# Transmitted Electric field

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

1. ### mo2015mo Thread Starter Member

May 9, 2013
157
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 ?// how can i show that mathematically?? if it was correct ?

plz help me and thanks in advance,,

2. ### studiot AAC Fanatic!

Nov 9, 2007
5,005
515
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)

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 ??

5. ### studiot AAC Fanatic!

Nov 9, 2007
5,005
515
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
1
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: Dec 15, 2013
7. ### studiot AAC Fanatic!

Nov 9, 2007
5,005
515
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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