--- title: "Pulse stuffing and complete TDM PCM system" subject: "Telecommunications" chapter: 3 key: "semester_8/telecommunications:multiplexing-pulse-stuffing-tdm-pcm" source: https://www.bctengineer.com/q/semester_8/telecommunications/multiplexing-pulse-stuffing-tdm-pcm site: BCT Engineering --- # Pulse stuffing and complete TDM PCM system Telecommunications · Chapter 3: Signal Multiplexing - Asked in: 2072 Chaitra, 2+2+4 marks - Video: [Multilevel multiplexing, pulse stuffing, synchronization bit in Time division multiplexing](https://www.youtube.com/watch?v=MzV5hk8AgmU) — Mathur Lectures - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/telecommunications/multiplexing-pulse-stuffing-tdm-pcm - Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-3 ## Question What is multiplexing? Why pulse stuffing is needed? Explain TDM of analog and digital sources and then show complete TDM PCM system with data rates. ## Short answer Multiplexing combines several signals into one composite signal. Pulse stuffing inserts dummy bits when independent digital streams have slightly different rates, preventing slips. For analog sources, sampling and interleaving yields PAM, then PCM; for digital sources, bits or words are interleaved. T1 PCM: 24 channels sampled at 8 kHz, 8-bit coding, plus one framing bit per 125 µs frame gives 1.544 Mbps. ## Answer **Multiplexing** is combining several signals into one composite signal for transmission over a single shared channel, and separating them again at the receiver. #### Why pulse stuffing is needed When digital tributaries with independent clocks (e.g. four E1 streams entering an E2 multiplexer) are combined, their bit rates differ slightly. The multiplexer reads them at a fixed, slightly higher rate; without correction its input buffers would run empty, causing slips (lost or repeated bits). **Pulse stuffing** inserts dummy bits whenever a tributary's buffer runs low; **stuffing control bits** (repeated and decided by majority vote) tell the demultiplexer which bits to remove, so the original stream and clock are recovered exactly. This is why $E2 = 8.448 > 4 \times 2.048$ Mbps. #### TDM of analog sources Analog signals are band-limited, then sampled in turn by a rotating switch (commutator) to give an interleaved PAM signal; each sample is usually quantised and coded (PCM). - Example: 4 voice channels, each limited to 3.4 kHz and sampled at 8 kHz, give $4 \times 8000 = 32\,000$ samples/s on the line. With 8-bit coding: $32\,000 \times 8 = 256$ kbps. - If sources have different bandwidths, a wider-band source is sampled several times per frame (super-commutation) and a narrow-band source only once every few frames (sub-commutation), so each sampling rate is a multiple or sub-multiple of the frame rate. #### TDM of digital sources Digital sources are already in bits, so they are interleaved directly, bit by bit or word by word. - If all sources have the same rate, each gets one slot per frame: 4 sources of 64 kbps → 256 kbps. - If rates differ but are multiples, faster sources get more slots per frame. Example: sources of 64, 64 and 128 kbps → frame with slots A, B, C, C → 256 kbps. - If rates are not exact multiples or not synchronous, **pulse stuffing** is used to bring each to its slot rate. #### Complete TDM–PCM system with data rates (T1, 24 channels) ```text ch1 -[LPF]-\ ch2 -[LPF]--[sampler 8 kHz]--[u-law 8-bit coder] ch24-[LPF]-/ (commutator) | [add F bit, AMI/B8ZS] | line 1.544 Mbps, regenerative repeaters | ch1..ch24 <-[LPF]<-[distributor]<-[decoder]<-[frame sync] ``` Data rates at each stage: $$ \begin{aligned} \text{Samples per channel} &= 8000\ \text{s}^{-1} \\ \text{Channel rate} &= 8000 \times 8 = 64\ \text{kbps} \\ \text{Frame} &= 24 \times 8 + 1 = 193\ \text{bits per } 125\ \mu\text{s} \\ \text{Line rate} &= 193 \times 8000 = 1.544\ \text{Mbps} \end{aligned} $$ The receiver locks onto the framing bits, splits the 8-bit words to the 24 channels, decodes and expands them, and low-pass filters to recover speech. Four such T1 streams, with pulse stuffing, form a T2 at 6.312 Mbps. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is pulse stuffing needed when multiplexing tributaries such as four E1 streams? A. To add error correction B. To remove DC from the line C. Tributary clocks differ slightly, so dummy bits are inserted to avoid buffer underflow/overflow (slips) D. To reduce the bit rate of the output Answer: C. The multiplexer reads at a fixed slightly higher rate, so dummy bits are inserted when a buffer runs low; this avoids slips. (Key point: Need for pulse stuffing) 2. What are stuffing control bits used for? A. To tell the demultiplexer which bits to remove B. To carry voice samples C. To set the sampling rate D. To encrypt the data Answer: A. Control bits, repeated and decided by majority vote, tell the demultiplexer which bits are dummy so the original stream is recovered. (Key point: Stuffing control bits) 3. Four voice channels of 3.4 kHz sampled at 8 kHz and coded with 8 bits give what line rate? A. 64 kbps B. 128 kbps C. 256 kbps D. 32 kbps Answer: C. 4 x 8000 = 32000 samples/s x 8 bits = 256 kbps. (Key point: TDM of analog sources) 4. Sources of 64, 64 and 128 kbps are time-multiplexed. How is the frame arranged? A. Slots A, B, C with equal length, giving 192 kbps B. Slots A, B, C, C, so the 128 kbps source gets two slots, giving 256 kbps C. Slots A, A, B, B, C giving 320 kbps D. One slot each plus pulse stuffing to 128 kbps each Answer: B. Faster sources get more slots per frame in proportion to their rate: 64+64+128 = 256 kbps. (Key point: Unequal digital rates) ## Related in Telecommunications - [Pulse stuffing in TDM synchronization](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Apulse-stuffing-tdm-sync) — Telecommunications, chapter 3 - [TDM types and pulse stuffing](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atdm-types-pulse-stuffing) — Telecommunications, chapter 3 - [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 - [Pulse stuffing; LED vs LASER sources](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Apulse-stuffing-led-laser) — Telecommunications, chapter 2 - [Multiplexing techniques and TDM standards](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Amultiplexing-techniques-tdm-standards) — 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 ## Related in other subjects - [PCM and analog-to-digital conversion](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Apcm-working) — Data Communication, chapter 5, asked 4× - [Data representation; analog vs digital system](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Adata-representation-analog-digital) — Data Communication, chapter 1 - [Digital transmission system; analog vs digital](https://www.bctengineer.com/question.md?key=semester_5%2Finstrumentation_ii%3Aanalog-digital-transmission-compare) — Instrumentation II, chapter 5 - [Multiplexing; synchronous vs asynchronous TDM](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Amux-compare-sync-async-tdm) — Data Communication, chapter 6, asked 6×