ω/2 Demodulation for a Parametric Oscillator

We often get questions from HF2LI lock-in amplifier customers who characterize MEMS and sometimes from those doing AFM scans on how to measure at half reference frequency using a lock-in amplifier. Half reference frequency lock-in measurement is often necessary when characterizing a parametric oscillator, for example. For those not familiar with parametric oscillators, a basic overview can be found on Wikipedia. In a nutshell, a resonance in a parametric oscillator at a frequency ωo  can be createdby applying an external force at 2ωo to one of its physical parameters. This is different from creating resonance by playing with instability in a regular resonator.

Luckily, HF2LI can be upgraded to include HF2LI-MF Multi-frequency option which can be easily configured to do ω/2 measurement. Here is how. The screenshot below shows an output of ω= 1MHz generated at Harm = 2, which means the output generated is actually at 2MHz and not at 1MHz as shown in FFT.

 Then to demodulate at ωo/2, one simply has to choose another demodulator and set Harm = 1 as shown in the next screenshot. Note that both the demodulator output oscillator and the demodulator input oscillator are the same (i.e. Osc=1). This ensures perfect phase coherence between the output signal generated and the demodulator reference. Voilà! It’s that simple.

On a side note, the HF2LI-MF option can be also used to generate phase shift even when generated at the harmonic of the interested fundamental frequency. On top of that, the phase can be swept as well in the Sweeper as shown below. This may be useful for AFM applications

The HF2LI-MF option is a very powerful tool for harmonic as well as phase shift analysis. Feel free to let us know if you want to share other imaginative ways to use HF2LI-MF.