# How to mesure phase in a signal

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#### kirgizz

##### Member level 2 Hello sinatra.

Thank you very much for the detailed answer.

Don't I need to eliminate the phase difference? This would be a great thing. I read something about "quadrature modulation" which is often mentioned as Y-output. (input signal multiplied with the 90 degree of ref. sine). I think that's what you meant.

#### sinatra

##### Full Member level 4 Hello Kirgizz.
The quadrature demodulation is a step further. Using this technique you can get amplitude and phase information.

Assuming your input signal is defined by:

vi = A0 sin ( wt + phi0 )

In the quadrature process you multiply the input signal by 2 local oscilator signals, one is with zero phase (reference) and the other one is in quadrature ( 90 degrees ):
vl1=Al sin (wl t)
vl2=Al sin (wl t - PI/2) = Al cos (wt )

At the output of those 2 multipliers we have:

vI = A0 sin ( wt + phi0 ) * Al sin (wl t) // this is the in-phase output

vQ= A0 sin ( wt + phi0 ) * Al cos (wl t) // this is the quadrature output

Expanding:
vI = (A0Al/2)[cos[(w-wl)t + phi0] - cos[(w+wl)t +phi0)]

vQ = (A0Al/2)[sin[(w+wl)t + phi0] + sin[(w-wl)t +phi0)]

Now, after passing the two output signals through low-pass filters to suppress the higher side band:

vI = (A0Al/2)cos[(w-wl)t + phi0] // this is the in-phase output

vQ = (A0Al/2)sin[(w-wl)t + phi0] // this is the quadrature output

Now with an extra processing it is easily shown that:

A0 = (1/Al) * sqrt ( vI**2 + vQ**2 ) // this the amplitude of the input signal found again after the demodulation process

And if we are sure that the local oscilator has the same frequency as the incoming signal we can say that
w=wl

Then we can find phi0:
phi0 = arctan (vI/vQ) // this is the phase of the input signal found after the demodulation process.

A DSP should be able to do this calculation quite easily.

This shows that the quadrature demodulation can get all the information from amplitude and phase modulation of the input signal provided that we know the frequency.

Greetings
S.

#### kirgizz

##### Member level 2 Hello sinatra.

Thank you, I appreciate it.
Now I think I know the right direction.

best regards

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