As we see in case of DSB-SC only sidebands are transmitted as they bear all informations about the signal. On the other hand, the two sidebands are identical and they carry same information. So, why not just send a single sideband and construct the other sideband from that.
Master SSB-SC Concepts
Explore our interactive tools and comparisons between DSB and SSB modulation techniques.
View Detailed ComparisonSSB-SC Modulator using Hilbert Transform
Single-sideband has the mathematical form of quadrature amplitude modulation (QAM) in the special case where one of the baseband waveforms is derived from the other, instead of being independent messages:
(t)·sin(2Ï€f0t)
Where s(t) is the message (real valued), 
(t) is the Hilbert transform, and f0 is the radio carrier frequency.
To understand this formula, we may express s(t) as real part of a complex valued function, with no loss of information.
(t)}
where j represents the imaginary unit. sa(t) is the analytical representation of s(t), which means that it comprises only the positive-frequency components of s(t)
Sa(f) = S(f) for f > 0; = 0 for f < 0
Therefore the frequency-translated function Sa(f – f0) contains only one side of S(f). Inverse Fourier transform results in:
ssb(t) = F -1 {Sa(f – f0)} = sa(t)·e2Ï€f0t
Using Euler’s formula:
= Re {[ s(t) + j·
(t)] · [cos(2Ï€f0t) + j·sin(2Ï€f0t)]} = s(t)·cos(2Ï€f0t) -
(t)·sin(2Ï€f0t)
Lower Sideband (LSB)
Similarly, the lower sideband can be expressed as:
(t)·sin(2Ï€f0t)
The sum of the two sideband signals is: susb(t) + slsb(t) = 2s(t)·cos(2Ï€f0t), which is the classic model of DSB-SC.
Other SSB-SC Modulators
Bandpass Filtering
One method of producing an SSB-SC signal is to remove one of its sidebands via filtering, leaving only either the upper sideband (USB) or the lower sideband (LSB). Most often, the carrier is suppressed.
Hartley Modulator
The Hartley modulator uses phasing to suppress the unwanted sideband. Two versions of the message are generated 90° out of phase, modulating carriers that are also 90° out of phase. Adding or subtracting the results yields the USB or LSB.
Weaver Modulator
The Weaver modulator uses only lowpass filters and quadrature mixers. It is favored in digital implementations. The band of interest is translated to be centered at zero, lowpass filtered, and then upconverted to the desired center frequency.
SSB-SC Detector
To recover the original signal, the sideband must be frequency-shifted back to its original baseband range using a product detector which mixes it with a Beat Frequency Oscillator (BFO).
Example Calculation
Receiver Intermediate Frequency (IF) = 45,000 Hz. Target Audio = 1,000 Hz.
BFO required = 44,000 or 46,000 Hz.
Detection involves choosing an FBFO that results in | Fif - Fbfo | = Fbaseband. Unwanted high-frequency components are removed with a lowpass filter.
Q & A and Summary
1. What is the primary difference between SSB-SC and DSB-SC?
The key difference is bandwidth. SSB-SC transmits only one sideband, requiring half the bandwidth of DSB-SC, while both suppress the carrier.
2. Explain the significance of the Hilbert transform \( \hat{m}(t) \) in SSB-SC.
The Hilbert transform generates the quadrature component of the message. This 90-degree phase shift allows for the mathematical cancellation of one sideband when combined with the original signal.
3. What role does the carrier suppression play?
Carrier suppression eliminates the redundant carrier component, saving power and allowing the modulation to focus exclusively on the information-bearing sideband.
4. How does the choice of USB or LSB affect the spectrum?
USB translates the spectrum upward from the carrier frequency, while LSB translates it downward. This determines where in the frequency band the signal resides.
5. Describe the demodulation process using coherent detection.
The received signal is multiplied by a local carrier of the same frequency and phase. This produces the message at baseband plus a high-frequency component at 2fc.
6. How does low-pass filtering contribute to demodulation?
It removes the high-frequency "double frequency" terms produced during the mixing process, leaving only the original message signal.
7. What are the advantages of SSB-SC over traditional AM?
Significant bandwidth efficiency (50% reduction) and power efficiency, making it ideal for long-range and satellite communications.
8. What is the significance of the trigonometric identities used in derivation?
Identities like \( \cos^2(\theta) \) help separate the baseband message from high-frequency carriers, simplifying the mathematical proof of recovery.