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Question on equation for instantaneous E field along the transmission medium.

  1. Jan 11, 2009 #1
    I am studying Poynting vectors. I run into question that I don't see any good explaination in all the books I have. All the books claimed
    E[tex]_{(z,t)}[/tex] =E[tex]_{(z=0)}[/tex] Re[e[tex]_{j(wt-\beta z)}[/tex] + [tex]\Gamma[/tex] e[tex]_{j(wt+\beta z)}[/tex]]

    But sinse E0 is complex so this is what I have and is not equal to what the book gives. In fact the Electromagnetic by Ulaby actually say ignor the phase angle of E0!! Below is what I have:

    Obviously the answer does not agree. This is particularly obvious when working on Poynting vectors. Please tell me what do I miss in this whole thing.

    Last edited: Jan 12, 2009
  2. jcsd
  3. Jan 11, 2009 #2
    Once you go into phasor domain, all information is just relative time. Therefore you can assume your Incident Phase Angle is zero. As well as that I believe that your book is assuming that maximum amplitude occurs at z=0(From your Latex Code). These two assumptions seem to be apparent in line 1, but not in line 3 of your derivations.
    Last edited: Jan 11, 2009
  4. Jan 11, 2009 #3
    But the book of Ulaby even expressly said that the incident E field at z=0 is complex and it has an angle. It just said they are going to ignor it!!! Ulaby simply say don't look at the phase angle of the incident E field and Cheng just ignor it.

    A phasor strip the time domain [tex]\omega[/tex]t out, but the phase angle of incident E field is absolute a spacial domain and cannot be ignor. The solution from the two cannot be made equal to justify that.

    I spent 2 days deriving the formulas and just can not make the two agree. I don't see how they can ignor the phase angle unless the incident E field at z=0 is always at maximum which is cosine(0)=1 like you suggested!!! But what is the justification that the forward travelling E field is ALWAYS maximum at z=0? I have modify my original equation drawing above, please take a look again.
    Last edited: Jan 12, 2009
  5. Jan 12, 2009 #4
    If you were given an oscilloscope, could you distinguish between the incident wave having a phase shift of 0 degrees, 10 degrees, 20 degrees, 30 degrees...?
  6. Jan 12, 2009 #5
    No!! This is EM wave, not the voltage and current phasor in transmission. They are the same though, the same question apply on voltage phasor at z=0 at the load. A directional coupler can separate the incident and reflected. But getting to the z=0 is easy to talk, impossible to get to!!!
  7. Jan 12, 2009 #6
    I have been looking up quite a few books today on both Plane Wave phasor and transmission line travelling wave phasor. All the books specified that the amplitude at z=0 is REAL. There is not phase angle. If the amplitude is real, then I agree with the book!!

    Can anyone give me a conclusive theory why the amplitude at z=0 is always real? The only book that claimed the value can be complex, that is Ulaby book.
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