For comparison of receivers or amplifiers working at different impedance levels the use of the equivalent noise resistance is misleading.

For example, it is hard to determine at a glance whether a receiver with an input impedance of 50ohms and $R_{eq}=90ohms$ is better, from the point of view of noise, than another receiver whose input impedance is 300ohms and $R_eq=400ohms$ .

As a matter of fact, the second receiver is the better one, as will be seen. Instead of equivalent noise resistance, a quality known as noise figure, sometimes called noise factor, is defined and used.

The noise figure F is defined as the ratio of the signal-to-noise power supplied to the input terminals of a receiver or amplifier to the signal-to-noise power supplied to the output or load resistor.

$Thus F= \frac{(Input \frac {S}{N})}{(Output \frac{S}{N})}$

The noise figure will be 1 for an ideal receiver. Practical receiver will generate some noise, and the $\frac{S}{N}$ will deteriorate as one moves toward the output.

Consequently, in a practical receiver ,the output $\frac{S}{N}$ will be lower than the input value, and so the noise figure will exceed 1.Hence,we have the alternative definition of noise figure, which states that F is equal to the $\frac{S}{N}$ of an ideal system divided by the $\frac{S}{N}$

At the output of the receiver or amplifier under test, both working at the same temperature over the same bandwidth and fed from the same source .

In addition, both must be linear. The noise figure may be expressed as an actual ratio or in decibels.