Figure 1: Focus on In-situ determination of fiber delay coefficient (alpha)
General
White Rabbit uses bidirectional wavelengths over a single fiber. Due to chromatic dispersion the forward- and backward propagation delay over the fiber differs. This difference is expressed in the WR asymmetry coefficient alpha (α) which is a fiber property, also known as fiber delay coefficient.
The relative delay curve of a typical optical fiber is non-linear and usually is described by fitting a 5-term Sellmeier equation. The slope of the relative delay curve (i.e. dispersion) determines the asymmetry (i.e. the fiber delay coefficient). The relative delay curve is nearly linear for the C-Band (1520-1577 [nm]) which is often used for long haul communication. For small wavelength offsets a linear 3-λ approximation of the fiber delay coefficient can be determined by probing the curve at two different wavelengths. The Master measures the Cable Round Trip Time (CRTT) at λ_{1} and λ_{2} while the Slave uses a fixed wavelength λ_{sm} (see figure 2).
This method uses the PTP time stamping capabilities that are already implemented in the devices. With the 3-λ approximation method the fiber delay coefficient of a deployed fiber can be determined and monitored insitu, i.e. without the need to have both fiber ends available at the same physical location, nor having the need for an extra link.
Figure 2: A Master and Slave device are connected via add/drop filters to the fiber under test. The Master is equipped with a tunable laser SFP.
The relative delay curve of a fiber under test can be measured with the test setup in figure 2. The tunable laser SFP in the Master can select λ_{1} and λ_{2} and measure the corresponding CRTTs δ(λ_{1}) and δ(λ_{2}). When the wavelength differences Δλ_{1} and Δλ_{2} are defined according to equation 1a and 1b:
\Delta\lambda_{1} = \lambda_{1} - \lambda_{sm}
\Delta\lambda_{2} = \lambda_{2} - \lambda_{sm}
Equation 1a, 1b: The wavelength differences between between λ_{1}, λ_{2} and λ_{sm}
then the fiber delay coefficient at λ_{1} can be calculated using equation 2:
\alpha(\lambda_{1}) = \frac{2{\Delta\lambda_{1}(\delta(\lambda_{1})-\delta(\lambda_{2}))}}{\delta(\lambda_{1})(\lambda_{1}-\lambda_{2})-(\delta(\lambda_{1})-\delta(\lambda_{2}))\Delta\lambda_{1}}
Equation 2: Calculation of the fiber delay coefficient when the Master uses λ_{1}, λ_{2} and the Slave uses fixed wavelength λ_{sm}. The fiber delay coefficient is a function of CRTT at λ_{1} and λ_{2} and the differences between λ_{1}, λ_{2} and λ_{sm}
Considerations
For the 3-λ approximation, theoretically small wavelength offsets perform better since large wavelength offsets suffer from chromatic dispersion non-linearity. However, the uncertainty in the CRTT measurements has a bigger impact on the 3-λ approximation method when small wavelength offsets are selected. Depending on measurement uncertainties one should find a balance between small and large wavelength offsets for optimal performance.
Propagation delay is affected by fiber temperature. CRTT measurements at λ_{1} and λ_{2} should therefore be performed as a combined set in a short period of time in order to keep temperature variations as small as possible.
Test results show that a 3-λ approximation determined fiber delay coefficient at properly selected wavelengths may results in a time errors below 100 ps for a 50 km fiber.
According to the PTP standard, for scalability reasons, all link calculations are done by the slave. When fixed and variable wavelength between master and slave are swapped then remote controlled wavelength tuning of the master is not needed. There is no objection to swap fixed and variable wavelength between master and slave, although the equations will slightly change:
\Delta\lambda_{1} = \lambda_{1} - \lambda_{ms}
\Delta\lambda_{2} = \lambda_{2} - \lambda_{ms}
Equation 3a, 3b: The wavelength differences between between λ_{1}, λ_{2} and λ_{ms}
\alpha(\lambda_{1}) = \frac{2{\Delta\lambda_{1}(\delta(\lambda_{1})-\delta(\lambda_{2}))}}{\delta(\lambda_{1})(\lambda_{2}-\lambda_{1})-(\delta(\lambda_{1})-\delta(\lambda_{2}))\Delta\lambda_{1}}
Equation 4: Calculation of the fiber delay coefficient when the Slave uses λ_{1}, λ_{2} and the Master uses fixed wavelength λ_{ms}
Documentation
A detailed description and overview of the 3-λ approximation method can be found in the ISPCS 2019 Best Paper Award winning article:
- Insitu determination of the fiber delay coefficient in time-dissemination networks, published in: 2019 IEEE International Symposium on Precision Clock Synchronization for Measurement, Control, and Communication (ISPCS).
Acknowledgements
Part of this work is funded by The 17IND14 project.
This project has received funding from the EMPIR programme co-financed by the Participating States and from the European Union’s Horizon 2020 research and innovation programme.
Contacts
Status
Date | Event |
---|---|
24-02-16 | Start of project |
17-07-17 | Made this sub sub-wiki page |
06-11-19 | Added ISPCS 2019 article and info |
Last updated: 6 Nov 2019