Communication Systems/Noise Figure

This page is going to talk about the effect of noise on transmission systems.

Noise Temperature

The amount of noise in a given transmission medium can be equated to thermal noise. Thermal noise is well-studied, so it makes good sense to reuse the same equations when possible. To this end, we can say that any amount of radiated noise can be approximated by thermal noise with a given effective temperature. Effective temperature is measured in Kelvin. Effective temperature is frequently compared to the standard temperature, $T_o$, which is 290 Kelvin.

Noise Figure

The noise figure of a given system, is denoted with a capital F. F is generally defined in terms of it's frequency characteristics. For any given system with frequency characteristic G(f), we can define the noise figure in terms of the noise spectrum as follows:

$F=\frac{S_{output}(f)}{G(f)S_{input}(f)}$

We can show that the noise figure and the equivalent temperature of a system are related through the following relationship:

$F=\frac{T_e+T_0}{T_0}$

Receiver Sensitivity

In a given bandwidth, W, we can show that the noise power N equals:

$N=F(k{T}_0)W$

From N, we can show that the sensitivity of the receiver is equal to

$SNR\times N$