# Diffraction and Fresnel Zones by Yh2SDXBu

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```									Diffraction and Fresnel Zones

Material Related to Chapter 11
Textbook Pages 358 - 359
Wavefront Encountering an Obstacle

Consider the obstacle shown in green to be a knife-edge of known height
( 0 to 3) and infinite width - into and out of the paper (your looking at the side)
Blockage Signal Levels

dB                                       Note leakage of signal into
but also that the field
strength above the top of the
obstacle ( 0 to -2) is also
disturbed.

ν is the dimensionless
Fresnel-Kirchoff diffraction
parameter. The graph shows
the loss in dB due to knife-
edge diffraction.

Signal Levels on the Far Side of the Shadowing Object
Huygens’ Principle

Representation of Radio Waves as Wavelets
Wavefront by Vector Summation

At a given point on the new wavefront at Point B, the signal vector is
determined by the vector addition of the contributions from the wavelets
The further distances introduce more time delay and hence the rotation of
the vectors as shown, e.g., vector contribution from + 2 point.
Cornu Spiral

Contribution
from vector
at point + 1
Fresnel Zones
   To visualize what happens to radio waves when they
encounter an obstacle, we have to develop a picture of the
wavefront after the obstacle as a function of the wavefront
just before the obstacle
   How much space around direct path between transmitter
and receiver should be clear of obstacles including the
ground?
   Objects within a series of concentric circles around the line of sight between
transceivers have constructive/destructive effects on communication
   A radio path has first Fresnel zone clearance if no objects
capable of causing significant diffraction penetrate the
corresponding ellipsoid
Fresnel Zones
    Assume that there is one object in the
Fresnel Zone, then we can look at the
resultant wavefront at destination B
    In terms of the Cornu spiral, the
upper half of the spiral is intact but
part of the lower half is absent due to
blockage by the object
    The resultant vector addition of all
components is near the free space
magnitude (i.e., no obstacle)
For point along the direct path, radius of first Fresnel zone (most serious
interference region):
SD
R
SD
S = distance from transmitter     D = distance from receiver
Fresnel Zone Formulation
   Rm = 17.3 [ SkmDkm/fGHz(Skm + Dkm) ]1/2

Note different units for R, f, S and D

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