---
title: "Talker and listener echo in four-wire circuit"
subject: "Telecommunications"
chapter: 2
key: "semester_8/telecommunications:four-wire-echo-numerical"
source: https://www.bctengineer.com/q/semester_8/telecommunications/four-wire-echo-numerical
site: BCT Engineering
---

# Talker and listener echo in four-wire circuit

Telecommunications · Chapter 2: Transmission Media

- Asked in: 2080 Baisakh, 3 marks
- Video: [Telecommunication Systems (11 - Transmission Impairments: Echo & Singing)](https://www.youtube.com/watch?v=9eN7sOCK8PY) — Dr. Samy S. Soliman
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/telecommunications/four-wire-echo-numerical
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-2

## Question

A four-wire circuit has a round-trip delay of 20 milliseconds. The propagation time for the two-wire circuit connected to each end is 1 millisecond, and its attenuation is 6 dB. The balance return loss is 3 dB and the stability margin is 3 dB. Calculate the attenuation of the talker echo, delay of talker echo, and attenuation of listener echo.

## Short answer

Four-wire loss L = S – B = 0 dB. Talker echo attenuation = 6 + L + B + L + 6 = 15 dB; delay = round-trip 20 ms + 2×1 ms = 22 ms. Listener echo attenuation relative to direct signal = 2S = 6 dB.

## Answer

**Assumptions (standard four-wire model):** $L$ = overall loss of the four-wire circuit between its two-wire terminals (hybrid to hybrid), $B$ = balance return loss of each hybrid, stability margin $S = L + B$ (half the loss round the four-wire loop). Each subscriber is joined to a hybrid by a two-wire circuit of 6 dB loss and 1 ms delay.

**Four-wire loss**
$$
L = S - B = 3 - 3 = 0\ \text{dB}
$$

```text
 Talker─[2W: 6dB,1ms]─H1══ 4-wire (L) ══H2─[2W]─Listener
           ^                               │ reflects (B)
           └──────── talker echo <─────────┘
```

**Talker echo** (talker's speech reflected at the far hybrid and heard by the talker):
$$
\begin{aligned}
A_{TE} &= 6 + L + B + L + 6 \\
&= 6 + 0 + 3 + 0 + 6 = 15\ \text{dB}
\end{aligned}
$$
$$
\begin{aligned}
\text{Delay}_{TE} &= 20\ \text{ms (4-wire round trip)} + 2 \times 1\ \text{ms (own 2-wire both ways)} \\
&= 22\ \text{ms}
\end{aligned}
$$

**Listener echo** (signal reflected at the far hybrid, then again at the near hybrid, reaching the listener late). Compared with the direct signal it travels once more round the four-wire loop:
$$
A_{LE} = 2L + 2B = 2S = 2 \times 3 = 6\ \text{dB below the direct signal}
$$
(absolute: $6 + 3L + 2B + 6 = 18$ dB from talker to listener, against 12 dB for the direct signal), delayed by 20 ms relative to it.

**Answer:** talker echo attenuation = **15 dB**, talker echo delay = **22 ms**, listener echo attenuation = **6 dB** (relative to the received speech, i.e. 18 dB overall).

## Check yourself

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

1. With stability margin S = L + B, S = 3 dB and B = 3 dB, what is the four-wire loss L?
   A. 6 dB
   B. 3 dB
   C. -3 dB
   D. 0 dB
   Answer: D. L = S - B = 3 - 3 = 0 dB. (Key point: Four-wire loss)

2. What is the talker echo attenuation for 6 dB two-wire loss at each end, L = 0 and B = 3 dB?
   A. 12 dB
   B. 15 dB
   C. 9 dB
   D. 18 dB
   Answer: B. A = 6 + L + B + L + 6 = 6 + 0 + 3 + 0 + 6 = 15 dB. (Key point: Talker echo attenuation)

3. What is the talker echo delay with a 20 ms four-wire round trip and 1 ms two-wire propagation at each end?
   A. 21 ms
   B. 20 ms
   C. 22 ms
   D. 24 ms
   Answer: C. 20 ms + 2 x 1 ms for the talker's own two-wire circuit both ways = 22 ms. (Key point: Talker echo delay)

4. How is the listener echo attenuation (relative to the direct signal) obtained?
   A. 2L + 2B = 2S = 6 dB
   B. L + B = 3 dB
   C. 6 + L + B = 9 dB
   D. 2S + 12 = 18 dB
   Answer: A. The echo makes an extra trip round the four-wire loop, so it is 2S = 6 dB below the direct signal. (Key point: Listener echo)

## Related in Telecommunications

- [Noise and two-wire to four-wire converter](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Anoise-two-four-wire-converter) — Telecommunications, chapter 2
- [Two-wire vs four-wire communication](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atwo-vs-four-wire) — Telecommunications, chapter 2
- [Wired vs wireless media; four-wire and hybrid](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Awired-wireless-four-wire-hybrid) — Telecommunications, chapter 2, asked 2×
- [Media types, four-wire system and hybrid](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Amedia-types-four-wire-hybrid) — Telecommunications, chapter 2
- [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
- [Guided vs unguided media; 2-wire to 4-wire](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aguided-unguided-two-four-wire) — Telecommunications, chapter 2, asked 2×

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