Attenuation Coefficient in an optical fibre

  • #1
594
12

Homework Statement


In a particular fibre, the attenuation coefficient for Rayleigh scattering is measured to be 0.30 dB/km at 1.20 μm.

(a) How large would it be expected to be at 0.80 μm?

(b) Ignoring other sources of attenuation, if a signal of a certain initial power was sent over a distance of 50 km of the fibre, what would be the power in the signal at the other end if the wavelength was 0.80 μm, as a fraction of the power that would be received at 1.20 μm?

Homework Equations


a = (10/L)log(Pin/Pout)

where L = distance
a= attenuation, units: dB/km

The Attempt at a Solution


a)

0.30 dB/km = (10/1.2*10-6)log(Pin/Pout)

0.30*10-6 / 10 = log(Pin/Pout)

3.0*10-8 = log(Pin/Pout)

a = (10/0.8*10-6)*3.0*10-8

a = 0.375 dB/km - this seems reasonable, as the distance is shorter, attenuation should be higher

b)
I don't really understand what b) is asking for though and am not really sure where to start.
 

Answers and Replies

  • #2
TSny
Homework Helper
Gold Member
12,608
3,004
The L in the formula represents the distance over which the signal travels. This will come into part (b).

I believe that 0.80 μm and 1.20 μm are wavelengths of the infrared light propagating in the fiber. To answer part (a), you need to know how the Rayleigh-scattering attenuation coefficient depends on wavelength. This link has some discussion

https://www.fiberoptics4sale.com/blogs/archive-posts/95048006-optical-fiber-loss-and-attenuation

Rayleigh scattering is discussed about halfway down the page. But, hopefully, this was covered in your textbook or lectures.
 
  • #3
594
12
The loss due to Rayleigh scattering is proportional to λ-4 and obviously decreases rapidly with increase in wavelength

a(λ)=a00/λ)4

a0 = 0.30 dB/km
λ0 = 1.20 μm

a(λ)=0.30(1.2*10-6/0.8*10-6)4

a = 1.51875 dB/km - answer for part a)
 
  • #4
TSny
Homework Helper
Gold Member
12,608
3,004
The loss due to Rayleigh scattering is proportional to λ-4 and obviously decreases rapidly with increase in wavelength

a(λ)=a00/λ)4

a0 = 0.30 dB/km
λ0 = 1.20 μm

a(λ)=0.30(1.2*10-6/0.8*10-6)4

a = 1.51875 dB/km - answer for part a)
That looks right to me.
Are all those digits in your answer significant?
 
  • #5
594
12
That looks right to me.
Are all those digits in your answer significant?
Oh no, I will probably just round it to 3 sig figs with a= 1.52 db/km

For b)
a = (10/L)log(Pin/Pout)
a(λ)=a00/λ)4

I'm still not entirely sure what b) is asking.

If the signal input has power X, wavelength of 0.80 μm, and was sent through the fibre for 50km, what would the power be at the output Y.

If the signal input has power A, wavelength of 1.20 μm, and was sent through the fibre for 50km, what would the power be at the output B.

I think it's also asking for a ratio between the output power of both 0.80 μm and 1.20 μm wavelengths.

0.30 = (10/50,000)log(Pin/Pout)

1.52 = (10/50,000)log(Pin/Pout)

I can solve for log(Pin/Pout) for both 0.30 db/km and 1.52 db/km and then get a ratio of the two?
 
  • #6
TSny
Homework Helper
Gold Member
12,608
3,004
Let P1, out be the output power of the 0.80 μm signal and let P2, out be the output power of the 1.20 μm signal.
Find the ratio of P2, out to P1, out assuming that the input power is the same for both wavelengths.

Since the attenuation coefficients are in units of dB/km, you will want to leave L in km.
 
  • #7
594
12
0.30 = (10/50,000)log(Pin/Pout)

1.52 = (10/50,000)log(Pin/Pout)

(50,000*0.30)/10 = log(Pin/Pout) = 1500

(50,000*1.52)/10 = log(Pin/Pout) = 7600

ratio: 1500/7600?
 
  • #8
TSny
Homework Helper
Gold Member
12,608
3,004
1.52 = (10/50,000)log(Pin/Pout)
It's a good idea to include units when you substitute in your numbers. You would then see that the units on the left side of the above equation don't match the units on the right side.

Once you fix the units, try to solve the equation for Pin/Pout.
 
  • #9
594
12
(50*0.30)/10 = log(Pin/Pout) = 1.5
e^log(Pin/Pout) = Pin/Pout
e1.5 = 4.48
(50*1.52)/10 = log(Pin/Pout) = 7.6
e7.6 = 1998
 
  • #10
TSny
Homework Helper
Gold Member
12,608
3,004
(50*0.30)/10 = log(Pin/Pout) = 1.5
e^log(Pin/Pout) = Pin/Pout
e1.5 = 4.48
(50*1.52)/10 = log(Pin/Pout) = 7.6
e7.6 = 1998
OK so far. Can you now find P2,out / P1,out if you assume Pin is the same for both signals?
 
  • #11
594
12
If i divide both numbers by each other i'm getting (P2, in/P2, out)/(P1, in/P1, out)

4.48/1998=0.002
 
  • #12
TSny
Homework Helper
Gold Member
12,608
3,004
If i divide both numbers by each other i'm getting (P2, in/P2, out)/(P1, in/P1, out)

4.48/1998=0.002
Looks good. But you have rounded the answer to only one significant figure.
 
  • #13
594
12
Looks good. But you have rounded the answer to only one significant figure.
4.48/1998 = 0.00224224224
 
  • #14
TSny
Homework Helper
Gold Member
12,608
3,004
4.48/1998 = 0.00224224224
How many significant figures would be appropriate?
 
  • #15
594
12
3 sig figs... so 0.00224
 
  • #16
TSny
Homework Helper
Gold Member
12,608
3,004
3 sig figs... so 0.00224
OK. 2 or 3 sig figs seems to me to be appropriate.

So, the question asks you to express P2, out as a fraction of P1, out.
 
  • #17
594
12
Would that just be 1/0.00224?
 
  • #18
TSny
Homework Helper
Gold Member
12,608
3,004
Not quite. You want to find a number c such that P2,out = c P1,out
 
  • #19
594
12
I don't quite follow...
 
  • #20
TSny
Homework Helper
Gold Member
12,608
3,004
You are asked to find P2, out as a fraction of P1, out.

Signal 2 has a larger attenuation constant. So, the output power of signal 2 will be less than the output power of signal 1. This can be expressed as saying that the output power of signal 2 is some fraction of the output power of signal 1.
That is, you could write P2, out = c P1, out for some number c. You just need to find c (which you have essentially done).

If c happened to equal .25, then you could say that the output power of signal 2 would be 1/4 the output power of signal 1.
You could write P2, out = 0.25 P1, out, or you could write P2, out = (1/4) P1, out
I think either way of writing it would be acceptable.

So, in your problem, what number should take the place of .25?
 
  • #21
594
12
P2, out=0.00224P1, out
 
  • #22
TSny
Homework Helper
Gold Member
12,608
3,004
Yes, that looks good.
 

Related Threads on Attenuation Coefficient in an optical fibre

Replies
1
Views
558
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
3
Views
405
  • Last Post
Replies
1
Views
7K
  • Last Post
Replies
2
Views
650
Replies
2
Views
672
Replies
1
Views
3K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
5
Views
614
Top