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Does the Poynting Vector imply wave propagation?

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lkformylove

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Poynting Vector

Does the Poynting Vector imply wave propagation?
 

biff44

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Re: Poynting Vector

I prefer the Burger's Vector, especially when I am really hungry!
 

jian

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Re: Poynting Vector

Hi, lkformylove:

Yes. Poynting vector basically tells you how the electromagnetic energy is flowing. We can represent the power as:

P = V * Conj(I)
P = |Inc*Inc| - |Ref * Ref|

They are not always precise. The V and I definition is only exact for TEM waves. The Inc and Ref defintions are only exact for idealized waveguides without loss in the transverse directions. When the waveguides have loss in the transverse direction, the Inc and Ref defintion of P is also an approximation. A typical example of loss in transverse direction is a rectangular waveguide with non-PEC conductor wall. In some sense, all waveguides in reality have loss in the transverse direction. Therefore, the above two definitions of P always involve approximation. Howver, for most waveguide structures, the loss is small and the two formulas are quite accurate. The only definition always precise is the Poynting vector. However, it is impractical to use such a definition in simulation and processing of data. More detail explanation in this topic can be found in the Appendix of IE3D User's Manual. Regards.
 

Dr_mas

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Re: Poynting Vector

hi jian i don't understand this sentence
When the waveguides have loss in the transverse direction, the Inc and Ref defintion of P is also an approximation

and what are you meaning by inc and ref >> are they power or volt?

there is a little error in your equation
We can represent the power as:

P = V * Conj(I)
which is not the real power >> P = real{V-rms x conj(I-rms)}
i think that it is only writing error ... thx
 

dowjones

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Poynting Vector

hello,

strictly speaking, poynting vector should be defined in terms of E and H fields, not V and I.

I suggest to refer to any electromagnetics book instead to a software manual.

rgdz
 

jian

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Re: Poynting Vector

Hi, Dr_Mas:

Yes. The formula I postered is for the same as yours:

P = Real [ V_rms * Conj( I_rms ) ] for TEM transmission lines only. However, I do think the Imag part may mean something. Basically, I can see that, when Imag = 0, the power is propagationg in one direction. It seems to me that the Real and Imag parts do indicate how good the system is matched.

Again, the true definition of P is:

P = Real{ Integral_On_Cross_Section[ E_rms X Conj( H_rms ) ] }

for a general case. When the field is a TEM field, the E in the cross-section is conservative and the double integral on the cross-section can be separated and you can write it as:

P = Real{ Integral_On_One_Croodinate( E_rms ) X Integral_On_Another_Coordinate[ Conj( H_rms ) ] }

V_rms = Integral_On_One_Croodinate( E_rms )
I_rms = Integral_On_Another_Coordinate[ Conj( H_rms ) ] with a different direction

Please understand that, from E and H to V and I is only good for TEM wave.

Hi, Dowejones: I hope we could find everything from textbooks. However, I have not found this derivation from textbook, and I have not found detailed explanation why and when the P = V * Conj( I ) can or can't be used. Same thing is true on complex Zc. All the textbooks assume Zc or the E/H in waveguide is a real number. You just can't find any text book to discuss it. That is the reason we documented it in the IE3D User's Manual. In fact, when E/H is no longer a pure real number, you will find that the whole waveguide theory is an approximation. A typical example is that walls of a rectangular waveguide (RWG) is no longer PEC. You will find that the field inside it can't be separated into incident wave (Inc) and reflected wave (Ref). When you try to find the power consumed in the material inside of a section of RWG, you will need to find it as:

P1 = Integration_on_cross_section_on_left + Integration_on_cross_section_on_right + Integration_on_all_side_walls

instead of:

P2 = Integration_on_cross_section_on_left + Integration_on_cross_section_on_right

which is documented in all Electromagnetic textbook.

The P2 formula leads:

P = |Inc*Inc| - |Ref*Ref|

and this formula is valid only conditionally. More precisely, Inc and Ref in a waveguide are valid only conditionally. There are many things involved when you allow losses on the side walls or RWG or there is loss in the transverse direction of a waveguide. Unfortunately, it is the real case in reality. Maybe I should write a book on it when I have time. Thanks!
 

dowjones

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Poynting Vector

hello,

to my understanding, the v-i definition is valid when you can define uniquely those v and i, and that is not the case in a waveguide, since there are no tem modes. therefore the E-H definition of the poynting vector should be used in waveguides

bye
 

No one

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Re: Poynting Vector

Hello lkformylove;
I advise you to read the the following book:

-Field and Wave Electromagnetics, Cheng.
 

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