--- title: "TST vs STS and three-stage design" subject: "Telecommunications" chapter: 4 key: "semester_8/telecommunications:tst-sts-design-crosspoints" source: https://www.bctengineer.com/q/semester_8/telecommunications/tst-sts-design-crosspoints site: BCT Engineering --- # TST vs STS and three-stage design Telecommunications · Chapter 4: Digital Switching - Asked in: 2075 Chaitra, 3+6 marks - Video: [Switching Engineering - Cross-points and Number of Switches - Calculations](https://www.youtube.com/watch?v=Bbm3lKI7O5Y) — KINEMARC - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/telecommunications/tst-sts-design-crosspoints - Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-4 ## Question Differentiate between TST and STS switch. Design a three stage switching system having 4 stage array of 5 input line and 6 second stage array. Also calculate the total number of cross points of the switching system. ## Short answer TST uses time-space-time with TSIs outside and a space switch center; STS uses space-time-space with TSIs in the center. For 4 first-stage arrays of 5x6, 6 middle arrays of 4x4, and 4 third-stage arrays of 6x5, total crosspoints = 120 + 96 + 120 = 336. ## Answer #### Difference between TST and STS switches | Point | TST | STS | |---|---|---| | Structure | Time – Space – Time | Space – Time – Space | | Outer stages | TSIs (memory) | Time-multiplexed space switches | | Centre stage | Time-multiplexed space switch | Array of TSIs | | Number of alternative paths | $l$ (internal time slots) | $k$ (centre TSIs) | | Expansion | Time expansion (cheap: faster memory) | Space expansion (costly: more crosspoints and TSIs) | | Blocking | Lower, $[1-(1-p')^2]^l$ | Higher, $[1-(1-p')^2]^k$ | | Control | Path search over time slots | Path search over centre TSIs | | Best for | Large exchanges, heavy traffic | Small exchanges, light traffic | #### Three-stage design **Reading of the data:** the first stage has 4 arrays with 5 input lines each, so $N = 4 \times 5 = 20$ lines, $n = 5$; the second stage has $k = 6$ arrays. - Stage 1: 4 arrays of $5 \times 6$ - Stage 2: 6 arrays of $4 \times 4$ (each middle array has one link from each of the 4 first-stage arrays) - Stage 3: 4 arrays of $6 \times 5$ ```text 5 in [5x6] \ / [6x5] 5 out 5 in [5x6] --> 6 x [4x4] --> [6x5] 5 out 5 in [5x6] --> middle --> [6x5] 5 out 5 in [5x6] / \ [6x5] 5 out (20 inputs) (20 outputs) ``` #### Crosspoints $$ \begin{aligned} N_1 &= 4 \times (5 \times 6) = 120 \\ N_2 &= 6 \times (4 \times 4) = 96 \\ N_3 &= 4 \times (6 \times 5) = 120 \\ N_x &= 120 + 96 + 120 = 336 \end{aligned} $$ Check: $N_x = 2Nk + k(N/n)^2 = 2(20)(6) + 6(4)^2 = 240 + 96 = 336$. A single-stage $20 \times 20$ switch needs 400 crosspoints, so the saving is 64 crosspoints (16%). Since $k = 6 < 2n - 1 = 9$, this network is **blocking**; 9 middle arrays would be needed for strict non-blocking. **Answer:** total crosspoints = **336**. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which statement correctly contrasts TST and STS? A. TST has TSIs at the outer stages and a space switch in the centre; STS the reverse B. TST has a space switch at the outer stages C. Both have identical stage order D. STS uses time expansion Answer: A. TST is Time-Space-Time and STS is Space-Time-Space. (Key point: TST vs STS structure) 2. For 4 first-stage arrays of 5 inputs and k = 6 middle arrays, the middle stage consists of A. 6 arrays of 4 x 4 B. 4 arrays of 6 x 6 C. 6 arrays of 5 x 5 D. 5 arrays of 4 x 4 Answer: A. Each middle array has one link from each of the 4 first-stage arrays, so it is 4 x 4, and there are 6 of them. (Key point: Stage sizes) 3. The total crosspoints for the design are A. 336 B. 400 C. 240 D. 96 Answer: A. 120 + 96 + 120 = 336, matching 2(20)(6) + 6(4)^2. (Key point: Total crosspoints) 4. Why is this network blocking? A. k = 6 is less than 2n - 1 = 9 B. N is too small C. It has three stages D. The middle arrays are 4 x 4 Answer: A. Strict non-blocking needs 2n - 1 = 9 middle arrays. (Key point: Blocking check) ## Related in Telecommunications - [Multistage switching; TST vs STS](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Amultistage-tst-sts-compare) — Telecommunications, chapter 4 - [Design 200×200 three-stage switch](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Athree-stage-200x200-clos) — Telecommunications, chapter 4 - [Crosspoints in three-stage switch (4 inputs, 5 arrays)](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Acrosspoints-4-input-5-second) — Telecommunications, chapter 4, asked 2× - [Switching functions and three-stage crosspoints](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aswitching-functions-crosspoints-4x4) — Telecommunications, chapter 4, asked 2× - [PCM switching and three-stage crosspoints](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Apcm-switching-crosspoints-4x5) — Telecommunications, chapter 4 - [Space and time switches; STS vs TST](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aspace-time-switch-sts-tst) — Telecommunications, chapter 4 ## Related in other subjects - [Interior cross wall design: three-storey, 150 mm slab](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Ainterior-cross-wall-three-storey-150mm) — Concrete Technology and Masonry Structure, chapter 8, asked 2× - [T/F: switching surge ratio vs system voltage](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atf-ssr-system-voltage) — Transmission and Distribution System Design, chapter 3, asked 4× - [First and second stage BOD](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Afirst-second-stage-bod-400) — Sanitary Engineering, chapter 5 - [Total station, features, data recording points](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atotal-station-features-recording-points) — Surveying II, chapter 9