3.7 Diffraction. allows RF signals to propagate to obstructed ( shadowed ) regions - over the horizon (around curved surface of earth) - behind obstructions received field strength rapidly decreases as receiver moves into obstructed region
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
3.7 Diffraction
Segments
3.7.1 Fresnel Zone Geometry
slit
knife edge
d = d1+ d2, where ,
di =
h
d
=
+
– (d1+d2)
TX
RX
d1
d2
ht
hobs
hr
Knife Edge Diffraction Geometry for ht = hr
Excess Path Length = difference between direct path & diffracted path
= d – (d1+d2)
3.54
3.55
=
=
h
h’
TX
d1
d2
RX
hobs
ht
hr
Knife Edge Diffraction Geometry ht > hr
Assume h << d1 , h <<d2 and h >> then by substitution and Taylor
Series Approximation
Phase Difference between two paths given as
tan(x)
TX
hobs-hr
ht-hr
RX
d1
d2
x
tan =
tan =
x = 0.4 rad tan(x) = 0.423
(0.4 rad ≈ 23o )
Equivalent Knife Edge Diffraction Geometry with hrsubtracted from all other heights
180-
when tan x x = +
v =
(3.56)
when is inunits of radians is given as
=
(3.57)
Eqn 3.55 for is often normalized using the dimensionless Fresnel-Kirchoffdiffraction parameter, v
d
λ/2 + d
λ + d
1.5λ + d
at 1 GHz λ = 0.3m
R
=
T
slice an ellipsoid with a plane yields circle with radius rn given as
h = rn =
then Kirchoffdiffraction parameter is given as
v =
=
thus for given rnvdefines an ellipsoid with constant = n/2
nthFresnel Zone is volume enclosed by ellipsoid defined for n andis defined
as relative to LOS path
Phase Difference, pertaining to nthFresnel Zone is
≤ Δ≤
(n-1)≤ ≤ n
d
d2
d1
Tx
Rx
For 2nd Fresnel Zone
Q
R
h
d2
O
T
d1
n
=n/2
1
/2
2
rn =
(3.58)
3
3/2
Excess Total Path Length, for each ray passing through nth circle
Rx
Tx
Assuming, d1& d2 >> rn radius of nth Fresnel Zone can be given in terms of n, d1,d2,
Rx
Tx
Diffraction Losses
e.g.
v =
excess path length
/2
3/2
RX
TX
h
d1
d2
and v are positive, thus h is positive
v =
RX
TX
h = 0 and v =0
RX
TX
d1
d2
h
d1
d2
and v are negative h is negative
3.7.2 Knife Edge Diffraction Model
Huygens 2nddry
source
h’
T
d1
R
d2
Knife Edge Diffraction Geometry, R located in shadowed region
= F(v) =
(3.59)
Electric field strength, Ed of knife-edge diffracted wave is given by:
Gd(dB) = Diffraction Gaindue to knife edge presence relative to E0
5
0
-5
-10
-15
-20
-25
-30
v
Graphical Evaluation
Gd(dB)
-3 -2 -1 0 1 2 3 4 5
Gd(dB)
v
0
-1
20 log(0.5-0.62v)
[-1,0]
20 log(0.5 e- 0.95v)
[0,1]
20 log(0.4-(0.1184-(0.38-0.1v)2)1/2)
[1, 2.4]
20 log(0.225/v)
> 2.4
Table for Gd(dB)
= 2.74
v =
3. path length difference between LOS & diffracted rays
e.g. Let: = 0.333 (fc = 900MHz), d1 = 1km, d2 = 1km, h = 25m
Compute Diffraction Loss at h = 25m
1. Fresnel Diffraction Parameter
1. Fresnel Diffraction Parameter
v =
= -2.74
3. path length difference between LOS & diffracted rays
e.g. Let: = 0.333 (fc = 900MHz), d1 = 1km, d2 = 1km, h = 25m
Compute Diffraction Loss at h = -25m
2. diffraction loss from graph is Gd(dB) 1dB
T
R
50m
100m
25m
10km
2km
T
v =
75m
25m
R
=
10km
2km
from graph, Gd(dB)= -25.5 dB
find h if Gd(dB)= 6dB
T
=0
h
25m
R
10km
2km
find diffraction loss
f = 900MHz = 0.333m
= tan-1(75-25/10000) = 0.287o
= tan-1(75/2000) = 2.15o
= + = 2.43o = 0.0424 radians
3.8 Scattering
h
hc =
(3.62)
h = standard deviation of surface height about mean surface height
rough= s
(3.65)
s =
(3.63)
s =
(3.64)
I0 is Bessel Function of 1st kind and 0 order
For h > hc reflected E-fields can be solved for rough surfaces using modified reflection coefficient
||
1.0
0.8
0.6
0.4
0.2
0.0
0 10 20 30 40 50 60 70 80 90
angle of incidence
Reflection Coefficient of Rough Surfaces
(1) polarization (vertical antenna polarization)
| |
1.0
0.8
0.6
0.4
0.2
0.0
angle of incidence
0 10 20 30 40 50 60 70 80 90
Reflection Coefficient of Rough Surfaces
(2) || polarization (horizontal antenna polarization)
power densityof signal scattered in direction of the receiver
RCS =
power density of radio wave incident upon scattering object
3.8.1 Radar Cross Section Model (RCS)
Pr(dBm) = Pt (dBm) + Gt(dBi) + 20 log() + RCS [dB m2]
– 30 log(4) -20 log dT - 20log dR