Better estimation of phase difference between two signals with variable frequency!

Question

Hello LabView Gurus, 
Being a power engineer and having just a little knowledge of signal processing and labview, I have been pulling my hair out for the last couple of days to get a better estimation of phase difference between two signals.
We have two analog voltage signals; 1. sine wave (50Hz ± 1Hz) and 2. a square wave with exactly half of sine wave frequency at any time.
At the starting point of operation (and simulation/acquisition) both signals will have no phase difference. However, the square wave's frequency changes unpredictably for a just a few millisecond but then it gets synchronized with sine wave's frequency again. This means that the square wave will be phased out from its original position. The task of the labview is to find the phase difference between the two signals continuously.
My approach to determine the phase difference is to measure the time when sine wave crosses zero amplitude and the time when the very next square wave changes amplitude from zero volts to +ve voltage (I have a 0.5volts threshold just to avoid any dramas from small line noise). The difference between these times is then divided by the time period and multiplied by 360 to get this phase difference in angles. 
As this part is just a small block of a big project, I can only allow 5000Hz sampling rate each for both signals. I read 500 samples (which means I read data from 5 cycles of sine wave and 2.5 cycles of square wave).
Now the problem is, as long as the frequency of sine wave stays constant at exactly 50Hz, I get a good estimation of the phase difference but when the frequency changes even a little (and it will happen in the real scenario i.e 50Hz ± 1Hz  and the square wave's frequency is dependent of sine wave's frequency), the estimation error increases.
I have attached my labview program. From front panel, you can set the phase of square wave (between -180 and 0) and you should see the labview's calculated phase in the indicator box named 'Phase'. Then you can press 'Real Frequency' switch that would cause the frequency to change like it would in real operation.
You can observe that the estimation error increases after you push the button. 
All I need to do is to reduce this estimation error and make it as close to the actual phase difference as possible. Any help would be greatly appreciated.
I am using LabView 2009 for this task.
The application is for electric machines and the stability/performance of machines under different faults.
Thank you for reading this far!
Regards,
Awais
Attachments:
v603.png ‏320 KB
v603.vi ‏186 KB

Answer 1

Jeff Bohrer wrote:
Basic math gives me a bit of pause on this approach.  You are sampling at 50 times the frequency of interest so you get 50 samples per cycle.  your phase resolution is 1/50th cycle or 7.2 degrees +/- noise.  You will need to samlpe faster to reduce phase resolution or average multiple readings (at a time cost that is signifigant)
Jeff- (Hardly Working)
I am sampling at 100 times the sine wave's frequency and 200 times the square wave's frequency.  Increasing the sampling rate completely solves my problem. But since I am acquiring several other inputs, I cannot afford a sampling rate higher than 5kHz.
F. Schubert wrote:
I'm not a signal processing expert, but here my basic understanding.
If you simulate sampling with 5kHz and a frequency of 50 Hz (and both are 'sync' by design), you always get an exact 5 periods. Any variation of your signals frequency gives you a propability to get 4 or 6 'trigger' events. That's an up or down of 20%!
The one measure to reduce such problems is using 'window functions'. They don't fit your current approach (counting instead of a DSP algorithm), so this needs to be reworked as well.
My approach would be to use the concept of a Locki-In amplifier. You need to phaseshift your ref-signal by 90°. Then multiply your measurement signal with the ref signal and the phase shifted ref signal. The obtained values for x/y coordinates of a complex number. Calculate the theta of the complex number (with the LV prim). Feed this in a low pass filter.
The trick on this is, that the square wave has harmonics in it, in this you are interested in the second harmonic which is the sine wave.
To get rid of the effect that the sync between sampling rate and ref signal frequency gives an error, you then can use the window I mentioned above (place it before the lock-in).
For a design that really plays well, use a producer-consumer design pattern to get the calculations done in parallel with the DAQ.
I suggest you to check on wikipedia for some of the keywords I mentioned. Go also for the external links which lead to great tutorials and AppNotes on the signal processing basics.
Sorry, it's not a simple solution I offer and we will have quite some conversation on this forum if you follow this path. Maybe someone else knows a simpler way.
Felix
www.aescusoft.de
My latest community nugget on producer/consumer design
My current blog: A journey through uml
An interesting view. the sine wave can indeed be looked as a second harmonic of the square wave. I will implement your idea and get back to you as soon as I get some results. But since I have very limited knowledge of signal processing, it might take me a while to get my hear around the solution you mentioned.