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What is T1, E1 and E3?

A T1 is the term used in reference to digital transmission at 1.544 Mb/s deployed by phone companies for carrying 24 transmission channels - each channel being a trunk. T1 can be translated as "Transmission #1". Above T1 speeds the next common Transmission Level is T3 corresponding to a bit rate of around 50 Mb/s.

Interestingly, in earlier developments of digital communications when telex and telegraph at 50 bits/sec was the norm, the first level transmission FDM multiplexed hierarchy was called a T1 and carried 24, 50bit/sec channels.

The 1,544,000 bits per second can be added up as follows: The intended application was voice telephony with a sampling rate of 8,000 samples per second, each producing an 8 bit byte, representing the amplitude of the sound at an instant, taken over 24 different channels. An extra bit called the framing bit is introduced with each sequence of 24, 8 bit bytes.

Thus we have:
(8 bits x 24 channels + 1) = 193 total bits that must pass in one Frame
8,000 Frames must pass in order to achieve 8,000 samples per second per channel:
193 bits/frame x 8,000 frames/s = 1,544,000 bits/s

In addition, earlier digital transmission systems used a methods referred to as bit-robbing, bit-stuffing or bit-insertion to maintain synchronization of the digital system in the event of too many "zero" bits in sequence. Later improvments used active an zero suppression algorythm - B8ZS - Binary 8-Zero Suppression, whereby a continuous sequence of 8 bits was indicated by the use of deliberate bipolar violations.

It is relevant to note that although common industry jargon will equate "T1" with a "1.544 Mb/s" bit stream, the actual payload is:
64kb/s x 24 = 1.536Mb/s
if bit robbing is not used - less. (56kb/s x 24 = 1.344Mb/s).

The T1, T3.. hierarchy developed in the United States.
In Europe and International transmission a different standard - E1, E2, E3, E4, E5 - developed.
E1 would carry some 32 channels. E2 would carry 4 E1s. E3 would carry 4 E2s. Etc.
Bit calculation for E1 is neat: 64kb/s x 32 = 2.048 Mb/s. Presto!

In the broader telecommunications industry evolution, there is a key inevitability about transmission history and technological advancement, which if recognised, is stragetically significant. To put it simply, transmission is in a manner of speaking - disappearing. In the early analog voice networks, a phone call, end-to-end ran over analog transmission elements, each of which had to perform and be kept performing up to standard. The switches first became digital; subsequently the transmission has become digital. Now, ideally, the core network as a whole introduces no analog distortion. The big heavy bulky character of transmission systems has disappeared. Ultimately, it's all just a bunch of electronics. The "switch" also is ultimately electronics. The distinction in the early days of analog telecommunications which led to the modularisation of a network into "Switching" and "Transmission" is no longer there. Switch manufacturers are making transmission equipment and vice-versa. Sooner or later the switch manufacturers are going to make "transmission" cards for their switches, consolidating their branching technologies simply because it is cheaper for them.