Discussion
The equivalent noise temperature of a network given the noise figure of the network or system is :
Answer: A
The equivalent noise temperature is \(T_{0}(F - 1)\).
The noise figure \(F\) is defined with the source at the reference temperature \(T_{0}\) (290 K). The noise the network adds, referred to its input, can be expressed as an extra temperature \(T_{e}\), so
\[ \begin{aligned} F &= \frac{T_{0} + T_{e}}{T_{0}} = 1 + \frac{T_{e}}{T_{0}} \\ \Rightarrow T_{e} &= T_{0}(F - 1) \end{aligned} \]
A noiseless network has \(F = 1\) and \(T_{e} = 0\), as it should. \(T_{0}(F + 1)\) and \(T_{0}F\) would give a noiseless network a non-zero noise temperature, and \(T_{0}/F\) would make a noisier network appear cooler.
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