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 sideband suppressed-carrier (SSB-SC) is 100% efficient.

Spectrum plot of a DSB-SC signal:

Image:Spectrum DSBSC.svg

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.

:$$

\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}}

Image:DSBSC Modulation.svg

In DSBSC, coherent demodulation is achieved by multiplying the DSB-SC signal with the carrier signal of the same phase as in the modulation process, analogous to the modulation process. This resultant signal is passed through a low pass filter to produce a scaled version of the original message signal:

:$$

\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}}

::$=\; \backslash left(\backslash frac\{1\}\{2\}V\_c\; V\text{'}\_c\backslash right)\backslash underbrace\{V\_m\; \backslash cos(\backslash omega\_m\; t)\}\_\{\backslash text\{original\; message\}\}\; +\; \backslash frac\{1\}\{4\}V\_c\; V\text{'}\_c\; V\_m\; \backslash left[\backslash cos((\backslash omega\_m\; +\; 2\backslash omega\_c)t)\; +\; \backslash cos((\backslash omega\_m\; -\; 2\backslash omega\_c)t)\backslash right]$

This equation 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 $\backslash omega\_c\; \backslash gg\; \backslash omega\_m$, 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.

For demodulation, the demodulation oscillator's frequency and phase must be exactly the same as the modulation oscillator's, otherwise, distortion and/or attenuation will occur.

To see this effect, take the following conditions:

• Message signal to be transmitted: $f(t)$
• Modulation (carrier) signal: $V\_c\backslash cos(\backslash omega\_c\; t)$
• Demodulation signal (with small frequency and phase deviations from the modulation signal): $V\text{'}\_c\backslash cos\backslash left[(\backslash omega\_c+\backslash Delta\backslash omega)t\; +\; \backslash theta\backslash right]$

The resultant signal can then be given by

:$f(t)\; \backslash times\; V\_c\backslash cos(\backslash omega\_c\; t)\; \backslash times\; V\text{'}\_c\backslash cos\backslash left[(\backslash omega\_c+\backslash Delta\backslash omega)t\; +\; \backslash theta\backslash right]$

::$=\backslash frac\{1\}\{2\}V\_c\; V\text{'}\_c\; f(t)\; \backslash cos\backslash left(\backslash Delta\backslash omega\backslash cdot\; t+\backslash theta\backslash right)\; +\; \backslash frac\{1\}\{2\}V\_c\; V\text{'}\_c\; f(t)\; \backslash cos\backslash left[(2\backslash omega\_c+\backslash Delta\backslash omega)t+\backslash theta\backslash right]$

::$\backslash xrightarrow\{\backslash text\{After\; low\; pass\; filter\}\}\; \backslash frac\{1\}\{2\}V\_c\; V\text{'}\_c\; f(t)\; \backslash cos\backslash left(\backslash Delta\backslash omega\backslash cdot\; t+\backslash theta\backslash right)$

The $\backslash cos\backslash left(\backslash Delta\backslash omega\backslash cdot\; t+\backslash theta\backslash right)$ terms results in distortion and attenuation of the original message signal. In particular, if the frequencies are correct, but the phase is wrong, contribution from $\backslash theta$ is a constant attenuation factor, also $\backslash Delta\backslash omega\backslash cdot\; t$ represents a cyclic inversion of the recovered signal, which is a serious form of distortion.

File:Demodulation distortion diagram.png

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.

Image:DSBSC Message Signal.png

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

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

Image:DSBSC Carrier Signal.png

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.

Image:DSBSC Modulated Output.png

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

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.

Image:DSBSC Spectrum.png

{{FS1037C MS188}}

• A DSBSC generation and demodulation instrument is described as side application of a commercial lock-in amplifier in [http://www.zhinst.com/blogs/sadik/2013/08/dsb-sc/ Double-sideband Suppressed-carrier Modulation].

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Category:Radio modulation modes