T1 and E1 frame structures and bit rates

Both systems use 8-bit PCM samples taken 8000 times per second, so each frame is 125 µs long and each voice channel is 64 kbps.

North American T1 frame

24 channels × 8 bits + 1 framing (F) bit. Signalling is robbed from the LSB of each channel in frames 6 and 12 of a 12-frame superframe.

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

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

European E1 frame

32 time slots × 8 bits; TS0 = frame alignment, TS16 = signalling, 30 voice slots.

+-----+-----+-----+------+------+-----+------+
| TS0 | TS1 | ... | TS15 | TS16 | ... | TS31 |
+-----+-----+-----+------+------+-----+------+
 sync  <-voice 1-15->  sig   <-voice 16-30->
<------ 32 x 8 = 256 bits in 125 us ------->

$$\begin{aligned} \text{Bits per frame} &= 32 \times 8 = 256\ \text{bits} \\ R_{E1} &= 256 \times 8000 = 2.048\ \text{Mbps} \end{aligned}$$

Multiplexing hierarchy and bit rates

North American:

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

European:

$$\begin{aligned} E2 &: 4 \times 2.048 = 8.192;\ \ 8.448 - 8.192 = 0.256\ \text{Mbps overhead} \\ E3 &: 4 \times 8.448 = 33.792;\ \ 34.368 - 33.792 = 0.576\ \text{Mbps overhead} \\ E4 &: 4 \times 34.368 = 137.472;\ \ 139.264 - 137.472 = 1.792\ \text{Mbps overhead} \\ E5 &: 4 \times 139.264 = 557.056;\ \ 564.992 - 557.056 = 7.936\ \text{Mbps overhead} \end{aligned}$$

The extra bits at each higher level are used for frame alignment, pulse stuffing (justification) control and alarms, because the tributaries are plesiochronous.