Reflection coefficient question.

[cdeguzma]

Hi...
I'm trying to solve a problem, and don't really know where to begin.
If you have freespace/material/freespace and are given permittivity, the thickness of material, and wavelength. How is one supposed to be able to calc the reflection coefficient? I vaguely understand how the wavelength effects it. Please help!

btw...if you haven't already guessed it...i'm a newbie at this.

thanks so much for your help

 

[flatulent]

There will be reflections from both boundaries where the impedance changes. The best way to approach this is from the standard transmission line equations which also apply.

 

[springf2000]

this is a complex question,y should tell me the concrete condition,for example the incident angle of the wave,the area of the material,etc,all these will effect the reflected coefficient

 

[cdeguzma]

To narrow down what I'm really confused about, a normal incident wave is travelling from free space into a medium then out to free space again. I'm trying to find the relationship between the width of the medium and permeability/permittivity so that I can calculate the reflection coefficient. I've tried 'google-ing' it but I've found nothing useful.

 

[dowjones]

hello.
this is a classical chapter in any electromagnetic text book. You can find the solution to that problem in the books of Pozar (MW engineering chap 1), Hayt (Engineering Electromagnetics chap 11), Collin (Field theory of guided waves chap 3),... The online ebook of Orfanidis includes SEVERAL chapters dealing with this problem (multilayered dielectrics).

the problem basically is that any material has an associated wave impedance, which is related to its electomagetic properties (permittivity, permeability, conductivity). A wave generated in a medium and incident in other medium sees a different wave impedance, and therefore part of the energy is reflected and part is transmitted. Boundary conditions at the interfaces give the amount of signal reflected and transmited.

(I have been trying to attch a pdf, but I have some problems with it. Ill continue trying). The pdf (which I try to attach) gives a quite good introduction on how the problem is solved. for oblique incidence check the previous references.

regards

 

[sergio mariotti]

If the wave is normal to the surface, the diffraction is small enough, tand=0, n=reflection index .

The max reflection on the 1st surface is given by:
R1=((n-1)/(n+1))^2

The max reflection on both surfaces, caused by re-reflections is given by:
R2=4*R1/((1+R1)^2)

 

[djalli]

Let start where you stopped:

Boundary of structure(2) is wave hitting wave comming from free space(1)? Is it microstrip or coaxial? or else which is important?

From free space going to another medium. Right?

Do you know figures as permetivity, do you have material uniform in structure?

At boundaries. Z0 of free space is 137ohms. Knowing magnetic permeability and electric permittivity of the boundary you can find Z0 (characteristic impedance of structure)

from there you can calculate the reflection coefficient.

now you say wave enters and leaves this structure and again to free space. You do the same thing.

But in this case Z0 is not free space but structure(1) wave is traveling and free space(2) is the load impedance. Roles get reversed.

This is a very classic transmission line problem.
Man post some figure and some details!

Reflection occurs where and when wave hits impedance discontinuity. So at boundaries.

else:
---------
Things do not fall as far as this. But above must be far enough for undergraduate sophmore knowledge.

When the wave hits impedance discontinuity some travels ahead but some travels back (this is the reflected wave) and at begining of the structure when original wave entered the reflected wave occurs another impedance dicontinuity and then some gets out and some gets reflected back and so forth and everything becomes a geometrical series.

 

[djalli]

And here is a picture for might be the question. Please provide details.

 

[cdeguzma]

If you have Pozar 2nd ed, it's problem 1.7.
Details of the problem: plane wave is normally incident on a dielectric slab of permittivity er and thickness d=lambda0/(4*sqrt(er)). lambda0 is the free space wavelength of the incident wave. if free space exists on both sides of the slab, find the reflection coefficient of the wave reflected from the front of the slab.

Don't know how to insert pictures but it looks like this: free spacee (e0)/medium(0=>d,e0er)/free space(e0)...along the z axis.

 

[DJ]

I think your question is how the wavelength has an influence on the reflection coeficient.
Let say the material has a constant dielectric constant over freq. The substrate has finit dimensions . For example there is reflection at the input (air to substrate) and another reflection at the output (subs to air). Actually there are many reflections between the two ends and the total reflection wave at the input is the summation of all the waves. It is a frequency dependend becous the substrate length.
The substrate width also has influence on freq. The surface is a magnetic wall and the distance between the walls has a frequency dependend reflections.

D.J

 

[djalli]

If you have Pozar 2nd ed, it's problem 1.7.
Details of the problem: plane wave is normally incident on a dielectric slab of permittivity er and thickness d=lambda0/(4*sqrt(er)). lambda0 is the free space wavelength of the incident wave. if free space exists on both sides of the slab, find the reflection coefficient of the wave reflected from the front of the slab.

Don't know how to insert pictures but it looks like this: free spacee (e0)/medium(0=>d,e0er)/free space(e0)...along the z axis.

I think all people in RF must keep David Pozar book under the pillow. heh.

Here is solution.

 

[djalli]

Hmmmm one error right-middle it says: d=/(4*sqrt(er)) I meant to write it d=lambda/(4*sqrt(er)).

 

[cdeguzma]

Thanks djalli for confirming my answer!