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

1. Jan 11, 2009

yungman

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$$_{(z,t)}$$ =E$$_{(z=0)}$$ Re[e$$_{j(wt-\beta z)}$$ + $$\Gamma$$ e$$_{j(wt+\beta z)}$$]

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.

Thanks

Last edited: Jan 12, 2009
2. Jan 11, 2009

ravioli

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
3. Jan 11, 2009

yungman

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 $$\omega$$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
4. Jan 12, 2009

ravioli

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...?

5. Jan 12, 2009

yungman

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!!!

6. Jan 12, 2009

yungman

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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