Transmitted Electric field

Discussion in 'Homework Help' started by mo2015mo, Dec 14, 2013.

  1. mo2015mo

    Thread Starter Member

    May 9, 2013
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    1
    Hi Guys,,

    My teacher was talking about the Wave reflection and transmission at Oblique incidence and said that

    "In many cases the transmitter electric field(Et) is larger than the incident electric field(Ei)"
    But i wonder how it happened?

    I analysed that as we know the transmitted , reflected and incident waves have to obey the conservation of Power ONLY .
    Pi = Pr + Pt
    BUt they do Not have to obey the conservation of electric filed
    so ?// :confused: how can i show that mathematically?? if it was correct ?

    plz help me and thanks in advance,,
     
  2. studiot

    AAC Fanatic!

    Nov 9, 2007
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    If the impedances are Zi for the incident medium and Zt for the reflected medium

    then

    Ei+Er = Et
    Hi+Hr = Ht
    Ei/Hi = Zi
    Er/Hr = -Zi
    Et/Ht = Zt

    Then the amplitude reflection coefficient is

    R = Er/Ei = (Zt-Zi)/(Zt+Zi)

    and the transmission coefficient is

    T = Et/Ei = 2Zt/(Zt+Zi)

    With suitable values for Zi and Zt this can be greater than one.

    What happens to T if the incident wave is travelling in a conductor? (hint Zi then = 0)
     
    Last edited: Dec 14, 2013
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  3. mo2015mo

    Thread Starter Member

    May 9, 2013
    157
    1
    If Zi = 0 thus R = 1 and T = 2 ( BUT How we can transfer a wave in a conducting media(shorting a wave) and we know If the 2nd medium is conducting Zt = 0 thus R= -1 and T= 0) :confused:
     
  4. mo2015mo

    Thread Starter Member

    May 9, 2013
    157
    1
    I got it :) we have two situations are
    Firstly T = 1 at Brewster angle (θB) OR when Zi = Zt
    Second T=Et/Ei > 1
    T = Et/Ei = 2Zt/(Zt+Zi) > 1
    2 Zt > Zt + Zi ==> Zt > Zi

    Is there any practical examples ?? :rolleyes:
     
  5. studiot

    AAC Fanatic!

    Nov 9, 2007
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    Think of a transmission line and its termination conditions.

    Think of open circuit and shorted in particular.
     
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  6. mo2015mo

    Thread Starter Member

    May 9, 2013
    157
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    open-circuited transmission line is a current node (zero point) and a voltage antinode (maximum amplitude)
    [​IMG]

    At the line termination of OC TL
    R=1 thus
    Vtotal = (V+) + (V-) = 2 Vout

    At the line termination of SC TL
    R=-1 thus
    Vtotal = (V+) + (V-) = ZERo
     
    Last edited: Dec 15, 2013
  7. studiot

    AAC Fanatic!

    Nov 9, 2007
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    Here is a sketch that may help further.
    It shows an EM wave travelling from left to right across tha pages and crossing a plane boundary from impedance Z1 to impedance Z2.
    E, H and (ExH) vectors and directions are shown for various vectors (transmitted, reflected when Z1>Z2 and when Z1<Z2).

    If an EM wave travelling in air is reflected normally from a conducting surface the transmitted magnetic wave is Ht = 2Hi and a magnetic standing wave then exists in the air with a very large standing wave ratio due to the reflected component.
    If the wave is initially travelling in the conductor then it is reflected from a conductor to air interface a similat Et = 2 Ei occurs.

    The first is the same as a short circuited transmission line
    The second is the same as on open circuit line.
     
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