A T1 is a a combination of 24 phone lines that are multiplexed to form roughly a 1. 53 Megabits per second wide area network connection, typically connected to the internet.
A T0 is 1 phone line (what goes to your house).
It consists of a 8 bit wide channel that is sampled at a rate of 2x the absolute frequency of the channel, 0Hz to 4000Hz, which is 8000 samples/second. On the first T0 channel, the phone company gives 7 of the 8 bits for data, and reserves the 8th bit for internal use (such as caller ID)
7bits * 8000 Samples/Second == 56,000 Bits/Second or 56k modem.
A T1 just combines 24 of these channels.
NOTE: on channels beyond the 1st channel, you get all 8 bits for data, therefore all channels from 2 and up are 64,000 b/s.
So...
If you take 56,000 + 23*64,000 ~== 1,529 Kb/s or 1. 5mbps link.
A T2 is just 4 T1s or 96 phone lines (Rarely used) == around 9. 6 Mbps
A T3 is just 28 T1s or 672 phone lines (more common) == around 45 Mbps
These numbers continue to get higher, but typically anything after a T3 becomes an OC (Fiber Optic) link due the higher frequencies required for more channels.
Hence the OC3, OC12, OC48, OC192, OC768 terms
The phone company achieves sending this signal over 1 phone line through a technique called Multiplexing. This can get a little complicated, but I will try to keep it simple.
When you make a phone call from your house, it goes to the local CO (Call Office). Everyone in your neighborhood connects to the same CO (could be a few thousand users). If the telephone company did not multiplex, each circuit (established call) would need a dedicated phone line between the Call Offices (and higher). This would require Millions of additional phone lines to be installed.
So...
Because each channel utilizes 4000Hz of frequency (to be picky, only 300Hz to 3300Hz), but the copper phone line can support frequencies upwards of many Mhz for relatively short distances (say a few miles), we have a significantly larger amount of bandwidth on the line that is not being used.
Multiplexing is a technique of shifting frequencies and stacking them. Call #1 gets frequency 0 --> 4000 Hz. When Caller #2 lifts the handset, the local CO MUX (short for Multiplexer), takes the incoming signal, and shifts it to 4000 --> 8000 Hz. The Third caller (or circuit) gets shifted to 8000 --> 12,000Hz.
Now, all 3 of these calls (or circuits) can be passed down the same copper line (between COs), just using the frequencies from 0Hz to 12,000Hz.
To give a little more detail for those of you who caught it, I originally stated the channel is 0 --> 4000 Hz (which at 7 bits, gives you exactly 56k), but I later reference only 300Hz --> 3300 Hz, which at 7 bits, you only get 42k, so how we really get 56k????
Because the majority of voice surrounds around say 800hz, with a little calculus, we can determine that is is more efficient to sample the frequency area around this more common area more often and less often say 2 or 3 standard deviations away from this point.
This is determined and sampled using a technique called u (Mu) law companding (not compounding) in the US and Alpha law companding abroad. Through these techniques, we can improve the signaling slightly, and re-achieve the theoretical limit of 56k.
The actual speed that your modem negotiates with say AOL, is based on many factors, the majority of them revolve around the amount of noise in the local loop (from the CO to your house) and the distance of that line. The closer you are to the CO (just like DSL) and the better quality of lines (typically y based on the age), the quieter the line, and the better quality connection or higher speed you will be able to obtain.
The funny thing is, this is exactly how the physical layer of DSL works. All the DSL Modem actually does (at the Physical layer), is act like a MUX, only called a Digital Subscriber Line Access Multiplexer (DSLAM). Every DSL Provider is different, and based on the bandwidth rates purchased, the frequencies used are different, but the principal is the same.
Between your house, and the local CO, you are just accessing more MHz of frequency on your local TeleCo loop. More frequency means more bandwidth.
Your Voice Transmission still occurs at 0 --> 4000 Hz, the data channel just occurs at a higher Frequency. That is why the DSL provider gives you those filters to put between the wall and the phone. With out these filters, you potentially could hear the actual data channel (the very bottom end). The filters also keep your voice (or any ambient noise) from interfering with the higher frequencies of the DSL.
Unfortunately, due to the laws of physics and higher frequencies not propagating as far as low frequencies (and the 20AWG wire of the phone system) and the average TeleCo loop being around 1. 25mi, you will not be able to maintain frequencies above about 10MHz efficiently.
As you get further away from the CO, the bandwidth capabilities of DSL drop (and not on a linear scale), which is why say Verizon can not make DSL available everywhere.
Cable Companies run a piece of RG8 (large piece of Coax) down the street, which is about an 8AWG copper cable (vs 20AWG for TelCo). Because the copper is so much larger, they can push much higher frequencies much further. Again with out getting into much detail, this is why the cable companies can provide higher band width and go farther from their Head In locations.
With the New FIoS technology (what in the TelCo industry is known as the "Last Mile") being installed into individuals homes, bandwidth limitations are virtually eliminated. The Fiber utilized for an OC3 (155Mbps) is the same Fiber used for an OC768 (39,813Mbps). The only difference is the "modem" or the Optical/Photonic switching equipment at the ends of the line.
One other thing to say (because I did not earlier), typically, when you purchase a T1 or a T3 from the phone company, they will bring you a F/O link, and put a DSLAM at your location, and then give you a copper link which will get connected to the Boarder Gateway Router (with the proper interface card). To upgrade this typically requires a change of adapters in the DSLAM and/or in your BGR.
But... This is in no way the guaranteed way of connecting. There are literally thousands of ways a WAN Link can be created, not all are necessarily connected to the "Internet" either. There are also many other technologies that can be thrown into this mix, such as ISDN, ATM, MPLS, SSH, Sonet, Frame Relay. Each one works differently, yet they are all related (most specifically to SDH/Sonet). They all can be private or public.
The distance limitations in Fiber Optic are also virtually eliminated (yes there is some loss, but it is typically less than 0. 4dB/Km).
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