Phase of FM signals

[Tomi]

Dear All,

I would like to measure the phase difference of two frequency modulated signals. The frequency of modulation is 3-10Hz but always the same for both singal at the same moment. The result frequency is 50-800Hz but in some cases it can be 4kHz. Additional problem is that the signals are noisy.
Because of the frequency changes it is difficult (for me) to take one channel as reference frequency for further calculations.

I attached some sample data files (*.acq) and my draft vi.

At the moment I search the place where the frequency is not changes too much, taken this frequeny and the peak positions of both signals and calculate the phase. I do not think that this is the best method.

I have an other idee. That is try to get th
e modulation frequency. Remove this frequency component from the modulated signals (how?). The signals should be constant frequency and use one phase analisys tool from labview library.

Is there any other method and tool what helps me to get the phase difference?
Thanks in advance,
Tomi

[johnsold]

It is difficult to define the phase of an FM signal, let alone measure it under noisy conditions. For a sinusoidal carrier modulated by a sinusoidal signal the voltage may be represented as:
v(t) = A*sin(2*pi*fc*t+B*sin(2*pi*fm*t)+theta)
where fc is the carrier frequency (assumed constant), fm is the modulating frequency (also constant), t is the time, and theta is a constant.
So what is the phase at time t1? 2*pi*t1/fc+B*sin(2*pi*fm*t)+theta
Now add some noise and a second, uncorrelated signal and it is not at all clear what you need to measure.

Can you clarify what you are trying to accomplish. Maybe some other measurement than phase is more appropriate.

Lynn

[Tomi]

Hi,

Thanks for your answer. I see that what I want is almost impossible and my question was not exact.
Let me desribe the situation, perhaps it generates some new idee.
I have a CD what rotates at a certain frequency. The speed is stable but unknown; it can be between 3-8Hz. The CD has excentricity. The centre of rotary notion is not the dimensional centre point of the CD. The difference can be 0-300um. Now i take this centre of rotary notion to the (0;0) descartes. On this simulation the motion on X axis is (Y:=0)
X=sqrt(E * (cos(t))^2 + r^2) + e * sin(t)

I think this is my modulation signal.

Let me go further. The CD contains a spiral. The pitch of spiral is 1.5-1.6um. (This spiral is the alternation of pits/land but now I take it just a simple
groove after LPF). I point to a certain point of CD surface with focused laser (coming from OPU) then I start to rotate the CD. Due to the eccentricity I get a signal where the carrier frequency is the groove signal and the modulation is the X movement of CD.

What I want to measure is a carrier phase of two satelite laser spots. The OPU generates 2 satelite spots (and one main spot). The satelite spots point to different place on the CD surface (difference is about 0.8um on radial (X) direction). The phase of the two spot signal is need. This is a quality parameter of OPU.

//The OPU is perfect if the phase is 180 degree.//

Tomi

[johnsold]

If I understand you correctly your ideal system is one where the laser spots look like this:
--------0-----O-----0----------
Whre the zero (0) represents the satellites and the upper case O is the main spot and the --- are a radial line from the center of rotation. And a poor system has the satellites at some other angle? or misaligned with the radial line?
--------0------O
\
\
0

Can you make a special test CD with a few radial grooves or scratches? If so your signal would be a single pulse at each groove for a perfectly aligned laser and centered CD. If the satellites were not aligned properly you would get multiple pulses or a broadened pulse at each groove. If
the CD were not centered on the rotational axis, there would be some "tilt" or multiple pulsing, but it would vary with the rotation and at two places the grooves would line up exactly with the radius, so this effect would be very predictable. If this is not clear I can generate some kind of drawing to illustrate my thinking.

Lynn

[Tomi]

Hi,


Thanks again for your reply.
Yes you are right, your simplified drawing is unambiguous.
General I have phase problem (what leads to reduced playability)
1 if the opu main spot does not travel on the radial line of CD.
2 the alignment of spots are not in the right angle to the radial line


On the attached picture the exact spot arrangemet is more understandable.
When I rotate the CD I get such signals what I have sent due to all CDs have certain eccentricity. And from these signals I have to calculate the phase difference. The CD is not changeable. The goal is to perform all additional tests with one predefined CD.


I understand the basis of Your idee but with my system it is not workable.

Tomi

[johnsold]

I looked at the data in your example and have an idea which may help. I extracted a segment about 0.2 seconds long which appears to represent 1 revolution of the CD. Then I did a Fourier transform of that segment. Both the magnitude and phase of the transforms vary somewhat from revolution to revolution. Perhaps if you looked at several data sets, some with good lasers and others with bad ones, you could determine the parameters which enable discrimination.

I did something like that with a vibration analyzer for a gear box many years ago. It required a combination of instrumentation and human judgement to establish the criteria (frequency bands and amplitude thresholds), but the final product gave the quality control ins
pector a yes/no decision that was reliable for years.

Lynn