--- title: "FDM hierarchy and T carrier system" subject: "Telecommunications" chapter: 3 key: "semester_8/telecommunications:fdm-hierarchy-t-carrier" source: https://www.bctengineer.com/q/semester_8/telecommunications/fdm-hierarchy-t-carrier site: BCT Engineering --- # FDM hierarchy and T carrier system Telecommunications · Chapter 3: Signal Multiplexing - Asked in: 2070 Chaitra, 3+5 marks - Video: [Unit 5 T1 Carrier system | A PCM-TDM System | T1 Digital system](https://www.youtube.com/watch?v=SY8ng74yEj4) — Techno Tutorials ( e-Learning) - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/telecommunications/fdm-hierarchy-t-carrier - Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-3 ## Question Explain FDM hierarchy. Describe T carrier system showing the frame structure of T1 level and different multiplexing levels with data rates. ## Short answer In FDM, voice channels are stacked by SSB: basic group 12 ch 60–108 kHz, supergroup 60 ch 312–552 kHz, mastergroup 300 ch, supermastergroup 900 ch. The T carrier system uses a T1 frame of 193 bits (1 framing + 24×8) every 125 µs, giving 1.544 Mbps. Higher levels: T2 6.312 Mbps (4 T1s), T3 44.736 Mbps (7 T2s), T4 274.176 Mbps (6 T3s). ## Answer #### 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: | Level | Made from | Voice channels | Frequency band | Bandwidth | |---|---|---|---|---| | Voice channel | – | 1 | 0–4 kHz | 4 kHz | | Basic group | 12 channels | 12 | 60–108 kHz | 48 kHz | | Basic supergroup | 5 groups | 60 | 312–552 kHz | 240 kHz | | Basic mastergroup | 5 supergroups | 300 | 812–2044 kHz | 1232 kHz | | Supermastergroup | 3 mastergroups | 900 | 8516–12388 kHz | 3872 kHz | (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.) ```text 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:** ```text 1 bit 8 bits 8 bits 8 bits +-----+-------+-------+-----+--------+ | F | Ch1 | Ch2 | ... | Ch24 | +-----+-------+-------+-----+--------+ <--------- 193 bits in 125 us --------> F = framing bit ``` $$ \begin{aligned} \text{Bits per frame} &= 24 \times 8 + 1 = 193\ \text{bits} \\ \text{Frame rate} &= 8000\ \text{frames/s}\ (T = 125\ \mu\text{s}) \\ R_{T1} &= 193 \times 8000 = 1.544\ \text{Mbps} \end{aligned} $$ - 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:** ```text 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) ``` | 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 | $$ \begin{aligned} T2 &: 4 \times 1.544 = 6.176;\ \ 6.312 - 6.176 = 0.136\ \text{Mbps overhead} \\ T3 &: 7 \times 6.312 = 44.184;\ \ 44.736 - 44.184 = 0.552\ \text{Mbps overhead} \\ T4 &: 6 \times 44.736 = 268.416;\ \ 274.176 - 268.416 = 5.76\ \text{Mbps overhead} \end{aligned} $$ The extra overhead at T2, T3 and T4 carries framing, pulse-stuffing control and alarm bits. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is the basic CCITT FDM group formed? A. 12 voice channels in 60-108 kHz by SSB B. 5 supergroups in 812-2044 kHz C. 24 channels by PCM D. 60 channels in 312-552 kHz Answer: A. 12 channels of 4 kHz are SSB-modulated into the 60-108 kHz (48 kHz) basic group; 5 groups make a 60-channel supergroup. (Key point: FDM hierarchy) 2. How many voice channels are in a CCITT basic mastergroup? A. 60 B. 300 C. 600 D. 900 Answer: B. A mastergroup is 5 supergroups x 60 = 300 channels. (Key point: Supergroup size) 3. What does a T1 frame contain? A. 32 slots of 8 bits B. 24 x 8 bits plus 1 framing bit = 193 bits in 125 µs C. 12 x 8 bits plus 2 framing bits D. 24 x 7 bits plus 1 bit Answer: B. 24 channels of 8 bits plus one F bit gives 193 bits per 125 µs, i.e. 1.544 Mbps. (Key point: T1 frame) 4. Why is T2 at 6.312 Mbps rather than 4 x 1.544 = 6.176 Mbps? A. Extra 136 kbps carries framing, stuffing control and alarm bits B. T2 carries 5 T1 streams C. T2 uses a higher sampling rate D. T2 uses 16-bit coding Answer: A. The difference of 0.136 Mbps is overhead for framing, pulse-stuffing control and alarms. (Key point: T2 overhead) ## Close variants set in other exams - [WDM and T carrier system](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Awdm-t-carrier-t1) — Telecommunications, chapter 3, asked 2× ## Related in Telecommunications - [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 principle and T1 carrier](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atdm-principle-t1-carrier) — Telecommunications, chapter 3 - [Digital carrier system and multiplexing techniques](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Adigital-carrier-multiplexing) — 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 - [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× - [Analog vs digital multiplexing; 24-channel system](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aanalog-digital-mux-24-channel) — Telecommunications, chapter 3 ## Related in other subjects - [T1 digital carrier system; adaptive delta modulation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3At1-hierarchy-adm) — Communication Systems, chapter 5 - [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 - [FDM hierarchy in telephone system](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Afdm-hierarchy-telephone) — Data Communication, chapter 6 - [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