--- title: "T1 and E1 TDM-PCM hierarchy with frame diagrams" subject: "Communication Systems" chapter: 5 key: "semester_6/communication_systems:t1-e1-frame-diagrams" source: https://www.bctengineer.com/q/semester_6/communication_systems/t1-e1-frame-diagrams site: BCT Engineering --- # T1 and E1 TDM-PCM hierarchy with frame diagrams Communication Systems · Chapter 5: Multiplexing Techniques - Asked in: 2080 Bhadra (CS II), 8 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_6/communication_systems/t1-e1-frame-diagrams - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-5 ## Question With the help of the frame diagrams, discuss T1 and E1 hierarchy of TDM-PCM telephony. ## Short answer The T1 frame has 24 channels of 8 bits plus 1 framing bit (193 bits) at 8000 Hz, giving 1.544 Mbps. The E1 frame uses 32 time slots (30 voice, 1 sync, 1 signaling) of 8 bits each, resulting in 256 bits/frame and 2.048 Mbps. ## Answer TDM-PCM telephony carries many 64 kb/s PCM voice channels on one line by interleaving their 8-bit samples in time. The two standards are **T1** (North America, Japan) and **E1** (Europe, ITU-T, used in Nepal). Both sample speech at 8 kHz, so each frame lasts $125$ µs. #### T1 frame ```text |<--------- one frame = 125 us = 193 bits --------->| +---+--------+--------+--------+-------+--------+ | F | Ch 1 | Ch 2 | Ch 3 | ... | Ch 24 | +---+--------+--------+--------+-------+--------+ 1 bit 8 bits 8 bits 8 bits 8 bits F = framing bit (pattern spread over 12 frames) ``` $$ \begin{aligned} \text{Bits per frame} &= 24 \times 8 + 1 = 193\ \text{bits} \\ \text{Frames per second} &= f_s = 8000\ \text{frames/s} \\ R_b &= 193 \times 8000 = 1\,544\,000\ \text{b/s} = 1.544\ \text{Mb/s} \end{aligned} $$ - 12 frames form a **superframe** (24 in the extended superframe, ESF). The F-bits of these frames carry the frame alignment pattern (100011011100 for the superframe). - Signalling uses the **robbed-bit** method: in frames 6 and 12, the LSB of every channel carries signalling (A and B bits). - µ-law companding ($\mu = 255$) and AMI/B8ZS line coding are used. #### E1 frame ```text |<-------- one frame = 125 us = 256 bits -------->| +-----+-----+-----+-----+------+------+-----+------+ | TS0 | TS1 | ... |TS15 | TS16 | TS17 | ... | TS31 | +-----+-----+-----+-----+------+------+-----+------+ sync voice voice signal voice voice each time slot = 8 bits; 32 slots per frame voice channels: TS1-TS15 and TS17-TS31 (30) ``` $$ R_b = 32 \times 8 \times 8000 = 2.048\ \text{Mb/s} $$ - **TS0** carries the frame alignment word (0011011) in alternate frames, plus alarm bits. - **TS16** carries channel-associated signalling. 16 frames form a **multiframe** of 2 ms. TS16 of frame 0 carries the multiframe alignment pattern, and TS16 of each of frames 1–15 carries the signalling bits of 2 channels (4 bits each). - A-law companding ($A = 87.6$) and HDB3 line coding are used. #### T1 hierarchy ```text 24 voice ch x 64 kb/s | [ DS1 / T1 ] 1.544 Mb/s 24 ch | x4 [ DS2 / T2 ] 6.312 Mb/s 96 ch | x7 [ DS3 / T3 ] 44.736 Mb/s 672 ch | x6 [ DS4 / T4 ] 274.176 Mb/s 4032 ch ``` #### E1 hierarchy ```text 30 voice ch x 64 kb/s (+ 2 overhead slots) | [ E1 ] 2.048 Mb/s 30 ch | x4 [ E2 ] 8.448 Mb/s 120 ch | x4 [ E3 ] 34.368 Mb/s 480 ch | x4 [ E4 ] 139.264 Mb/s 1920 ch | x4 [ E5 ] 564.992 Mb/s 7680 ch ``` At each higher level, the higher rate is a little more than (number of inputs × lower rate). The extra bits are used for framing and **bit stuffing** (justification), which align input streams whose clocks differ slightly. For example, $4 \times 1.544 = 6.176$ Mb/s, but DS2 runs at 6.312 Mb/s. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is a T1 frame laid out? A. 1 framing bit then 24 x 8-bit channels = 193 bits B. 32 x 8 bits C. 24 x 8 bits with no framing D. 8 framing bits then 24 channels Answer: A. One F bit plus 24 channels of 8 bits makes 193 bits in 125 us. (Key point: T1 frame) 2. How does T1 carry signalling? A. Robbed bit: LSB of each channel in frames 6 and 12 B. A dedicated TS16 C. In the framing bit D. Separate wire Answer: A. In frames 6 and 12 of the superframe the LSB of each channel carries A and B signalling bits. (Key point: T1 signalling) 3. What is the E1 multiframe? A. 16 frames (2 ms) with TS16 carrying signalling for 2 channels per frame B. 12 frames with robbed bits C. 24 frames in ESF D. 32 frames of 4 ms Answer: A. 16 x 125 us = 2 ms; each frame's TS16 carries signalling for two channels. (Key point: E1 multiframe) 4. What does TS0 carry in E1? A. Frame alignment word (0011011) in alternate frames plus alarm bits B. Voice channel 1 C. Signalling D. Stuffing bits Answer: A. TS0 provides frame synchronisation; TS16 does signalling. (Key point: E1 TS0) 5. Why does the higher-order rate exceed the sum of inputs (4 x 1.544 = 6.176 vs 6.312)? A. Framing and bit-stuffing bits align streams with slightly different clocks B. Higher sampling rate C. More bits per sample D. Companding Answer: A. Justification bits handle clock differences and framing adds overhead. (Key point: Bit stuffing) ## Related in Communication Systems - [Companding; T1 hierarchy of TDM-PCM telephony](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Acompanding-t1) — 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 - [E1 hierarchy; PCM of 4.2 MHz TV signal with 512 levels](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ae1-pcm-tv-4-2mhz-512) — Communication Systems, chapter 4 - [E1 digital hierarchy; SQNR in uniformly quantized PCM](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ae1-hierarchy-sqnr-uniform-pcm) — Communication Systems, chapter 5, asked 2× - [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 - [TDM vs FDM for voice; E1 and T1 hierarchies](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Atdm-fdm-voice-e1-t1) — Communication Systems, chapter 5 ## Related in other subjects - [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× - [T1 and E1 frame structures and bit rates](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3At1-e1-frame-structures) — Telecommunications, chapter 3 - [TDM and T1/E1 carrier standards](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atdm-t1-e1-carriers) — Telecommunications, chapter 3 - [TDM principle and T1 carrier](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atdm-principle-t1-carrier) — Telecommunications, chapter 3