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### High accuracy Phase Difference calculations between two sine waves

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```Hi,

I am trying to find the phase difference between two sine waves using matlab to an accuracy of 4 decimal places. That means I want to be able to detect a phase difference as small as 1e-4 radians. I am using a 12bit A/D. Both signals are of the same frequency(50Hz), and the SNR is 2:1(yes, its a high noise environment). I have tried many different ways but cant get an accuracy of more than 2 decimal places. Some methods I have tried are -:

1. I have tried to find the zerocrossing  and hence detect the time difference to find the phase but doesn't work for high accuracy.

2.I have also tried to find the cross-correlation of the two signals and detect the max time lag at the peak. This method give me a 3 decimal accuracy but still not good enough.

For the these two methods I used a high sampling frequencies like 50KHz 500Khz 1MHz and 100Mhz. The last one gave me the best results which is understandable as the closer the samples the more accurate they will be but at that high a sampling frequency designing filters for a 50Hz signal with 500 to 5Khz range of noise is hard, almost impossible in matlab. I am not sure what filter to use there.

3. I also tried sina*sinb, the product to sum rule. I took the time avg. of the resulting wave to eliminate  the time varying component and tried taking the arccos of the DC component that contained teh phase information.

4. I also tried sina+sinb, the sum to product rule and then took the magnitude to calculate the phase difference.

The problem I faced with the above two methods is that the arccosine function is extremely sensitive and hence the accuracy is there but the stability is not due to noise.

For the above described problem I have a the following questions -:

Q.1 Is A/D vertical resolution high enough for the accuracy I want?

Q.2 What sampling freqeuncy would ideal be ideal for filtering as well as calulcation?

Q.3 What kind of filters should I use?

Q.4 Are there nay other ways of calulating phase difference with that high an accuracy?

-Karan Uppal
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7/23/2012 5:51:06 PM