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Signal to Noise Ratio S/N

 

Signal To Noise Ratio

When signals are detected, processed or amplified is essential to know the the signal integrity that could be affected by any undesirable signal or noise produced internally in the circuits or system or picked up externally, in order to measure the signal strength against the noise the concept of “signal to noise ratio” was established.

The signal to noise ratio is the ratio of a signal level versus a noise level, and it is normally expressed in decibels as it is illustrated below, the signal to noise ratio can be represented in the frequency or time domains.

 

                          Signal level =  60 dbm

                                                                                                                                                                                                   A               

                            Signal                           

                                                                B   

                                                                                    Average noise level = 10 dbm              

                                                                                       

                                                         

The above picture represents the signal to noise ratio in the frequency domain as can be seen in a spectrum analyzer for a signal with a power of 60 dbm and average noise of 10 dbm. For most practical purposes the average noise level is considered, but for critical operation the noise pick levels provide a safer signal to noise ratio analysis specially for random high noise spikes.

A = Signal to noise level considering the picks of the noise  

B = Signal to noise level considering the average of the noise

From the picture the signal to noise ratio considering the average noise level is 50 dbs since the signal is 50 dbs above the noise level.

The minimum signal to noise ratio specifications will depend on the specific system requirements and application, while for most commercial application a signal to noise ratio of few dbs could be sufficient, for others systems could not, is the job of the engineer to verify the proper signal to noise requirement for the system, for example the S/N ratio for the reception of ananalog TV signal must be superior to 40 db to guaranty a noise free image.

When  the signal under consideration is a signal carrier then is called the carrier to noise ratio or C/N.

 

 

 

 

 

 

 

 

The above picture represents the signal to noise ratio as could be seen in a oscilloscope, since an oscilloscope normally do not display signal amplitudes in decibels, the S/N in decibels can be calculated by using the relationship:

20 Log10  (S/N)

Example:

What is the S/N ratio in decibels of a signal with an amplitude of  one volts and a noise amplitude of 50 millivolts?

S=1 V

N= .050 V

S/N in decibels = 20 Log10 (1/.050) = 26.02 decibels

Be aware that the wider the channel bandwidth the more noise power density will pass, so noise is also a function the bandwidth, see also thermal noise.

 

Signal to Noise Ratio Displayed in the Frequency Domain

Signal

Noise amplitude

Signal to Noise Ratio Displayed in the Time

Domain

Signal amplitude