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Addition of waves

  1. Mar 16, 2008 #1
    hi i know how to add 90degree phase shifts but i can't remember how to add two simple waveforms...

    i need to express v1 + v2 if;

    v1 = 96sin(120[tex]\Pi[/tex]t+ [tex]\pi[/tex]/6)
    v2 = 90sin(120[tex]\Pi[/tex]t-[tex]\pi[/tex]/3)

    can anyone help please!?
  2. jcsd
  3. Mar 16, 2008 #2


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    A sinusoid can be represented in either rectangular notation or polar notation.
  4. Mar 16, 2008 #3
    yeah but the polar for this is just overcomplicating things (im just not good at it) but i cant remember the calcultion method...
  5. Mar 16, 2008 #4


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    Well if you know a method that does not over complicate things, then let me know. For now, you should know that addition of sinusoidal waveforms is best done using rectangular notation.

    [tex]x = r \cdot cos(\theta)[/tex]
    [tex]y = r \cdot sin(\theta)[/tex]

    x - real part
    y - imaginary part
    r - magnitude of the sinusoid
    [itex]\theta[/itex] - phase
  6. Mar 16, 2008 #5
    yeah i really can't remember how to use this method... which is embarrassing
    id say im pretty screwed really
    i have no idea how id adapt that to what i have.

    thanks anyways tho
  7. Mar 16, 2008 #6


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    Okay. What you want to do is add V1 and V2. Both of these are sinusoidal waveforms. Such waveforms can be expressed in two different ways. We can use phasor notation, where our signal is in a complex exponential form. Or we can represent our waveform in rectangular (cartesian) notation. Rectangular notation is of the form x + jy. Where real{x + jy} = x and imaginary{x + jy} = y.

    Rectangular notation makes addition of V1 and V2 easy. Just convert V1 and V2 to rectangular notation (see my initial post). To add in rectangular form, just add the real parts together and add the imaginary parts together.

    http://en.wikipedia.org/wiki/Phasor_(electronics [Broken]) (phasors)
    http://en.wikipedia.org/wiki/Polar_coordinate_system (review of coordinate system; includes cartesian notation and complex exponentials)
    Last edited by a moderator: May 3, 2017
  8. Mar 17, 2008 #7


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    Staff: Mentor

    ranger is giving you some pretty good help -- does it make more sense now? Using phasors or complex numbers to represent time-domain waveforms helps you to keep the "sin"-phase and "cos"-phase components separate. For the waveforms you are trying to add, you need to split each one up into its sin-phase and cos-phase components, and add those separately.

    If you're still confused after reading Ranger's references, please re-post here and show us your attempt at expressing your original two waveforms as phasors for addition of components....
  9. Mar 19, 2008 #8

    You'll get it, if you went up to someone on the street and asked them chances are they would have no clue what you are even talking about.

    I honestly forget how to do this stuff too but if you brush up on it and work at it it will come back to you.
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