Tue 22nd Nov: Optical Fibre Info (2)

I apologise if some of this (and the pictures I have used this week) seems familiar to what I did last week. What I have done this week is taken the additional knowledge I have gained and applied it to better explain some of the concepts and redo some of the calculations to provide more accurate answers.


(I am not entirely sure why this post is all in capitals but something seems to have happened when publishing..)

Taking the statement I made in the previous week

So since we are restricted to using LEDs the best we can use so far seems to be a 4-core (full duplex) OM2 multimode graded index loose optical fibre. (Loose Tube C S T Armoured 50/125 LSOH).

It has come to my attention that we do not need to receive signals, merely transmit them, so we do not need a full duplex system but rather a half duplex one instead.

The reason why I have chosen 4 core is because when considering optical fibres for communications over lengths of 45km I get the feeling it is quite unusual to request a single core. Nearly all of the single core optical fibres that I have found do not come armour plated or have very good resistances to temperature or moisture. However, I have had an idea, instead of only using one core and letting the other 3 go to waste, I propose we use them in the following way. Suppose we want to transmit a file of 20Mb over a line that could transmit at a maximum rate of 20Mbps, now if we had a single core we could transmit 20 million bits per second. However, why not split the file we want to send into 4 pieces of 5Mb. Then we can send each of the 5Mb files down their own optical fibre core. As you can see, one 20Mb file will take 1 second to go down one 20Mbps core, or we can send 4 5Mb files down their own core at a speed of 5Mbps to give the same result. However, if we know that each core can handle a maximum speed of 20Mbps why not simply send all 4 5Mb files at 20Mbps down their own core? This mean we can transmit a signal 4 times faster without having to increase the bandwidth (and hence increase the signal dispersion).

I asked Ross and we are not allowed to do this.

I chose multimode because we are severely restricted in what we can choose here due to the parameters of the problem given to us i.e we are not allowed to use single mode fibres.

I chose the graded fibre because it greatly reduces the amount of dispersion, as explained later.

Loose optical fibre:

http://www.premiumline-cabling.com/download/catalog_PL_FO_final.pdf

We need a loose optical fibre because it provides us with very high resistances to temperature and moisture. The gel acts as an insulating layer which prevents the propagation of water into the system. Also, if the cable is flexed or stressed it reduces the damage done to the cores by acting as a cushion. The reason why I want to choose a high armoured (Kevlar) outer shell is because of its high durability and so there is much less chance of rodents/creatures chewing into or getting to the fibre optic core.

I've looked around and found that the company will provide us with rolls of length 2km.

So to reach a distance of 45km we will need 22 splices and no connectors because this system is designed to be secure.

Power Loss Calculation Again

I am now going to redo the calculation for the power loss in the optical fibre because I have more accurate numbers now.

The attenuation of our cable is 0.5dB/km (at a wavelength of 1300nm), the splice loss is 0.02dB/slice (Can you give me a better value than the one I found Natalie?), no connectors, a 0.3dB error for irregularities in the fibre and finally a 3dB safety margin to ensure that the signal has some strength when it reaches the receiving end.

http://communications.draka.com/sites/eu/Datasheets/MMF%20-%20Graded-Index%20Multimode%20Optical%20Fiber%20%2850_125%20%C2%B5m%29.pdf

This gives me so far a total power loss of 25.8dB(=0.384W). So we need to transmit with AT THE VERY LEAST this power. As more accurate values become available I will continue to improve on this number, but for now this is not too bad.

 

Maximum Bandwidth Calculation

What limits are bandwidth is how badly the signal gets "smeared" or dispersed inside the optical fibre as it travels the 45km distance. There are a few forms of dispersion which need to be considered:

Modal Dispersion:

This is the most important one and is due to the fact that light entering the system at different angles will have to travel different distances and hence will take different times to reach the receiver.

This causes the signal to disperse and means that we lose this sharp "high" "low" signal into a stretched out signal which is less obvious and so we lose data.

Graded index fibres greatly reduce this effect but not entirely.

 Material Dispersion:

This is where light of different wavelengths travel at different velocity through the medium. Even though we are using a monochromatic light source there are always errors in how the light is produced giving us a range of wavelengths about the quoted value which is also emitted (i.e the light source has a spectral width).

http://spie.org/Documents/Publications/00%20STEP%20Module%2007.pdf

Where λ_{0} is the wavelength of the light emitted. We also that that n(λ_{0}) is the refractive index of the inner core, n_{g} is the group refractive index and D_{m} represents the material dispersion in picoseconds per kilometre of length of the fibre per nanometre spectral width of the source.

Waveguide Dispersion:

Seeing as how Material Dispersion results from the dependence on wavelength of the refractive index of the fibre material, even if we assume the core and cladding refractive indices are to be independent of wavelength, the group velocity of each would still depend on the wavelength due to the geometry of the fibre, this is called waveguide dispersion. The waveguide dispersion and the material dispersion together are called intramodal dispersion.

The group velocity is different from the velocity of the individual wave packets.  The group velocity is the speed of the wave packet whereas the phase velocity is the speed of the individual waves.

http://www.slideshare.net/sir2011Anonymous/optical-fiber-dispersion-8807357

http://spie.org/Documents/Publications/00%20STEP%20Module%2007.pdf

However, we do not need to consider waveguide dispersion here because we are using a multimode fibre.

http://www.linktionary.com/f/fiber-optic.html

Just to get an idea of the order of magnitude I used this value:

http://www.teraxion.com/imports/_uploaded/White%20pape-Dispersion%20control%20for%20ultrafast%20optics.pdf

Note that I had to use this example value because manufacturers just don't quote the waveguide dispersion in multimode fibres and you will see in a moment why.

So using the experimentally determined value for pure silica I found (3ps²/(nmkm)), obviously the true value of our optical fibre will be different from this value however I want an order of magnitude. Over 45km, with a spectral width of 30nm this means we will have a rise time of 0.064ns, which is tiny in comparison to the other forms of dispersion.

 

Polarisation Dispersion:

Polarization mode dispersion (PMD) is a form of modal dispersion where two different polarizations of light in a waveguide, which normally travel at the same speed, travel at different speeds due to random imperfections and asymmetries, causing random spreading of optical pulses. Unless it is compensated, which is difficult, this ultimately limits the rate at which data can be transmitted over a fibre. This is more of a problem for single mode fibres rather than multimode fibres.

http://en.wikipedia.org/wiki/Polarization_mode_dispersion

 

The calculation:

The optical fibre I have found has an "overfilled modal bandwidth" of 1200Mhz.km, so over the distance of 45km this implies that the maximum frequency we can obtain just considering the modal dispersion is: (1200/45)=26.6MHz. However, it will be easier to compare all of the different dispersion types if I consider their rise times instead. The rise time is defined as the time required for the signal to change from 10% to 90% of its maximum value. the system rise time is determined by the data rate and the code format.

Notice that figure (a) has a signal with a sufficient rise time, even though the pulses are rounded the signal is still detectable. However in figure (b) the transmitted signal takes too long to respond to the input signal. This has a strong effect on the data rate:

If the response time is not sufficient then we lose information on transmitted data.

To prevent this distortion, an acceptable criterion is to require that a system have a rise time t_{s} of no more than 70% of the pulse width T_{p}:

t_s <= (0.7T_p)

Now there are many different digital encoding schemes, the most popular being Return to zero (RZ) and non-Return to zero (NRZ) The NRZ requires only one transition per symbol whereas RZ requires two transition for each data bit. This implies that the required bandwidth for RZ must be twice that of NRZ, this is shown below.

A non-return-to-zero (NRZ) code is a binary code in which "1s" are represented by one significant condition and "0s" are represented by some other significant condition, with no other neutral or rest condition. The RZ format uses twice the bandwidth to achieve the same data-rate as compared to non-return-to-zero format. But NRZ requires a more complex demodulator since the clock can't be extracted from the signal as it can in RZ.

http://in.answers.yahoo.com/question/index?qid=20080411132348AARdnVl

To avoid this demodulation problem we are going to use a RZ encoding system. This means that the rise time will be given by:

t_s <= 0.7T/2 = 0.35/B_r

Note that the B_{r} is the bit rate and it equals 1/T.

So as mentioned above, due to the modal dispersion our maximum bit rate will be 26.67MHz, meaning the rise time will be 1.31x10^-8s=13.1ns.

I know that for the optical fibre the material dispersion is given by 0.105ps/(nm²km). After speaking with John he suggests that the spectral width of the light sources will be around 30nm-50nm. Taking the lower end of this estimate over a distance of 45km gives us a rise time of 4.25ns.

So the total rise time will be:

Total rise time t_t = SQRT(13.1^2 + 4.25^2) = 13.77ns

This means our maximum bandwidth considering these two factors will be 25.4MHz, to be on the safe side I recommend transmitting with a frequency of no more than 22MHz.

So our maximum bandwidth so far is 22MHz.

If I were to take the upper estimate given to me by John of a spectral width of 50nm then our maximum bandwidth would be 19.8MHz, but to be on the safe side it should be no more than 17MHz.