# Radio Signal to Noise S/N Ratio, SNR

The signal to noise ratio, SNR or S/N ratio is one of the most straightforward methods of measuring radio receiver sensitivity.

It defines the difference in level between the signal and the noise for a given signal level. The lower the noise generated by the receiver, the better the signal to noise ratio.

As with any sensitivity measurement, the performance of the overall radio receiver is determined by the performance of the front end RF amplifier stage. Any noise introduced by the first RF amplifier will be added to the signal and amplified by subsequent amplifiers in the receiver. As the noise introduced by the first RF amplifier will be amplified the most, this RF amplifier becomes the most critical in terms of radio receiver sensitivity performance. Thus the first amplifier of any radio receiver should be a low noise amplifier.

## Concept of signal to noise S/N ratio SNR

Although there are many ways of measuring the sensitivity performance of a radio receiver, the S/N ratio or SNR is one of the most straightforward and it is used in a variety of applications. However it has a number of limitations, and although it is widely used, other methods including noise figure are often used as well. Nevertheless the S/N ratio or SNR is an important specification, and is widely used as a measure of receiver sensitivity

The difference is normally shown as a ratio between the signal and the noise, S/N, and it is normally expressed in decibels. As the signal input level obviously has an effect on this ratio, the input signal level must be given. This is usually expressed in microvolts. Typically a certain input level required to give a 10 dB signal to noise ratio is specified.

## Signal to noise ratio formula

The signal to noise ratio is the ratio between the wanted signal and the unwanted background noise. It can be expressed in its most basic form using the S/N ratio formula below:

It is more usual to see a signal to noise ratio expressed in a logarithmic basis using decibels with the formula below:

${\mathrm{SNR\left(dB\right)}}_{}=10{\mathrm{log}}_{10}\left(\frac{{P}_{\mathrm{signal}}}{{P}_{\mathrm{noise}}}\right)$

If all levels are expressed in decibels, then the formula can be simplified to the equation below:

$\mathrm{SNR}\left(\mathrm{dB}\right)={P}_{\mathrm{signal}}\left(\mathrm{dB}\right)-{P}_{\mathrm{noise}}\left(\mathrm{dB}\right)$

The power levels may be expressed in levels such as dBm (decibels relative to a milliwatt, or to some other standard by which the levels can be compared.

## Effect of bandwidth on SNR

A number of other factors apart from the basic performance of the set can affect the signal to noise ratio, SNR specification. The first is the actual bandwidth of the receiver. As the noise spreads out over all frequencies it is found that the wider the bandwidth of the receiver, the greater the level of the noise. Accordingly the receiver bandwidth needs to be stated.

Additionally it is found that when using AM the level of modulation has an effect. The greater the level of modulation, the higher the audio output from the receiver. When measuring the noise performance the audio output from the receiver is measured and accordingly the modulation level of the AM has an effect. Usually a modulation level of 30% is chosen for this measurement.

## Signal to noise ratio specifications

In view of the fact that the actual SNR experienced at any time is governed by a number of factors, the conditions under which the signal to noise ratio is experienced need to be stated.

In this way the S/N ratio is stated to include all these conditions. To enable the S/N ratio for different receivers to be compared, generally the performance is stated for set parameters. Typically the input voltage for a signal to noise ratio of 10dB is stated. Other factors like the bandwidth also need to be included along with the type of transmission and for AM the modulation depth (typically 30% is used).

Typically one might expect to see a figure in the region of 0.5 microvolts for a 10 dB S/N in a 3 kHz bandwidth for SSB or Morse. For AM a figure of 1.5 microvolts for a 10 dB S/N in a 6 kHz bandwidth at 30% modulation might be seen.

## Points to note when measuring signal to noise ratio

SNR, signal to noise ratio is a very convenient method of quantifying the sensitivity of a receiver, but there are some points to note when interpreting and measuring signal to noise ratio.

To investigate these it is necessary to look at the way the measurements of signal to noise ratio, SNR are made. A calibrated RF signal generator is used as a signal source for the receiver. It must have an accurate method of setting the output level down to very low signal levels. Then at the output of the receiver a true RMS AC voltmeter is used to measure the output level.

• S/N and (S+N)/N When measuring signal to noise ratio there are two basic elements to the measurement. One is the noise level and the other is the signal. As a result of the way measurements are made, often the signal measurement also includes noise as well, i.e. it is a signal plus noise measurement. This is not normally too much of a problem because the signal level is assumed to be much larger than the noise. In view of this some receiver manufacturers will specify a slightly different ratio: namely signal plus noise to noise (S+N/N). In practice the difference is not large, but the S+N/N ratio is more correct.
• PD and EMF Occasionally the signal generator level in the specification will mention that it is either PD or EMF. This is actually very important because there is a factor of 2:1 between the two levels. For example 1 microvolt EMF. and 0.5 microvolt PD are the same. The EMF (electro-motive force) is the open circuit voltage, whereas the PD (potential difference) is measured when the generator is loaded. As a result of the way in which the generator level circuitry works it assumes that a correct (50 Ohm) load has been applied. If the load is not this value then there will be an error. Despite this most equipment will assume values in PD unless otherwise stated, but it is always worth checking if possible.

While there are many parameters that are used for specifying the sensitivity performance of radio receivers, the signal to noise ratio is one of the most basic and easy to comprehend. It is therefore widely used for many radio receivers used in applications ranging from broadcast reception to fixed or mobile radio communications.