you for your contribution! You can also upload a video entry or images related to this topic.

Do you have a full video?

Are you sure to Delete?

Cite

If you have any further questions, please contact Encyclopedia Editorial Office.

HandWiki. Antenna Gain. Encyclopedia. Available online: https://encyclopedia.pub/entry/28599 (accessed on 19 July 2024).

HandWiki. Antenna Gain. Encyclopedia. Available at: https://encyclopedia.pub/entry/28599. Accessed July 19, 2024.

HandWiki. "Antenna Gain" *Encyclopedia*, https://encyclopedia.pub/entry/28599 (accessed July 19, 2024).

HandWiki. (2022, October 10). Antenna Gain. In *Encyclopedia*. https://encyclopedia.pub/entry/28599

HandWiki. "Antenna Gain." *Encyclopedia*. Web. 10 October, 2022.

Copy Citation

In electromagnetics, an antenna's power gain or simply gain is a key performance number which combines the antenna's directivity and electrical efficiency. In a transmitting antenna, the gain describes how well the antenna converts input power into radio waves headed in a specified direction. In a receiving antenna, the gain describes how well the antenna converts radio waves arriving from a specified direction into electrical power. When no direction is specified, gain is understood to refer to the peak value of the gain, the gain in the direction of the antenna's main lobe. A plot of the gain as a function of direction is called the gain pattern or radiation pattern. Antenna gain is usually defined as the ratio of the power produced by the antenna from a far-field source on the antenna's beam axis to the power produced by a hypothetical lossless isotropic antenna, which is equally sensitive to signals from all directions. Usually this ratio is expressed in decibels, and these units are referred to as decibels-isotropic (dBi). An alternative definition compares the received power to the power received by a lossless half-wave dipole antenna, in which case the units are written as dBd. Since a lossless dipole antenna has a gain of 2.15 dBi, the relation between these units is [math]\displaystyle{ \mathrm{Gain(dBd)} = \mathrm{Gain(dBi)} - 2.15 }[/math]. For a given frequency, the antenna's effective area is proportional to the power gain. An antenna's effective length is proportional to the square root of the antenna's gain for a particular frequency and radiation resistance. Due to reciprocity, the gain of any reciprocal antenna when receiving is equal to its gain when transmitting. Directive gain or directivity is a different measure which does not take an antenna's electrical efficiency into account. This term is sometimes more relevant in the case of a receiving antenna where one is concerned mainly with the ability of an antenna to receive signals from one direction while rejecting interfering signals coming from a different direction.

dipole antenna
electrical efficiency
dipole

**Power gain** (or simply **gain**) is a unitless measure that combines an antenna's efficiency *[math]\displaystyle{ \epsilon_{antenna} }[/math]* and directivity *D*:

- [math]\displaystyle{ G = \epsilon_{antenna} \cdot D. }[/math]

The notions of efficiency and directivity depend on the following.

The **efficiency** [math]\displaystyle{ \epsilon_{antenna} }[/math] of an antenna is the **total radiated power** [math]\displaystyle{ P_o }[/math] divided by the input power at the feedpoint

- [math]\displaystyle{ \epsilon_{antenna} = {P_o \over P_{in}} }[/math]

A transmitting antenna is supplied power by a feedline, a transmission line connecting the antenna to a radio transmitter. The **input power** [math]\displaystyle{ P_{in} }[/math] to the antenna is typically defined to be the power supplied to the antenna's terminals (the *feedpoint*), so antenna power losses do not include power lost due to joule heating in the feedline and reflections back down the feedline due to antenna/line impedance mismatches.

The electromagnetic reciprocity theorem guarantees that the electrical properties of an antenna, such as efficiency, directivity, and gain, are the same when the antenna is used for receiving as when it is transmitting.

An antenna's directivity is determined by its radiation pattern, how the radiated power is distributed with direction in three dimensions. All antennas are directional to a greater or lesser extent, meaning that they radiate more power in some directions than others. The direction is specified here in spherical coordinates [math]\displaystyle{ (\theta,\phi) }[/math], where [math]\displaystyle{ \theta }[/math] is the **altitude** or angle above a specified reference plane (such as the ground), while [math]\displaystyle{ \phi }[/math] is the **azimuth** as the angle between the projection of the given direction onto the reference plane and a specified reference direction (such as north or east) in that plane with specified sign (either clockwise or counterclockwise).

The distribution of output power as a function of the possible directions [math]\displaystyle{ (\theta,\phi) }[/math] is given by its radiation intensity [math]\displaystyle{ U(\theta,\phi) }[/math] (in SI units: watts per steradian, W⋅sr^{−1}). The output power is obtained from the radiation intensity by integrating the latter over all solid angles [math]\displaystyle{ d\Omega = \cos\theta \, d\theta \, d\phi }[/math]:

- [math]\displaystyle{ P_o =\int_{-\pi}^\pi\int_{-\pi/2}^{\pi/2}U(\theta,\phi) \, d\Omega = \int_{-\pi}^\pi\int_{-\pi/2}^{\pi/2}U(\theta,\phi) \cos \theta \, d\theta \, d\phi. }[/math]

The **mean radiation intensity** [math]\displaystyle{ \overline U }[/math] is therefore given by

- [math]\displaystyle{ \overline U =\frac{P_o}{4\pi}~~ }[/math] since there are 4π steradians in a sphere
- [math]\displaystyle{ =\frac{\epsilon_{antenna}\cdot P_{in}}{4\pi} }[/math] using the first formula for [math]\displaystyle{ P_o }[/math].

The directive gain or **directivity** [math]\displaystyle{ D(\theta,\phi) }[/math] of an antenna in a given direction is the ratio of its radiation intensity [math]\displaystyle{ U(\theta,\phi) }[/math] in that direction to its mean radiation intensity [math]\displaystyle{ \overline U }[/math]. That is,

- [math]\displaystyle{ D(\theta,\phi)=\frac{U(\theta,\phi)}{\overline U}. }[/math]

An isotropic antenna, meaning one with the same radiation intensity in all directions, therefore has directivity, D = 1, in all directions independent of its efficiency. More generally the maximum, minimum, and mean directivities of any antenna are always at least 1, at most 1, and exactly 1. For the half-wave dipole the respective values are 1.64 (2.15 dB), 0, and 1.

When the directivity [math]\displaystyle{ D }[/math] of an antenna is given independently of direction it refers to its maximum directivity in any direction, namely

- [math]\displaystyle{ D=\max_{\theta, \, \phi}D(\theta,\phi). }[/math]

The power gain or simply **gain** [math]\displaystyle{ G(\theta,\phi) }[/math] of an antenna in a given direction takes efficiency into account by being defined as the ratio of its radiation intensity [math]\displaystyle{ U(\theta,\phi) }[/math] in that direction to the mean radiation intensity of a perfectly efficient antenna. Since the latter equals [math]\displaystyle{ P_{in}/4\pi }[/math], it is therefore given by

- [math]\displaystyle{ G(\theta,\phi)=\frac{U(\theta,\phi)}{P_{in}/4\pi} }[/math]
- [math]\displaystyle{ =\epsilon_{antenna}\cdot\frac{U(\theta,\phi)}{\overline U} }[/math] using the second equation for [math]\displaystyle{ \overline U }[/math]
- [math]\displaystyle{ =\epsilon_{antenna}\cdot D(\theta,\phi) }[/math] using the equation for [math]\displaystyle{ D(\theta,\phi). }[/math]

As with directivity, when the gain [math]\displaystyle{ G }[/math] of an antenna is given independently of direction it refers to its maximum gain in any direction. Since the only difference between gain and directivity in any direction is a constant factor of [math]\displaystyle{ \epsilon_{antenna} }[/math] independent of [math]\displaystyle{ \theta }[/math] and [math]\displaystyle{ \phi }[/math], we obtain the fundamental formula of this section:

- [math]\displaystyle{ G=\epsilon_{antenna}\cdot D. }[/math]

If only a certain portion of the electrical power received from the transmitter is actually radiated by the antenna (i.e. less than 100% efficiency), then the directive gain compares the power radiated in a given direction to that reduced power (instead of the total power received), ignoring the inefficiency. The directivity is therefore the maximum directive gain when taken over all directions, and is always *at least* 1. On the other hand, the power gain takes into account the poorer efficiency by comparing the radiated power in a given direction to the actual power that the antenna receives from the transmitter, which makes it a more useful figure of merit for the antenna's contribution to the ability of a transmitter in sending a radio wave toward a receiver. In every direction, the power gain of an isotropic antenna is equal to the efficiency, and hence is always *at most* 1, though it can and ideally should exceed 1 for a directional antenna.

Note that in the case of an impedance mismatch, *P _{in}* would be computed as the transmission line's incident power minus reflected power. Or equivalently, in terms of the rms voltage

- [math]\displaystyle{ P_{in} = V^2 \cdot \text{Re} \left\lbrace \frac{1}{Z_{in}} \right\rbrace }[/math]

where *Z _{in}* is the feedpoint impedance.

Published numbers for antenna gain are almost always expressed in decibels (dB), a logarithmic scale. From the gain factor G, one finds the gain in decibels as:

- [math]\displaystyle{ G_{dBi} = 10 \cdot \log_{10}\left(G\right). }[/math]

Therefore, an antenna with a peak power gain of 5 would be said to have a gain of 7 dBi. dBi is used rather than just dB to emphasize that this is the gain according to the basic definition, in which the antenna is compared to an isotropic radiator.

When actual measurements of an antenna's gain are made by a laboratory, the field strength of the test antenna is measured when supplied with, say, 1 watt of transmitter power, at a certain distance. That field strength is compared to the field strength found using a so-called *reference antenna* at the same distance receiving the same power in order to determine the gain of the antenna under test. That ratio would be equal to G if the reference antenna were an isotropic radiator(irad).

However a true isotropic radiator cannot be built, so in practice a different antenna is used. This will often be a half-wave dipole, a very well understood and repeatable antenna that can be easily built for any frequency. The directive gain of a half-wave dipole is known to be 1.64 and it can be made nearly 100% efficient. Since the gain has been measured with respect to this reference antenna, the difference in the gain of the test antenna is often compared to that of the dipole. The gain relative to a dipole is thus often quoted and is denoted using dBd instead of dBi to avoid confusion. Therefore, in terms of the true gain (relative to an isotropic radiator) G, this figure for the gain is given by:

- [math]\displaystyle{ G_{dBd} = 10 \cdot \log_{10}\left(\frac{G}{1.64}\right). }[/math]

For instance, the above antenna with a gain G=5 would have a gain with respect to a dipole of 5/1.64 = 3.05, or in decibels one would call this 10 log(3.05) = 4.84 dBd. In general:

- [math]\displaystyle{ G_{dBd} = G_{dBi} - 2.15dB }[/math]

Both dBi and dBd are in common use. When an antenna's maximum gain is specified in decibels (for instance, by a manufacturer) one must be certain as to whether this means the gain relative to an isotropic radiator or with respect to a dipole. If it specifies dBi or dBd then there is no ambiguity, but if only dB is specified then the fine print must be consulted. Either figure can be easily converted into the other using the above relationship.

Note that when considering an antenna's directional pattern, gain with respect to a dipole does *not* imply a comparison of that antenna's gain in each direction to a dipole's gain in that direction. Rather, it is a comparison between the antenna's gain in each direction to the *peak* gain of the dipole (1.64). In any direction, therefore, such numbers are 2.15 dB smaller than the gain expressed in dBi.

**Partial gain** is calculated as power gain, but for a particular polarization. It is defined as the part of the radiation intensity [math]\displaystyle{ U }[/math] corresponding to a given polarization, divided by the total radiation intensity of an isotropic antenna.^{[1]}

The partial gains in the [math]\displaystyle{ \theta }[/math] and [math]\displaystyle{ \phi }[/math] components are expressed as

- [math]\displaystyle{ G_{\theta} = 4\pi\left(\frac{U_\theta}{P_{\mathrm{in}}}\right) }[/math]

and

- [math]\displaystyle{ G_{\phi} = 4\pi\left(\frac{U_\phi}{P_{\mathrm{in}}}\right) }[/math],

where [math]\displaystyle{ U_{\theta} }[/math] and [math]\displaystyle{ U_{\phi} }[/math] represent the radiation intensity in a given direction contained in their respective [math]\displaystyle{ E }[/math] field component.

As a result of this definition, we can conclude that the total gain of an antenna is the sum of partial gains for any two orthogonal polarizations.

- [math]\displaystyle{ G = G_{\theta} + G_{\phi} }[/math]

Suppose a lossless antenna has a radiation pattern given by:

- [math]\displaystyle{ U = B_0\,\sin^3(\theta). }[/math]

Let us find the gain of such an antenna.

**Solution**:

First we find the peak radiation intensity of this antenna:

- [math]\displaystyle{ U_{\mathrm{max}} = B_0 }[/math]

The total radiated power can be found by integrating over all directions:

- [math]\displaystyle{ P_{\mathrm{rad}} = \int_0^{2\pi}\int_0^{\pi}U(\theta,\phi)\sin(\theta) \, d\theta \,d\phi = 2 \pi B_0 \int_0^{\pi}\sin^4(\theta) \, d\theta = B_0\left(\frac{3\pi^2}{4} \right) }[/math]

- [math]\displaystyle{ D = 4\pi\left(\frac{U_{\mathrm{max}}}{P_{\mathrm{rad}}}\right) = 4\pi\left[\frac{B_0}{B_0\left(\frac{3\pi^2}{4}\right)}\right] = \frac{16}{3\pi} = 1.698 }[/math]

Since the antenna is specified as being lossless the radiation efficiency is 1. The maximum gain is then equal to:

- [math]\displaystyle{ G = \epsilon_{antenna} \, D = (1)(1.698) = 1.698 }[/math] .

- [math]\displaystyle{ G_{dBi} = 10 \, \log_{10}(1.698) = 2.30 \, \mathrm{dBi} }[/math]

Expressed relative to the gain of a half-wave dipole we would find:

- [math]\displaystyle{ G_{dBd} = 10 \, \log_{10}(1.698/1.64) = 0.15 \, \mathrm{dBd} }[/math].

According to IEEE Standard 145–1993,^{[2]} **realized gain** differs from the above definitions of gain in that it is "reduced by the losses due to the mismatch of the antenna input impedance to a specified impedance." This mismatch induces losses above the dissipative losses described above; therefore, realized gain will always be less than gain.

Gain may be expressed as **absolute gain** if further clarification is required to differentiate it from realized gain.^{[2]}

**Total radiated power** (TRP) is the sum of all RF power radiated by the antenna when the source power is included in the measurement. TRP is expressed in watts or the corresponding logarithmic expressions, often dBm or dBW.^{[3]}

When testing mobile devices, TRP can be measured while in close proximity of power-absorbing losses such as the body and hand of the user.^{[4]}

The TRP can be used to determine body loss (BoL). The body loss is considered as the ratio of TRP measured in the presence of losses and TRP measured while in free space.

- Balanis, Constantine A. (2016). Antenna theory : analysis and design (4th ed.). Hoboken, New Jersey. pp. 63. ISBN 978-1-119-17898-9. OCLC 933291646. https://www.worldcat.org/oclc/933291646.
- "IEEE Standard Definitions of Terms for Antennas". IEEE STD 145-1993: 1–32. 1993-07-01. doi:10.1109/IEEESTD.1993.119664. ISBN 978-0-7381-0555-0. https://dx.doi.org/10.1109%2FIEEESTD.1993.119664
- "CTIA Test Plan for Wireless Device Over-the-Air Performance Rev. 3.4.2". CTIA. May 2015. http://www.ctia.org/docs/default-source/default-document-library/ctia_ota_test_plan_rev_3_4_2.pdf?sfvrsn=2.
- Mobile Broadband Multimedia Networks: Techniques, Models and Tools for 4G by Luís M. Correia

More

Information

Subjects:
Others

Contributor
MDPI registered users' name will be linked to their SciProfiles pages. To register with us, please refer to https://encyclopedia.pub/register
:

View Times:
7.3K

Entry Collection:
HandWiki

Update Date:
10 Oct 2022