FDM hierarchy and T carrier system

FDM hierarchy

In analogue telephone networks voice channels (0.3–3.4 kHz, 4 kHz slots) are stacked in frequency in steps, by SSB modulation, to form larger and larger groups. The CCITT (ITU-T) hierarchy:

(The Bell/AT&T system uses a 600-channel mastergroup of 10 supergroups at 564–3084 kHz, and a 3600-channel jumbo group of 6 mastergroups.)

 12 x voice --[SSB mod]--> GROUP      (12 ch, 60-108 kHz)
  5 x group --[SSB mod]--> SUPERGROUP (60 ch, 312-552 kHz)
  5 x SG    --[SSB mod]--> MASTERGROUP(300 ch)
  3 x MG    --[SSB mod]--> SUPERMASTER(900 ch)

Standard building blocks let equipment from different makers interconnect, and whole groups can be routed together.

T carrier system

The T carrier is the North American digital TDM hierarchy. Each voice channel (DS0) is PCM coded at $8000 \times 8 = 64$ kbps with µ-law companding.

T1 frame structure:

 1 bit  8 bits  8 bits        8 bits
+-----+-------+-------+-----+--------+
|  F  |  Ch1  |  Ch2  | ... |  Ch24  |
+-----+-------+-------+-----+--------+
<--------- 193 bits in 125 us -------->
F = framing bit

$$\begin{aligned} \text{Bits per frame} &= 24 \times 8 + 1 = 193\ \text{bits} \\ \text{Frame rate} &= 8000\ \text{frames/s}\ (T = 125\ \mu\text{s}) \\ R_{T1} &= 193 \times 8000 = 1.544\ \text{Mbps} \end{aligned}$$

• 12 frames form a superframe (D4); the F-bits form an alignment pattern.
• In frames 6 and 12 the LSB of every channel is robbed for signalling.
• Line code: AMI/B8ZS on twisted pair.

Multiplexing levels:

24 x DS0 --> [MUX] --> T1  1.544 Mbps (24 ch)
 4 x T1  --> [M12] --> T2  6.312 Mbps (96 ch)
 7 x T2  --> [M23] --> T3  44.736 Mbps (672 ch)
 6 x T3  --> [M34] --> T4  274.176 Mbps (4032 ch)

$$\begin{aligned} T2 &: 4 \times 1.544 = 6.176;\ \ 6.312 - 6.176 = 0.136\ \text{Mbps overhead} \\ T3 &: 7 \times 6.312 = 44.184;\ \ 44.736 - 44.184 = 0.552\ \text{Mbps overhead} \\ T4 &: 6 \times 44.736 = 268.416;\ \ 274.176 - 268.416 = 5.76\ \text{Mbps overhead} \end{aligned}$$

The extra overhead at T2, T3 and T4 carries framing, pulse-stuffing control and alarm bits.