Noise Figure (NF) represents the performance of amplifier in receiver system.

Noise figure is the ratio of input S/N to output S/N:

\[f = \frac{S_{in}/N_{in}}{S_{out}/N_{out}}\]

where \(f\) is the true value of noise figure.

The strength of output signal can be obtained as the following equation:

\[S_{out} = GS_{in}\]

where \(G\) is the gain of the amplifier.

Noise power at input is given by:

\[N_{in} = kT_{0}B\]

where \(T_{0}\) is ambient temperature, \(k\) is Boltzman constant, \(B\) is bandwidth.

Also, noise power at output is given by:

\[N_{out} = G(kT_{0}B+kT_{G}B)\]

where \(T_{G}\) is the equivalent input noise temperature of the amplifier.

Thus, \(f\) can be obtained:

\[f = \frac{S_{in}/kT_{0}B}{GS_{in}/G(kT_{0}B+kT_{G}B)}\]

\[f = 1+\frac{T_{G}}{T_{0}}\]

From this equation, it is clear that \(f\) should be more than 1.

Furthermore, \(T_{G}\) can be written as:

\[T_{G} = (f-1)T_{0}\]