# What is noise figure

### RF Sensitivity Tutorial Includes

There are a number of methods of determining the sensitivity of radio receivers and their associated elements within radio communications systems. Of these methods, the noise figure is one of the most widely used methods. Not only is it widely used to assess the sensitivity performance or receivers, but it can be applied to complete receiving systems or to elements such as RF amplifiers. Thus it is possible to use the same notation to measure the noise performance of a whole receiver, or an RF amplifier. This makes it possible to determine whether a low noise amplifier may be suitable for a particular radio communications system by judging their relative levels of performance.

In view of this noise figure is a particularly important parameter for a wide variety of radio communications systems from fixed or mobile radio communications systems, two way radio communications systems, and satellite radio communications systems.

## Noise figure basics

Essentially the measurement assesses the amount of noise each part of the system or the system as a whole introduces. This could be the radio receiver, or an RF amplifier for example. If the system were perfect then no noise would be added to the signal when it passed through the system and the signal to noise ratio would be the same at the output as at the input. As we all know this is not the case and some noise is always added. This means that the signal to noise ratio or SNR at the output is worse than the signal to noise ratio at the input. In fact the noise figure is simply the comparison of the SNR at the input and the output of the circuit.

A figure known as the noise factor can be derived simply by taking the SNR at the input and dividing it by the SNR at the output. As the SNR at the output will always be worse, i.e. lower, this means that the noise factor is always greater than one.

The noise factor is rarely seen in specifications. Instead the noise figure is always seen. This is simply the noise factor expressed in decibels.

Noise figure

In the diagram S1 is the signal at the input, N1 is the noise at the input
and S2 is the signal at the output and N2 the noise at the output

As an example if the signal to noise ratio at the input was 4:1, and it was 3:1 at the output then this would give a noise factor of 4/3 and a noise figure of 10 log (4/3) or 1.25 dB. Alternatively if the signal to noise ratios are expressed in decibels then it is quite easy to calculate the noise figure simply by subtracting one from another because two numbers are divided by subtracting their logarithms. In other words if the signal to noise ratio was 13 dB at the input and only 11 dB at the output then the circuit would have a noise figure of 13 - 11 or 2 dB.

## Typical examples

The specifications of different pieces of equipment used for different types of radio communications systems will vary quite widely. A typical HF radio receiver may have a noise figure of 15 dB of more and function quite satisfactorily. A better level of performance is not necessary because of the high level of atmospheric noise. However receiver used for narrow band applications at VHF or above might have a noise figure of 3 or 4 dB. Narrow band RF amplifiers often have a noise figure of around 1 dB. However it is interesting to note that even the best professional wide-band VHF UHF receivers may only have a noise figure of around 8 dB.

Noise figure is a very important specification used in a variety of radio communications applications. It may be quoted for radio receivers, individual components, or for a complete receiver system within a fixed or mobile radio communications system. In view of its versatility noise figure is one of the most important parameters for radio communications applications when assessing sensitivity.

By Ian Poole

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