---
title: "Space switch and why TST is used"
subject: "Telecommunications"
chapter: 4
key: "semester_8/telecommunications:space-switch-why-tst"
source: https://www.bctengineer.com/q/semester_8/telecommunications/space-switch-why-tst
site: BCT Engineering
---

# Space switch and why TST is used

Telecommunications · Chapter 4: Digital Switching

- Asked in: 2069 Bhadra (old course), 6+6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/telecommunications/space-switch-why-tst
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-4

## Question

With a block and logical diagram, explain the working principle of space switch (S) used in digital switching system. Justify, why TST switch and why not TS or ST switch are used in digital switching system?

## Short answer

A digital space switch uses time-multiplexed gates and control memories to connect input highways to output highways per time slot, changing highways but not time slots. TS/ST have single path and high blocking; TST provides multiple internal slot paths, reducing blocking to (1-(1-p')^2)^l. It is preferred over STS because time expansion (faster memory) is cheaper than space expansion.

## Answer

#### Space (S) switch in a digital switching system
A digital space switch is a **time-multiplexed space switch (TMS)**. It connects $N$ incoming PCM highways to $M$ outgoing highways. Its crosspoints are electronic gates, and the connection pattern changes every time slot under the control of control memories. It changes the highway of a sample but keeps its time slot.

#### Block diagram
```text
 Incoming          Crosspoint           Outgoing
 highways          matrix               highways
 HW1 ------->+--------------------+---> OHW1
 HW2 ------->|   N x M gates      |---> OHW2
  ...        |   (or M x N:1 MUX) |      ...
 HWN ------->+--------------------+---> OHWM
                ^    ^        ^
             [CM1] [CM2] ... [CMM]   c words each
                ^
         time-slot counter <--- clock (frame sync)
                ^
         call-control processor (writes CMs)
```

#### Logical diagram (one output column)
Each output is in effect an $N$-to-1 multiplexer whose select lines come from its control memory.
```text
  I1 --|AND|--+
  I2 --|AND|--+
   ...        +--[OR]--> output Oj
  IN --|AND|--+
        ^
   decoder (log2 N -> N lines)
        ^
   CMj word for current slot
```
Only the AND gate selected by the decoder is enabled in a slot, so only that input reaches the output.

#### Working principle
1. Each control memory has $c$ words, one per slot; word $t$ of CM$_j$ holds the address of the input highway to connect to output $j$ in slot $t$.
2. The time-slot counter, synchronised to the frame, steps $t = 0 \dots c-1$.
3. In slot $t$, every CM is read; each decoder enables one gate, so input $I_a$ is connected to output $O_j$ for the duration of slot $t$ (about 3.9 µs for a 32-slot frame).
4. In the next slot different gates may be enabled, so each crosspoint is shared by up to $c$ calls.
5. At call set-up the processor writes the input number into the right CM word; at release it clears it.

**Example:** CM$_2$ word 5 = 3 → in slot 5, I3 is connected to O2. Word 6 = 1 → in slot 6, I1 is connected to O2.

Control memory size: $M \times c \times \lceil\log_2 N\rceil$ bits (or with one-hot words, $N$ bits each).

#### Why TST and not TS or ST
**Problem of two-stage TS and ST:**
- **TS:** the TSI moves the sample to the output slot $j$, then the S stage must connect the highways in slot $j$. If slot $j$ on the output highway is already taken by a call from another input highway, the call is blocked.
- **ST:** the S stage must connect the highways in the input slot $i$; if slot $i$ is already busy into that output highway, the call is blocked.
- Only **one path** exists, so blocking is about equal to link occupancy $p$ (e.g. 0.3 to 0.7), far above an acceptable grade of service (e.g. 0.002).

**TST gives many paths:** the input TSI can move the sample to any free internal slot $x$, the S stage switches in slot $x$, and the output TSI moves it to slot $j$. There are $l$ paths:
$$
P_B = \left[1 - (1 - p')^2\right]^{l}, \quad p' = \frac{pc}{l}
$$
For example, $c = l = 32$, $p = 0.5$: $P_B = 0.75^{32} \approx 1.0 \times 10^{-4}$.

**Why TST rather than STS:**
1. Paths in TST come from time slots; increasing $l$ (time expansion) needs only faster memory and logic, which is cheap.
2. In STS, more paths need more centre TSIs and more crosspoints (space expansion), which is costly.
3. Non-blocking needs only $l \ge 2c - 1$, easily met (e.g. 64 internal slots for 32-slot links).
4. The space stage is small ($N \times N$ highways), and the time stages are just memories, so TST is cheaper, more modular and suits large exchanges.
5. Path search is simple: find one internal slot free on two links; the reverse path can use slot $x + l/2$.

Hence practical digital exchanges use TST (or its extension TSST) instead of two-stage TS or ST switches.

## Check yourself

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

1. In a digital time-multiplexed space switch, what does a sample undergo when it passes through?
   A. Its time slot changes but the highway stays the same
   B. Its highway changes but its time slot stays the same
   C. Both its highway and time slot change
   D. Neither changes; only the sample amplitude is regenerated
   Answer: B. The crosspoint matrix moves the sample from one highway to another within the same time slot. Changing slots is the job of a time switch. (Key point: What a space switch changes)

2. How does the control memory (CM) of output j decide which input is connected in slot t?
   A. Word t of CM j holds the address of the input highway to connect to output j in slot t
   B. CM j stores the actual speech samples for output j
   C. CM j holds a fixed input number used in all slots
   D. CM j counts the slots and resets the frame
   Answer: A. Each CM has one word per slot; the word is decoded to enable one AND gate so only that input reaches the output. This lets each crosspoint be shared by up to c calls. (Key point: Role of control memory)

3. Why does a two-stage TS or ST switch have high blocking?
   A. The TSI memory is too slow
   B. There is only one path, so the space stage must use a fixed slot that may already be busy
   C. The control memory is too small to store addresses
   D. Crosspoints cannot be shared between calls
   Answer: B. With one path per call, the S stage must use slot j (TS) or slot i (ST). If that slot is busy toward the output highway, the call is blocked, giving blocking about equal to occupancy p. (Key point: Why TS/ST block)

4. Why is TST preferred over STS in practice?
   A. TST has fewer paths per call
   B. More paths in TST come from time expansion, which needs only faster memory, whereas STS needs more TSIs and crosspoints
   C. STS cannot change the time slot
   D. TST needs no control memory
   Answer: B. Time expansion in TST is cheap because it just uses faster memory and logic. STS gets extra paths only by adding centre TSIs and crosspoints, which is costly. (Key point: Why TST is preferred over STS)

## Related in Telecommunications

- [Time division switching and space switch](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atime-division-space-switch) — Telecommunications, chapter 4
- [ST and TS drawbacks solved by STS](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Ast-ts-drawbacks-sts) — 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×
- [Multistage switching; TST vs STS](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Amultistage-tst-sts-compare) — 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
- [Time and space switch drawbacks](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atime-space-switch-drawbacks) — Telecommunications, chapter 4

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