Double Sideband Suppressed Carrier (DSB-SC) Modulation

DSB-SC is a modulation technique that eliminates the carrier component from the transmitted signal, dedicating all power to the information-carrying sidebands. This dramatically improves power efficiency compared to conventional AM, making it the preferred choice for point-to-point communication systems.

Mathematical Representation

The DSB-SC signal is simply the product of the message and carrier:

s(t) = Ac · m(t) · cos(2πfc·t)

For a single-tone message m(t) = Am·cos(2πfm·t):

s(t) = Ac·Am·cos(2πfm·t)·cos(2πfc·t)

Using trigonometric identity:

s(t) = (AcAm/2)·cos[2π(fc+fm)·t] + (AcAm/2)·cos[2π(fc-fm)·t]

Notice: No carrier component at fc — only USB and LSB remain.

DSB-SC Waveform

Key Differences from Standard AM

Frequency Spectrum

Power Analysis

Since the carrier is suppressed:

Total transmitted power = Sideband power only

For single-tone modulation:

• PT = Ac²Am²/(4R) = Pc·m² (where Pc would be the carrier power)
• PUSB = PLSB = Ac²Am²/(8R)

Efficiency = 100% (all transmitted power is useful)

Generation of DSB-SC Signals

Balanced Modulator (Ring Modulator)

Operating Principle:

• When carrier is positive: D1, D2 conduct → output = +m(t)
• When carrier is negative: D3, D4 conduct → output = -m(t)
• Net effect: output = m(t) × sign[c(t)] ≈ m(t)·c(t) after filtering

Balanced Modulator using Transistors

Two identical AM modulators are arranged so their carrier components cancel while sidebands add constructively.

Coherent (Synchronous) Demodulation

Since the envelope of DSB-SC is |m(t)| (not m(t)), a simple envelope detector fails. Coherent detection is mandatory.

Mathematical Analysis:

Input: s(t) = Ac·m(t)·cos(2πfc·t)

Multiply by local oscillator: v(t) = s(t)·cos(2πfc·t)

v(t) = Ac·m(t)·cos²(2πfc·t)

v(t) = (Ac/2)·m(t) + (Ac/2)·m(t)·cos(4πfc·t)

After low-pass filtering (removes the 2fc component):

Output = (Ac/2)·m(t) ← Original message recovered!

Effect of Phase and Frequency Errors

Phase Error (φ)

If local oscillator has phase error: cos(2πfc·t + φ)

Output = (Ac/2)·m(t)·cos(φ)

• For φ = 0°: Full output
• For φ = 90°: Zero output (quadrature null)
• Attenuation factor: cos(φ)

Frequency Error (Δf)

If local oscillator frequency is fc + Δf:

Output = (Ac/2)·m(t)·cos(2πΔf·t)

The output is the message multiplied by a slowly varying cosine, causing a "beat" distortion that makes speech unintelligible.

Costas Loop for Carrier Recovery

The error signal is proportional to sin(2φ), which drives the VCO to lock at φ = 0.

Solved Example 1

Problem: A DSB-SC signal is generated using a carrier of 100 kHz and message signal of bandwidth 5 kHz. The carrier amplitude is 10V and message amplitude is 4V. Calculate the total transmitted power across a 50Ω load and the bandwidth.

Solution:

DSB-SC signal: s(t) = 10 × 4 × cos(2πfm·t) × cos(2π×100000·t)

Peak amplitude of each sideband = AcAm/2 = 10×4/2 = 20V

Power in each sideband = (20)²/(2×50) = 400/100 = 4W

Total power = 2 × 4 = 8W

Bandwidth = 2 × fm(max) = 2 × 5000 = 10 kHz

Solved Example 2

Problem: In a DSB-SC demodulator, the local oscillator has a phase error of 30°. What is the signal loss in dB?

Solution:

Output attenuation factor = cos(30°) = 0.866

Signal loss in dB = 20·log10(1/0.866) = 20·log10(1.155) = 20 × 0.0625 = 1.25 dB

At 60° phase error: loss = 20·log10(1/cos60°) = 20·log10(2) = 6.02 dB

Applications of DSB-SC

1. Stereo FM Broadcasting: The L-R difference signal is transmitted as DSB-SC on a 38 kHz subcarrier
2. Color Television: Chrominance signals (I and Q) use DSB-SC modulation
3. Instrumentation: Phase-sensitive detection in lock-in amplifiers
4. Data Communication: BPSK is essentially DSB-SC with a binary message

Interview Questions

Q1: Why can't an envelope detector be used for DSB-SC demodulation?

The envelope of a DSB-SC signal is |m(t)|, not m(t). At every zero crossing of the message, the carrier undergoes a 180° phase reversal. An envelope detector would output the absolute value of the message, introducing severe distortion. Coherent detection is essential to recover the actual sign of m(t) by using phase information from a synchronized local oscillator.

Q2: What is the Costas loop and why is it needed?

The Costas loop is a carrier recovery circuit for DSB-SC signals. Since DSB-SC has no discrete carrier component in its spectrum, the receiver cannot simply filter out the carrier for synchronization. The Costas loop uses two parallel demodulation paths (I and Q channels) and generates an error signal that drives a VCO to synchronize with the suppressed carrier. It effectively performs both carrier recovery and demodulation simultaneously.

Q3: How does DSB-SC achieve 100% efficiency compared to AM's 33%?

In standard AM, the carrier consumes 2/3 of the power but carries no information. DSB-SC eliminates the carrier entirely, so all transmitted power goes to the sidebands which carry the information. The tradeoff is receiver complexity — AM allows simple envelope detection while DSB-SC requires coherent detection with carrier recovery, adding cost and complexity to every receiver.

Q4: What is the quadrature null problem in coherent detection?

If the local oscillator phase drifts to exactly 90° (quadrature) relative to the received carrier, the output becomes zero regardless of the message signal strength. This happens because cos(90°) = 0 in the demodulation equation. The Costas loop prevents this by continuously tracking the carrier phase.