---
title: "Three-stage combination switch"
subject: "Telecommunications"
chapter: 4
key: "semester_8/telecommunications:combination-switch-3-stage"
source: https://www.bctengineer.com/q/semester_8/telecommunications/combination-switch-3-stage
site: BCT Engineering
---

# Three-stage combination switch

Telecommunications · Chapter 4: Digital Switching

- Asked in: 2071 Shrawan, 2+6 marks
- Video: [THREE STAGE COMBINATION SWITCHING - STS & TST SWITCH by RITU SHARMA GPC SIKAR](https://www.youtube.com/watch?v=h9Hh3igh1XY) — GPCSIKAR E-LECTURES
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/telecommunications/combination-switch-3-stage
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-4

## Question

What do you mean by combination switch? Explain the working principle of 3-stage combination switch with its block diagram.

## Short answer

A combination switch merges T and S stages to change both highway and slot. In TST, input TSIs, an N×N space stage, and output TSIs. To connect, a free internal slot x is found; input TSI moves sample to x, space closes crosspoint at x, output TSI moves sample to desired outgoing slot. Blocking PB = [1-(1-p')^2]^l, non-blocking if l ≥ 2c-1.

## Answer

#### Combination switch
A **combination switch** is a digital switch built by combining **time (T) stages** and **space (S) stages**. A pure time switch is limited by memory speed and a pure space switch cannot change time slots, so the two are combined to get a large switch that can change both the highway and the time slot of a sample. Examples: TS, ST (two-stage), TST, STS (three-stage), TSST, TSSST.

#### Three-stage combination switch (TST)
The most common three-stage combination switch is **Time–Space–Time**.

```text
         Input T       Space S        Output T
 HW1 --->[TSI A1]--+-------------+--[TSI B1]---> HW1
 HW2 --->[TSI A2]--|  N x N TMS  |--[TSI B2]---> HW2
  ...      ...     |  (control   |    ...
 HWN --->[TSI AN]--|  memory)    |--[TSI BN]---> HWN
                   +-------------+
  c slots each      l internal slots    c slots
```

**Block functions**
- **Input time stage:** one TSI per incoming highway; moves a sample from its external slot to a chosen internal slot.
- **Space stage:** a time-multiplexed $N \times N$ space switch; in each internal slot it connects any input highway to any output highway.
- **Output time stage:** one TSI per outgoing highway; moves the sample from the internal slot to the required outgoing slot.
- **Control unit:** finds a free internal slot and writes all three control memories.

#### Working principle
Connect slot 4 of highway 1 (caller A) to slot 22 of highway N (called B):
1. The processor searches for an internal slot $x$ that is free at the output of TSI-A1 and at the input of TSI-BN, say $x = 10$.
2. **Input T:** TSI-A1 control memory set so the sample from slot 4 is read out in slot 10.
3. **Space:** control memory of column N set to "1" for slot 10; the crosspoint (1, N) closes in slot 10.
4. **Output T:** TSI-BN control memory set so the sample arriving in slot 10 is sent out in slot 22.
5. The B→A direction uses another internal slot, often $x + l/2$, so one search serves both directions.
6. On release, the control memory entries are cleared.

#### Blocking
There are $l$ alternative paths (internal slots). With link occupancy $p$ and $p' = pc/l$:
$$
P_B = \left[1 - (1 - p')^2\right]^{l}
$$
Non-blocking when $l \ge 2c - 1$.

**Advantages:** low blocking, cheap time expansion, small space stage, good for large exchanges. The other three-stage form, **STS**, uses space stages outside and TSIs in the middle, but needs more hardware for the same blocking.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why combine T and S stages?
   A. Pure time is limited by memory speed and pure space cannot change slots
   B. To avoid using memory
   C. To remove control memory
   D. To use analog signals
   Answer: A. Combination gives large switches that change both highway and slot. (Key point: Why combine)

2. In a TST switch, what is the role of the space stage?
   A. Change the slot from external to internal
   B. Connect input highway to output highway in the chosen internal slot
   C. Move sample to outgoing slot
   D. Find free slots
   Answer: B. The N x N space stage connects the highways during internal slot x. (Key point: TST roles)

3. To connect slot 4 of HW1 to slot 22 of HW N, what must the processor first find?
   A. A free internal slot x at TSI-A1 output and TSI-BN input
   B. A free centre TSI
   C. A free external slot
   D. Spare memory
   Answer: A. An internal slot free on both sides is required before writing the three control memories. (Key point: Setting up a call)

4. When is TST non-blocking?
   A. l >= c
   B. l >= 2c - 1
   C. l >= c/2
   D. l >= 2c + 1
   Answer: B. With l internal slots and c external slots, l >= 2c - 1 gives non-blocking. (Key point: Non-blocking condition)

## Related in Telecommunications

- [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×
- [Space switch and two-stage S-T drawbacks](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aspace-switch-two-stage-st) — Telecommunications, chapter 4
- [Digital exchange and three-stage crosspoints](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Adigital-exchange-crosspoints) — Telecommunications, chapter 4
- [Time switch and two-stage T-S network](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atime-switch-two-stage-ts) — Telecommunications, chapter 4
- [Working principle of a digital telephone exchange](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Adigital-telephone-exchange-principle) — Telecommunications, chapter 4, asked 4×

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