Transmitted Electric field

Thread Starter

mo2015mo

Joined May 9, 2013
157
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,,
 

studiot

Joined Nov 9, 2007
4,998
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:

Thread Starter

mo2015mo

Joined May 9, 2013
157
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)
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:
 

Thread Starter

mo2015mo

Joined May 9, 2013
157
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:
 

Thread Starter

mo2015mo

Joined May 9, 2013
157
Think of a transmission line and its termination conditions.

Think of open circuit and shorted in particular.
open-circuited transmission line is a current node (zero point) and a voltage antinode (maximum amplitude)


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:

studiot

Joined Nov 9, 2007
4,998
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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