Attenuation in Fiber Communications Systems

I'm teaching a fiber optics communications course this semester and - like just about every communications course - we started out talking about attenuation.

Attenuation is just a fancy word for loss. In any communications system you've got a certain amount of signal strength going in and a certain amount of signal strength coming out. If there is no amplification in a system there is always going to be loss and the output signal will always be weaker than the input signal.

In fiber systems attenuation is caused by three things:

1. Absorption - Glass, whether it is fiber or the windows in your house, will always absorb a small amount of light going through it. The amount depends on the wavelength of light and what the glass is made of.
2. Scattering - Atoms in glass cause a certain amount of scattering of light and scattered light will not emerge at the output.
3. Leakage - Light will leak out of fiber, especially if the are a lot of bends in the fiber.

Fiber manufacturers typically provide specifications for all three of these, along with total attenuation per kilometer.

One of the primary goals in any communications system is to keep the attenuation to a minimum. Even so, there will always be a loss in signal intensity when comparing output power to input power. Calculating attenuation in a system is pretty simple. Attenuation is cumulative so basically you just add up the signal loss for each component in the system. Here's an example:

Question: A 50 km fiber run has been spec'd at 99% transmission per km. What percentage of light will emerge at the output?

Answer:

The fiber run is transmitting 99% per km so after the first km 99% of the input signal will be available, after the second km, 99% of what's left after the first km will be available, etc. So we can say:

60.5% of the original input signal strength will emerge at the output.

How To Put Your iPhone Into Field Test Mode & Compare Signal Strength Bars To Actual Signal Levels

In a previous post I showed how to do Decibel (dB) calculations when both the input power and output power are known for a transmission system. We learned that a 50% decrease between input and output power results in a power loss of -3 dB with the negative sign indicating the loss in power.

These calculations work great if you know both the input and output power but - what if you don't know the input power? And, because dB calculations are made based on an output power to input power ratio, they really don't tell you much when it comes to things like actual signal strength. What's the solution? Something called a dBm calculation. dBm calculations are done in basically the same way we do dB calculations, the only real difference being we replace the input power value in the equation with a 1 mW constant:

P_signal in dBm = 10 x log₁₀(P_{signal in Watts}/1mW)

Where P_{signal in Watts} is the signal strength measured in Watts. This equation can be simplified using some basic math since 1mW is now a constant, yielding:

P_signal in dBm = 10 x (log₁₀P_{signal in Watts}) + 30

Pretty simple, the dBm level of a signal that has been measure in Watts is just ten times the base-10 log of the measured signal plus 30. It's actually so simple it's much more common to measure and indicate communications signals in dBm. In fact, you can take some measurements yourself if you happen to own an iPhone. Let's learn how.

The iPhone has the ability to go into something called Field Test mode. Once in this mode you can look at signal strength in both signal bars (what we are all used to seeing) and also in dBm. To put an iPhone into Field Test mode just punch in the following number on the phone keypad, including the "star" and "pound sign" keys:

*3001#12345#*

After you punch these numbers and symbols in, hit the Call button on the keypad and you'll end up with your iPhone screen looking like this:

Lots of interesting stuff here but - for now - let's ignore everything but the upper left hand corner of the screen. Take a look at where you usually see the signal bars and you'll see a negative number - this is the actual cell signal strength your phone is receiving in dBm referenced to 1 mW. In the above screen shot I'm measuring -113 dBm. Touch that signal strength number once and it toggles to the familiar signal strength bars:


Touch it again and it flips back to the strength number. You get the idea. What constitutes a good signal? Here's some rough signal strength guidelines:

Full Signal:-70 or lower
Optimal Signal:-70 to -75
Fair Signal:-75 to -85
Poor Signal: -85 or higher

Remember as a negative number increases in its numeric value it is actually decreasing with reference to zero. This means a -70 dBm signal is stronger than a -85 dBm signal.

This is interesting to experiment with - check your signal strength in different locations see and how it correlates to the numbers of bars you are getting. Does it match up? Not always based on my experience!

To exit out of Field Test mode on the iPhone just hit the Home button.

Have a Blackberry? (I don't so proceed with this one at your own risk) I've been told you can do something similar using the secret code Alt-NMLL to convert your bars to numbers. To convert back to signal strength bars just enter the same secret code again.

Have a phone other than an iPhone or Blackberry? Most phones will allow you to go into some sort of field mode to see actually signal strength numbers. Check your manual or do some searching on the web to find out how.


7/6/10 Update: This function appears to be disabled after completing the iOS 4 Software Update

What The Heck Is A Decibel?

Maybe "decibel" is not part of your normal vocabulary but it is a term we all occasionally read or hear used. Typically it has to do with noise levels - we use decibels to describe loud or soft sounds. US government research even suggests a safe exposure sound limit of 85 decibels for eight hours a day. We frequently hear the term but - have you ever wondered what a "decibel" really is? Let's take a look.

Decibel (abbreviated dB) measurement is a logarithmic measurement typically of a output/input ratio of power or voltage. According to Wikipedia, the decibel originates from methods used to quantify reductions in audio levels in telephone circuits. Over distance any type of transmission media (copper wire, fiber optic lines, wireless) signal gets lost. The simplest way to think of a transmission system is as a box with signal going in and signal coming out the other end. In the diagram below we'll use P_in for our input signal and P_out for our output signal.
P_loss in the diagram is the power lost as the signal moves from the input to the output of the system. Any communications system signal is going to lose strength as it moves from one point to another due to things like resistance, capacitance and inductance that are all integral parts of any transmission system. Heat (as in hot days) can be a major problem for cable and telephone companies because wire resistance increases with heat causing more power to be lost in the delivery system. Sometimes signal loss is so significant amplifiers have to be added to a communications links to clean up and boost signal strength. Let's take a look at how decibels are calculated.

Power loss in dB is calculated by multiplying 10 times the base-10 log of the output power (P_out) divided by the input power (P_in). Let's look at an example where P_in is 20 Watts (or 20W) and a P_out is 15W.

P_loss in dB = 10 x log₁₀(P_out/P_in)

P_loss in dB = 10 x log₁₀(15W/20W)

P_loss in dB = 10 x log₁₀(.75)

Using a calculator to take the base-10 log of .75 we get -.125 Don't miss the negative sign - it is important here - it indicates power is being lost in the transmission system. Continuing with our equation.

P_loss in dB = 10 x (-.125)

P_loss in dB = -1.25dB

So, in this transmission system example, our output signal is said to be down (referencing the negative sign) 1.25 dB.

Let's work one more calculation, this time using a P_in of 16W and a P_out of 8W. Not a very efficient transmission system if we are losing half the power we put in. Let's see what we get for decibel loss working through the equation.

P_loss in dB = 10 x log₁₀(P_out/P_in)

P_loss in dB = 10 x log₁₀(8W/16W)

P_loss in dB = 10 x log₁₀(.5)

Using a calculator to take the base-10 log of .5 we get -.3 Again - don't forget the negative sign. Continuing with our equation.

P_loss in dB = 10 x (-.3)

P_loss in dB = -3dB

In this example, the system is losing half the input power and our output signal is said to be 3dB down. This is important to remember - for every 3 dB power decreases or increases by 50%. How do we know if it is increases or decreases? By that very important positve or negative sign!

In a future post we'll take power calculations a little further and discuss something called the dBm Scale.

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Update 01/25/10

Homework: If P_in is 7W and P_out is 5W what is the P_loss in dB?


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