I am programming a phase-locked loop to track the resonance of a tuning fork so that the tuning fork is always on resonance. This will be used in condensed matter physics through atomic force microscopy.

Now, I am not certain about how to carry this out, so I was wondering if someone here could help me.

I have programmed an FPGA to output an arbitrary driving voltage, and this drives a tuning fork. This tuning fork then generates a signal that is eventually converted to a voltage and read by my device. Now, I also have a lock-in amplifier to detect the phase lag between my DAC (technically, the NCO that outputs via DAC) and ADC signals. I have made a graph of the phase difference after taking 4000 steps around the resonance frequency. Also, there is a graph of the LIA's detected magnitude*2.

I do not know what any of the transfer functions are, I apologize.

enter image description here Phase difference (phase lag) graph on left. Resonance centered at 32.7635 kHz enter image description here However, my phase difference graph is likely incorrect. I found the following that displays continuous "pretty" graph that may be what I am supposed to have.

Phase lag in blue

Does anyone know why phase graph has a max/min of 1/-1? If so, does anyone know how I may fix it?

Thank you
  • $\begingroup$ Your phase in the Labview plot, is in normalized radians, right? That is +1 = 180 degrees and -1 = 180 degrees? $\endgroup$
    – Ben
    Feb 9 at 18:53
  • $\begingroup$ I would assume so. However, I did not explicitly specify for the detected phase to be normalized, nor did I normalize the data. $\endgroup$ Feb 9 at 18:54
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    $\begingroup$ You could unwrap the phase, and the discontinuity would go away $\endgroup$
    – Ben
    Feb 9 at 19:06
  • $\begingroup$ I tried using the LabVIEW "Unwrap Phase PtByPt" subVI, but it produces the same output zone.ni.com/reference/en-XX/help/371361R-01/ptbypt/… $\endgroup$ Feb 9 at 19:18
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    $\begingroup$ the VI expects an input with a ±pi range. You have a ± 1 range. You should miltiply your phase by $\pi$ $\endgroup$
    – Ben
    Feb 9 at 19:19

You seem to have 3 problems

1 - You have a phase wrap. It happens when the phase goes past 180 degrees. The phase will wrap back to -180 degrees. You can fix this by unwrapping the phase.

2 - Your phase is in normalized radians instead of being in radians or degrees. This is not a problem per se but when you try to unwrap the phase, you should be aware that phase unwrap blocks usually expect a phase in radians, not in normalized radians.

3 - The measured phase seems to be inverted compared to what you expect.


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