# how t o measure the phase difference of two signals

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#### chin

##### Member level 1 measure phase difference of sinusoidal signals

Hi all...

I have two sinusoidal signal of same frequency, i would like to measure the phase difference.
Can anyone tell me how to find the phase difference of these two sinusoids.

chin

#### ieropsaltic

##### Full Member level 4 measure phase of two signals

You can use an XOR gate. First, you need to change both signals into square waves then use an XOR gate with each input connected to one of the signals. The output of the XOR gate will have an average equal to the absolute of the phase difference ,so, if you place a LPF after the XOR gate, you'll get this average.

You may also use a mixer for both sinusoids. When s1(t)=sin(wt) and s2(t)=sin(wt+θ), mixer o/p(after LPF)=.5*cos(θ) which equals 0 at θ (error)=π/2 i.e error is proportional to phase shifts from π/2.

#### Dmitrij

##### Advanced Member level 4 phase difference measures

Imagine, 2 harmonic signals are given (it's expected here, that you can visualize both of them using any mathematical resource, such as Matlab or Mathcad, for example):

s1(t) = sin(wt)
s2(t) = sin (wt+phi) if necessary you may convert sinus to cosinus with the use of well-known trigonometric formulas:

Let's find the difference of 2 signals by subtracting s2(t) from s1(t) and transform the result, connecting the functions of double and sinle arguments:

s(t) = s1(t) - s2(t) = sin(wt) - sin(wt+phi) = 2sin(-phi/2)*cos(wt+phi/2).
s(t=0) = 2sin(-phi/2)*cos(phi/2)=-sin(phi) = A. A may be defined from yhe graphic plot, using machine computation. Then

phi = -arcsin(A)

2) Find the time delay of one signal respectively to the other. Mark this time-shift as delta_t and signal's period - T. Then the following formula is true:

phi/360 = delta_t / T,

phi = 360 * (delta_t / T)

3) Also more complicated methods may be used. However most of them require the presense and usage of special equippment. Provided you possess the oscillograph (analogue or digital , it doesn't matter), it's possible to send the 1st signal to the 1st channel and the 2nd signal to the 2nd. On the screen you'll observe the Lissagu figures. These figures may be a line, a point, a circle, an ellips, etc. and each unique figure corresponds to the distinct phase shift. If the value is apriori non-exact, then the result will also have some error, which must be involved in the computation algorithm,

4) Also, you can use digital ways of measuring the phase shift, such as transforming it to the voltage, which is shown on the scale of voltmeter or other apparatus, capable of measuring voltage. Take any book on metrology in order to look through this topic.

With respect,

Dmitrij

### chin

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