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Accurate phase measurement with relativly low sampling frequency

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Newbie level 4
Feb 17, 2013
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To give some more information on what I am to use this for: I have two signals. Both are periodic sine waves with the same frequency, but with a constant phase difference. Let's call one of the signals for ref (reference) and the other sig (signal). They can look like this:

ref(t) = sin(2*pi*f*t)

sig(t) = sin(2*pi*f*t + θ)

where f = 300 000 Hz.

I sample the two signals simultaneously, multiply them and low pass filter in the micro controller. This way I get the in-phase component. To get the out-of-phase component I shift ref with θ = 90°, multiply ref with sig and low pass filter to remove the high frequency component.

I understand how this works when having a sampling rate that is for example 360 times the signal frequency (in this case 360*300 000 = 108MSPS), which would give close to 1° accuracy over one period.

I am trying to understand how I can do accurate phase measurement of a signal with a sampling frequency that is for example only 5 times the signal frequency. I have been doing some reading and have found that this is to be possible by sampling more than one period of the periodic sine wave signal and do some averaging, but I am struggling finding a good explaination/examples on this.

So far I have figured out that to do this over several periods I have to satisfy the equation:

fs/fsig = N/M

where fs = sampling frequency, fsig = signal frequency, N = total number of samples, M = periods.

For my example fs could be 2.5MHz, N = 25 and M = 3. This will give a phase difference between each sample of:

Φ = 2*pi * (fsig/fs) = 2*pi * (M/N) = 43.2°

So for 3 periods we have 25 samples with a constant phase difference of 43.2°.

From this point I need some help what to do next. I want to know if someone can point me to a link, book, ebook or anything that explains this technique, tell me if this technique has a name (that would help my googling a lot) or can take some time explaining this in a short or long text.


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