Sunday, 28 April 2019

Intro to Data Comms

The proper title of this subject is Data Communications and Net-centric computing, and a lot of people shortened the title to DCNC. Honestly, I didn't particularly think all that much about that, so instead I simply referred to it as data comms. Anyway, you know how we seem to magically be able to connect to a computer on the other side of the world and be able to access the information on that computer almost instantaneously. Well, this subject is designed to actually demystify all of that technobabble and actually demonstrate how it is done. Mind you, one of the reasons that we are able to access Netflix has more to do with there being a server here in Australia as opposed to actually downloading the information directly from the United States. One of the reasons that this isn't all that feasible, despite this information traveling at, or at least pretty close to, the speed of light has something to do with there not actually being a direct cable between Australia and the US.

Here is a map of where all of the submarine cables are located across the world that enable us to be interconnected in a way that we haven't been before. Oh, and before you ask, satellite transmission is so painfully slow that we simply don't bother with it, despite the fact that once again the signals travel at, or at least pretty close to, the speed of light.

Bell's Invention

So, let's consider a little history here. Sure, we could say that Alexander Graham Bell 'invented' the telephone, but honestly, people were sending messages electronically long before he made that famous call to the guy in the next room. The thing is that before the telephone there was the telegraph, which was used to transmit messages across long distances. Before that, with the exception of the Greeks (or was it the Persians) using bonfires to transmit messages, the fastest way to send a message from one place to another was by horse. Actually, the United States had this method known as the Pony Express, where a rider would ride a certain distance, and when he reached a checkpoint, he would hand the parcel to a much more rested horse and rider. Still, that was a pretty slow way of transmitting messages.

Now we have the telephone. The way the telephone works (and after I discovered this I can never look at that device the same again) is that there is a diaphragm in the speaker that vibrates when you speak. The vibration then causes a circuit to connect, though the strength of the circuit will depend upon the strength of the diaphragm hitting the circuit. This is how our voice is modulated into an electronic signal. The signal then travels down a wire, through a system known as the PTSN, or public telephone switching network, to the destination. The electric pulses will then hit a magnet which will grow strong and weak based upon the strength of the signal hitting it. This magnet will cause another diaphragm to vibrate, and this vibration, not surprisingly, produces sound. In fact the sound that is produced is a replication of the sound that was originally spoken into the telephone.

The other thing is how the telephone actually knows where to connect to. Well, originally you would have to dial the switch board and tell the operator who you wanted to connect to. When I was young we had these rotary phones, and later push button phones (which is why we use the term 'to dial a number', and the term 'ring' comes from the fact that a bell in the phone would ring when we called somebody - much different to the Beyonce that comes out of our modern phones). Each of the numbers would take a certain amount of time for the dial to return to its previous spot, and that length would tell the operator, and later the computer, the number that was requested. Put them all together and you get a telephone number. This was similar to the push button phones, except each of the buttons would send a signal down the line that was slightly different to the others. When the signal reached the exchange, the computer would interpret these signals and work out the number that was wanted.

Another thing with the phone number is that it is divided into sections - take this phone number 08 8245 2212. The first two digits is the area code (this is an Australian phone number), and tells the exchange which state they want. The next four numbers (originally it was three, but we run out of numbers so added another number to the front) tells the exchange what exchange is wanted. The last for digits is the actual number of the phone that is being dialed.

The thing is that this world is analog in nature, but computers, or at least the computers that we are currently using, really only understand the world as a series of 0s and 1s (or ons and offs, or true and false, but you get the idea). So the trick here is basically attempting to translate what is in effect analog, or continuous, into digital, or discrete.

Sine Waves

So, this is a sine wave, or more appropriately a sinusoidal wave.

I would have pulled the pictures from the notes to show how the sine wave comes from a circle, that is pulled apart and then placed along an axis (which is what is above) but the video below is so much better.

So, the sine wave is basically a continuous line that goes up and down. The wave is made up of a crest, the section above the x-axis, which is the time axis, and the trough which is the area below the x-axis. The peak to peak amplitude is the distance from the bottom of the trough to the top of the peak, and one whole cycle, namely the amount of time it takes for the wave to go to each of the peak and the trough and back to its original position (even if the original position is at one of the peaks) is known as the wavelength.

A sine wave can be rendered mathematically as follows:

x(t) = A.sin(2.π.f.t + φ)

Now, we can reduce that by including the angular frequency, which is:

ω = 2.π.f

so, the formula becomes:

 x(t) = A.sin(ω.t + φ)

The following values are as follows:

A = amplitude
f = frequency
t= time (in seconds) 
φ = phase (in radians)
ω= angular momentum
Π = pi, a constant, of 3.14 (though it is an irrational number, meaning that it goes on forever).

So, the amplitude is the y-axis, and is usually measured in volts.
The frequency is measured as the number of wavelengths in one second. The phase is determined by how far along the x-axis the intersection is (that is where the amplitude is 0). A phase of 0 is where the wave starts at t=0 and A=0 (and goes up)..

Let us put that into practice by looking at some sine waves:

So, looking at this we can see that the peak of the waves (or both of them) is 2, so A=2. It takes 100 ms to complete one entire wavelength, so that means that there are 10 waves in a second, so the frequency is 10. With regards to the red wave, the wave begins at t=0, so the phase is 0. The angular momentum, which is 2πf is 2* 3.14*10 = 62.8.

So, plotting the red wave into the formula, we get v1(t) = 2sin(62.8t), and φ=0.

Now that we have the details of the first, red, wave we can calculate the details of the second wave. To do that we need to work out the change, so:

φ = -2π 🛆t/T

Now, 🛆t is the change, and T is the time for one wave length we can work out the change, namely because we have a reference point, so 🛆t = 70-50 = 20. T=100, and we can convert 2π into degrees easily enough, since it will be 360o. So, we have φ = -360*20/100 = -7200/100 = -72o. So, we now know that the phase is -72 degrees.

This, the mathematical formula for our second wave is v2(t) = 2 sin(62.8t - 72).

Now that we have played around with a hypothetical sine way, let us take this into the real world and work out the instantaneous voltage of power supply in Australia. Now, we have two types: AC, or alternating current, and DC, or direct current. Direct current doesn't change (and operates at 230v) so at any point along the time axis the instantaneous voltage will always be 230v.

For alternating current, that is somewhat different. The frequency is 50 hz (that is 50 cycles per second). However, the voltage is 230v, though this isn't the peak voltage, but the root mean square. To find the peak voltage, we use the following equation:

Vp = Vrms(√2/2)

Yep, we have that ugly number there. So, Vp = 230*(√2/2) which gives us approximately 325 volts.

Now that we have the amplitude, we can plug all the values in.

V(t) = 325 sin (314t)

The phase is 0, so all we need to do to work out the instantaneous voltage is add in the time.

At 0s, V(t) = 325 sin (314*0) = 0v.

At 10ms, V(t) = 325 sin ([314rad/s][0.01s]) =  -200V

Anyway, enough of this and lets move onto something different, namely Internet Protocols.
Creative Commons License

Intro to Data Comms by David Alfred Sarkies is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. This license only applies to the text and any image that is within the public domain. Any images or videos that are the subject of copyright are not covered by this license. Use of these images are for illustrative purposes only are are not intended to assert ownership. If you wish to use this work commercially please feel free to contact me

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