What is the relation between noise temperature introduced by beam TB and the antenna temperature TA when the solid angle obtained by the noise source is greater than antenna solid angle?

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What is the relation between noise temperature introduced by beam TB and the antenna temperature TA when the solid angle obtained by the noise source is greater than antenna solid angle?

(a) TA= TB

(b) TA > TB

(c) TA < TB

(d) TA « TB

I had been asked this question in class test.

My question comes from Antenna Noise Temperature in portion Antenna Parameters – II of Antennas

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Correct option is (a) TA= TB

The explanation is: When the solid angle obtained by the noise source ΩB is greater than antenna solid angle ΩA, then relation between noise temperature introduced by beam TB and the antenna temperatureTA  is given by

TA= TB (If Lossless antenna).

For radio astronomy, ΩB<ΩA and TA≠ TB; ΔTA=$\frac{\Omega_B}{\Omega_A}T_B$

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