Double-sideband Suppressed-carrier Modulation

Double-sideband Suppressed-carrier (DSB-SC) modulation is an amplitude modulation, which consists only of the two symmetrical sidebands and no carrier band. I came across this scheme in an ultra-sound application, where the power utilization can be maximized when all power is available on the sidebands. I turns out that DSB-SC modulation can easily be generated and demodulated using the MOD option available for the HF2LI and UHFLI lock-in amplifiers. The MOD option is a feature unique to Zurich Instruments lock-in amplifiers and allows to do a direct sideband synthesis and demodulation based on a given carrier and the modulation frequency. The fact that not the sideband frequencies are specified but rather the center or carrier and the modulation (distance between carrier and sideband) are specified has enormous consequences. These are:

  • you can easily sweep the modulation frequency, e.g., for Bode plots
  • the phase relation between the two sidebands is always defined because the sidebands are constructed using the same oscillator
  • the carrier and modulation frequencies can be controlled by, e.g., a PLL and still the phase relations will be defined at all times

The generation part is straight forward, the required settings can be seen in the screenshot below.

UHFLI LabOne MOD

Figure: (click to enlarge) LabOne User Interface of the UHFLI 600 MHz Lock-in Amplifier with UHF-MOD option, configured to generate a DSB-SC modulated signal (top) and the standard Spectrum Analyzer shows the the spectrum around 1 MHz where the sidebands are clearly visible at ±20 kHz.

The demodulation part is straight forward when only amplitudes are of interest but does get a bit tricky when the modulation phase is of interest, too. This is because the phase of the sidebands is relative to the carrier and the modulation oscillators, but since we do not have a carrier band to measure, we don’t know what its phase is. Fortunately we can use the knowledge that in AM the sidebands are in-phase, which we can apply to the problem.

φc, φlo and φup are directly measured by the lock-in and are the phases of the carrier, the lower sideband and the upper sideband, respectively. The quantity of interest is the phase of the modulation, φmod, which is determined by the first 2 equations below. The third equation stems from the assumption that we have a pure AM modulation and that we can assume in-phase sidebands.

  1. φmod up = φup − φc
  2. φmod lo = −(φlo − φc)
  3. φmod lo − φmod up = 0  ⇔  φmod = φmod lo = φmod up

 
And thus

φmod = (φup − φlo) / 2

More details on DSB-SC, especially for transmission applications can be found at http://en.wikipedia.org/wiki/Double-sideband_suppressed-carrier_transmission.