Consider two EDFA amplifiers in cascade. Each EDFA has an average input signal power of 10 mW and an average noise power of 1 mW. What is the OSNR of the system at the receiver.

The Optical Signal-to-Noise Ratio (OSNR) for a system with a cascade of N identical amplifiers, where each amplifier's gain compensates for the preceding fiber span's loss, is calculated by dividing the input signal power by the total accumulated noise. The total noise is the sum of the noise generated by each amplifier. Given: Input Signal Power (Pin) = 10 mW Noise Power per amplifier (PASE) = 1 mW Number of amplifiers (N) = 2 The total accumulated noise power (Pnoisetotal) is N PASE = 2 1 mW = 2 mW. The system OSNR in linear scale is: OSNRlinear = Pin / Pnoisetotal = 10 mW / 2 mW = 5 Converting to decibels (dB): OSNR (dB) = 10 log10(5) ≈ 6.99 dB, which is rounded to 7 dB.

A. 20 dB is incorrect. This value might result from erroneously adding the OSNR of each stage in dB (10 dB + 10 dB), which is physically incorrect as noise accumulates and degrades the OSNR.
B. 10 dB is incorrect. This represents the OSNR for a single amplifier stage (10 mW / 1 mW = 10, or 10 dB), but it fails to account for the noise added by the second amplifier.
D. 5 dB is incorrect. This value corresponds to a linear OSNR of approximately 3.16, which does not align with the correct calculation of noise accumulation from the two amplifier stages.

1. Agrawal, G. P. (2021). Fiber-Optic Communication Systems (5th ed.). Wiley. In Chapter 6, Section 6.4.2, "Cascaded Amplifiers," the text explains that for a chain of N amplifiers where gain compensates for loss, the total accumulated amplified spontaneous emission (ASE) power is approximately N times the ASE power of a single amplifier. The system OSNR is then calculated as OSNR ≈ Pin / (N PASE). This directly supports the calculation: OSNR = 10 mW / (2 1 mW) = 5, or ~7 dB. (See Equation 6.4.8 and the surrounding discussion on page 238).

2. Nokia (2018). Application Note: OSNR and its role in optical network performance management. This document explains that OSNR is a critical parameter that degrades along a multi-span link due to the accumulation of noise from each amplifier. This principle confirms that the OSNR of a two-amplifier system must be lower than that of a single-amplifier system, invalidating options A and B. (See section "OSNR in optical networks", page 3).