Phase cancellation of Sine wave

[Uhdap]

Hi,

I was trying to check the phase cancellation of the sine wave by adding two sine waves generated.

The phase gets cancelled and shows zero deg at the output of the combined signal, when the phase input was +10deg and -10deg. This hold good until the phase inputs till +89deg and -89deg.

When the phase inputs are changed to +90deg and -90deg the phase pout of the combined signal is not zero and it shows 180deg for inputs beyond +95deg and -95deg.

Why its behaving like this. Can someone explain please.

[Bob_Schor]

I'll try to do this with a "word picture".  Imagine you have two runners on a circular track, both running at exactly the same speed.  Start them running together, and they keep on running together.

Now start them a yard apart.  They keep on running a yard apart.  The runners circling the track are your two sine waves (look at their position from a long distance away -- they "run to the left, then run to the right, then run to the left, etc." in a sinusoidal fashion.  Your "Phase cancellation" is an attempt to replace the two runners with an "average" (or "midway-between") runner.

Start increasing the (constant) distance between the runners.  You are doing it by having one start "10 degrees" (or 1/36 of the track circumference) ahead, the other "10 degrees" behind (for example).  Where is the midpoint?  Why, right between them, measured by the shorter distance (1/36 of the track circumference).  Now increase the distance until they are on opposite sides of the track, what you are calling 90 degrees.  Now where is the midpoint?  Is it at the original "starting point", or at 180 degrees?  And if you separate them by more than half the track distance, then isn't it logical to put the distance between them as the shorter distance?

If you like "doing the math", explore the expression sin (2 pi f t + phi), which is a sine wave with frequency f and phase phi.  Write down and simplify the "cancellation" you are proposing (namely sin (2 pi f t + phi) + sin (2 pi f t - phi)) and see the surprising thing that happens if phi = 90°.  What would you call the phase of the resulting (not a) sinusoid?

Bob Schor

[billko]

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@Bob_Schor wrote:

I'll try to do this with a "word picture".  Imagine you have two runners on a circular track, both running at exactly the same speed.  Start them running together, and they keep on running together.

Now start them a yard apart.  They keep on running a yard apart.  The runners circling the track are your two sine waves (look at their position from a long distance away -- they "run to the left, then run to the right, then run to the left, etc." in a sinusoidal fashion.  Your "Phase cancellation" is an attempt to replace the two runners with an "average" (or "midway-between") runner.

Start increasing the (constant) distance between the runners.  You are doing it by having one start "10 degrees" (or 1/36 of the track circumference) ahead, the other "10 degrees" behind (for example).  Where is the midpoint?  Why, right between them, measured by the shorter distance (1/36 of the track circumference).  Now increase the distance until they are on opposite sides of the track, what you are calling 90 degrees.  Now where is the midpoint?  Is it at the original "starting point", or at 180 degrees?  And if you separate them by more than half the track distance, then isn't it logical to put the distance between them as the shorter distance?

If you like "doing the math", explore the expression sin (2 pi f t + phi), which is a sine wave with frequency f and phase phi.  Write down and simplify the "cancellation" you are proposing (namely sin (2 pi f t + phi) + sin (2 pi f t - phi)) and see the surprising thing that happens if phi = 90°.  What would you call the phase of the resulting (not a) sinusoid?

Bob Schor

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I like to picture them as runners running in a "circle", but with an added time dimension, which makes them run in a corkscrew fashion, as shown here in my favorite discussion about IQ data.

[Bob_Schor]

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@Uhdap wrote:

Hi,

I was trying to check the phase cancellation of the sine wave by adding two sine waves generated.

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When I was taking Freshman Physics (I think it was), we had a quiz, or a homework problem ( don't recall the exact details) that most of us "got wrong".  One of my Classmates uttered an unforgettable Quote:  "Answer Analysis reveals that the Question is Wrong!".

I just realized (after reading Billko's response to my latest post) that I, too, was answering the "Wrong Question".  What I believe @Uhdap was really asking is "How do I plot (or express) my Sine Wave to cancel out its Phase Shift" (or, alternatively, "How do I shift the Phase of my Sinusoidal Signal to an arbitrary value?".

The answer is simple.  A sinusoidal signal of arbitrary phase can be expressed as a sum of a sine wave of some amplitude and a cosine wave of some amplitude, with the phase being simply the angle whose tangent is the sine amplitude divided by the cosine amplitude.  [This is Sine Wave, or Fourier, Analysis].  For a signal whose frequency is known, fitting sines and cosines of the known frequency and determining the phase angle is simple.  For an unknown signal, you can do Fourier Analysis of the signal (LabVIEW has functions to do this, but you should know something about Signal Analysis before attempting this blindly) and determine the phase of the strongest Sinusoid in your sample (the rest you can consider to be "noise").

Once you have the dominant frequency and the phase (at that frequency) of your signal, you can "phase-cancel" your signal by simply delaying it by the amount of time corresponding to that phase.  For example, if you are sampling at 1 kHz, or 1000 points a second, and your signal is a 10 Hz sinusoid (so 100 points per sinusoid) and you determine that its phase is 45° (which I, not being an Engineer, would call a phase lead, and would result in the signal being shifted to the left (i.e. earlier in time), you simply move the plot to the right by 45°, or one-eighth of a Cycle (which would be 100/8 = 12.5 points, oops, how do you plot half-a-point, but you get the idea, I hope).

Bob Schor (this is probably all I have to say about this topic -- go learn some Signal Theory).

[Uhdap]

Thank for your reply Bob and bilko, am just trying to understand from the explanation what have you shared.. Let me work out.