# Does carriers lifetime introduce any dispersion to a LED diode emitter?

I'm asked to calculate the maximum chromatic dispersion coefficient D for which an optical cable is able to transmit at a 100 Mbps bitrate working in SMS.

The maximum bitrate is given by

B≤1/2∆τ, where ∆τ is the intramodal dispersion and B is the maximum bitrate.

The thing is that I'm given the LED diode carriers lifetime, τ', and I'm not sure what is the effect on the dispersion. My idea is that lifetime just introduces another dispersion, which makes total dispersion ∆τ+τ', but I'm not sure at all.

The other option is that τ' affects the intramodal dispersion somehow. Since ∆τ=D·L·∆λ, is that possible that τ' and ∆λ are related?

Update:

Since it seems the question may be a little ambiguous, this is original problem:

Given a system made by L=72km optical cable and a LED diode emitter with λ=1330 nm, ∆λ=10nm and carriers lifetime τ'=1ns, which the maximum value of the chromatic dispersion coefficient so the system works at a 100Mbps bitrate.

The thing is that I don't know how to deal with the carriers lifetime.

Thanks!

• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
Commented Nov 15, 2022 at 14:36

The various things that spread out the pulse, drive electronic rise, carrier lifetime, chromatic dispersion, receiver response time, etc. all wind up convolved with your signal.

The achievable bitrate also depends on the nature of your modulation and your signal/noise ratio. So, the problem is an ill-posed idealization, and without further information about what is intended it cannot be answered.

The chromatic dispersion coefficient (CDC) is a standard value for any manfactured fiber. The method to determine it is by using CD analyzers to measure the time delay, in ps, as a function of the wavelength and then drawing CDC, in ps/(nm*km), from the slope of this delay curve and from the length of the link. The delay curve plotted by CD analyzers is a fitted trace based on the acquired time delays at discrete wavelength points.

Typically, carriers lifetime limits the bitrate and dispersion limits the distance of transmission at specific bitrate.

Usually, Single mode system has a dispersion tolerance of 17𝑝𝑠/(𝑛𝑚*𝑘𝑚) which determines the maximum distance for specific bitrates.

However, you can determine the maximum tolerable dispersion for this system using procedure in similar tutorial problems in following link

https://www.slideshare.net/Hharishassan/tutorial-design-of-optical-communication-systems

Another useful resource

https://dl.cdn-anritsu.com/en-us/test-measurement/files/Technical-Notes/White-Paper/Disp_in_Opt_Fibers_PMD_CD.pdf