---
title: "Short note: Coherent detector"
subject: "Communication Systems"
chapter: 2
key: "semester_6/communication_systems:short-note-coherent-detector"
source: https://www.bctengineer.com/q/semester_6/communication_systems/short-note-coherent-detector
site: BCT Engineering
---

# Short note: Coherent detector

Communication Systems · Chapter 2: Amplitude Modulation

- Asked in: 2072 Magh (CS I), 4 marks
- Video: [Coherent Detection of DSB-SC or DSB-SC Detection (Basics, Working, Block Diagram & Impotence)](https://www.youtube.com/watch?v=uiTHa7g5ssg) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/communication_systems/short-note-coherent-detector
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-2

## Question

Write a short note on coherent detector.

## Short answer

A coherent detector multiplies the incoming signal by a locally generated carrier of identical frequency and phase, then low‑pass filters. For DSB‑SC, output = (Ac/2)m(t)cosφ; a phase error φ reduces amplitude and quadrature null occurs at 90°. Carrier recovery uses a Costas loop or squaring loop; works for all linear modulations but requires complex synchronisation.

## Answer

A **coherent (synchronous) detector** recovers the message by multiplying the received modulated signal with a locally generated carrier of the **same frequency and phase** as the transmitted carrier, followed by a low-pass filter. It is needed for DSB-SC, SSB and VSB, and can also detect DSB-FC.

```text
 s(t) ---->( X )----> LPF ----> vo(t)
             ^       (0 to W)
             |
     cos(wc t + phi)  <-- carrier recovery
                          (Costas loop / PLL)
```

**For DSB-SC**, $s(t) = A_cm(t)\cos\omega_ct$:

$$
\begin{aligned}
v(t) &= A_cm(t)\cos\omega_ct\cos(\omega_ct + \phi) \\
&= \frac{A_c}{2}m(t)\cos\phi + \frac{A_c}{2}m(t)\cos(2\omega_ct + \phi)
\end{aligned}
$$

After LPF: $v_o(t) = \tfrac{A_c}{2}m(t)\cos\phi$.

**Effect of errors**

- Phase error $\phi$: output reduced by $\cos\phi$; at $\phi = 90^\circ$ output is zero (quadrature null).
- Frequency error $\Delta\omega$: output $\propto m(t)\cos\Delta\omega t$ (beating); for SSB it shifts the audio pitch.

**Carrier recovery:** pilot carrier, squaring loop, or Costas loop.

**Merits:** works for all AM types, linear, better noise performance than envelope detection at low SNR. **Demerits:** complex and costly because of the synchronisation circuit.

## Check yourself

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

1. A coherent detector recovers the message by:
   A. Multiplying by a local carrier of the same frequency and phase, then low-pass filtering
   B. Rectifying and smoothing the input
   C. Differentiating the input
   D. Squaring and band-pass filtering
   Answer: A. The product contains the message plus a 2fc term, and the LPF keeps the message. (Key point: Principle)

2. For DSB-SC with phase error phi, the detector output is:
   A. Ac m(t)
   B. (Ac/2) m(t) sin(phi)
   C. (Ac/2) m(t) cos(phi)
   D. (Ac/2) m(t) cos(2 phi)
   Answer: C. After the LPF the product gives (Ac/2) m(t) cos(phi). (Key point: Output with phase error)

3. At phi = 90 degrees the output of the coherent detector is:
   A. Maximum
   B. Half of maximum
   C. Inverted message
   D. Zero
   Answer: D. cos(90 degrees) = 0, giving the quadrature null. (Key point: Quadrature null)

4. Which is a method of carrier recovery for coherent detection?
   A. Envelope detector
   B. Costas loop, squaring loop or pilot carrier
   C. AGC circuit
   D. Discriminator
   Answer: B. The local carrier is derived by a pilot carrier, squaring loop or Costas loop. (Key point: Carrier recovery)

## Related in Communication Systems

- [SNR gain of non-coherent FM detector](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Anoncoherent-fm-gain) — Communication Systems, chapter 9, asked 2×