Temperatures
Keywords: clic

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Temperatures

The power received by an antenna in a bandwidth is conveniently expressed in term of antenna temperature, , which is the temperature for which an equivalent resistor would give the same power , following the Nyquist noise formula:

| (2)

As the quantity is affected by the atmospheric absorption and the antenna foward coupling factor , we define the quantity through:

| (3)

The , where is the image band rejection factor, accounts for a single sideband signal.

Brightness temperature, , is the Rayleigh-Jeans temperature of an equivalent blackbody which would give the same power per unit area per unit frequency and per unit solid angle as the celestial source:

| (4)

For a resolved source, the antenna temperature is equal to the sky brightness temperature. For an unresolved source, the coupling between antenna temperature and source flux density is:

| (5)

where is the antenna efficiency.

The noise temperature is the sum of the various noise contributions:

| (6)

where is the cosmic background, is the sky noise, is the ground noise pickup and is the receiver noise temperature. The forward efficiency is a property of the antenna that indicates how much coupling there is in the forward hemisphere with respect to the full sphere. With an atmosphere at a physical tempeture and with an opacity at the observed frequency, the sky noise and ground pickup temperature are expressed as:

|  |  | (7)
|  |  | (8)

is the system temperature, the noise equivalent temperature of the receiving chain refered to a perfect antenna located outside the atmosphere and for a single sideband signal:

| (9)

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