Double-sideband suppressed-carrier transmission

DSB-SC is basically an amplitude modulation wave without the carrier, therefore reducing power waste, giving it a 50% efficiency. This is an increase compared to normal AM transmission (DSB) that has a maximum efficiency of 33.333%, since 2/3 of the power is in the carrier which conveys no useful information and both sidebands containing identical copies of the same information. Single Side Band Suppressed Carrier (SSB-SC) is 100% efficient.

Spectrum plot of a DSB-SC signal:

DSB-SC is generated by a mixer. The signal produced is the product of the message signal and a carrier signal. The mathematical representation of this process is shown below, where the product-to-sum trigonometric identity is used.

${\displaystyle \underbrace {V_{m}\cos \left(\omega _{m}t\right)} _{\mbox{Message}}\times \underbrace {V_{c}\cos \left(\omega _{c}t\right)} _{\mbox{Carrier}}=\underbrace {{\frac {V_{m}V_{c}}{2}}\left[\cos \left(\left(\omega _{m}+\omega _{c}\right)t\right)+\cos \left(\left(\omega _{m}-\omega _{c}\right)t\right)\right]} _{\mbox{Modulated Signal}}}$

For DSBSC, Coherent Demodulation is done by multiplying the DSB-SC signal with the carrier signal (with the same phase as in the modulation process) just like the modulation process. This resultant signal is then passed through a low pass filter to produce a scaled version of the original message signal.

${\displaystyle \overbrace {{\frac {V_{m}V_{c}}{2}}\left[\cos \left(\left(\omega _{m}+\omega _{c}\right)t\right)+\cos \left(\left(\omega _{m}-\omega _{c}\right)t\right)\right]} ^{\mbox{Modulated Signal}}\times \overbrace {V'_{c}\cos \left(\omega _{c}t\right)} ^{\mbox{Carrier}}}$

${\displaystyle =\left({\frac {1}{2}}V_{c}V'_{c}\right)\underbrace {V_{m}\cos(\omega _{m}t)} _{\text{original message}}+{\frac {1}{4}}V_{c}V'_{c}V_{m}\left[\cos((\omega _{m}+2\omega _{c})t)+\cos((\omega _{m}-2\omega _{c})t)\right]}$

The equation above shows that by multiplying the modulated signal by the carrier signal, the result is a scaled version of the original message signal plus a second term. Since ${\displaystyle \omega _{c}\gg \omega _{m}}$, this second term is much higher in frequency than the original message. Once this signal passes through a low pass filter, the higher frequency component is removed, leaving just the original message.

This is best shown graphically. Below is a message signal that one may wish to modulate onto a carrier, consisting of a couple of sinusoidal components with frequencies respectively 800 Hz and 1200 Hz.

The equation for this message signal is ${\displaystyle s(t)={\frac {1}{2}}\cos \left(2\pi 800t\right)-{\frac {1}{2}}\cos \left(2\pi 1200t\right)}$.

The carrier, in this case, is a plain 5 kHz (${\displaystyle c(t)=\cos \left(2\pi 5000t\right)}$) sinusoid—pictured below.

The modulation is performed by multiplication in the time domain, which yields a 5 kHz carrier signal, whose amplitude varies in the same manner as the message signal.

${\displaystyle x(t)=\underbrace {\cos \left(2\pi 5000t\right)} _{\mbox{Carrier}}\times \underbrace {\left[{\frac {1}{2}}\cos \left(2\pi 800t\right)-{\frac {1}{2}}\cos \left(2\pi 1200t\right)\right]} _{\mbox{Message Signal}}}$

The name "suppressed carrier" comes about because the carrier signal component is suppressed—it does not appear in the output signal. This is apparent when the spectrum of the output signal is viewed. In the picture shown below we see four peaks, the two peaks below 5000 Hz are the lower sideband (LSB) and the two peaks above 5000 Hz are the upper sideband (USB), but there is no peak at the 5000 Hz mark, which is the frequency of the suppressed carrier.

 This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 2022-01-22. (in support of MIL-STD-188).

• A DSBSC generation and demodulation instrument is described as side application of a commercial lock-in amplifier in Double-sideband Suppressed-carrier Modulation.