Double-Sideband Suppressed-Carrier Modulation

August 28, 2013 by Sadik Hafizovic

Double-sideband suppressed-carrier (DSB-SC) modulation is an amplitude modulation that consists only of the two symmetrical sidebands and no carrier band. I came across this scheme in an ultrasound application, where power utilization can be maximized when all power is available on the sidebands. It 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 enables direct sideband synthesis and demodulation based on a given carrier and modulation frequency. Importantly, it isn't the sideband frequencies that are specified but rather the center or carrier and the modulation (the distance between carrier and sideband). This has enormous consequences:

  • The modulation frequency can be swept easily, 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 a PLL, for example, and still the phase relations will be defined at all times.

The generation part is straightforward: the required settings are shown in Figure 1.

UHFLI LabOne MOD

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

The demodulation part is also straightforward when only amplitudes are of interest, but it 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 as we have no carrier band to measure we don't know what its phase is. Fortunately, we can use the fact that in amplitude modulation (AM) sidebands are in-phase. φc, φlo and φup are directly measured by the lock-in amplifier 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 two equations below. The third equation stems from the assumption that we have pure AM 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

Hence:

φmod = (φup − φlo) / 2