--- title: "T1 and E1 frame structures and bit rates" subject: "Telecommunications" chapter: 3 key: "semester_8/telecommunications:t1-e1-frame-structures" source: https://www.bctengineer.com/q/semester_8/telecommunications/t1-e1-frame-structures site: BCT Engineering --- # T1 and E1 frame structures and bit rates Telecommunications · Chapter 3: Signal Multiplexing - Asked in: 2076 Asoj, 6 marks - Video: [North American (T1), Europe (E1) System & Hierarchy Principles of Communication Board Soln In Nepali](https://www.youtube.com/watch?v=XiEB5dKF_Ec) — OPengineer - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/telecommunications/t1-e1-frame-structures - Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-3 ## Question Clarify the North American (T1) and European (E1) frame structures along with their multiplexing hierarchy, and for each hierarchical level provide the bit rate calculation. ## Short answer T1 frame: 24x8+1=193 bits per 125 us, rate 1.544 Mbps; E1 frame: 32x8=256 bits, rate 2.048 Mbps. NA hierarchy: T1 1.544, T2 6.312, T3 44.736, T4 274.176 Mbps. European: E1 2.048, E2 8.448, E3 34.368, E4 139.264, E5 564.992 Mbps. ## Answer 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. ```text 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. ```text +-----+-----+-----+------+------+-----+------+ | 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:** | Level | Made from | Voice channels | Bit rate | Overhead | |---|---|---|---|---| | DS0 | 1 voice channel | 1 | 64 kbps | – | | DS1 (T1) | 24 DS0 | 24 | 1.544 Mbps | 8 kbps (framing) | | DS2 (T2) | 4 DS1 | 96 | 6.312 Mbps | 136 kbps | | DS3 (T3) | 7 DS2 | 672 | 44.736 Mbps | 552 kbps | | DS4 (T4) | 6 DS3 | 4032 | 274.176 Mbps | 5.76 Mbps | $$ \begin{aligned} T2 &: 4 \times 1.544 = 6.176;\ \ 6.312 - 6.176 = 0.136\ \text{Mbps overhead} \\ T3 &: 7 \times 6.312 = 44.184;\ \ 44.736 - 44.184 = 0.552\ \text{Mbps overhead} \\ T4 &: 6 \times 44.736 = 268.416;\ \ 274.176 - 268.416 = 5.76\ \text{Mbps overhead} \end{aligned} $$ **European:** | Level | Made from | Voice channels | Bit rate | Overhead | |---|---|---|---|---| | E0 | 1 voice channel | 1 | 64 kbps | – | | E1 | 30 voice + 2 TS | 30 | 2.048 Mbps | 128 kbps (TS0, TS16) | | E2 | 4 E1 | 120 | 8.448 Mbps | 256 kbps | | E3 | 4 E2 | 480 | 34.368 Mbps | 576 kbps | | E4 | 4 E3 | 1920 | 139.264 Mbps | 1.792 Mbps | | E5 | 4 E4 | 7680 | 564.992 Mbps | 7.936 Mbps | $$ \begin{aligned} E2 &: 4 \times 2.048 = 8.192;\ \ 8.448 - 8.192 = 0.256\ \text{Mbps overhead} \\ E3 &: 4 \times 8.448 = 33.792;\ \ 34.368 - 33.792 = 0.576\ \text{Mbps overhead} \\ E4 &: 4 \times 34.368 = 137.472;\ \ 139.264 - 137.472 = 1.792\ \text{Mbps overhead} \\ E5 &: 4 \times 139.264 = 557.056;\ \ 564.992 - 557.056 = 7.936\ \text{Mbps overhead} \end{aligned} $$ The extra bits at each higher level are used for frame alignment, pulse stuffing (justification) control and alarms, because the tributaries are plesiochronous. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is common to T1 and E1 frames? A. Both have 193 bits B. 8000 frames/s of 125 us, 8-bit PCM samples, 64 kbps per channel C. Both have 32 slots D. Both use the same signalling Answer: B. Both sample at 8 kHz with 8-bit words, but differ in channel count and overhead. (Key point: Common basis) 2. How is E2 overhead found? A. 8.448 - 4 x 2.048 = 0.256 Mbps B. 8.448 - 2.048 = 6.4 Mbps C. 4 x 8.448 - 34.368 D. 8.448 - 30 x 64 kbps Answer: A. 4 x 2.048 = 8.192 Mbps, so 8.448 - 8.192 = 0.256 Mbps of overhead. (Key point: E2 overhead) 3. How is E3 formed and what is its rate? A. 7 x E2 = 44.736 Mbps B. 4 x E2 = 34.368 Mbps (480 channels) C. 4 x E1 = 34.368 Mbps D. 6 x E2 = 139.264 Mbps Answer: B. Every E level multiplexes four lower tributaries; E3 is 4 x E2 giving 34.368 Mbps and 480 channels. (Key point: E-hierarchy) 4. In a 12-frame T1 superframe, which frames carry signalling and how? A. Frames 1 and 7 use TS16 B. Every frame uses the F bit C. Frames 6 and 12, by robbing the LSB of each channel D. Frame 12 only, using a separate slot Answer: C. Robbed-bit signalling occurs in frames 6 and 12 of the superframe. (Key point: T1 signalling) ## Related in Telecommunications - [North American T1 vs European E1 hierarchy](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3At1-e1-hierarchy-compare) — Telecommunications, chapter 3, asked 2× ## Related in other subjects - [T1 and E1 TDM-PCM hierarchy with frame diagrams](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3At1-e1-frame-diagrams) — Communication Systems, chapter 5 - [T1 and E1 bit rate and bandwidth; DPCM encoder](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3At1-e1-bitrate-dpcm) — Communication Systems, chapter 5 - [E1 frame, TDM hierarchy and signaling rate](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ae1-frame-hierarchy) — Communication Systems, chapter 5 - [Short note: T1 and E1 hierarchy](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ashort-note-t1-e1-hierarchy) — Communication Systems, chapter 5