F B9 f A9 f W

The received power p can be expressed as the temperature TA of a matched resistor at the antenna terminals ("radiation resistance") through the Nyquist (1928) formula p = k Ta (W Hz-1).

where k = 1.38 . 10 23 WK-1 Hz 1 is Boltzmann's constant.

We call this fictitious temperature the antenna temperature. Note that the antenna temperature is a measure of the received power by the antenna and is not related to the physical temperature of the antenna structure.

In a similar fashion we can express the source brightness in terms of a temperature, which we call brightness temperature, denoted by Tb . It is defined as the equivalent Rayleigh-Jeans blackbody temperature:

The brightness temperature is also a fictitious quantity and will not be related to the physical temperature of the source apart from the case where the source can be characterised as a blackbody in the Rayleigh-Jeans approximation (e.g. the planets at radio wavelengths). Before we link the expressions for the power emitted by the source and that received by the antenna, we must remember that only half of the randomly polarised blackbody radiation will be received by the linearly (or circularly) polarised antenna. Combining Eqs. (5.8 - 5.10) we obtain

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