JPL's Wireless Communication Reference Website 

Chapter: Wireless Channels 
Section: Path Loss, Plane earth loss.


Angle of incidence Y

            hr+ht
 tan(Y) =  -----
             d
For d >> hr+ht, tan(Y) and sin (Y) approximately equal Y. Meanwhile cos(Y) is about 1.

Reflection coefficient

For a horizontally-polarized wave incident on the surface of a perfectly smooth earth,

,

where er is the relative dielectric constant of the earth, Y is the angle of incidence (between the radio ray and the earth surface) and x = s/(2 p fc e0) with s the conductivity of the ground and e0 the dielectric constant of vacuum. So, x = s/(we0)=18 109s/f.

 

For vertical polarization

 

 SurfaceConductivity sRelative Dielectric Constant er
 
Dry Poor Ground
10-3
4-7
 
Average Ground
5 10-3
15
 
Wet Good Ground
2 10-2
25-30
 
Fresh Water
10-2
81
 
Sea Water
5
81

Exercise

Show that the reflection coefficient tends to -1 for angles close to 0. Verify that for horizontal polarization, abs(Rc) > 0.9 for Y < 10 degrees. For vertical polarization, abs( Rc) > 0.5 for Y < 5 degrees and abs( Rc) > 0.9 for Y < 1 degree.

Reflection Coefficient Calculator

Input parameters:
Carrier Frequency:  MHz
Distance: meter
Tx ant. height:  meter
Rx ant. height:  meter
er  
s  

Run calculation:

  

Results:
Angle degree
Horizontal Polarization
abs(R)		  
ang(R) degree
Vertical Polarization
abs(R)		  
ang(R) degree

Disclaimer: Executable software programs are provided with no guarantee whatsoever. Some browsers do not support Java applets or JavaScript 1.2. See License.

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JPL's Wireless Communication Reference Website © Jean-Paul M.G. Linnartz, 1993, 1995.