Double Sideband Suppressed Carrier (DSB-SC) Modulation - Communication

Definition

DSB-SC stands for Double Sideband Suppressed Carrier. It is an amplitude-modulation scheme in which the two sidebands that carry the information are transmitted but the carrier component is intentionally not transmitted (it is suppressed). The carrier contains no information; transmitting it wastes transmitter power. By suppressing the carrier, the available transmitter power is concentrated in the sidebands that carry the modulating information, improving power efficiency.

• Reason for suppression: the carrier contains no information and its transmission wastes power, therefore it is removed in DSB-SC to save power.
• Power and bandwidth trade-off: DSB-SC reduces power wasted in the carrier while occupying the same spectral bandwidth as a conventional DSB full-carrier (DSB-FC) transmission; the transmitted spectrum consists only of the upper and lower sidebands.
• Comparison: a DSB-FC (conventional AM) transmits the carrier and both sidebands; DSB-SC transmits only the two sidebands and so avoids the carrier power loss.

Generation of a DSB-SC signal

A common method to generate a DSB-SC signal is by using a product (multiplier) modulator. The modulated signal is the product of the baseband (modulating) signal and a sinusoidal carrier.

If the baseband (message) signal is x(t) and the carrier is cos(ω_ct), the transmitted DSB-SC signal is produced by multiplying these two signals. Using the frequency-shifting property of the Fourier transform, multiplication in time corresponds to frequency translation (convolution) in the frequency domain.

By the frequency-shifting property of the Fourier transform:

The result of multiplication with a cosine carrier places copies of the baseband spectrum around +ω_c and -ω_c, producing only the two sidebands and no carrier impulse at ω = 0.

Mathematical expression and spectrum

Consider a sinusoidal message (for clarity of algebra) and a sinusoidal carrier:

x(t) = A_x cos(2πf_xt)

c(t) = A_c cos(2πf_ct)

The product at the modulator output is s(t) = x(t)·c(t).

Derivation (each step on a separate line):

A_x cos(2πf_xt) · A_c cos(2πf_ct)

= A_xA_c · cos(2πf_xt) cos(2πf_ct)

= (A_xA_c/2) · [cos 2π(f_c + f_x)t + cos 2π(f_c - f_x)t]

Thus the modulated signal consists of two sinusoidal components at frequencies f_c + f_x (upper sideband) and f_c - f_x (lower sideband).

From the frequency locations:

f_max = f_c + f_x

f_min = f_c - f_x

Bandwidth, BW = f_max - f_min = 2 f_x

Hence, for a baseband signal whose highest frequency is f_x, the DSB-SC transmission occupies a total bandwidth of 2 f_x, symmetrically placed about the carrier frequency.

Carrier suppression using a balanced modulator

To remove the carrier while preserving the sidebands, a balanced modulator (balanced mixer) is commonly used. The principle is that a nonlinear device produces products (sum and difference frequencies) when two signals are applied; a balanced arrangement cancels the carrier terms while retaining the desired product terms that give the sidebands.

A balanced modulator can be implemented using diodes, transistors or FETs in a bridge/transformer arrangement so that carrier components cancel at the output.

In the diode balanced modulator shown, the message x(t) is applied such that the two diode legs see the carrier with opposite phase for the message component. The instantaneous inputs at the two diode legs may be written as:

v₁ = cos ω_ct + x(t)

v₂ = cos ω_ct - x(t)

Each diode is a nonlinear device. Represent its I-V characteristic by a power series (Taylor expansion) about the operating point:

i(v) = a v + b v² + higher-order terms

The diode currents are therefore (writing the first two nonzero terms):

i₁ = a [cos ω_ct + x(t)] + b [cos ω_ct + x(t)]² + ...

i₂ = a [cos ω_ct - x(t)] + b [cos ω_ct - x(t)]² + ...

The output voltage across the load R is proportional to the difference of these diode currents:

v_o = R [i₁ - i₂]

On expanding and cancelling identical terms the even powers of the carrier that are common to i₁ and i₂ are removed, while terms odd in x(t) remain. Keeping the dominant terms gives:

v_o = 2 a R x(t) + 4 b R x(t) cos ω_ct + higher-order products

Interpretation:

• The term 2 a R x(t) is a copy of the baseband message (an unwanted feedthrough term at baseband).
• The term 4 b R x(t) cos ω_ct is the desired DSB-SC component (product of message and carrier producing only sidebands).

The unwanted baseband feedthrough is usually removed by a band-pass filter (tuned LC network) centred at the carrier frequency, leaving the DSB-SC output:

v_o ≈ K x(t) cos ω_ct, where K = 4 b R

Detection (Demodulation) of DSB-SC

Because the carrier is suppressed, envelope detectors (which rely on a carrier envelope) cannot recover the message from DSB-SC. Synchronous (coherent) detection is required; this means the receiver must multiply the received DSB-SC signal by a locally generated carrier having the same frequency and phase as the transmitter carrier, then low-pass filter the product to obtain the baseband.

Suppose the received DSB-SC signal is r(t) = K x(t) cos ω_ct (noise and channel effects omitted). The receiver multiplies r(t) by a locally generated carrier cos(ω_ct + φ):

r(t) · cos(ω_ct + φ) = K x(t) cos ω_ct · cos(ω_ct + φ)

= (K/2) x(t) [cos φ + cos(2 ω_ct + φ)]

After passing this product through a low-pass filter, the high-frequency term cos(2 ω_ct + φ) is removed and the recovered baseband is:

(K/2) x(t) cos φ

Therefore demodulation requires the receiver carrier to be phase-synchronised with the transmitter carrier (φ ≈ 0). A phase error reduces recovered amplitude by a factor cos φ and can even invert polarity for large phase errors. Practical receivers use carrier-recovery techniques such as Costas loops or pilot carriers where available.

Power and bandwidth considerations

Power: in DSB-SC all transmitted power appears in the sidebands that carry information; the carrier component carries no power because it is not transmitted. This is why DSB-SC is often described as having very high modulation efficiency: none of the transmitted power is wasted on an uninformative carrier.

Bandwidth: the DSB-SC signal occupies a bandwidth equal to twice the highest frequency present in the baseband (BW = 2 f_m,max). This is the same occupied bandwidth as a DSB-FC system (DSB-SC simply removes the carrier spectral line but leaves the sidebands unchanged in width).

Advantages

• High modulation efficiency: transmitted power is used for information-bearing components only (carrier power is not transmitted).
• Less transmitter power wasted: because the carrier is suppressed, more of the transmitter power is available for the sidebands.
• Spectral use: DSB-SC transmits the same useful sideband information as DSB-FC but avoids the carrier component.

Disadvantages

• Requires coherent detection: the receiver must regenerate the carrier with accurate phase and frequency; this adds complexity.
• Carrier recovery difficulty: recovering a carrier in the presence of noise and channel distortions can be challenging.
• Receiver cost/complexity: synchronous demodulators and carrier recovery loops increase receiver complexity and cost compared with simple envelope detectors used for ordinary AM.

Applications

• Digital modulation building block: DSB-SC operation forms the basis of several digital modulation techniques (for example, components of phase-shift keying implementations use suppressed-carrier representations).
• Stereo FM multiplexing: the standard FM stereo multiplex system uses a suppressed-carrier DSB (38 kHz) subcarrier to transmit the L - R difference signal; the carrier is suppressed and the sidebands carry the difference information.
• Intermediate stages in communication systems: mixers and balanced modulators producing DSB-SC are widely used in frequency conversion and modulation stages in transmitters and receivers.

Practical notes and concluding remarks

DSB-SC is a fundamental modulation technique taught in communication systems because it illustrates multiplication in time, spectral translation, and the need for coherent detection. It offers better power efficiency than conventional AM but at the expense of receiver complexity. Balanced modulators and mixers are practical implementations that cancel unwanted carrier components while producing the desired sideband products. Understanding DSB-SC prepares one for related techniques such as single-sideband (SSB) modulation and coherent digital modulation schemes.