# Use basic concepts to determine antenna noise temperature.

USE BASIC CONCEPTS TO DETERMINE ANTENNA NOISE TEMPERATURESensitivity in any receiving system is ultimately limited by noise in the system. In most RF systems, external noise enters through the antenna and adds to internal noise generated by the low noise amplifier (LNA) and resistive losses from filters and couplers (Figure 1). The noise contributed by the antenna is generated by the sky, earth and antenna resistive loss. A common figure of merit for a receiving system is G/T, where G is the antenna gain and T is the noise temperature of the combined sources.

It is generally easier to control the internal system noise than the noise received by the antenna. Antenna noise can be minimized to some extent through careful design and prudent choice of RF frequency. However, in many systems, the receiver antenna design and RF frequency are fixed by other system requirements and thus cannot be optimized for minimum noise. In these cases, the expected antenna temperature must be calculated and then other system parameters, such as transmitter power and LNA noise figure, are specified appropriately to achieve a viable link.

A large amount of data is available in literature to assist the engineer in evaluating the level of antenna noise. However, the noise is highly dependent on the antenna characteristics and operational situation, so the data must be interpreted and applied properly to yield an accurate result. Improper interpretation of published data can lead to a system that is over-or under-specified. This can particularly be a problem at lower frequencies where system noise is dominated by the antenna rather than internal components.

The term "antenna noise temperature" is used frequently in RF systems work, but its physical meaning is often not fully understood. From basic physics, it is known that a blackbody radiation source will emit electromagnetic radiation according to Planck's law. At RF and microwave frequencies, the flux density can be determined by making use of the Raleigh-Jeans approximation to Planck's law: F = (2kT/[lambda.sup.2])[omega]

where: F = flux density (W/[m.sup.2]-Hz) k = Boltzmann's constant (1.38 x [10.sup.-23] J/K) T = physical temperature of the blackbody (K) [lambda] = wavelength of the RF radiation (m) and [omega] = solid angle subtended by the blackbody source (steradians).

In a given direction, the noise-power density received by the antenna will be equal to one-half of the flux density multiplied by the effective area of the antenna in that direction. The total received noise-power density will be an average over all directions. The factor of one-half is needed because the blackbody flux density contains all polarizations, while the antenna receives only one polarization.

If an antenna with a matched load resistor is immersed inside a blackbody radiator, the flux density will be constant from all directions. By noting that the effective area of an antenna is equal to G[lambda.sup.2]/4[pi] (where G is the gain) and integrating over all 4[pi] steradians of space, the total power delivered to the load can be calculated. This calculation yields a simple result which can be applied to any antenna with a matched load resistor:

N = kTB

where: N = noise power (W) and B = noise bandwidth (Hz).

This result is independent of the antenna radiation pattern due to the fact that the flux density is constant from all directions.

In a real-world situation, the antenna will receive noise from a variety of sources at different frequencies. At the RF frequency of interest, these sources are treated as blackbody radiators even though in most cases they are not. The total noise power into the load resistor is measured and divided by kB to obtain an equivalent blackbody temperature. This equivalent blackbody temperature is referred to as the antenna temperature ([T.sub.a]).

[T.sub.a] is not a physical quantity because neither the antenna nor its surroundings are at that temperature. It does, however, quantify the noise power into the load resistor at the RF frequency of interest. [T.sub.a] should not be confused with another commonly used term, "brightness temperature," [T.sub.b]. This value is used to characterize the noise flux density that emanates from specific parts of the sky and earth at various frequencies. It normally assumes an antenna with infinitely narrow bandwidth (perfect resolution). [T.sub.a] is equal to a weighted average of all brightness temperatures seen by the antenna radiation pattern plus an additional amount due to resistive loss.

NOISE SOURCES

The noise power received by a given antenna is normally generated by a combination of sources. Understanding and characterizing each source is fundamental to correct estimation of antenna noise temperature.

For most applications above 50 MHz, the significant sources of noise are the galaxy, sun, earth, atmospheric absorption and antenna resistive loss. Below 50 MHz, significant noise is also generated by the hundreds of lightning strikes that occur continually throughout the world. Galactic noise is dominant at frequencies below 1 GHz. This noise comes from the millions of stars that make up the Milky Way galaxy. The magnitude of this noise depends on the RF frequency and the direction that the antenna is pointed. Galactic noise is greatest when the antenna is pointed towards the galactic center and lowest when the antenna is pointed towards the galactic poles. The brightness temperature of this noise decreases with rising RF frequency.

Radio astronomers have made maps of the sky to quantify galactic noise power. This is normally accomplished by placing a high-gain antenna (very narrow beamwidth) at a fixed elevation angle and then measuring the noise power out of the antenna as the earth rotates. This is repeated at various elevation angles until a large portion of the sky has been swept by the antenna beam.

A formula can be used to approximate the average brightness temperature of galactic noise:

[T.sub.gal] = 2.6 x [10.sup.19]/[f.sup.2]

where: f = RF frequency (Hz).

This average value is useful for calculations involving wide-beamwidth antennas, but should be used with caution when applied to narrow-beamwidth antennas.

At frequencies above 1 GHz, noise caused by absorption and reradiation of energy by oxygen and water vapor in the earth's atmosphere becomes significant. The brightness temperature due to this noise depends on the RF frequency and elevation angle. At low elevation angles, the antenna beam passes through more of the atmosphere than it does at high angles. As a result, the brightness temperature will be largest at low angels and will decrease as the antenna is elevated from the horizon. Between 1 and 10 GHz, the brightness temperature is relatively constant for a fixed elevation angle. At 5 [Degrees] elevation, temperature is about 30 K. At 90 [Degrees] elevation (zenith), the temperature drops to about 3 K. These temperatures assume a very narrow antenna beamwidth so that the beam is focused on a small area of the sky.

The sun is a discrete source of antenna noise. From the earth, it subtends an angle of only about 0.5 [Degrees]. The brightness temperature of the sun decreases with increasing RF frequency and can vary widely with solar flare activity. During quiet periods of solar activity, the temperature of the sun can be modeled as:

[T.sub.sun] = 1.96 x [10.sup.14]/f

For example, at 2 GHz the brightness temperature of the sun is 98,000 K. A high-gain antenna aimed directly at the sun will have a large antenna temperature. Many antennas, however, have a beamwidth that is much larger than 0.5 [Degrees], so the high temperature of the sun is averaged with the cool space that surrounds it.

For these types of antennas, the sun appears as a point source of noise and can be described more conveniently by its noise flux density. By combining equations and noting that a 0.5 [Degrees] cone angle is equivalent to 6 x [10.sup.-5] steradians, an expression can be obtained for the noise flux density of the sun (in W/[m.sup.2]-Hz):

[F.sub.sun] = 3.6 x [10.sup.-30]f

The earth can be approximated as a blackbody radiator with an average temperature of 290 K. If an antenna had its entire radiation pattern directed toward the ground, [T.sub.a] would be approximately 290 K. The precise temperature will vary somewhat with the local terrain and the physical temperature of the earth's surface.

Antenna resistive loss is generated by a variety of sources, including surface resistivity, RF cables and rotary joints. The antenna temperature due to this loss, referenced at the antenna output, is given by:

[T.sub.a] = [T.sub.p] (L - 1)/L

where: [T.sub.p] = physical temperature of the antenna (K) and L = resistive loss.

For example, a 2-dB loss at room temperature would produce an antenna temperature of 107 K.

In theory, the antenna noise temperature can be calculated by integrating the product of the gain and brightness temperature over a unit sphere about the antenna. In practice, however, neither the gain pattern nor the brightness temperature may be known analytically. Calculations can still be performed, however, with the help of some approximations. For a low-gain antenna, the sky can be broken up into smaller sections over which the gain and brightness temperature are relatively constant. Antenna temperature can then be approximated by:

[T.sub.a] = (1/4[pi])[[alpha.sub.1G.sub.1T.sub.1] + [alpha.sub.2G.sub.2T.sub.2] + ....]

where: [alpha] = the solid angle over which the gain and noise temperature are constant [G.sub.1, G.sub.2] = section gain values and [T.sub.1, T.sub.2] = section brightness temperature values.

For example, if a lossless isotropic antenna had half of its radiation pattern pointed at the earth ([T.sub.b] = 290 K) and the other half pointed at a cool area of space ([T.sub.b] = 100 K), the antenna temperature would be:

[T.sub.a] = (1/4[pi])[(2[pi])(1)(290) + (2[pi])(1)(100)] = 195 K

Noise from discrete sources such as the sun is normally handled differently from galactic, atmospheric and earth noise. For a discrete source, the noise flux density is an easier quantity to work with than brightness temperature because the antenna beam is typically wider than the noise source. By noting that the effective area of an antenna is equal to G[lambda.sup.2]/4[pi], the antenna temperature can be expressed in terms of flux density and antenna gain:

[T.sub.a] = ([lambda.sup.2]/8[pi]k)FG

This equation assumes the antenna beam to be wider than the angle subtended by the noise source. A high-gain antenna can have a very large noise temperature if pointed directly at a discrete source such as the sun. A low-gain antenna will be much less affected, even when the source falls within the beamwidth of the antenna.

The equations governing antenna noise temperature might imply that [T.sub.a] is a direct function of antenna gain; this is not necessarily true. Increasing gain will not result in greater antenna temperature unless the increased gain causes the beam to be more focused on a hot spot in the sky. For instance, a low-gain antenna may be pointed toward a section of space where the brightness temperature (and noise flux density) is constant. As the gain is increased, the noise power received from along the boresight increases. However, the overall antenna temperature remains constant because the beamwidth decreases.

PHOTO : FIGURE 1 RF SYSTEM NOISE IS THE SUM OF NOISES DERIVED FROM EXTERNAL SOURCES AND INTERNAL COMPONENTS

Robert S. Bokulic is a senior engineer at the Johns Hopkins University Applied Physics Laboratory.

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Title Annotation: | EW Design Engineers' Handbook & Manufacturers Directory |
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Author: | Bokulic, Robert S. |

Publication: | Journal of Electronic Defense |

Date: | Jan 1, 1992 |

Words: | 1953 |

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