Signal-to-noise ratio (S/N or SNR) definition
Posted by Margaret Rouse
Contributor(s): John Burke
In analog and digital communications, signal-to-noise ratio, often written S/N or SNR, is a measure of signal strength relative to background noise. The ratio is usually measured in decibels (dB).
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If the incoming signal strength in microvolts is Vs, and the noise level, also in microvolts, is Vn, then the signal-to-noise ratio, S/N, in decibels is given by the formula
S/N = 20 log10(Vs/Vn)
If Vs = Vn, then S/N = 0. In this situation, the signal borders on unreadable, because the noise level severely competes with it. In digital communications, this will probably cause a reduction in data speed because of frequent errors that require the source (transmitting) computer or terminal to resend some packets of data.
Ideally, Vs is greater than Vn, so S/N is positive. As an example, suppose that Vs = 10.0 microvolts and Vn = 1.00 microvolt. Then
S/N = 20 log10(10.0) = 20.0 dB
which results in the signal being clearly readable. If the signal is much weaker but still above the noise -- say 1.30 microvolts -- then
S/N = 20 log10(1.30) = 2.28 dB
which is a marginal situation. There might be some reduction in data speed under these conditions.
If Vs is less than Vn, then S/N is negative. In this type of situation, reliable communication is generally not possible unless steps are taken to increase the signal level and/or decrease the noise level at the destination (receiving) computer or terminal.
Communications engineers always strive to maximize the S/N ratio. Traditionally, this has been done by using the narrowest possible receiving-system bandwidth consistent with the data speed desired. However, there are other methods. In some cases, spread spectrum techniques can improve system performance. The S/N ratio can be increased by providing the source with a higher level of signal output power if necessary. In some high-level systems such as radio telescopes, internal noise is minimized by lowering the temperature of the receiving circuitry to near absolute zero (-273 degrees Celsius or -459 degrees Fahrenheit). In wireless systems, it is always important to optimize the performance of the transmitting and receiving antennas.
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