July 2, 2026
Most engineers working on optical transceivers, long-haul transmission, and amplifier testing learn the so-called "58 Formula" from senior colleagues when they first enter the industry. It is a quick calculation method for noise figure (NF) and optical signal-to-noise ratio (OSNR). However, in practical testing, engineers often find that the noise figure calculated via the 58 Formula deviates significantly from the actual readings measured by an optical spectrum analyzer (OSA). This article derives the origin of the constant "58" starting from fundamental formulas, and clarifies scenarios where the 58 Formula is valid and cases that demand precise calculation algorithms instead.
Noise figure is a core metric for evaluating the performance of optical amplifiers in optical communication systems, which quantifies the extra noise generated by an optical amplifier. Per the international standard IEC 61290-3-1:2003 Optical Amplifiers – Part 3: Noise figure parameters, the standard formula for noise figure is defined as:
Parameter Definitions
Rearranging the formula yields:
Parameter Definitions
The following noise figure test of our high-power polarization-maintaining SOA (Model JSA-BT525G35-PM) illustrates why the 58 Formula produces inconsistent results against OSA measurements.
The yellow and cyan curves in the spectrum plot represent the input and output optical spectra, respectively. Key measured parameters are listed below:
Step 1: Calculation Using the 58 Formula
This result shows a large discrepancy against the OSA reading, proving the formula yields invalid data here.
The root cause is that the OSA resolution bandwidth in this test is not 0.1 nm, so the constant termis no longer equal to 58 dBm. The standard original formula must be adopted for accurate computation:
Step 2: Precise Calculation via Standard Formula
This result closely matches the NF value displayed on the OSA.
The number 58 is not a universal constant. It is only valid for the combination of 1550 nm wavelength and 0.1 nm reference bandwidth. The constant must be recalculated whenever the operating wavelength or OSA resolution bandwidth changes.
The constant value of 58 fromis calculated for a 1550 nm wavelength and a 12.5 GHz reference bandwidth. Early optical amplifiers were primarily deployed in long-haul transmission systems operating within the C-band, making the 58 Formula suitable for those applications. However, the emergence of semiconductor optical amplifiers (SOAs) has expanded amplifier operating wavelengths to 800–2000 nm, where the 58 Formula loses its validity.
- Traditional EDFA-based long-haul DWDM systems operating near the C-band 1550 nm window;
- Rough engineering estimation of system OSNR, adopting the industry-standard 0.1 nm reference bandwidth
- Linear transmission links free from optical nonlinear interference
- Preliminary performance estimation of C-band SOAs during scheme design.
- Non-C-band optical amplifiers: O/S/L/U-band amplifiers, SOAs operating at 800–1400 nm or above 1600 nm;
- Noise figure testing with an OSA resolution bandwidth other than 0.1 nm (e.g., 0.069 nm, 0.05 nm as shown in the case);
- Distributed Raman amplification systems, whose noise models differ fundamentally from EDFAs and SOAs;
- High-speed long-distance transmission links with severe nonlinear effects requiring precise simulation;
- High-precision laboratory component testing and factory calibration of finished products, which mandate the original standard formula.
Tianjin Janhoo Optoelectronics Technology Co., Ltd is a high-tech enterprise specializing in the R&D and manufacturing of domestic semiconductor optical amplifiers (SOAs). We currently supply a full lineup of SOA products covering 850 nm, 1060 nm, 1270 nm, 1310 nm, 1550 nm and 1625 nm, as well as reflective SOA (RSOA) gain chips at 850 nm, 1310 nm and 1550 nm.
Our facility features a Class 10,000 cleanroom laboratory equipped with complete equipment for optical chip fabrication, testing and packaging. We possess hybrid integrated micro-packaging capabilities for optical chips, and are conducting R&D on hybrid integrated devices combining narrow-linewidth external cavity lasers (NLL/ECL) with SOAs, alongside high-power SOA devices. We also provide third-party services including optoelectronic component testing, packaging and processing.
Chinese Site: http://www.tj.jhbf.cc/
English Site: www.soaamplifier.com
Email: chenying@tjjhbf.cc
