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