# SNR calculating

The SNR is calculated using the logarithm.

For example, the SNR of a signal is 30 dB when it traverses one OA. If the signal power is S and the noise is N, the signal power is 10lgS, and the noise power is 10lgN. Before the signal traverses the OA, the noise is low and is negligible. After the signal traverses the OA, the noise increases sharply to N. Therefore, the SNR changes sharply.

When the signal traverses the second OA, the SNR is: 10lgS/2N = 10lgS/N �?10lg2. When the signal traverses the third OA, the SNR is: 10lgS/3N = 10lgS/N �?10lg3.

The number of OAs determines how many times the noise N is multiplied.

Assume that the SNR is 20 dB when the signal traverses the tenth OA and that all OAs cause the same impact on the noise. At the first OA, the SNR is: 10lgS/N = 30.

At the second OA, the SNR is: 10lgS/2N = 10lgS/N �?10lg2 = 30 �?10lg2 = 27, and the change is 3.

At the third OA, the SNR is: 30 �?10lg3 = 25.2, and the change is 1.8.

At the fourth OA, the SNR is: 30 �?10lg4 = 24, and the change is 1.2.

At the fifth OA, the SNR is: 30 �?10lg5 = 23, and the change is 1.

At the sixth OA, the SNR is: 30 �?10lg6 = 22.2, and the change is 0.8.

At the seventh OA, the SNR is: 30 �?10lg7 = 21.5, and the change is 0.7.

At the eighth OA, the SNR is: 30 �?10lg8 = 21, and the change is 0.5.

At the ninth OA, the SNR is: 30 �?10lg9 = 20.4, and the change is 0.6.

At the tenth OA, the SNR is: 30 �?10lg10 = 20, and the change is 0.4.

The noise varies significantly according to the input optical power, gain, and OA model. An OA with higher noise has greater impact on the entire SNR.

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