#### Signal-to-noise ratio

signal amplitude

noise amplitude

Figure 1: Measurement of signal amplitudes to calculate a signal-to-noise ratio

signal amplitude

noise amplitude

Figure 1: Measurement of signal amplitudes to calculate a signal-to-noise ratio

#### Signal-to-noise ratio

The signal-to-noise ratio (abbreviated to SNR or S/N) is the ratio of the average signal power to the power of the average noise level. As a ratio of quantities of the same unit of measurement, a signal-to-noise ratio is a dimensionless number used to evaluate reception quality and an achievable receiver sensitivity. In radar technology, the signal-to-noise ratio is represented on a logarithmic scale:

SNR = 10 log | signal power | = 10 log | P_{S} |
(1) |

noise power | P_{R} |

By emphasizing average signal power and average noise power, practically both quantities are reduced to the same unit of time. However, since an oscilloscope does not display power but voltage values of the respective pulse amplitudes, these measured values must be squared to calculate power. This is possible because both signals are present on the same line, i.e. they have the same impedance, which is reduced away by the ratio:

SNR = 10 log | (U_{signal })^{2} |
(2) |

(U_{noise })^{2} |

Therefore, instead of a signal-to-noise ratio, it is better to state amplitude values directly in tuning specifications.
(Even if this means a signal-to-noise ratio as a power ratio).
For example, the much smaller echo signal in Figure 1 has exactly an SNR of 3 dB.
The power is twice the noise level by a factor of 2,
even if the signal amplitude is less than twice the noise amplitude:
2· (0,42 noise)^{2} = (0,6 signal)^{2}.