Help with Phasors

Discussion in 'General Electronics Chat' started by Pramu, Feb 29, 2012.

  1. Pramu

    Thread Starter New Member

    Feb 29, 2012
    1
    0
    Im having a little trouble with phasor multiplication at the moment;
    Let v(t)=Vm cos (ωt+θ);
    Phasor of this is taken as V=Vm exp(jθ)

    in phasor notation, V^2 = Vm exp(jθ) * Vm exp(jθ) = Vm^2 exp(2jθ) => v(t)^2= Vm^2 * (cos 2ωt+2θ)

    But from trignomatry, v(t)^2 = Vm^2 * cos^(ωt+θ)
    Why am i getting two different answers? Where have i gone wrong. Please give me an answer. Thanx :)
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    On reflection I don't think one can directly equate non-linear transformations between the time & frequency domains. Although it would be worth reviewing the means by which the computation of power in the two domains is consistently resolved.
     
    Last edited: Feb 29, 2012
  3. bretm

    Member

    Feb 6, 2012
    152
    24
    Vm cos (ωt+θ)

    is not equal to

    Vm exp(jθ)

    The first is strictly real-valued and the second is complex-valued. When you square each of them you'll get different results as well.

    The first is a time-varying wave with frequency ω and phase θ. The second is just a single point in the complex plane at angle θ from the real axis and distance Vm from the origin.
     
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