---
title: "DSB-SC vs SSB; synchronous demodulation of DSB-SC"
subject: "Communication Systems"
chapter: 2
key: "semester_6/communication_systems:dsbsc-vs-ssb-synchronous-demod"
source: https://www.bctengineer.com/q/semester_6/communication_systems/dsbsc-vs-ssb-synchronous-demod
site: BCT Engineering
---

# DSB-SC vs SSB; synchronous demodulation of DSB-SC

Communication Systems · Chapter 2: Amplitude Modulation

- Asked in: 2080 Chaitra (CS I), 3+6+3 marks
- Video: [Demodulation of DSB SC Synchronous Detector | Hindi/Urdu | Communication System by Raj Kumar Thenua](https://www.youtube.com/watch?v=mooa-UaN2zo) — Learn By Watch Electronics
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/communication_systems/dsbsc-vs-ssb-synchronous-demod
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-2

## Question

Compare and contrast DSB-SC and SSB. Explain the synchronous demodulation for DSB-SC signal along with its requirements and limitations.

## Short answer

DSB-SC transmits both sidebands (bandwidth 2W) while SSB transmits one sideband (bandwidth W); both require coherent detection. Synchronous demodulation multiplies the received signal by a local carrier of identical frequency and phase, then low-pass filters to recover the message. Requires carrier recovery (e.g., Costas loop). Limitations: phase error scales output by cosφ (zero at 90°), frequency error causes beating distortion, and receiver is more complex than envelope detection.

## Answer

#### Comparison of DSB-SC and SSB

Both suppress the carrier and need coherent detection; they differ in the number of sidebands sent.

| Point | DSB-SC | SSB-SC |
|---|---|---|
| Expression | $A_cm(t)\cos\omega_ct$ | $\frac{A_c}{2}[m(t)\cos\omega_ct \mp \hat m(t)\sin\omega_ct]$ |
| Sidebands | USB + LSB | USB or LSB only |
| Bandwidth | $2W$ | $W$ |
| Power | Both sidebands (redundant) | Half of DSB-SC for the same message |
| Generation | Simple: balanced or ring modulator | Complex: sharp filter or phase-shift method |
| Detection | Coherent (Costas loop possible) | Coherent; small frequency error shifts pitch |
| Low-frequency messages | Handled easily | Hard with filter method (needs a gap near DC) |
| Uses | Stereo FM sub-carrier, QAM | HF voice links, telephony |

Similarity: both save carrier power, both give the same output SNR as baseband for the same transmitted power.

#### Synchronous (coherent) demodulation of DSB-SC

The received wave is multiplied by a locally generated carrier of **exactly the same frequency and phase**, and the product is low-pass filtered.

```text
 s(t) ----->( X )----- v(t) ----> LPF ----> vo(t)
              ^                  (0 to W)
              |
        Local oscillator
        cos(wc t + phi)
```

Let $s(t) = A_cm(t)\cos\omega_ct$ and local carrier $\cos(\omega_ct + \phi)$:

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

The LPF removes the $2\omega_c$ term:

$$
v_o(t) = \frac{A_c}{2}\cos\phi\; m(t)
$$

With $\phi = 0$: $v_o(t) = \tfrac{A_c}{2}m(t)$, the message is recovered exactly.

#### Requirements

- The local oscillator must be **synchronised in frequency and phase** with the transmitter carrier.
- LPF cut-off at $W$, and $f_c \gg W$ so spectra do not overlap.
- A carrier-recovery circuit (pilot carrier, squaring loop or Costas loop) is needed because no carrier is transmitted.

#### Limitations

- **Phase error:** output scales by $\cos\phi$. At $\phi = 90^\circ$ the output is zero (**quadrature null effect**). A slowly varying $\phi$ causes fading.
- **Frequency error** $\Delta\omega$: output becomes $\tfrac{A_c}{2}m(t)\cos(\Delta\omega t)$, a beating distortion.
- Receiver is costlier and more complex than an envelope detector.

## Check yourself

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

1. How do DSB-SC and SSB compare in bandwidth?
   A. Both need 2W
   B. DSB-SC needs 2W and SSB needs W
   C. DSB-SC needs W and SSB needs 2W
   D. Both need W
   Answer: B. SSB sends only one sideband. (Key point: Bandwidth and power)

2. With a local carrier cos(wc t + phi), what is the LPF output for a DSB-SC input?
   A. Ac m(t) sin(phi)
   B. (Ac/2) m(t) cos(2 wc t)
   C. Ac m(t)
   D. (Ac/2) m(t) cos(phi)
   Answer: D. The product contains a baseband term (Ac/2)m cos phi and a 2wc term which the LPF removes. (Key point: Synchronous detection output)

3. What happens when the phase error is 90°?
   A. Output is zero (quadrature null effect)
   B. Output is maximum
   C. Output is doubled
   D. Output is the 2wc term
   Answer: A. cos 90° = 0. (Key point: Quadrature null)

4. What is needed because the carrier is not transmitted?
   A. An envelope detector only
   B. A wider LPF with cut-off above fc
   C. A carrier recovery circuit such as a Costas loop or squaring loop
   D. No extra circuit
   Answer: C. The local carrier must match the transmitted one in frequency and phase. (Key point: Requirement)

## Related in Communication Systems

- [DSB-AM, DSB-SC and SSB spectra; synchronous detection](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adsbam-dsbsc-ssb-spectrum-synchronous) — Communication Systems, chapter 2
- [Compare DSB-AM, DSB-SC, SSB, VSB; SSB by phase discrimination](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Acompare-am-variants-ssb-phase) — Communication Systems, chapter 2
- [Compare DSB-AM, DSB-SC and SSB](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Acompare-dsbam-dsbsc-ssb) — Communication Systems, chapter 2
- [Detection gain of SSB-SC vs DSB-SC](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adetection-gain-ssbsc-dsbsc) — Communication Systems, chapter 9, asked 2×
- [DSB-AM vs SSB; ring modulator for DSB-SC](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adsbam-ssb-compare-ring-modulator) — Communication Systems, chapter 2
- [DSB-FC vs DSB-SC; phase shift method for SSB](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adsbfc-dsbsc-ssb-phase-shift) — Communication Systems, chapter 2

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