# Which expression suits best when the solid angle obtained by the noise source is less than antenna solid angle?

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Which expression suits best when the solid angle obtained by the noise source is less than antenna solid angle?

(a) PA ΩA=PB ΩB  and ΔTA=$\frac{\Omega_B}{\Omega_A} T_B$

(b) PA ΩB=PB ΩA and ΔTA=$\frac{\Omega_B}{\Omega_A} T_B$

(c) ΔTA=$\frac{\Omega_A}{\Omega_B} T_B$ and PA ΩB=PB ΩA

(d) ΔTA=$\frac{\Omega_A}{\Omega_B} T_B$ and PA ΩA=PB ΩB

I have been asked this question in class test.

This intriguing question comes from Antenna Noise Temperature topic in portion Antenna Parameters – II of Antennas

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Right answer is (a) PA ΩA=PB ΩB  and ΔTA=$\frac{\Omega_B}{\Omega_A} T_B$

To elaborate: When the solid angle obtained by the noise sourceΩB 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=$\frac{\Omega_B}{\Omega_A} T_B$ and PA ΩA=PB ΩB

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