284 Radio Engineering for Wireless Communication and Sensor Applications
amplifier and mixer types are able to operate only at very low temperatures, for example, a maser and a superconductor-insulator-superconductor (SIS) quasiparticle mixer. Figure 11.6 presents noise temperatures of different microwave amplifiers and mixers.
11.2.2 Antenna Noise Temperature
Besides the useful signal, an antenna also receives noise power from its surroundings. The antenna noise temperature TA is defined as the temperature of such a matched resistive termination, which provides the same noise power as the noise power available from the antenna terminals, which is equal to the noise power received by the antenna in case of a lossless antenna. In the following we assume a lossless antenna.
A so-called black surface does not reflect any radiation incident on it. At optical wavelengths such a surface is black in color. In a thermal equilib-
Figure 11.6 Noise temperatures versus frequency of microwave amplifiers and mixers at different physical temperatures. Natural background noise values as a reference.
rium, the black surface must emit the same power as it absorbs. At temperature T its brightness, or the power radiated per square meter, hertz, and steradian, is [7]
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B = |
2hf 3 |
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c 2 |
e hf /kT − 1 |
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At radio frequencies hf << kT, and therefore |
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B ≈ |
2kT |
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l 2 |
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Let us consider a situation like that in Figure 11.7, where a black surface fully surrounds a lossless antenna. The noise power received by the antenna in a bandwidth of df is
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Gmax |
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P = |
1 |
A ef df |
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B (u, f) |
G (u, f) |
d V |
(11.25) |
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4p |
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where A ef is the effective aperture area of the antenna, G (u, f) is the antenna gain in a direction (u, f ), and Gmax is the maximum antenna gain. The
Figure 11.7 A receiving antenna surrounded by a black surface.
286 Radio Engineering for Wireless Communication and Sensor Applications
factor of 1/2 is due to the fact that an antenna has a certain polarization but the polarization of noise is random. Therefore, one-half of the noise power is in a given polarization. By substituting (11.24) into (11.25) we get
P = |
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A ef df |
2kT |
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4p |
= kT df |
(11.26) |
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l2 |
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Gmax |
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Thus, TA = T, and the received noise power is independent of the antenna gain and is directly proportional to the temperature of the black surface and to the bandwidth. If the temperature of the black surface depends on the direction within the radiation pattern of the antenna, the received noise power is calculated by integrating from (11.25).
The antenna receives noise from everywhere, including from space and the atmosphere. For these it is possible to define an equivalent black surface temperature, which depends on frequency and direction, as shown in Figure 11.8.
Figure 11.8 Noise temperature of the sky.
