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 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: ==Generation==

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}} ==Demodulation==

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}} ::= \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] 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 \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. Distortion and attenuation 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\cos(\omega_c t) • Demodulation signal (with small frequency and phase deviations from the modulation signal): V'_c\cos\left[(\omega_c+\Delta\omega)t + \theta\right] The resultant signal can then be given by :f(t) \times V_c\cos(\omega_c t) \times V'_c\cos\left[(\omega_c+\Delta\omega)t + \theta\right] ::=\frac{1}{2}V_c V'_c f(t) \cos\left(\Delta\omega\cdot t+\theta\right) + \frac{1}{2}V_c V'_c f(t) \cos\left[(2\omega_c+\Delta\omega)t+\theta\right] ::\xrightarrow{\text{After low pass filter}} \frac{1}{2}V_c V'_c f(t) \cos\left(\Delta\omega\cdot t+\theta\right) The \cos\left(\Delta\omega\cdot t+\theta\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 \theta is a constant attenuation factor, also \Delta\omega\cdot t represents a cyclic inversion of the recovered signal, which is a serious form of distortion. ==Waveforms==

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 s(t) = \frac{1}{2}\cos\left(2\pi 800 t\right) - \frac{1}{2}\cos\left( 2\pi 1200 t\right). The carrier, in this case, is a plain 5 kHz (c(t) = \cos\left( 2\pi 5000 t \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. x(t) = \underbrace{\cos\left( 2\pi 5000 t \right)}_\mbox{Carrier} \times \underbrace{\left[\frac{1}{2}\cos\left(2\pi 800 t\right) - \frac{1}{2}\cos\left( 2\pi 1200 t\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 5,000 Hz are the lower sideband (LSB) and the two peaks above 5,000 Hz are the upper sideband (USB), but there is no peak at the 5,000 Hz mark, which is the frequency of the suppressed carrier. ==References==